This paper presents a sampling-based planning algorithm for in-hand manipulation of a grasped object using a series of external pushes. A high-level sampling-based planning framework, in tandem with a low-level inverse contact dynamics solver, effectively explores the space of continuous pushes with discrete pusher contact switch-overs. We model the frictional interaction between gripper, grasped object, and pusher, by discretizing complex surface/line contacts into arrays of hard frictional point contacts. The inverse dynamics problem of finding an instantaneous pusher motion that yields a desired instantaneous object motion takes the form of a mixed nonlinear complementarity problem. Building upon this dynamics solver, our planner generates a sequence of pushes that steers the object to a goal grasp. We evaluate the performance of the planner for the case of a parallel-jaw gripper manipulating different objects, both in simulation and with real experiments. Through these examples, we highlight the important properties of the planner: respecting and exploiting the hybrid dynamics of contact sticking/sliding/rolling and a sense of efficiency with respect to discrete contact switch-overs.
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