Convex and Combinatorial Optimization for Dynamic Robots in the Real World

Abstract

Humanoid robots walking across intermittent terrain, robotic arms grasping multifaceted objects, UAVs darting left or right around a tree, or autonomous vehicles making discrete navigation decisions in traffic, many of the dynamics and control problems we face today have both rich nonlinear dynamics and an inherently combinatorial structure. In this talk, I'll review some recent work on optimization-based planning and control methods which address these two challenges simultaneously. All of these can be modeled as hybrid systems, but in some cases more efficient optimizations are possible by using alternative formulations, such as (measure-) differential inclusions. I'll present our explorations with mixed-integer convex-, semidefinite-programming-relaxations, and satisfiability-modulo- theory(SMT)-based methods applied to hard problems in legged locomotion over rough terrain, grasp optimization, and UAVs flying through highly cluttered environments.