Optimization for control and planning of multi-contact dynamic motion

Whether a robot is assisting a person to move about the home, or packing containers in a warehouse, the fundamental promise of robotics centers on the ability to productively interact with a complex and changing environment in a safe and controlled fashion. However, current robots are largely limited to basic tasks in structured environments-operating slowly and cautiously, afraid of any incidental contact with the outside world. Dynamic interaction, encompassing both legged locomotion and manipulation, poses significant challenges to traditional control and planning techniques. Discontinuities from impact events and dry friction make standard tools poorly suited in scenarios with complex or uncertain contacts between robot and environment. I will present approaches that leverage the interplay between numerical optimization and the mathematical structure of contact dynamics to avoid the combinatorial complexity of mode enumeration. This will include a tractable algorithm for trajectory optimization, without an a priori encoding of the contact sequence, and an approach utilizing sums-of-squares programming to design and provably verify controllers that stabilize systems making and breaking contact.