C1-Smooth Multi-Contact Dynamics for Robotics

PASSCODE: 295251

When a robot forms multiple contact points with its environment near-simultaneously, small perturbations can change the anticipated order of contact, which can lead to vastly different outcomes. These “multi-contact dynamics” have eluded convenient mathematical analysis, despite posing no issue for a plethora of terrestrial organisms ranging from ants to elephants. Classically, simulating a three-legged hopping robot a mere 2 hops into the future would require solving over 1,000 separate differential equations. This dissertation leverages recent theoretical work to show that many multi-contact dynamics are – in practice – easier to model, control, and simulate than previously believed. We begin by introducing a three-legged hopping robot and showing experimentally that its flight-to-triple-stance impact map is linearizable (C1) near the triple-contact trajectory. Using this result, we employ smooth system identification and control tools to successfully steer the hopper in the plane in real-time, even in the presence of significant disturbances. Finally, we present a numerical method for rapidly and accurately solving initial value problems for the more general class of “event-selected [multi-contact] systems” that performs on-par with the state-of-the-art via a comparison with MuJoCo.

CHAIR: Shai Revzen