Reactive Gait Composition with Stability: Dynamic Walking amidst Static and Moving Obstacles

This paper presents a modular approach to motion planning with provable stability guarantees for robots that move through changing environments via periodic locomotion behaviors. We focus on dynamic walkers as a paradigm for such systems, although the tools developed in this paper can be used to support general compositional approaches to robot motion planning with Dynamic Movement Primitives (DMPs). Our approach ensures a priori that the suggested plan can be stably executed. This is achieved by formulating the planning process as a Switching System with Multiple Equilibria (SSME) and proving that the system's evolution remains within explicitly characterized trapping regions in the state space under suitable constraints on the frequency of switching among the DMPs. These conditions effectively encapsulate the low-level stability limitations in a form that can be easily communicated to the planner to guarantee that the suggested plan is compatible with the robot's dynamics. Furthermore, we show how the available primitives can be safely composed online in a receding horizon manner to enable the robot to react to moving obstacles. The proposed framework is applied on 3D bipedal walking models under common modeling assumptions, and offers a modular approach towards stably integrating readily available low-level locomotion control and high-level planning methods.Comment: 18 pages, 10 figure

Stabilizing Momopedal Robot Running: Reduction-by-Feedback and Compliant Hybrid Zero Dynamics.

As an alternative to traditional wheeled and tracked ground vehicles, biologically-inspired legged systems are becoming increasingly common. On a macroscopic level, locomotion on land can be understood through the introduction of archetypical reductive models, capable of capturing the salient characteristics of the task-level behavior, e.g., walking or running. Unfortunately, these reductive models provide no information of the control mechanisms, through which the multiple joints and limbs of the high-degree-of-freedom-plant are coordinated to produce the observed behavior. The coordinated recruitment of the plant into a low-degree-of-freedom target model constitutes the central problem addressed in this dissertation, which aims at offering a mathematically precise feedback control solution to this problem for the particular setting of monopedal robot running. The robotic monopod Thumper, recently constructed in a collaborative effort between the University of Michigan and Carnegie Mellon University, offers a unique platform for exploring advanced feedback control strategies for running on compliant monopedal robots. The control law proposed for Thumper grows out of rigorous nonlinear controller synthesis ideas, and it coordinates the actuated degrees of freedom of the robot so that a lower-dimensional hybrid subsystem, i.e., a reductive model that encodes running, emerges from the closed-loop dynamics. This subsystem effectively governs the behavior of the robot.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/62418/1/poulakas_1.pd

On the passive dynamics of quadrupedal running

In this thesis, the dynamics of quadrupedal running via the bounding gait is studied. To analyse the properties of the passive dynamics of Scout II, a model consisting of a body and two massless spring-loaded prismatic legs is introduced. A return map is derived to study the existence of periodic system motions. Numerical studies of the return map show that passive generation of cyclic motion is possible. Most strikingly, local stability analysis of the return map shows that the dynamics of the open loop passive system alone can confer stability of the motion. Stability improves at higher speeds, a fact which is in agreement with recent results from biomechanics showing that the dynamics of the body become dominant in determining stability when animals run at high speeds. Furthermore, pronking is found to be more unstable than bounding, which explains why Scout II shows a "preference" for the bounding gait. These results can be used in developing a general control methodology for legged robots, resulting from the synthesis of feed-forward and feedback models that take advantage of the mechanical system

Passive quadrupedal bounding with a segmented flexible torso

Abstract — This paper examines the effect of torso flexibility on the dynamics of quadrupedal running with a bounding gait. A reduced-order passive and conservative model with a segmented flexible torso and compliant legs is introduced to study torso-leg coordination. Numerical return map studies reveal that a large variety of cyclic bounding motions can be realized passively, as a natural mode of the system. Despite the simplicity of the model, the resulting motions correspond to torso bending movements that resemble those in galloping mammals without explicit reliance on the fine structural and morphological details. This way, the proposed model offers a unifying description of the task-level locomotion behavior, and can be used to inform feedback control synthesis by serving as a behavioral target for the control system. I