Synthesizing Dynamical Behaviors for Physical Systems Using Phase-Space Method

Desired dynamics for physical systems can be synthesized from the phase-space geometric point of view. We have developed a phase-space method for synthesizing control strategies and implemented the method for a class of nonlinear dynamical systems. In this paper, we examine how the phase-space method can be applied to analyze and synthesize control laws for physical systems that exhibit distinct phases of operation. Examples of such systems includes walking and hopping machines successfully constructed by Marc Raibert and power regulators containing switching elements. We outline how useful control strategies for these systems can be explored in phase space using geometric constraints. The phase-space synthesis relies on knowledge of applied mathematics and control theory and techniques of geometric reasoning. We describe additional components that are necessary for making this approach practical.