Koopman global linearization of contact dynamics for robot locomotion and manipulation enables elaborate control

Controlling robots that dynamically engage in contact with their environment is a pressing challenge. Whether a legged robot making-and-breaking contact with a floor, or a manipulator grasping objects, contact is everywhere. Unfortunately, the switching of dynamics at contact boundaries makes control difficult. Predictive controllers face non-convex optimization problems when contact is involved. Here, we overcome this difficulty by applying Koopman operators to subsume the segmented dynamics due to contact changes into a unified, globally-linear model in an embedding space. We show that viscoelastic contact at robot-environment interactions underpins the use of Koopman operators without approximation to control inputs. This methodology enables the convex Model Predictive Control of a legged robot, and the real-time control of a manipulator engaged in dynamic pushing. In this work, we show that our method allows robots to discover elaborate control strategies in real-time over time horizons with multiple contact changes, and the method is applicable to broad fields beyond robotics.