A Method for Sub-Minimal-Time Trajectory Planning of Redundant Dual manipulator Systems

This paper describes a method for sub-minimal-time trajectory planning of a dual manipulator system required to move a rigid task object from one spatial point to another. In this method, in order to transform the time optimal control problem into a non-linearly constrained optimisation problem, a piece-wise constant function is used to approximate the third derivatives of the generalised coordinates of the active joints of the dual manipulator system. However, the system is underspecified due to the redundancy, which is inherent to the system. A technique to overcome the problem, in which an excessive torque is used as optimisation variables, is proposed accordingly. A numerical example involving two SCARA type manipulators handling a long beam was used to illustrate the proposed scheme and results showed the effectiveness of the proposed technique.