Optimal Planning of a Collision-free Trajectory of Redundant Manipulators

Abstract

In this study, global planning of a collision-free trajectory (simultaneous planning of geometric path and its time para meterization) involving potential functions and direct kinematic and dynamic equations of the manipulator is presented. This planning is based on using the necessary conditions of min imum for an integral type criterion. General transversality conditions corresponding to the boundary ones (resulting from the task to be performed) are derived. Thus, closed systems of boundary dependences fully specifying differential equations, which arise from the necessary conditions of extreme for the above criterion, are obtained. As a result, this system renders it possible to reduce the collision-free trajectory planning problem to a two-point boundary value problem. A numerical example involving a manipulator of three-revolute kinematic pairs of the Vth class is considered.