Planning Velocities of Free Sliding Objects as a Free Boundary Value Problem

In this paper, a novel planning method is proposed to solve initial velocities of the free sliding object for given initial and final configurations. Finding the desired initial velocities for free sliding objects is a key step for implementing impulse manipulation and multi-agent dynamic cooperative manipulation. The motion of free sliding objects on a plane is governed by friction forces and the initial state of the object; this motion can be modeled by a set of six first-order differential equations. In this paper, the planning problem is formulated as a free boundary value problem (FBVP). In order to solve the problem, the FBVP is first reduced to a standard two-point boundary value problem, then quasi-Newton based optimization procedures are utilized to solve the planning problem. The proposed method does not require qualitative motion characteristics; thus, it can be used for objects with general shape and arbitrary pressure distribution. Numerical and experimental results on objects with different geometries and pressure distributions are used to demonstrate the performance of the proposed planner. KEY WORDS—object manipulation, free sliding free boundary value problem, two-point boundary value problem, shooting method