Feedback Control of the Pusher-Slider System: A Story of Hybrid and Underactuated Contact Dynamics

This paper investigates real-time control strategies for dynamical systems\nthat involve frictional contact interactions. Hybridness and underactuation are\nkey characteristics of these systems that complicate the design of feedback\ncontrollers. In this research, we examine and test a novel feedback controller\ndesign on a planar pushing system, where the purpose is to control the motion\nof a sliding object on a flat surface using a point robotic pusher. The\npusher-slider is a simple dynamical system that retains many of the challenges\nthat are typical of robotic manipulation tasks.\n Our results show that a model predictive control approach used in tandem with\ninteger programming offers a powerful solution to capture the dynamic\nconstraints associated with the friction cone as well as the hybrid nature of\nthe contact. In order to achieve real-time control, simplifications are\nproposed to speed up the integer program. The concept of Family of Modes (FOM)\nis introduced to solve an online convex optimization problem by selecting a set\nof contact mode schedules that spans a large set of dynamic behaviors that can\noccur during the prediction horizon. The controller design is applied to\nstabilize the motion of a sliding object about a nominal trajectory, and to\nre-plan its trajectory in real-time to follow a moving target. We validate the\ncontroller design through numerical simulations and experimental results on an\nindustrial ABB IRB 120 robotic arm.\n