Motor Sizing for Legged Robots Using Dynamic Task Specification

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 as a design parameter. This approach permits an analytical proof that continuous operation yields superior thermal performance to intermittent operation. We compare the results of motor sizing using our proposed method with more conventional techniques such as using the continuously permissible current specification. Our simulations are run across a database of commercially available motors, and we envision that our results might be of immediate use to robot designers for motor as well as gearbox selection.

On the Comparative Analysis of Locomotory Systems with Vertical Travel

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 compensation term in order to offset the gravitational potential gained or lost during locomotion. We observe that this modification requires an additional, experimentally fitted model estimating the efficiency at which a system is able to transfer energy to and from gravitational potential. This paper introduces a family of such models, thus introducing methods to allow fair comparisons of locomotion on level ground, sloped, and vertical surfaces, for any vehicle which necessarily gains or loses potential energy during travel.

Characterization of Dynamic Behaviors in a Hexapod Robot

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 tripod stance dynamics of the robot which are identified by a purely jointspace-driven estimation method introduced in this paper. Our results establish a strong relationship between energetic efficiency (simultaneous reduction in power consumption and in- crease in speed) and the dynamical structure of an alternating tripod gait as measured by its fidelity to the SLIP mechanics—a dynamical pattern exhibit- ing characteristic exchanges of kinetic and spring-like potential energy [3]. We conclude that gaits that are dynamic in this manner give rise to better uti- lization of energy for the purposes of locomotion.

This work is supported in part by the National Science Foundation (NSF) under a FIBR Award 0425878. Yasemin Ozkan Aydin is supported by International Research Fellowship Programme of the Scientific and Technological Research Council of Turkey (TUBITAK).

For more information: Kod*Lab

X-RHex: A Highly Mobile Hexapedal Robot for Sensorimotor Tasks

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 physical volume and a comparable footprint and weight. Furthermore, X-RHex is designed to be easier to build and maintain by using a variety of commercial off-the-shelf (COTS) components for a majority of its internals. This document describes the X-RHex architecture and design, with a particular focus on the new ability of this robot to carry modular payloads as a laboratory on legs. X-RHex supports a variety of sensor suites on a small, mobile robotic platform intended for broad, general use in research, defense, and search and rescue applications. Comparisons with previous RHex platforms are presented throughout, with preliminary tests indicating that the locomotive capabilities of X-RHex can meet or exceed the previous platforms. With the additional payload capabilities of X-RHex, we claim it to be the first robot of its size to carry a fully programmable GPU for fast, parallel sensor processing.

Sprawl Angle in Simplified Models of Vertical Climbing: Implications for

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 in animals and in robots by examining the stability and power advantages of variously more and less sprawled limb morphologies when driven by conventional motors in contrast with animal-like muscles. For open loop models of gait generation inspired by the neural-deprived regimes of high stride-frequency animal climbing, our results corroborate earlier hypotheses that sprawled posture may be required for stability. For quadratic-in- velocity power output actuation models typical of commercially available electromechanical actuators, our results suggest the new hypothesis that sprawled posture may confer significant energetic advantage. In notable contrast, muscle-powered climbers do not experience an energetic benefit from sprawled posture due to their sufficiently distinct actuator characteristics and operating regimes. These results suggest that the potentially significant benefits of sprawled posture climbing may be distinctly different depending upon the details of the climber’s sensorimotor endowment. They offer a cautionary instance against mere copying of biology by engineers or rote study of physical models by biologists through this reminder of how even simple questions addressed by simple models can yield nuanced answers that only begin to hint at the complexity of biological designs and behaviors.

Disturbance Detection, Identification, and Recovery by Gait Transition in Legged

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 simple finite state machine identifies disturbances as due either to an expected ground contact, a missing ground contact indicating leg fault, or an unexpected “wall” contact. Recovery proceeds as necessary by means of a recently developed topological gait transition coordinator. We demonstrate the efficacy of this system by presenting preliminary data arising from two reactive behaviors — wall avoidance and leg-break recovery. We believe that extensions of this framework will enable reactive behaviors allowing the robot to function with guarded autonomy under widely varying terrain and self-health conditions.

Classification and Identification of Environment Through Dynamic Coupling

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 with temporal resolution of measurement updates determined by the periodicity of the limit behavior. While the basic concept has a wide application spectrum, our discussion focuses on terrestrial locomotion where contact properties, such a compliance, damping, sheer friction and surface topology, are important environmental markers. Accurate identification of environmental parameters enables two types of applications. In behavioral control, availability of measurements on environmental parameterization can facilitate better adaptation of actuation strategy. In localization and map building applications, such mechanical characteristics of the environment, which are typically hard to attain, can serve as a new set of classifiers. Presented approach is founded on the observation that locomotive behaviors, and particularly the dynamic ones, emerge from the interaction between the active actuation actions of the mechanism with its environment. To evaluate our concept in a systematic fashion we constructed a simplified numerical model of a dynamic hexapod robot. We present results on numerical simulations and outline a path for a physical implementation on dynamic hexapod robot.

A Self-Exciting Controller for High-Speed Vertical Running

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 additional internal clock or reference signal. Specifically, we show that this “self-exciting” controller does indeed generate an “almost” globally asymptotically stable limit cycle: the attractor basin is as large as topologically possible and includes all the state space excluding a set with empty interior. We offer an empirical comparison of the resulting climbing behavior to that achieved by a more conventional clock-generated gait trajectory tracker. The new, self-exciting gait generator exhibits a marked improvement in vertical climbing speed, in fact setting a new benchmark in dynamic climbing by achieving a vertical speed of 1.5 body lengths per second.

For more information: Kod*Lab

Design of a Tunable Stiffness Composite Leg for Dynamic Locomotion

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 improve the speed and stability of these robots in changing environmental conditions. However, to date, the mechanical complexities of designing usefully robust tunable passive compliance into legs has precluded their implementation on practical running robots. This paper describes a new design of a ”structurally controlled variable stiffness” leg for a hexapedal running robot. This new leg improves on previous designs’ performance and enables runtime modification of leg stiffness in a small, lightweight, and rugged package. Modeling and leg test experiments are presented that characterize the improvement in stiffness range, energy storage, and dynamic coupling properties of these legs. We conclude that this variable stiffness leg design is now ready for implementation and testing on a dynamical running robot.

Gait Transitions for Quasi-Static Hexapedal Locomotion on Level Ground

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 modest use of classical group theory to replace combinatorial search and optimization with a computationally simpler and conceptually more straightforward appeal to elementary algebra. We decompose the space of all periodic legged gaits into a cellular complex indexed using “Young Tableaux”, making transparent the proximity to steady state orbits and the neighborhood structure. We encounter the simple task of transitioning between these gaits while locomoting over level ground. Toward that end, we arrange a family of dynamical reference generators over the “Gait Complex” and construct automated coordination controllers to force the legged system to converge to a specified cell’s gait, while assessing the relative static stability of gaits by approximating their stability margin via transit through a “Stance Complex”. To integrate these two different constructs—the Gait Complex describing possible gaits, the Stance Complex defining safe locomotion—we utilize our compositional lexicon to plan switching policies for a hybrid control approach. Results include automated gait transitions for a variety of useful gaits, shown via tests on a hexapedal robot.