Control Synthesis for Dynamic Contact Manipulation

We explore the control synthesis problem for a robot dynamically manipulating an object in the presence of multiple frictional contacts. Contacts occur both between the object and the robot, and between the object and the environment. Two sets of constraints govern the evolution of the system — contact velocity constraints that prevent separation and cause rolling, and, contact force constraints that arise from Coulomb friction. We combine the constraints in the space of contact accelerations, obtaining bounds on the robot acceleration as a function of the system state. We solve the motion planning problem by providing a feasible path for the system and generating the controls and the system trajectory by time-scaling the feasible path. We provide examples that illustrate the merits and limitations of our technique and discuss some of the open problems