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 correctness of this approach, an open question, has been demonstrated in simpler settings and is further suggested by the extensive experiments reported here using an actual working implementation with EDAR—a mobile robot operating in a purely feedback-based event-driven manner. These results verify the reliability of this approach against uncertainties in sensory information and unanticipated changes in workspace configuration.
Stability Analysis of Legged Locomotion Models by Symmetry-Factored Return Maps
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 non-integrability of the SLIP dynamics, we obtain a necessary condition for asymptotic stability (and a sufficient condition for instability) at a fixed point, formulated as an exact algebraic expression in the physical parameters. We use this expression to characterize analytically the sensory cost and stabilizing benefit of various feedback schemes previously proposed for the 2DoF SLIP model, posited as a low-dimensional representation of running.We apply the result as well to a 3DoF SLIP model that will be treated at greater length in a companion paper as a descriptive model for the robot RHex.
Toward a 6 DOF Body State Estimator for a Hexapod
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 performance using a visual ground truth measurement system. As an independent assessment of our estimator’s quality we also compare its odometry performance to sensorless averaged open loop distance-per-stride estimates.
Level Sets and Stable Manifold Approximations for Perceptually Driven Nonholonomically
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.
Model-Based Dynamic Self-Righting Maneuvers for a Hexapedal Robot
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 strategy that overcomes actuator torque limitations, resulting in robust flipping behavior over a wide range of surfaces. We present simulations and experiments to validate the model and characterize the performance of the new controller.
Multi-point Contact Models for Dynamic Self-Righting of a Hexapod Robot
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 and show that for our specific application, it yields dynamics which are well-defined. We then present a feedback controller that achieves “maximal” performance under morphological and actuation constraints, while ensuring the validity of the model by staying away from singularities. Finally, through systematic experiments, we demonstrate that our controller is capable of robust flipping behavior.
For more information: Kod*Lab
Automated Gait Adaptation for Legged Robots
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 descent while managing its self-experiments and measuring the outcome by visual servoing within a partially engineered environment. The resulting performance gains extend considerably beyond what we have managed with hand tuning. For example, the hest hand tuned alternating tripod gaits never exceeded 0.8 m/s nor achieved specific resistance helow 2.0. In contrast, Nelder-Mead based tuning has yielded alternating tripod gaits at 2.7 m/s (well over 5 body lengths per second) and reduced specific resistance to 0.6 while requiring little human intervention at low and moderate speeds. Comparable gains have been achieved on the much larger ruggedized version of this machine.
Legged Odometry from Body Pose in a Hexapod Robot
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 degree of freedom vision based ground truth measurement system (GTMS). We also compare the performance to that of sensorless odometry schemes — both legged as well as on a wheeled version of the robot — using GTMS measurements of elapsed distance.
For more information: Kod*Lab
Towards a factored analysis of legged locomotion models
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 those models, which is formulated as an exact algebraic expression despite the non-integrability of the SLIP dynamics. We outline the application of this analysis to other models of legged locomotion and its importance for the stability of legged robots and animals.
A leg configuration sensory system for dynamical body state estimates
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 frame. We compare against ground truth measurement the performance of the model operating on real-time leg strain data generated under completely realistic operating conditions. We introduce an algorithm for computing six degree of freedom body posture measurements in world frame coordinates from the outputs of the six leg configuration models, together with a priori information about the ground. We discuss the manner in which such stance phase configuration estimates will be fused with other sensory data to develop the continuous time full body state estimates for RHex.