Planning velocities of free sliding objects for dynamic manipulation

In this paper, a novel numerical approach is proposed to solve the initial velocities of the free sliding object for given initial and final configurations. To find the desired initial velocities for free sliding objects is a key step for implementing dynamic manipulation. In order to plan the initial velocities, the motion of free sliding objects is modeled as a set of 6 first order differential equations, and the planning problem is formulated as a free boundary value problem (FBVP). Through a simple transformation, the FBVP is reduced to a standard Two-point boundary value (TPBV) problem. Quasi-Newton based optimization procedures are utilized to solve the planning problem. Unlike existing approaches, the proposed method does not require qualitative motion characteristics, thus it can be used for objects with general shape and arbitrary pressure distribution. Simulation results on polygonal objects with three to five vertices are used to demonstrate the planning method.