Technical Report on: Towards Reactive Control of Simplified Legged Robotics Maneuvers

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

Morphology and the gradient of a symmetric potential predicts gait transitions of dogs

Gaits and gait transitions play a central role in the movement of animals. Symmetry is thought to govern the structure of the nervous system, and constrain the limb motions of quadrupeds. We quantify the symmetry of dog gaits with respect to combinations of bilateral, fore-aft, and spatio-temporal symmetry groups. We tested the ability of symmetries to model motion capture data of dogs walking, trotting and transitioning between those gaits. Fully symmetric models performed comparably to asymmetric with only a 22% increase in the residual sum of squares and only one-quarter of the parameters. This required adding a spatio-temporal shift representing a lag between fore and hind limbs. Without this shift, the symmetric model residual sum of squares was 1700% larger. This shift is related to (linear regression, n = 5, p = 0.0328) dog morphology. That this symmetry is respected throughout the gaits and transitions indicates that it generalizes outside a single gait. We propose that relative phasing of limb motions can be described by an interaction potential with a symmetric structure. This approach can be extended to the study of interaction of neurodynamic and kinematic variables, providing a system-level model that couples neuronal central pattern generator networks and mechanical models

Technical Report on: Anchoring Sagittal Plane Templates in a Spatial Quadruped

This technical report provides a more thorough treatment of the proofs and derivations in the authors\u27 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 details

Composition of Templates for Transitional Legged Behaviors

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 interactions with the environment [4,5] has been limited by our inability to find appropriate constituent models (“templates” [6]) from which to construct these complex behaviors

Anchoring Sagittal Plane Templates in a Spatial Quadruped

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 admits formal guarantees of stability with some modest assumptions. Experimental results validate the reliable execution of those planar template-based maneuvers, even in the face of large lateral, yaw, and roll incurring disturbances. This spatial anchor, fixed in parallel composition with a variety of different parallel and sequential compositions of sagittal plane templates, illustrates the robust portability of provably interoperable modular control components across a variety of hardware platforms and behaviors. For more information: Kod*la

Sequential Composition of Dynamically Dexterous Robot Behaviors

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 blocked by an obstacle that disconnects the free space formed when the ball and paddle remain in contact, forcing the machine to “let go” for a time to bring the ball to the desired state. The controller compositions we create guarantee that a ball introduced in the “safe workspace” remains there and is ultimately brought to the goal. We report on experimental results from an implementation of these formal composition methods, and present descriptive statistics characterizing the experiments.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67990/2/10.1177_02783649922066385.pd

Level Sets and Stable Manifold Approximations for Perceptually Driven Nonholonomically Constrained Navigation

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 propose a general hybrid procedure that adapts to the constrained motion setting the standard feedback controller arising from a navigation function in the fully actuated case by switching back and forth between moving down and across the associated gradient field toward the stable manifold it induces in the constrained dynamics. Guaranteed to avoid obstacles in all cases, we provide some reasonably general sufficient conditions under which the new procedure guarantees convergence to the goal. Simulations are provided for perceptual models previously introduced by other authors

Visual Registration and Navigation using Planar Features

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 visually cued goal without ever losing sight of the beacons that define it. Since the horizontal plane behavior of RHex can be represented as a unicycle, feeding back the navigation function gradient avoids loss of beacons, but does not yield an asymptotically stable goal. We address new problems arising from the configuration of the beacons and present preliminary experimental results that illustrate the discrepancies between the idealized and physical robot actuation capabilities

Sensitive dependence of the motion of a legged robot on granular media

Legged locomotion on flowing ground ({\em e.g.} granular media) is unlike locomotion on hard ground because feet experience both solid- and fluid-like forces during surface penetration. Recent bio-inspired legged robots display speed relative to body size on hard ground comparable to high performing organisms like cockroaches but suffer significant performance loss on flowing materials like sand. In laboratory experiments we study the performance (speed) of a small (2.3 kg) six-legged robot, SandBot, as it runs on a bed of granular media (1 mm poppy seeds). For an alternating tripod gait on the granular bed, standard gait control parameters achieve speeds at best two orders of magnitude smaller than the 2 body lengths/s ($\approx 60$ cm/s) for motion on hard ground. However, empirical adjustment of these control parameters away from the hard ground settings, restores good performance, yielding top speeds of 30 cm/s. Robot speed depends sensitively on the packing fraction $\phi$ and the limb frequency $\omega$, and a dramatic transition from rotary walking to slow swimming occurs when $\phi$ becomes small enough and/or $\omega$ large enough. We propose a kinematic model of the rotary walking mode based on generic features of penetration and slip of a curved limb in granular media. The model captures the dependence of robot speed on limb frequency and the transition between walking and swimming modes but highlights the need for a deeper understanding of the physics of granular media.Comment: 4 figure