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This technical report provides a more thorough treatment of the proofs and derivations in the authors' paper "Anchoring Sagittal Plane Templates in a Spatial Quadruped." The description of the anchoring controller is reproduced here without abridgement, and additional appendices provide a clearer account of the implementation [Read more →]

This paper introduces a new controller that stabilizes the motion of a spatial quadruped around sagittal-plane templates. It enables highly dynamic gaits and transitional maneuvers formed from parallel and sequential compositions of such planar templates in settings that require significant out-of-plane reactivity. The controller [Read more →]

This paper develops a three degree-of-freedom sagittal-plane hybrid dynamical systems model of a Groucho-style bounding quadrupedal run. Simple within-stance controls using a modular architecture yield a closed form expression for a family of hybrid limit cycles that represent bounding behavior over a range of user-selected [Read more →]

Origami processes can generate both rigid and compliant structures from the same homogeneous sheet material. In this article, we advance the origami robotics literature by showing that it is possible to construct an arbitrary rigid kinematic chain with prescribed joint compliance from a single tubular sheet. Our “Kinegami” [Read more →]

We physically demonstrate a reactive sensorimotor architecture for mobile robots whose behaviors are generated by motivation dynamics. Motivation dynamics uses a continuous dynamical system to reactively compose low-level control vector fields using valuation functions which capture the potentially competing influences of external [Read more →]

Complex manipulation tasks, such as rearrangement planning of numerous objects, are combinatorially hard problems. Existing algorithms either do not scale well or assume a great deal of prior knowledge about the environment, and few offer any rigorous guarantees. In this paper, we propose a novel hybrid control architecture for [Read more →]

PURPOSE For children with mobility impairments, without cognitive delays, who want to participate in outdoor activities, existing assistive technology (AT) to support their needs is limited. In this review, we investigate the control and design of a selection of robotic walkers while exploring a selection of legged robots to [Read more →]

Robotics is an emerging synthetic science concerned with programming work. Robot technologies are quickly advancing beyond the insights of the existing science. More secure intellectual foundations will be required to achieve better, more reliable and safer capabilities as their penetration into society deepens. Presently missing [Read more →]

Using mechanical design inspired by the Ghost Minitaur and the open-source motor controller hardware from the Stanford Doggo, we built an open-source two-degree-of-freedom hopping robot. The robot hops using a Raibert-inspired reactive controller on the leg length and velocity. This technical report documents the project and [Read more →]

Natural environments are often filled with obstacles and disturbances. Traditional navigation and planning approaches normally depend on finding a traversable “free space” for robots to avoid unexpected contact or collision. We hypothesize that with a better understanding of the robot–obstacle interactions, these collisions [Read more →]

This paper presents a reactive planning system that enriches the topological representation of an environment with a tightly integrated semantic representation, achieved by incorporating and exploiting advances in deep perceptual learning and probabilistic semantic reasoning. Our architecture combines object detection with [Read more →]

Compositional methods for developing, analyzing and synthesizing robot behaviors construed as controlled hybrid dynamical systems with regular properties [1] has proven an effective framework for achieving steady state gaits [2,3]. Exploiting their potential for programming transitional behaviors, requiring more complicated [Read more →]

We report on experiments with a laptop-sized (0.23m, 2.53kg), paper origami robot that exhibits highly dynamic and stable two degree-of-freedom (circular boom) hopping at speeds in excess of 1.5 bl/s (body-lengths per second) at a specific resistance O(1) while achieving aerial phase apex states 25% above the stance height over [Read more →]

Evidence from empirical literature suggests that explainable complex behaviors can be built from structured compositions of explainable component behaviors with known properties. Such component behaviors can be built to directly perceive and exploit affordances. Using six examples of recent research in legged robot locomotion, we [Read more →]

We study a quadrupedal robot traversing a structured (i.e., periodically spaced) obstacle field driven by an open-loop quasi-static trotting walk. Despite complex, repeated collisions and slippage between robot legs and obstacles, the robot’s horizontal plane body orientation (yaw) trajectory can converge in the absence of any [Read more →]

We present an approach to overcoming challenges in dynamical dexterity for robots through programmably compliant origami mechanisms. Our work leverages a one-parameter family of flat sheet crease patterns that folds into origami bellows, whose axial compliance can be tuned to select desired stiffness. Concentrically arranged [Read more →]

Despite substantial evidence for the crucial role played by an active backbone or spine in animal locomotion, its adoption in legged robots remains limited because the added mechanical complexity and resulting dynamical challenges pose daunting obstacles to characterizing even a partial range of potential performance benefits. [Read more →]

Abstract. We document the reliably repeatable dynamical mounting and dismounting of wheeled stools and carts, and of fixed ledges, by the Minitaur robot. Because these tasks span a range of length scales that preclude quasi-static execution, we use a hybrid dynamical systems framework to variously compose and thereby [Read more →]

Predicting the susceptibility of soil to wind erosion is difficult because it is a multivariate function of grain size, soil moisture, compaction, and biological growth. Erosive agents like plowing and grazing also differ in mechanism from entrainment by fluid shear; it is unclear if and how erosion thresholds for each process are [Read more →]

A Gibsonian theory of affordances commits to direct perception and the mutuality of the agent-environment system. We argue that there already exists a research program in robotics which incorporates Gibsonian affordances. Controllers under this research program use information perceived directly from the environment with little or [Read more →]

This abstract was accepted to the Robot Design and Customization workshop at ICRA 2019. For more information: Kod*lab.

We work with geoscientists studying erosion and desertification to improve the spatial and temporal resolution of their data collection over long transects in difficult realworld environments such as deserts. The Minitaur robot, which can run quickly over uneven terrain and use a single leg to measure relevant ground properties [Read more →]

This paper proposes a new multi-input brushless DC motor current control policy aimed at robotics applications. The controller achieves empirical improvements in steady-state torque and power-production abilities relative to conventional controllers, while retaining similarly good torque-tracking and stability characteristics. [Read more →]

We propose a variant of iterated belief revision designed for settings with limited computational resources, such as mobile autonomous robots. The proposed memory architecture---called the universal memory architecture (UMA)---maintains an epistemic state in the form of a system of default rules similar to those studied by Pearl [Read more →]

This paper presents a provably correct method for robot navigation in 2D environments cluttered with familiar but unexpected non-convex, star-shaped obstacles as well as completely unknown, convex obstacles. We presuppose a limited range onboard sensor, capable of recognizing, localizing and (leveraging ideas from constructive [Read more →]

Robots capable of dynamic locomotion behaviors and high-bandwidth sensing with their limbs have a high cost of transport, especially when locomoting over highly dissipative substrates such as sand. We formulate the problem of reducing the energetic cost of locomotion by a Minitaur robot on sand, reacting to robot state variables [Read more →]

In the field of haptics, conditions for mechanical “transparency”[1] entail such qualities as “solid virtual objects must feel stiff” and “free space must feel free”[2], suggesting that a suitable actuator is able both to do work and readily have work done on it. In this context, seeking actuator transparency has come [Read more →]

We demonstrate the physical rearrangement of wheeled stools in a moderately cluttered indoor environment by a quadrupedal robot that autonomously achieves a user's desired configuration. The robot's behaviors are planned and executed by a three layer hierarchical architecture consisting of: an offline symbolic task and motion [Read more →]

This paper applies an extension of classical averaging methods to hybrid dynamical systems, thereby achieving formally specified, physically effective and robust instances of all virtual bipedal gaits on a quadrupedal robot. Gait specification takes the form of a three parameter family of coupling rules mathematically shown to [Read more →]

We present the first fully spatial hopping gait of a 12 DoF tailed biped driven by only 4 actuators. The control of this physical machine is built up from parallel compositions of controllers for progressively higher DoF extensions of a simple 2 DoF, 1 actuator template. These template dynamics are still not themselves integrable, [Read more →]

In practice, the mobile sensor networks have two important tasks: firstly, sensors should be able to locate themselves close to where major events are happening so that event tracking becomes possible; secondly, the sensor networks should also maintain a good area coverage over the environment in order to detect new events. [Read more →]

We construct a sensor-based feedback law that provably solves the real-time collision-free robot navigation problem in a compact convex Euclidean subset cluttered with unknown but sufficiently separated and strongly convex obstacles. Our algorithm introduces a novel use of separating hyperplanes for identifying the robot’s local [Read more →]

This paper considers the problem of completing assemblies of passive objects in nonconvex environments, cluttered with convex obstacles of unknown position, shape and size that satisfy a specific separation assumption. A differential drive robot equipped with a gripper and a LIDAR sensor, capable of perceiving its environment only [Read more →]

We describe the Nomadic Monument for Women in Robotis (NMWR), a project celebrating women pioneers in robotics. NMWR is a 13’ semi-transparent geodesic dome with illustrations and descriptions of the women and their research on the inside faces of the triangles. Visitors can see rough outlines of the illustrations from the [Read more →]

We extend a smooth dynamical systems averaging technique to a class of hybrid systems with a limit cycle that is particularly relevant to the synthesis of stable legged gaits. After introducing a definition of hybrid averageability sufficient to recover the classical result, we illustrate its applicability by analysis of first a [Read more →]

The efficiency of sampling-based motion planning algorithms is dependent on how well a steering procedure is capable of capturing both system dynamics and configuration space geometry to connect sample configurations. This paper considers how metrics describing local system dynamics may be combined with convex subsets of the free [Read more →]

A challenge of pan/tilt/zoom (PTZ) camera networks for efficient and flexible visual monitoring is automated active network reconfiguration in response to environmental stimuli. In this paper, given an event/activity distribution over a convex environment, we propose a new provably correct reactive coverage control algorithm for [Read more →]

We develop a dynamical systems approach to prioritizing multiple tasks in the context of a mobile robot. We take navigation as our prototypical task, and use vector field planners derived from navigation functions to encode control policies that achieve each individual task. We associate a scalar quantity with each task, [Read more →]

The art practice of play uses spontaneity and surprise to communicate meaningful content and inspire critical thinking (1-3). We describe three engineering education outreach efforts that use play to communicate legged robotics research concepts. In the first workshop, Penn engineering students were motivated to learn how to [Read more →]

We propose the idea of a discrete navigation problem – consisting of controlling the state of a discrete-time control system to reach a goal set while in the interim avoiding a set of obstacle states – to approximate a simplified class of transitional legged robotic tasks such as leaping which have no well established [Read more →]

This paper demonstrates a fully sensor-based reactive homing behavior on a physical quadrupedal robot, using onboard sensors, in simple (convex obstacle-cluttered) unknown, GPS-denied environments. Its implementation is enabled by our empirical success in controlling the legged machine to approximate the (abstract) unicycle [Read more →]

Though multi-functional robot hardware has been created, the complexity in its functionality has been constrained by a lack of algorithms that appropriately manage flexible and autonomous reconfiguration of interconnections to physical and behavioral components. Raibert pioneered a paradigm for the synthesis of planar hopping [Read more →]

This technical report provides proofs and calculations for the paper "Towards Reactive Control of Simplified Legged Robotics Maneuvers," as well as implementation notes and a discussion on robustness.

Models of aeolian processes rely on accurate measurements of the rates of sediment transport by wind, and careful evaluation of the environmental controls of these processes. Existing field approaches typically require intensive, event-based experiments involving dense arrays of instruments. These devices are often cumbersome and [Read more →]

This thesis addresses how the local geometry of the workspace around a system state can be combined with local metrics describing system dynamics to improve the connectivity of the graph produced by a sampling-based planner over a fixed number of configurations. This development is achieved through generalization of the concept of [Read more →]

We document empirically stable bounding using an actively powered spine on the Inu quadrupedal robot, and propose a reduced-order model to capture the dynamics associated with this additional, actuated spine degree of freedom. This model is sufficiently accurate as to roughly describe the robots mass center trajectory during a [Read more →]

We study the spatial sampling strategies employed by field scientists studying aeolian processes, which are geophysical interactions between wind and terrain. As in geophysical field science in general, observations of aeolian processes are made and data gathered by carrying instruments to various locations and then deciding when [Read more →]

This paper contributes to quantifying the notion of robotic fitness by developing a set of necessary conditions that determine whether a small quadruped has the ability to open a class of doors or climb a class of stairs using only quasi-static maneuvers. After verifying that several such machines from the recent robotics [Read more →]

In robotics, it is often practically and theoretically convenient to design motion planners for approximate low-order (e.g., position- or velocity-controlled) robot models first, and then adapt such reference planners to more accurate high-order (e.g., force/torque-controlled) robot models. In this paper, we introduce a novel [Read more →]

Anti-virus software based on unsupervised hierarchical clustering (HC) of malware samples has been shown to be vulnerable to poisoning attacks. In this kind of attack, a malicious player degrades anti-virus performance by submitting to the database samples specifically designed to collapse the classification hierarchy utilized by [Read more →]

Sampling-based algorithms offer computationally efficient, practical solutions to the path finding problem in high-dimensional complex configuration spaces by approximately capturing the connectivity of the underlying space through a (dense) collection of sample configurations joined by simple local planners. In this paper, we [Read more →]

In this paper we introduce and study three new measures for efficient discriminative comparison of phylogenetic trees. The NNI navigation dissimilarity $d_{nav}$ counts the steps along a “combing” of the Nearest Neighbor Interchange (NNI) graph of binary hierarchies, providing an efficient approximation to the (NP-hard) NNI [Read more →]

This paper develops a comparative framework for the design of an actuated inertial appendage for planar reorientation. We define the Inertial Reorientation template, the simplest model of this behavior, and leverage its linear dynamics to reveal the design constraints linking a task with the body designs capable of completing it. [Read more →]

For direct-drive legged robots operating in unstructured environments, workspace volume and force generation are competing, scarce resources. In this paper we demonstrate that introducing geared core actuation (i.e., proximal to rather than distal from the mass center) increases workspace volume and can provide a disproportionate [Read more →]

Spatial point process models are a commonly-used statistical tool for studying the distribution of objects of interest in a domain. We study the problem of deploying mobile robots as remote sensors to estimate the parameters of such a model, in particular the intensity parameter lambda which measures the mean density of points in [Read more →]

The Jerboa, a tailed bipedal robot with two hip-actuated, passive-compliant legs and a doubly actuated tail, has been shown both formally and empirically to exhibit a variety of stable hopping and running gaits in the sagittal plane. In this paper we take the first steps toward operating Jerboa as a fully spatial machine by [Read more →]

Rigid bodies, plastic impact, persistent contact, Coulomb friction, and massless limbs are ubiquitous simplifications introduced to reduce the complexity of mechanics models despite the obvious physical inaccuracies that each incurs individually. In concert, it is well known that the interaction of such idealized approximations [Read more →]

In robotics, it is essential to model and understand the topologies of configuration spaces in order to design provably correct motion planners. The common practice in motion planning for modelling configuration spaces requires either a global, explicit representation of a configuration space in terms of standard geometric and [Read more →]

We construct a sensor-based feedback law that provably solves the real-time collision-free robot navigation problem in a compact convex Euclidean subset cluttered with unknown but sufficiently separated and strongly convex obstacles. Our algorithm introduces a novel use of separating hyperplanes for identifying the robot’s local [Read more →]

In distributed mobile sensing applications, networks of agents that are heterogeneous respecting both actuation as well as body and sensory footprint are often modelled by recourse to power diagrams — generalized Voronoi diagrams with additive weights. In this paper we adapt the body power diagram to introduce its “free [Read more →]

We reconsider the problem of reactive navigation in sphere worlds, i.e., the construction of a vector field over a compact, convex Euclidean subset punctured by Euclidean disks, whose flow brings a Euclidean disk robot from all but a zero measure set of initial conditions to a designated point destination, with the guarantee of no [Read more →]

In robotics, it is essential to model and understand the topologies of configuration spaces in order to design provably correct motion planners. The common practice in motion planning for modelling configuration spaces requires either a global, explicit representation of a configuration space in terms of standard geometric and [Read more →]

This paper explores the applicability of a Linear Quadratic Regulator (LQR) controller design to the problem of bipedal stance on the Minitaur [1] quadrupedal robot. Restricted to the sagittal plane, this behavior exposes a three degree of freedom (DOF) double inverted pendulum with extensible length that can be projected onto the [Read more →]

An elementary geometric construction, known as Napoleon’s theorem, produces an equilateral triangle, obtained from equilateral triangles erected on the sides of any initial triangle: The centers of the three equilateral triangles erected on the sides of the arbitrarily given original triangle, all outward or all inward, are the [Read more →]

We introduce the use of hierarchical clustering for relaxed, deterministic coordination and control of multiple robots. Traditionally an unsupervised learning method, hierarchical clustering offers a formalism for identifying and representing spatially cohesive and segregated robot groups at different resolutions by relating the [Read more →]

RHex is one of very few legged robots being used for realworld rough-terrain locomotion applications. From its early days, RHex has been shown to locomote successfully over obstacles higher than its own hip height [1], and more recently, on sand [2] and sand dunes [3], [4] (see Figure 1). The commercial version of RHex made by [Read more →]

This letter introduces Minitaur, a dynamically running and leaping quadruped, which represents a novel class of direct-drive (DD) legged robots. We present a methodology that achieves the well-known benefits of DD robot design (transparency, mechanical robustness/efficiency, high-actuation bandwidth, and increased specific power), [Read more →]

We propose a self-organizing memory architecture (UMA) for perceptual experience provably capable of supporting autonomous learning and goal-directed problem solving in the absence of any prior information about the agent’s environment. The architecture is simple enough to ensure (1) a quadratic bound (in the number of available [Read more →]

We empirically investigate the implications of applying Raibert’s Scissor algorithm to the Spring Loaded Inverted Pendulum (SLIP) model in combination with other controllers to achieve transitional maneuvers. Specifically, we are interested in how the conjectured neutral stability of Raibert’s algorithm allows combined [Read more →]

This paper examines the design of a parallel spring-loaded actuated linkage intended for dynamically dexterous legged robotics applications. Targeted at toe placement in the sagittal plane, the mechanism applies two direct-drive brushless dc motors to a symmetric five bar linkage arranged to power free tangential motion and [Read more →]

We develop a stochastic framework for modeling and analysis of robot navigation in the presence of obstacles. We show that, with appropriate assumptions, the probability of a robot avoiding a given obstacle can be reduced to a function of a single dimensionless parameter which captures all relevant quantities of the problem. This [Read more →]

We introduce the use of hierarchical clustering for relaxed, deterministic coordination and control of multiple robots. Traditionally an unsupervised learning method, hierarchical clustering offers a formalism for identifying and representing spatially cohesive and segregated robot groups at different resolutions by relating the [Read more →]

This paper presents preliminary results of a semi-autonomous building exploration behavior using the hexapedal robot RHex. Stairwells are used in virtually all multi-floor buildings, and so in order for a mobile robot to effectively explore, map, clear, monitor, or patrol such buildings it must be able to ascend and descend [Read more →]

We have built a 4DOF tailed monoped that hops along a boom permitting free sagittal plane motion. This underactuated platform is powered by a hip motor that adjusts leg touchdown angle in flight and balance in stance, along with a tail motor that adjusts body shape in flight and drives energy into the passive leg shank spring [Read more →]

Measurements used to study wind shear stress and turbulence, surface roughness, sand flux, and dust emissions are typically obtained from stationary instrumentation, and are thus limited spatially. They are also dependent on deployment of instrumentation for specific events and thus the are limited temporally. We have been [Read more →]

This paper explores the design space of simple legged robots capable of leaping culminating in new behaviors for the Penn Jerboa, an underactuated, dynamically dexterous robot. Using a combination of formal reasoning and physical intuition, we analyze and test successively more capable leaping behaviors through successively more [Read more →]

We have built a 12DOF, passive-compliant legged, tailed biped actuated by four brushless DC motors. We anticipate that this machine will achieve varied modes of quasistatic and dynamic balance, enabling a broad range of locomotion tasks including sitting, standing, walking, hopping, running, turning, leaping, and more. Achieving [Read more →]

We refine and advance a notion of parallel composition to achieve for the first time a stability proof and empirical demonstration of a steady-state gait on a highly coupled 3DOF legged platform controlled by two simple (decoupled) feedback laws that provably stabilize in isolation two simple 1DOF mechanical subsystems. [Read more →]

This paper addresses the coordinated navigation of multiple independently actuated disk-shaped robots-all placed within the same disk-shaped workspace. Assuming perfect sensing, shared-centralized communications and computation, as well as perfect actuation, we encode complete information about the goal, obstacles, and workspace [Read more →]

Researchers in a variety of fields, including aeolian science, biology, and environmental science, have already made use of stationary and mobile remote sensing equipment to increase their variety of data collection opportunities. However, due to mobility challenges, remote sensing opportunities relevant to desert environments and [Read more →]

Desertification is a long-standing issue in China, but research on the processes of desertification is limited by availability of personnel and technical equipment. This suggests a perfect application and further testing ground for the mobile desert sensing technology described in a previous technical report. We describe here the [Read more →]

We present a centralized online (completely reactive) hybrid navigation algorithm for bringing a swarm of n perfectly sensed and actuated point particles in Euclidean d space (for arbitrary n and d) to an arbitrary goal configuration with the guarantee of no collisions along the way. Our construction entails a discrete abstraction [Read more →]

We introduce a recursive (“anytime”) distributed algorithm that iteratively restructures any initial spanning tree of a weighted graph towards a minimum spanning tree while guaranteeing at each successive step a spanning tree shared by all nodes that is of lower weight than the previous. Each recursive step is computed by a [Read more →]

We introduce an agility measure enabling the comparison of two very different leaping-from-rest transitions by two comparably powered but morphologically different legged robots. We use the measure to show that a flexible spine outperforms a rigid back in the leaping- from-rest task. The agility measure also sheds light on the [Read more →]

We consider the problem of visually servoing a legged vehicle with unicycle-like nonholonomic constraints subject to second-order fore-aft dynamics in its horizontal plane. We target applications to rugged environments characterized by complex terrain likely to perturb significantly the robot’s nominal dynamics. At the same [Read more →]

We propose a new anytime hierarchical clustering method that iteratively transforms an arbitrary initial hierarchy on the configuration of measurements along a sequence of trees we prove for a fixed data set must terminate in a chain of nested partitions that satisfies a natural homogeneity requirement. Each recursive step [Read more →]

Robots are often modeled as hybrid systems providing a consistent, formal account of the varied dynamics associated with the loss and gain of kinematic freedom as a machine impacts and breaks away from its environment.

We prove convergence of an approximate Bayesian estimator for the (scalar) location estimation problem by recourse to a histogram approximant. We exploit its tractability to present a simple strategy for managing the tradeoff between accuracy and complexity through the cardinality of the underlying partition. Our theoretical [Read more →]

Many locomotion tasks on real, complex terrain are poorly modeled as deviations from limit cycles of steady state running. As obstacles become larger and larger relative to leg length, every step is novel and challenging: the leap onto a ledge in Fig. 1 is quite unlike any running step. We seek to organize and systematically [Read more →]

We propose a new paradigm for reactive wallfollowing by a planar robot taking the form of an actively steered sensor model that augments the robot’s motion dynamics. We postulate a foveated sensor capable of delivering third-order infinitesimal (range, tangent, and curvature) data at a point along a wall (modeled as an unknown [Read more →]

As dynamic robot behaviors become more capable and well understood, the need arises for a wide variety of equally capable and systematically applicable transitions between them. We use a hybrid systems framework to characterize the dynamic transitions of a planar “legged” rigid body from rest on level ground to a fully aerial [Read more →]

We document initial experiments with Canid, a freestanding, power-autonomous quadrupedal robot equipped with a parallel actuated elastic spine. Research into robotic bounding and galloping platforms holds scientific and engineering interest because it can both probe biological hypotheses regarding bounding and galloping mammals [Read more →]

Humans and animals adapt their leg impedance during running for both internal (e.g., loading) and external (e.g., surface) changes. To date, the mechanical complexity of designing usefully robust tunable passive compliance into legs has precluded their implementation on practical running robots. This work describes the design of [Read more →]

This paper introduces self-manipulation as a new formal design methodology for legged robots with varying ground interactionsRead more → This work was supported by the ARL/GDRS RCTA project under Cooperative Agreement Number W911NF-10–2−0016. For further information, visit Kod*lab.

We propose a self-organizing database for per- ceptual experience capable of supporting autonomous goal- directed planning. The main contributions are: (i) a formal demonstration that the database is complex enough in principle to represent the homotopy type of the sensed environment; (ii) some initial steps toward a formal [Read more →]

On challenging, uneven terrain a legged robot’s open loop posture will almost inevitably be inefficient, due to uncoordinated support of gravitational loads with coupled internal torques. By reasoning about certain structural properties governing the infinitesimal kinematics of the closed chains arising from a typical stance, we [Read more →]

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In this paper we explore the design space of tails intended for self-righting a robot’s body during free fall. Conservation of total angular momentum imposes a dimensionless index of rotational efficacy upon the robot’s kinematic and dynamical parameters whose selection insures that for a given tail rotation, the body rotation [Read more →]

This technical report is a companion document to the CLAWAR 2012 paper of the same name, for which we explicitly write out a full derivation of the kinematics and dynamics. Please refer to that document for motivation, experimentation, and discussion.

For mobile robots, the essential units of actuation, computation, and sensing must be designed to fit within the body of the robot. Additional capabilities will largely depend upon a given activity, and should be easily reconfigurable to maximize the diversity of applications and experiments. To address this issue, we introduce a [Read more →]

This paper describes the inspiration, design, analysis, implementation of and experimentation with the first dynamical vertical climbing robot. Biologists have proposed a pendulous climbing model that abstracts remarkable similarities in dynamic wall scaling behavior exhibited by radically different animal species. We study [Read more →]

Granular media (GM) present locomotor challenges for terrestrial and extraterrestrial devices because they can flow and solidify in response to localized intrusion of wheels, limbs and bodies. While the development of airplanes and submarines is aided by understanding of hydrodynamics, fundamental theory does not yet exist to [Read more →]

This report presents the apex state achieved after performing a variety of jumps with the XRL robot. A full account of the behaviors and the theoretical basis is given in another paper, this document is intended to simply provide higher resolution copies of those figures, and present the results in numerical form.

We propose a dynamical reference generator equipped with an augmented transient “replanning” subsystem that modulates a feedback controller’s efforts to force a mechanical plant to track the reference signal. The replanner alters the reference generator’s output in the face of unanticipated disturbances that drive up the [Read more →]

This paper documents near-autonomous negotiation of synthetic and natural climbing terrain by a rugged legged robot, achieved through sequential composition of appropriate perceptually triggered locomotion primitives. The first, simple composition achieves autonomous uphill climbs in unstructured outdoor terrain while avoiding [Read more →]

We develop robust methods that allow specification, control, and transition of a multi-legged robot’s stepping pattern—its gait—during active locomotion over natural terrain. Resulting gaits emerge through the introduction of controllers that impose appropriately-placed repellors within the space of gaits, the torus of [Read more →]

Biomechanical studies suggest that animals’ abilities to tune their effective leg compliance in response to changing terrain conditions plays an important role in their agile, robust locomotion. However, despite growing interest in leg compliance within the robotics literature, little experimental work has been reported on [Read more →]

We explore an approach to incorporating task and motor thermal dynamics in the selection of actuators for legged robots, using both analytical and simulation methods. We develop a motor model with a thermal component and apply it to a vertical climbing task; in the process, we optimally choose gear ratio and therefore eliminate it [Read more →]

This paper investigates the relationship between energetic effi- ciency and the dynamical structure of a legged robot’s gait. We present an experimental data set collected from an untethered dynamic hexapod, EduBot [1] (a RHex-class [2] machine), operating in four distinct manually selected gaits. We study the robot’s single [Read more →]

This paper revisits the concept of specific resistance, a dimensionless measure of locomotive efficiency often used to compare the transport cost of vehicles (Gabrielli & von Karman 1950), and extends its use to the vertical domain. As specific resistance is designed for comparing horizontal locomotion, we introduce a [Read more →]

This paper revisits the concept of specific resistance, a dimensionless measure of locomotive efficiency often used to compare the transport cost of vehicles (Gabrielli & von Karman 1950), and extends its use to the vertical domain. As specific resistance is designed for comparing horizontal locomotion, we introduce a [Read more →]

We report on the design and development of X-RHex, a hexapedal robot with a single actuator per leg, intended for real-world mobile applications. X-RHex is an updated version of the RHex platform, designed to offer substantial improvements in power, run-time, payload size, durability, and terrain negotiation, with a smaller [Read more →]

Empirical data taken from fast climbing sprawled posture animals reveals the presence of strong lateral forces with significant pendulous swaying of the mass center trajectory in a manner captured by a recently proposed dynamical template. In this simulation study we explore the potential benefits of pendulous dynamical climbing [Read more →]

We present a framework for detecting, identifying, and recovering within stride from faults and other leg contact disturbances encountered by a walking hexapedal robot. Detection is achieved by means of a software contactevent sensor with no additional sensing hardware beyond the commercial actuators’ standard shaft encoders. A [Read more →]

This paper presents a methodology enabling robotic systems to classify and identify their environment according to the mechanical properties of the local contact dynamics. Described approach employs existing proprioceptive sensors and requires no additional specialized hardware. Identification process is performed in real-time [Read more →]

Traditional legged runners and climbers have relied heavily on gait generators in the form of internal clocks or reference trajectories. In contrast, here we present physical experiments with a fast, dynamical, vertical wall climbing robot accompanying a stability proof for the controller that generates it without any need for an [Read more →]

Passively compliant legs have been instrumental in the development of dynamically running legged robots. Having properly tuned leg springs is essential for stable, robust and energetically efficient running at high speeds. Recent simulation studies indicate that having variable stiffness legs, as animals do, can significantly [Read more →]

As robot bodies become more capable, the motivation grows to better coordinate them—whether multiple limbs attached to a body or multiple bodies assigned to a task. This paper introduces a new formalism for coordination of periodic tasks, with specific application to gait transitions for legged platforms. Specifically, we make [Read more →]

This paper introduces the problem of determining through distributed consensus the fastest mixing Markov chain with a desired sparsity pattern. In contrast to the centralized optimization-based problem formulation, we develop a novel distributed relaxation by constructing a dynamical system over the cross product of an [Read more →]

This paper describes the development of a legged robot designed for general locomotion of complex terrain but specialized for dynamical, high-speed climbing of a uniformly convex cylindrical structure, such as an outdoor telephone pole. This robot, the RiSE V3 climbing machine—mass 5.4 kg, length 70 cm, excluding a 28 cm tail [Read more →]

Ability to translate to a goal position under the constrains imposed by complex environmental conditions is a key capability for biological and artificial systems alike. Over billions of years evolutionary processes have developed a wide range of solutions to address mobility needs in air, in water and on land. The efficacy of [Read more →]

Legged locomotion on flowing ground (e.g., granular media) is unlike locomotion on hard ground because feet experience both solid- and fluid-like forces during surface penetration. Recent bioinspired legged robots display speed relative to body size on hard ground comparable with high-performing organisms like cockroaches but [Read more →]

We are interested in the development of a variety of legged robot platforms intended for operation in unstructured outdoor terrain. In such settings, the traditions of rational engineering design, driven by analytically informed and computationally assisted studies of robot-environment models, remain ineffective due to the [Read more →]

Arthropods with their extraordinary locomotive capabilities have inspired roboticists, giving rise to major accomplishments in robotics research over the past decade. Most notably bio-inspired hexapod robots using only task level open-loop controllers [22, 9] exhibit stable dynamic locomotion over highly broken and unstable [Read more →]

This paper presents an integrated, systems-level view of several novel design and control features associated with the biologically inspired, hexapedal, RiSE (Robots in Scansorial Environments) robot. RiSE is the first legged machine capable of locomotion on both the ground and a variety of vertical building surfaces including [Read more →]

Our objective is to provide experimentalists with neuromechanical control hypotheses that can be tested with kinematic data sets. To illustrate the approach, we select legged animals responding to perturbations during running. In the following sections, we briefly outline our dynamical systems approach, state our over-arching [Read more →]

This paper addresses problems of robot navigation with nonholonomic motion constraints and perceptual cues arising from onboard visual servoing in partially engineered environments. We propose a general hybrid procedure that adapts to the constrained motion setting the standard feedback controller arising from a navigation [Read more →]

Legged robots are by nature strongly non-linear, high-dimensional systems whose full complexity permits neither tractable mathematical analysis nor comprehensive numerical study. In consequence, a growing body of literature interrogates simplified “template” [1], [2] models—to date almost exclusively confined to sagittal- or [Read more →]

Recent developments in dynamic legged locomotion have focused on encoding a substantial component of leg intelligence into passive compliant mechanisms. One of the limitations of this approach is reduced adaptability: the final leg mechanism usually performs optimally for a small range of conditions (i.e. a certain robot weight, [Read more →]

This paper reviews a template for dynamical climbing originating in biology, explores its stability properties in a numerical model, and presents empirical data from a physical prototype as evidence of the feasibility of adapting the dynamics of the template to robot that runs vertically upward. The recently proposed pendulous [Read more →]

We present our approach to undergraduate engineering education, “A contexualized, social, self-paced, engineering education for life-long learners” through a look at a new two course introductory sequence for the freshman year. As the centerpiece of these courses, we use a smaller version of our advanced research platform, [Read more →]

We report on a hybrid 12-dimensional full body state estimator for a hexapod robot executing a jogging gait in steady state on level terrain with regularly alternating ground contact and aerial phases of motion. We use a repeating sequence of continuous time dynamical models that are switched in and out of an extended Kalman [Read more →]

Simple mathematical models or ‘templates’ of locomotion have been effective tools in understanding how animals move and have inspired and guided the design of robots that emulate those behaviors. This paper describes a recently proposed biologically-based template for dynamic vertical climbing, and evaluates the feasibility [Read more →]

We discuss the gait generation and control architecture of a bioinspired climbing robot that presently climbs a variety of vertical surfaces, including carpet, cork and a growing range of stucco-like surfaces in the quasi-static regime. The initial version of the robot utilizes a collection of gaits (cyclic feed-forward motion [Read more →]

Cheetahs and beetles run, dolphins and salmon swim, and bees and birds fly with grace and economy surpassing our technology. Evolution has shaped the breathtaking abilities of animals, leaving us the challenge of reconstructing their targets of control and mechanisms of dexterity. In this review we explore a corner of this [Read more →]

We report on a continuous-time rigid-body pose estimator for a walking hexapod robot. Assuming at least three legs remain in ground contact at all times, our algorithm uses the outputs of six leg-configuration sensor models together with a priori knowledge of the ground and robot kinematics to compute instantaneous estimates of [Read more →]

We review a large multidisciplinary effort to develop a family of autonomous robots capable of rapid, agile maneuvers in and around natural and artificial vertical terrains such as walls, cliffs, caves, trees and rubble. Our robot designs are inspired by (but not direct copies of) biological climbers such as cockroaches, geckos, [Read more →]

This paper introduces a framework for representing, generating, and then tuning gaits of legged robots. We introduce a convenient parametrization of gait generators as dynamical systems possessing designer specified stable limit cycles over an appropriate torus. This parametrization affords a continuous selection of operation [Read more →]

A collection of unactuated disk-shaped "parts" must be brought by an actuated manipulator robot into a specified configuration from arbitrary initial conditions. The task is cast as a noncooperative game played among the parts—which in turn yields a feedback-based event-driven approach to plan generation and execution. The [Read more →]

We present a new stability analysis for hybrid legged locomotion systems based on the “symmetric” factorization of return maps.We apply this analysis to two-degrees-of-freedom (2DoF) and threedegrees- of-freedom (3DoF) models of the spring loaded inverted pendulum (SLIP) with different leg recirculation strategies. Despite the [Read more →]

This paper addresses problems of robot navigation with nonholonomic motion constraints and perceptual cues arising from onboard visual servoing in partially engineered environments. We focus on a unicycle motion model and a variety of artificial beacon constellations motivated by relevance to the autonomous hexapod, RHex. We [Read more →]

We report on a continuous time full body state estimator for a hexapod robot operating in the dynamical regime (entailing a significant aerial phase) on level ground that combines a conventional rate gyro with a novel leg strain based body pose estimator. We implement this estimation procedure on the robot RHex and evaluate its [Read more →]

We report on the design and analysis of a controller that can achieve dynamical self-righting of our hexapedal robot, RHex. Motivated by the initial success of an empirically tuned controller, we present a feedback controller based on a saggital plane model of the robot. We also extend this controller to develop a hybrid pumping [Read more →]

In this paper, we report on the design of a model-based controller that can achieve dynamical self-righting of a hexapod robot. Extending on our earlier work in this domain, we introduce a tractable multi-point contact model with Coulomb friction. We contrast the singularities inherent to the new model with other available methods [Read more →]

Gait parameter adaptation on a physical robot is an error-prone, tedious and time-consuming process. In this paper we present a system for gait adaptation in our RHex series of hexapedal robots that renders this arduous process nearly autonomous. The robot adapts its gait parameters by recourse to a modified version of Nelder-Mead [Read more →]

We report on a continuous time odometry scheme for a walking hexapod robot built upon a previously developed leg-strain based body pose estimator. We implement this estimation procedure and odometry scheme on the robot RHex and evaluate its performance at widely varying speeds and over different ground conditions by means of a 6 [Read more →]

In this paper, we introduce a hexapedal locomotion controller that simulation evidence suggests will be capable of driving our RHex robot at speeds exceeding five body lengths per second with reliable stability and rapid maneuverability. We use a low dimensional passively compliant biped as a "template" -- a control target for the [Read more →]

In this paper, we report on a new stability analysis for hybrid legged locomotion systems based on factorization of return maps. We apply this analysis to a family of models of the Spring Loaded Inverted Pendulum (SLIP) with different leg recirculation strategies. We obtain a necessary condition for the asymptotic stability of [Read more →]

This paper addresses the problem of registering the hexapedal robot RHex, relative to a known set of beacons, by real-time visual servoing. A suitably constructed navigation function represents the task, in the sense that for a completely actuated machine in the horizontal plane, the gradient dynamics guarantee convergence to the [Read more →]

We report on a novel leg strain sensory system for the autonomous robot RHex [Saranli U. et al., 2001] implemented upon a cheap, high performance local wireless network [H. Komsuoglu, 2002]. We introduce a model for RHex's 4-bar legs [E.Z. Moore, 2001] relating leg strain to leg kinematic configuration in the body coordinate [Read more →]

The spring-loaded inverted pendulum (SLIP), or monopedal hopper, is an archetypal model for running in numerous animal species. Although locomotion is generally considered a complex task requiring sophisticated control strategies to account for coordination and stability, we show that stable gaits can be found in the SLIP with [Read more →]

The class of continuous piecewise linear (PL) functions represents a useful family of approximants because invertibility can be readily imposed, and if a PL function is invertible, then it can be inverted in closed form. Many applications, arising, for example, in control systems and robotics, involve the simultaneous construction [Read more →]

This paper presents a general framework for representing and generating gaitsfor legged robots. We introduce a convenient parametrization of gait generators as dynamical systems possessing specified stable limit cycles over an appropriate torus. Inspired by biology, this parametrization affords a continuous selection of operation [Read more →]

Planar, underactuated, biped walkers form an important domain of applications for hybrid dynamical systems. This paper presents the design of exponentially stable walking controllers for general planar bipedal systems that have one degree-of-freedom greater than the number of available actuators. The within-step control action [Read more →]

This paper presents a framework for visual servoing that guarantees convergence to a visible goal from almost every initially visible configurations while maintaining full view of all the feature points along the way. The method applies to first- and second-order fully actuated plant models. The solution entails three components: [Read more →]

The zero dynamics of a hybrid model of bipedal walking are introduced and studied for a class of N-link, planar robots with one degree of underactuation and outputs that depend only on the configuration variables. Asymptotically stable solutions of the zero dynamics correspond to asymptotically stabilizable orbits of the full [Read more →]

We report on the design and analysis of a controller which can achieve dynamical self-righting of our hexapedal robot, RHex. We present an empirically developed control procedure which works reasonably well on indoor surfaces, using a hybrid energy pumping strategy to overcome torque limitations of its actuators. Subsequent [Read more →]

We address the problem of coupling cyclic robotic tasks to produce a specified coordinated behavior. Such coordination tasks are common in robotics, appearing in applications like walking, hopping, running, juggling and factory automation. In this paper we introduce a general methodology for designing controllers for such [Read more →]

This paper introduces the use of vector fields to design, optimize, and implement reactive schedules for safe cooperative robot patterns on planar graphs. We consider automated guided vehicles (AGVs) operating upon a predefined network of pathways. In contrast to the case of locally Euclidean configuration spaces, regularization [Read more →]

The dynamics of a Spring Loaded Inverted Pendulum (SLIP) \template” [1] approximate well the center of mass (COM) of running animals, humans, and of the robot RHex [2]. Running control can therefore be ierarchically structured as a high level SLIP control and the anchoring of SLIP in the complex morphology of the physical [Read more →]

It is now well established that running animals’ mass centers exhibit the characteristics of a Spring Loaded Inverted Pendulum (SLIP) in the sagittal plane (Blickhan and Full, 1993). What control policy accomplishes this collapse of dimension by which animals solve the “degrees of freedom problem” (Bernstein, 1967)Read more → How [Read more →]

Animals execute locomotor behaviors and more with ease. They have evolved these breath-taking abilities over millions of years. Cheetahs can run, dolphins can swim and flies can fly like no artificial technology can. It is often argued that if human technology could mimic nature, then biological-like performance would follow. [Read more →]

EDAR (event-driven assembler robot) — a mobile robot capable of moving a collection of disk-shaped parts located on a two-dimensional workspace from an arbitrary initial configuration to a desired configuration while avoiding collisions in a purely reactive manner, is presented. Since EDAR uses a higher-level scheduler to switch [Read more →]

The flexibility of computer vision is attractive when designing manipulation systems which must interact with otherwise unsensed objects. However, occlusions introduce significant challenges to the construction of practical vision-based control systems. This paper provides empirical validation of a vision based control strategy [Read more →]

In this paper, the authors describe the design and control of RHex, a power autonomous, untethered, compliant-legged hexapod robot. RHex has only six actuators—one motor located at each hip—achieving mechanical simplicity that promotes reliable and robust operation in real-world tasks. Empirically stable and highly [Read more →]

We describe a method for the decentralized phase regulation of two coupled hybrid oscillators. In particular, we prove that the application of this synchronization method to two hopping robots, each of which individually achieves only asymptotically stable hopping, results in an asymptotically stable limit cycle for the coupled [Read more →]

We report on our progress in extending the behavioral repertoire of RHex, a compliant leg hexapod robot. We introduce two new controllers, one for climbing constant slope inclinations and one for achieving higher speeds via pronking, a gait that incorporates a, substantial aerial phase. In both cases, we make use of an underlying [Read more →]

We propose an event-driven algorithm for the control of simple robot assembly problems based on noncooperative game theory. We examine rigorously the simplest setting — three bodies with one degree of freedom and offer extensive simulations for the 2 DOF extension. The initial analysis and the accompanying simulations suggest [Read more →]

Many tasks in robotics and automation require a cyclic exchange of energy between a machine and its environment. Since most environments are "under actuated"—that is, there are more objects to be manipulated than actuated degrees of freedom with which to manipulate them—the exchange must be punctuated by intermittent repeated [Read more →]

This paper presents the first evidence that the Spring Loaded Inverted Pendulum (SLIP) may be “anchored ” in our recently designed compliant leg hexapod robot, RHex. Experimentally measured RHex center of mass trajectories are fit to the SLIP model and an analysis of the fitting error is performed. The fitting results are [Read more →]

We investigate the stability of a one degree of freedom mechanical spring-mass system modulated by a feed-forward "clock" that stiffens and relaxes a Hooke's law potential force according to a periodic rhythm. At the present early stage of inquiry, we offer sufficient conditions for local asymptotic stability of an isolated [Read more →]

We report in this paper a relatively simple means of generating closed-form approximants to the return map associated with a family of nonintegrable Hamiltonian systems. These systems arise in consideration of legged locomotion by animals and robots. The approximations proceed through the iterated application of the mean value [Read more →]

Visual servo controllers in the literature rarely achieve provably large domains of attraction, and seldom address two important sensor limitations: (i) susceptibility to self-occlusions and (ii) finite field of view (FOV). We tackle the problem of global, occlusion-free visual servoing of a fully actuated rigid body by recourse [Read more →]

Stable and robust autonomous dynamic locomotion is demonstrated experimentally in a four and a six-legged robot. The Scout II quadruped runs on flat ground in a bounding gait, and was motivated by an effort to understand the minimal mechanical design and control complexity for dynamically stable locomotion. The RHex 0 hexapod runs [Read more →]

The class of piecewise linear homeomorphisms (PLH) provides a convenient functional representation for many applications wherein an approximation to data is required that is invertible in closed form. In this paper we introduce the graph intersection (GI) algorithm for "learning" piecewise linear scalar functions in two settings: [Read more →]

We introduce tools which help one to compose concurrent, hybrid control programs for a class of distributed robotic systems, assuming a palette of controllers for individual tasks is already constructed. These tools, which combine the backchaining of continuous robot behaviors with Petri nets, expand on successful work in [Read more →]

We report on our empirical studies of a new controller for a two-link brachiating robot. Motivated by the pendulum-like motion of an ape's brachiation, we encode this task as the output of a "target dynamical system." Numerical simulations indicate that the resulting controller solves a number of brachiation problems that we term [Read more →]

We present the design, modeling and preliminary control of RHex, an autonomous dynamically stable hexapod possessing merely six actuated degrees of freedom (at the hip attachment of each leg). Our design emphasizes mechanical simplicity as well as power and computational autonomy, critical components for legged robotics [Read more →]

This paper is concerned with the parts’ moving problem based on an event-driven planning and control. We are interested in developing feedback based approaches to the automatic generation of actuator commands that cause the robot to move a set of parts from an arbitrary initial disassembled configuration to a specif ed final [Read more →]

We propose the "minvar" algorithm for computing continuous, continuously invertible, piecewise linear (PL) approximations of color space transformations that can serve as functional replacements wherever look-up tables are presently used. After motivating the importance of invertible approximants in color space management [Read more →]

The University of Michigan and Xerox's Wilson Research Center have been collaborating on problems in color management systems since 1996, supported in part by an NSF GOALI grant. The paper is divided into three sections. The first discusses the basics of xerography and areas where systems methodology can have a potential impact. [Read more →]

Locomotion results from complex, high-dimensional, non-linear, dynamically coupled interactions between an organism and its environment. Fortunately, simple models we call templates have been and can be made to resolve the redundancy of multiple legs, joints and muscles by seeking synergies and symmetries. A template is the [Read more →]

In this paper, we report on a "hybrid" scheme for regulating the swing up behavior of a two degree of freedom brachiating robot. In this controller, a previous "target dynamics" controller and a mechanical energy regulator are combined. The proposed controller guarantees the boundedness of the total energy of the system. [Read more →]

We report on our efforts to develop a sequential robot controller composition technique in the context of dexterous “batting” maneuvers. A robot with a flat paddle is required to strike repeatedly at a thrown ball until the ball is brought to rest on the paddle at a specified location. The robot’s reachable workspace is [Read more →]

We have previously developed a brachiation controller that allows a two degree of freedom robot to swing from handhold to handhold on a horizontal ladder with evenly space rungs as well as swing up from a suspended posture using a "target dynamics" controller. In this paper, we extend this class of algorithms to handle the much [Read more →]

We describe a hybrid planar image-based servo algorithm which, for a simplified planar convex rigid body, converges to a static goal for all initial conditions within the workspace of the camera. This is achieved by using the sequential composition of a palette of continuous image based controllers. Each sub-controller, based on a [Read more →]

We address the problem of controlling large distributed robotic systems such as factories. We introduce tools which help us compose local, hybrid control programs for a class of distributed robotic systems, assuming a palette of controller for individual tasks is already constructed. These tools, which combine backchaining [Read more →]

We consider the use of linear splines with variable knots for the approximation of unknown functions from data, motivated by control and estimation problems arising in color systems management. Unlike most popular nonlinear-in-parameters representations, piecewise linear (PL) functions can be simply inverted in a closed form. For [Read more →]

We describe work-in-progress toward a nonlinear image-based rigid body dynamic triangulator which we believe tracks a moving target from "essentially all" initial conditions (all initial conditions except a set of measure zero). The dynamic triangulator depends on the goal state only through its image plane position and velocity [Read more →]

We report on our recent empirical success in the study of a two-link brachiating robot. The "target dynamics" controller developed in our previous work (1997) is implemented on a physical system in our laboratory. The swing locomotion and swing-up behavior of the robot as well as continuous locomotion have been successfully [Read more →]

We propose a new family of controllers for multi-jointed planar monoped runners, based on approximate but accurate models of the stance phase dynamics of a two degree of freedom "SLIP" leg. Unlike previous approaches, the new scheme gives control over all parameters of the system including the hopping height, forward speed and [Read more →]

This paper explores the possibility of using vector fields to design and implement reactive schedules for safe cooperative robot patterns on graphs. The word "safe" means that obstacles - designated illegal portions of the configuration space - are avoided. The word "cooperative" connotes situations wherein physically distributed [Read more →]

We present a system for generation and recognition of oscillatory gestures. Inspired by gestures used in two representative human-to-human control areas, we consider a set of oscillatory (circular) motions and refine from them a 24 gestures lexicon. Each gesture is modeled as a dynamic system with added geometric constraints to [Read more →]

We characterize equilibrium gaits of a small knee monoped in terms of manifest parameters by recourse to approximate closed form expressions. We first eliminate gravity during stance and choose a very special model of potential energy storage in the knee. Next, we introduce simple closed form approximations, motivated by the mean [Read more →]

We report on our preliminary studies of a new controller for a two-link brachiating robot. Motivated by the pendulum-like motion of an ape's brachiation, we encode this task as the output of a "target dynamical system". Numerical simulations indicate that the resulting controller solves a number of brachiating problems that we [Read more →]

We present a simplified state-space model of a once-through supercritical boiler turbine power plant. This phenomenological model has been developed from a greatly simplified application of the first principles of physical laws. When we fit our model to a far more complex and physically accurate simulation model commissioned by [Read more →]

This paper presents some preliminary results from a research collaboration concerning the modeling and control of color xerography. In this first communication of our work, we describe our efforts to develop a model for a monochrome marking engine. We adopt the technique of principal component analysis for choice of output [Read more →]

We present a working implementation of a dynamics based architecture for visual sensing. This architecture provides field rate estimates of the positions and velocities of two independent falling balls in the face of repeated visual occlusions and departures from the field of view. The practical success of this system can be [Read more →]

We present a system for generation and recognition of oscillatory gestures. Inspired by gestures used in two representative human-to-human control areas, we consider a set of oscillatory motions and refine from them a 24 gesture lexicon. Each gesture is modeled as a dynamical system with added geometric constraints to allow for [Read more →]

We report on our efforts to develop robot controller composition techniques in the context of dexterous “batting” maneuvers. A robot with a flat paddle is required to strike repeatedly at a falling ball until it is brought to zero velocity at a a specified position. The robot’s workspace is cluttered with obstacles that [Read more →]

This paper reports on our present achievement toward the intelligent control of a boiler-turbine power-plant based on switching control scheme, recently revived by some active reports. To overcome strong nonlinearity emerging in load following operations of boiler-turbine power plants, which is not efficiently compensated by the [Read more →]

We propose an event-driven approach to planning and control of robot assembly problems using ideas from non-cooperative game theory. We report on the results of an extensive simulation study for a very simple two degree of freedom case - the arrangement of disks on a plane by a disk shaped robot.

We report on our initial efforts to build robot feedback controllers that develop increased capability from simpler constituent controllers. Previous work with our three degree of freedom robot has resulted in a machine that exhibits various dynamically dexterous skills of superlative ability but very narrow behavioral scope. We [Read more →]

A simplified lossless model of the Raibert planar hopper is introduced for the purpose of analytically studying the control of forward velocity. A closed-form return map describing the robot's state at the next hop as a function of that at the current hop is derived. The Raibert forward velocity controller is introduced and the [Read more →]

In this paper we demonstrate that a passive vibration strategy can bring a 1 degree of freedom ball to a known trajectory from all possible initial configurations. We draw motivation from the problem of parts feeding in sensorless assembly. We provide simulation results suggesting the relevance of our analytical results to the [Read more →]

This paper explores the problem of building robot navigation plans via scalar valued functions in the face of incomplete information about the configuration space such as might be available from onboard sensors. It seems as though syntactical aspects of navigation function construction may play an important role. This problem [Read more →]

This paper describes a simple visual servoing control algorithm capable of robustly positioning a three degree of freedom end effector based only on information from a stereo vision system. The proposed control algorithm does not require estimates of the gripper’s spatial position, a significant source of calibration [Read more →]

In this paper we discuss a robotic task requiring dynamical safety in the face of an intermittent environment. We define and offer examples of this notion. We then construct a dynamically safe composite controller from dynamically safe constituents, and present empirical evidence of its effectiveness. For more information: Kod*Lab

In this paper we demonstrate that a passive vibration strategy can bring a one-degree-of-freedom ball to a specified periodic trajectory from all initial conditions. We draw motivation from the problem of parts feeding in sensorless assembly. We provide simulation results suggesting the relevance of our analysis to the parts [Read more →]

In previous papers we have reported successful laboratory implementations of a family of juggling algorithms. In all but the one degree of freedom case, these empirically successful algorithms have so far resisted our analytical efforts to explain why they work. This is in large measure a consequence of our inability to write down [Read more →]

A new class of control algorithms—the “mirror algorithms”— gives rise to experimentally observed juggling and catching behavior in a planar robotic mechanism. The simplest of these algorithms (on which all the others are founded) is provably correct with respect to a simplified model of the robot and its environment. This [Read more →]

Assembly problems require that a robot with fewer actuated degrees of freedom manipulate an environment containing a greater number of unactuated degrees of freedom. From the perspective of control theory, these problems hold considerable interest because they are characterized by the presence of non-holonomic constraints that [Read more →]

This paper presents a stability analysis of a simple Shannon juggler and contrasts its properties with those of a mirror juggler. It discusses the need to develop a systems theory for strongly coupled tunable oscillators. For more information: Kod*Lab

In the recent successful effort to achieve the spatial two-juggle - batting two freely falling balls into independent stable periodic vertical orbits by repeated impacts with a three degree of freedom robot arm, the authors have found it necessary to introduce a dynamical window manager into their real-time stereo vision. This [Read more →]

We report on our recently achieved spatial two-juggle: the ability to bat two freely falling balls into stable periodic vertical trajectories with a single three degree of freedom robot arm using a real-time stereo camera system for sensory input. After a brief review of the previously reported one-juggle, we describe our initial [Read more →]

This paper presents a new model-based adaptive controller and proof of its global asymptotic stability with respect to the standard rigid-body model of robot-arm dynamics. Experimental data from a study of one new and several established globally asymptotically stable adaptive controllers on two very different robot arms 1) [Read more →]

We discuss the sensory management strategy that has evolved over the course of our efforts to build a three degree of freedom robot capable of juggling two balls at once . A field rate stereo camera system passes estimates of the balls’ positions to a juggling algorithm that drives the robot’s joint actuators. In order to meet [Read more →]

We present a new methodology for exact robot motion planning and control that unifies the purely kinematic path planning problem with the lower level feedback controller design. Complete information about the freespace and goal is encoded in the form of a special artificial potential function - a navigation function - that [Read more →]

An approach to the problem of controlling automated assembly tasks using artificial potential functions is described. The authors address the automatic generation of actuator commands for a robot manipulator that result in the motion of a collection of rigid-body parts from disassembled initial configurations to an assembled final [Read more →]

How is navigating a unicycle amidst obstacles like manipulating beads on a necklaceRead more → This paper addresses that question by introducing a simple control system that appears to offer a common dynamical model for both situations. System (1) consists of a trivially controlled set of “steering” state variables and an additional set [Read more →]

We review our progress to date in eliciting dynamically dexterous behaviors from a three degree of freedom direct drive robot manipulator whose real-time stereo cameras provide 60 Hz sampled images of multiple freely falling bodies in highly structured lighting conditions. At present, the robot is capable of forcing a single [Read more →]

An autonomous machine requires a description of its designated task in a language that it ‘understands’. The machine language of robots — physical mechanisms endowed with actuators and sensory devices for the purpose of performing work — is the language of dynamical systems. Since the diversity of robotic tasks is immense [Read more →]

This paper presents two setpoint regulation problems that may be distinguished from the traditional preview of feedback design by the a priori impossibility of building a smooth bounded controller whose closed loop yields asymptotic stability while preserving configuration constraints. An appeal to the theoretical ideas introduced [Read more →]

This article offers some analytical results concerning simplified models of Raibert's hopper. We represent the task of achieving a recurring hopping height for an actuated "ball" robot as a stability problem in a nonlinear discrete dynamical control system. We model the properties of Raibert's control scheme in a simplified [Read more →]

This paper concerns a simple extension of Lord Kelvin's observation that energy decays in a dissipative mechanical system. The global limit behavior ofsuch systems can be made essentially equivalent to that of much simpler gradient systems by the introduction of a "navigationfunction" in the role of an artificial field. This [Read more →]

An intelligent machine is autonomous. An autonomous machine can operate successfully in a diversity of situations without resort to intervention by “higher level” processes, for example, humans. Physical machines are ultimately force or torque controlled dynamical systems: the specification of input torques, whether via [Read more →]

An approach to the problem of automated assembly planning and control using artificial potential functions is described. A simple class of tasks, 2D sphere assemblies, is examined. A constructive theory for the planning and control of this class of tasks is presented. Computer simulations demonstrate that the approach may provide [Read more →]

A Euclidean Sphere World is a compact connected submanifold of Euclidean n-space whose boundary is the disjoint union of a finite number of (n — 1) dimensional Euclidean spheres. A Star World is a homeomorph of a Euclidean Sphere World, each of whose boundary components forms the boundary of a star shaped set. We construct a [Read more →]

In a continuing program of research in robotic control of intermittent dynamical tasks, we have constructed a three degree of freedom robot capable of juggling a ball falling freely in the earth’s gravitational field. This work is a direct extension of that previously reported in [7, 3, 5, 4]. The present paper offers a [Read more →]

This paper presents a new adaptive controller and proof of its global asymptotic stability with respect to the standard rigid body model of robot arm dynamics. Experimental data from a study of this and other globally asymptotically stable adaptive controllers on two very different robot arms (i) reconciles several previous [Read more →]

Assembly problems require that a robot with a few actuated degrees of freedom manipulate an environment with a greater number of unactuated degrees of freedom. Since the dynamical coupling between degrees of freedom in this setting is a function of their relative configuration, the motion of such systems is subject to constraints [Read more →]

Programming machines to operate flexibly and autonomously in the physical world seems to require a sophisticated representation that encodes simultaneously the nature of a task, the nature of the environment within which the task is to be performed, and the nature of the robot’s capabilities with respect to both. We seek a [Read more →]

Assembly problems require that a robot with a few actuated degrees of freedom manipulate an environment with a greater number of unactuated degrees of freedom. Since the dynamical coupling between degrees of freedom in this setting is a function of their relative configuration, the motion of such systems is subject to constraints [Read more →]

In a continuing program of research in robotic control of intermittent dynamical tasks, we have constructed a three degree of freedom robot capable of “juggling” a ball freely in the earth’s gravitational field. This work is a direct extension of that previously reported in [5, 1, 4, 3, 2, 7]. The system consists of four [Read more →]

This paper concerns the construction of a class of scalar valued analytic maps on analytic manifolds with boundary. These maps, which we term navigation functions, are constructed on an arbitrary sphere world—a compact connected subset of Euclidean n-space whose boundary is formed from the disjoint union of a finite number of (n [Read more →]

An advanced robot control system joining a GMF A-500 industrial arm with a network of Inmos Transputers is described in the context of the developing field of robotics. The robot system is used to experimentally compare conventional linear control algorithm performance with both the advanced “computer torque” inverse dynamics [Read more →]

A program of research in robotics that seeks to encode abstract tasks in a form that simultaneously affords a control scheme for the torque-actuated dynamical systems, as well as a proof that the resulting closed-loop behavior will correctly achieve the desired goals, is reviewed. Two different behaviors that require dexterity and [Read more →]

Assembly problems require that a robotic system with fewer actuated degrees of freedom manipulate an environment with a greater number of unactuated degrees of freedom. This paper explores the possibilities of combining a navigation plan for an “animated” version of the environment with a juggling plan that mediates between [Read more →]

The performance of real-time distributed control systems is shown to depend critically on both communication and computation costs. A taxonomy for distributed system performance measurement is introduced. A roughly accurate method of performance prediction for simple systems is presented. Experimental results demonstrate the [Read more →]

Recent results of dynamical systems theory are used to derive strong predictions concerning the global properties of a simplified model of a planar juggling robot. In particular, it is found that certain lower-order local (linearized) stability properties determine the essential global (nonlinear) stability properties, and that [Read more →]

A navigation function is an artificial potential energy function on a robot configuration space (C-space) which encodes the task of moving to an arbitrary destination without hitting any obstacle. In particular, such a function possesses no spurious local minima. In this paper we construct navigation functions on forests of stars: [Read more →]

This article develops a formalism for describing and analyzing a very simple representative class of robotic tasks that require "dynamical dexterity" - among them, the task of juggling. The authors review their empirical success, to date, with a new class of control algorithms for this task domain, called "mirror algorithms." The [Read more →]

A new class of control algorithms - “mirror algorithms” - give rise to experimentally observedjuggling behavior in a simple robotic mechanism. The simplest of these algorithms (upon which all the others are founded) is provably correct with respect to a simplified model of the robot and its environment. This paper reviews the [Read more →]

We have developed a formalism for describing and analyzing a very simple representative of a class of robotic tasks which involve repeated robot-environment interactions, among then the task of juggling. We review our empirical success to date with a new class of control algorithms for this task domain that we call “mirror [Read more →]

This paper reviews the theory of navigation functions and the attendant use of natural control techniques with emphasis upon applications to mobile autonomous robots. Results to date will be discussed in the context of a larger program of research that seeks effective parameterizations of uncertainty in robot navigation problems. [Read more →]

This paper illustrates the use of the Yale XP/DCS - a dual board real-time distributed control module based upon the INMOS Transputer family of micoprocessors - for high performance real-time motion control applications. The XP/DCS complements the the Transputer’s 1.5 Mflop computational rate and four independent on-chip 20 Mbps [Read more →]

The authors consider the construction of navigation functions on configuration spaces whose geometric expressiveness is rich enough for navigation amidst real-world obstacles. They describe a general methodology which extends the construction of navigation functions on sphere worlds to any smoothly deformable space. According to [Read more →]

Cyclops is a distributed real-time vision system. It is "real-time" as for most vision tasks, it can be configured with enough processing nodes as to allow an update rate of 60 Hz with a maximum latency of 1/30s. This allows the system to be used directly as a feedback sensor for motion control. Even though Cyclops was built [Read more →]

Examination of total energy shows that the global limit behavior of a dissipative mechanical system is essentially equivalent to that of its constituent gradient vector field. The class of “navigation functions” is introduced and shown to result in “almost global” asymptotic stability for closed loop mechanical control [Read more →]

A description is given of a dual-board real-time distributed control module based on the INMOS T414/T800 transputers. The CPU board provides fast external memory, support for the four 10-MHz serial transputer links including two fiber-optic links, and an I/O expansion connector. The board's backplane connector is pin-compatible [Read more →]

This paper reviews certain theoretical results in robot task planning and control obtained with the support of NSF Research Initiation Grant DMC-8505160. The “natural control” paradigm is reviewed and detailed attention is focused upon the specific task of robot navigation in a cluttered environment. The paper concludes with [Read more →]

There mingle in the contemporary field of robotics a great many disparate currents of thought from a large variety of disciplines. Nevertheless, a largely unspoken understanding seems to prevail in the field to the effect that certain topics are conceptually distinct. In general, methods of task planning are held to be unrelated [Read more →]

The introduction of "error coordinates" and a "tracking potential" on the rotations affords a global nonlinear version of inverse dynamics for attitude tracking. The resulting algorithm produces "almost global" asymptotically exact tracking: this convergence behavior is as strong as the topology of the phase space can allow. A new [Read more →]

This article describes a modular computational engine that has become the workhorse for almost all real-time motion control tasks that we encounter in the Yale Robotics Laboratory. Roughly speaking, these tasks amount to the marshalling of various data - from external sensors; from user specified commands; from motor joint [Read more →]

We investigate the computational needs of advanced real-time robot control. First, sampling rate issues in the control of nonlinear systems are discussed. Second, a representative nonlinear robot control algorithm using an explicit robot dynamical model is derived. Some typical terms of the exact equations are given for two [Read more →]

We develop a formalism for describing and analyzing a very simple representative of a class of robotic tasks which require "dynamical dexterity," among them the task of juggling. We introduce and report on our preliminary empirical experience with a new class of control algorithms for this task domain that we call "mirror [Read more →]

A navigation function is a scalar valued function on a robot configuration space which encodes the task of moving to a desired destination without hitting any obstacles. Our program of research concerns the construction of navigation functions on a family of configuration spaces whose “geometric expressiveness” is rich enough [Read more →]

The introduction of “error coordinates” and a “tracking potential” on the rotations affords a global nonlinear version of inverse dynamics for attitude tracking. The resulting algorithm produces “almost global” asymptotically exact tracking: this convergence behavior is as strong as the topology of the phase space can [Read more →]

A novel Lyapunov function is introduced. The author treats the PD compensated mechanical system, which is defined on a configuration space which admits a trivial tangent bundle. Previous results are derived in a simpler form, namely, that such systems are exponentially stable, hence BIBO stable, and steady-state ouptut magnitudes [Read more →]

We offer some preliminary analytical results concerning simplified models of Raibert’s hopper. We represent the task of achieving a recurring hopping height for an actuated “ball” robot as a stability problem in the setting of a nonlinear discrete dynamical system. We model the properties of Raibert’s control scheme in a [Read more →]

The juggling work takes its place within a larger program of research concerned with the development of unified methodologies for robot task representation, planning, and control. The talk will summarize this large context, and then provide a more detailed look at progress in juggling to date. For more information: Kod*Lab

The utility of artificial potential functions is explored as a means of translating automatically a robot task description into a feedback control law to drive the robot actuators. A class of functions is sought which will guide a point robot amid any finite number of spherically bounded obstacles in Euclidean n-space toward an [Read more →]

The authors construct a simplified model of a dynamically dexterous robot, M.H. Raibert's hopper, and investigate its elegant, physically based control strategies. Analysis of induced discrete dynamics leads to strong conclusions concerning global limiting properties. These conclusions are then verified by computer simulation of [Read more →]

We explore a very simple representative of a class of of robotic tasks which require "dynamic dexterity", among them the task of "juggling". In this initial paper we propose a formal definition of a "vertical one juggle", report a few preliminary analytical results, and offer illustrative simulations. This analysis is being [Read more →]

Strict Lyapunov functions are constructed for a class of nonlinear feedback compensated mechanical systems, requiring no à priori information concerning the initial conditions of the closed-looped system. These Lyapunov functions may be used to design a stable adaptive version of the "computed-torque" algorithm for tracking a [Read more →]

The “mechanical systems” define a large and important class of highly nonlinear dynamical equations which, for example, encompasses all robots. In this report it is shown that a strict Lyapunov Function suggested by the simplest examplar of the class - a one degree of freedom linear time invariant dynamical system - may be [Read more →]

The limits in global navigation capability of potential function based robot control algorithms are explored. Elementary tools of algebraic and differential topology are used to advance arguments suggesting the existence of potential functions over a bounded planar region with arbitrary fixed obstacles possessed of a unique local [Read more →]

The practice of automatic control has its origins in antiquity. It is only recently - within the middle decades of this century - that a body of scientific theory has been developed inform and improve that practice. Control theorists tend to divide their history into two periods. A "classical" period, prior to the sixties [Read more →]

Asymptotically stable linear time invariant systems are capable of tracking arbitrary reference signals with a bounded error proportional to the magnitude of the reference signal (and its derivatives). It is shown that a similar property holds for a general class of nonlinear dynamical systems which includes all robots. As in the [Read more →]

A feedback control strategy for the command of robot motion includes some limited automatic planning capabilities. These may be seen as sequential solution algorithms implemented by the robot arm interpreted as a mechanical analog computer. This perspective lends additional insight into the manner in which such control techniques [Read more →]

This paper introduces a class of linearizing coordinate transformations for mechanical systems whose moment of inertia matrix has a square root which is a jacobian. The transformations, when they exist, define a local isometry from joint space to euclidean space, hence, may afford further insight into the transient behavior of [Read more →]

Earlier results of this author and others demonstrate that a broad range of robotic tasks can be commanded through relatively simple feedback controllers with a guarantee of global asymptotic stability. A weakness of such methods is the requirement that exact values of all dynamical parameters be available, since they are used to [Read more →]

This paper describes some initial steps toward the development of more natural control strategies for free motion of robot arms. The standard lumped parameter dynamical model of an open kinematic chain is shown to be stabilizable by linear feedback, after nonlinear gravitational terms have been cancelled. A new control algorithm [Read more →]

Since Hilbert posed the problem of systematically counting and locating lhe limit cycle of polynomial systems on the plane in 1900, much efTort has been expended in its investigation. A large body of literature - chiefly by Chinese and Soviet authors - has addressed this question in the context of differential equations whose [Read more →]

This note states necessary and sufficient conditions for the existence of a linear state feedback controller such that a second-order bilinear system has a globally asymptotically stable closed loop. A suitable controller is constructed for each system which satisfies the conditions.

This paper investigates the stability properties of second-order systems, x. = ƒ(x), where ƒ(x) contains either quadratic terms-system (1)-or linear and quadratic terms-system (2)-in x. The principal contributions are summarized in two theorems which give necessary and sufficient conditions for stability and asymptotic stability [Read more →]

The concept of an automaton operating in a multi-teacher environment is introduced, and several interesting questions that arise in this context are examined. In particular, we concentrate on the consequences of adding a new teacher to an existing n-teacher set as it affects the choice of a switching strategy. The effect of this [Read more →]