Mechanics and Control of Biomimetic Locomotion

Joel Burdick
Department of Mechanical Engineering

"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.

A significant body of research has been developed in the area of robotic locomotion. Prior studies have often focused either on a particular set of assumptions (such as quasi-static motion) or a particular robot morphology (such as a biped or quadruped). To date there exists no unifying methodology for analyzing or controlling robotic locomotion. Ultimately, we seek a "mechanics theory" and a "control theory" for robotic locomotion which is both rigorous and uniformly applicable to a broad class of locomotory problems. This talk summarizes some recent work on the development of unifying principles for a broad class of locomotion problems.

In order to establish notation and key ideas, the talk will begin with a review of the basic mechanics underlying biomimetic locomotion. In particular, ideas from the geometric mechanics literature, such as principal fiber bundles and their associated 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. Extensions to controllability theory that are adapted to biomimetic locomotion systems will be reviewed. 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 new controllability framework, the second part of the talk will describe trajectory generation methods.