Solving hybrid control problems: level sets and behavioral programming

Abstract

Hybrid systems include both continuous dynamics and discrete events. We represent the continuous dynamics by differential equations and represent the events by a discrete transition model. We describe computational approaches to solving optimal hybrid control problems using two techniques: a fast marching level set method and behavioral programming. We review our extension of the fast marching level set method to the hybrid setting, including its formalization, a constructive proof of its correctness, approximation errors to the analog solution, and upper- and lower-bounding approximate solutions. Our work also explores an idea known as behavioral programming. We review the theoretical underpinnings and then perform some experiments using this technique to solve a specific problem in robotic assembly, the peg-in-hole problem. We demonstrate the abstraction of primitive actions into behaviors, try out several strategies for combining behaviors, and compare their optimality and computational effort vis-a-vis primitive actions.