Technical Report: Control and Design of an Open-Source Two-Degree-of-Freedom Hopping

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 provides a guide to others interested in building similar research robots.

An obstacle disturbance selection framework: emergent robot steady states under

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 and disturbances can be exploited as opportunities to improve robot locomotion in complex environments. In this article, we propose a novel obstacle disturbance selection (ODS) framework with the aim of allowing robots to actively select disturbances to achieve environment-aided locomotion. Using an empirically characterized relationship between leg–obstacle contact position and robot trajectory deviation, we simplify the representation of the obstacle-filled physical environment to a horizontal-plane disturbance force field. We then treat each robot leg as a “disturbance force selector” for prediction of obstacle-modulated robot dynamics. Combining the two representations provides analytical insights into the effects of gaits on legged traversal in cluttered environments. We illustrate the predictive power of the ODS framework by studying the horizontal-plane dynamics of a quadrupedal robot traversing an array of evenly-spaced cylindrical obstacles with both bounding and trotting gaits. Experiments corroborate numerical simulations that reveal the emergence of a stable equilibrium orientation in the face of repeated obstacle disturbances. The ODS reduction yields closed-form analytical predictions of the equilibrium position for different robot body aspect ratios, gait patterns, and obstacle spacings. We conclude with speculative remarks bearing on the prospects for novel ODS-based gait control schemes for shaping robot navigation in perturbation-rich environments.

Reactive Semantic Planning in Unexplored Semantic Environments Using Deep Perceptual

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 semantic SLAM, affording robust, reactive logical as well as geometric planning in unexplored environments. Moreover, by incorporating a human mesh estimation algorithm, our system is capable of reacting and responding in real time to semantically labeled human motions and gestures. New formal results allow tracking of suitably non-adversarial moving targets, while maintaining the same collision avoidance guarantees. We suggest the empirical utility of the proposed control architecture with a numerical study including comparisons with a state-of-the-art dynamic replanning algorithm, and physical implementation on both a wheeled and legged platform in different settings with both geometric and semantic goals.

For more information: Kod*lab

A Tendon-Driven Origami Hopper Triggered by Proprioceptive Contact Detection

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 thousands of cycles. Three conventional brushless DC motors load energy into the folded paper springs through pulley-borne cables whose sudden loss of tension upon touchdown triggers the release of spring potential that accelerates the body back through liftoff to flight with a 20W powerstroke, whereupon the toe angle is adjusted to regulate fore-aft speed. We also demonstrate in the vertical hopping mode the transparency of this actuation scheme by using proprioceptive contact detection with only motor encoder sensing. The combination of actuation and sensing shows potential to lower system complexity for tendon-driven robots.

For more information: Kod*lab (link to

Examples of Gibsonian Affordances in Legged Robotics Research Using an

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 suggest that robots can be programmed to effectively exploit affordances without developing explicit internal models of them. We use a generative framework to discuss the examples, because it helps us to separate—and thus clarify the relationship between—description of affordance exploitation from description of the internal representations used by the robot in that exploitation. Under this framework, details of the architecture and environment are related to the emergent behavior of the system via a generative explanation. For example, the specific method of information processing a robot uses might be related to the affordance the robot is designed to exploit via a formal analysis of its control policy. By considering the mutuality of the agent-environment system during robot behavior design, roboticists can thus develop robust architectures which implicitly exploit affordances. The manner of this exploitation is made explicit by a well constructed generative explanation.

Modulation of Robot Orientation via Leg-Obstacle Contact Positions

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 body level feedback to stable steady state patterns. We classify these patterns into a series of “types” ranging from stable locked equilibria, to stable periodic oscillations, to unstable or mixed period oscillations. We observe that the stable equilibria can bifurcate to stable periodic oscillations and then to mixed period oscillations as the obstacle spacing is gradually increased. Using a 3D-reconstruction method, we experimentally characterize the robot leg-obstacle contact configurations at each step to show that the different steady patterns in robot orientation trajectories result from a self-stabilizing periodic pattern of leg-obstacle contact positions. We present a highly-simplified coupled oscillator model that predicts robot orientation pattern as a function of the leg-obstacle contact mechanism. We demonstrate that the model successfully captures the robot steady state for different obstacle spacing and robot initial conditions. We suggest in simulation that using the simplified coupled oscillator model we can create novel control strategies that allow multi-legged robots to exploit obstacle disturbances to negotiate randomly cluttered environments. For more information: Kod*lab (link to

A Programmably Compliant Origami Mechanism for Dynamically Dexterous Robots

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 cylinder pairs reliably manifest additive stiffness, extending the programmable range by nearly an order of magnitude and achieving bulk axial stiffness spanning 200–1500 N/m using 8 mil thick polyester-coated paper. Accordingly, we design origami energy-storing springs with a stiffness of 1035 N/m each and incorporate them into a three degree-of-freedom (DOF) tendon-driven spatial pointing mechanism that exhibits trajectory tracking accuracy less than 15% rms error within a (2 cm)^3 volume. The origami springs can sustain high power throughput, enabling the robot to achieve asymptotically stable juggling for both highly elastic (1 kg resilient shotput ball) and highly damped (“medicine ball”) collisions in the vertical direction with apex heights approaching 10 cm. The results demonstrate that “soft” robotic mechanisms are able to perform a controlled, dynamically actuated task.

Extended Version of Simple Sagittal Running: Stability of a Quadrupedal

This paper develops a three degree-of-freedom sagittal-plane hybrid dynamical systems model of a bounding quadruped. Simple within-stance controls yield a closed form expression for a family of hybrid limit cycles that represent bounding behavior over a range of user-selected fore-aft speeds as a function of the model’s kinematic and dynamical parameters. Controls acting on the hybrid transitions are structured so as to achieve a cascade composition of in-place bounding driving the fore-aft degree of freedom thereby decoupling the linearized dynamics of an approximation to the stride map. Careful selection of the feedback channels used to implement these controls affords infinitesimal deadbeat stability which is relatively robust against parameter mismatch. Experiments with a physical quadruped reasonably closely match the bounding behavior predicted by the hybrid limit cycle and its stable linearized approximation.

Composition of Templates for Transitional Pedipulation Behaviors

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 systematically reuse a small lexicon of templates (low degree of freedom behavioral primitives). The resulting behaviors comprise the key competences beyond mere locomotion required for robust implementation on a legged mobile manipulator of a simple version of the warehouseman’s problem.

Coronal Plane Spine Twisting Composes Shape To Adjust the Energy

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. This paper takes a next step toward such a characterization by exploring the quasistatic terrestrial self-righting mechanics of a model system with coronal plane spine twisting (CPST). Reduction from a full 3D kinematic model of CPST to a two parameter, two degree of freedom coronal plane representation of body shape affordance predicts a substantial benefit to ground righting by lowering the barrier between stable potential energy basins. The reduced model predicts the most advantageous twist angle for several cross-sectional geometries, reducing the required righting torque by up to an order of magnitude depending on constituent shapes. Experiments with a three actuated degree of freedom physical mechanism corroborate the kinematic model predictions using two different quasistatic reorientation maneuvers for both elliptical and rectangular shaped bodies with a range of eccentricities or aspect ratios. More speculative experiments make intuitive use of the kinematic model in a highly dynamic maneuver to suggest still greater benefits of CPST achievable by coordinating kinetic as well as potential energy, for example as in a future multi-appendage system interacting with a contact-rich 3D environment.