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This paper investigates real-time control strategies for dynamical systemsthat involve frictional contact interactions. Hybridness and underactuation arekey characteristics of these systems that complicate the design of feedbackcontrollers. In this research, we examine and test a novel feedback controllerdesign on a planar pushing system, where the purpose is to control the motionof a sliding object on a flat surface using a point robotic pusher. Thepusher-slider is a simple dynamical system that retains many of the challengesthat are typical of robotic manipulation tasks.  Our results show that a model predictive control approach used in tandem withinteger programming offers a powerful solution to capture the dynamicconstraints associated with the friction cone as well as the hybrid nature ofthe contact. In order to achieve real-time control, simplifications areproposed to speed up the integer program. The concept of Family of Modes (FOM)is introduced to solve an online convex optimization problem by selecting a setof contact mode schedules that spans a large set of dynamic behaviors that canoccur during the prediction horizon. The controller design is applied tostabilize the motion of a sliding object about a nominal trajectory, and tore-plan its trajectory in real-time to follow a moving target. We validate thecontroller design through numerical simulations and experimental results on anindustrial ABB IRB 120 robotic arm.

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