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