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Talk Abstract
Controllability and Trajectory Planning for Biomimetic Locomotion

Joel Burdick, California Institute of Technology

"Biomimetic locomotion" is the movement of robotic mechanisms in ways that are analogous to the patterns of movement found in nature. Practically speaking, it is movement that does not rely upon wheels, jets, thrusters, or propellers. Biomimetic locomotion is typically generated by a coupling of periodic internal body deformations to an external constraint. In order to establish notation and key ideas, the talk will begin with a review of the basic mechanics underlying biomimetic locomotion. In particular, the role of principal fiber bundles and connections will be stressed.

A biomimetic locomotion mechanism is "controllable" if there exists an admissible set of controls which drives the system from its current configuration to any nearby configuration. Controllability is a key issue that must be addressed by any comprehensive theory of biomimetic locomotion engineering. Unfortunately, standard controllability methods from nonlinear control theory, such as Chow's theorem, are not well suited to the analysis of biomimetic locomotors. For example, in the case of legged robot mechanisms, the governing mechanics of foot placement are discontinuous. However, conventional controllability tests rely upon differentiation. In order to overcome this difficulty, we present an extension of Chow's theorem to the case of ``stratified'' configuration spaces, which can be used to model the discontinuous nature of legged locomotion. Even in the cases where the governing mechanics are smooth, standard controllability results are inefficient because they do not take advantage of the inherent structure in biomimetic locomotion configuration spaces. We also present a version of Chow's theory that is adapted to biomimetic locomotion systems.

While controllability is a key issue in the design and analysis of biomimetic locomotion systems, trajectory generation is a primary practical problem for the deployment of complex biomimetic locomotors. Using the controllability framework established in the first part of the talk, the second part of the talk will described trajectory generation methods.

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