Collision free trajectory planning for cooperative multiple manipulators

We propose a method of planning collision free trajectories for cooperative multiple manipulators. The dynamic equations of manipulators and the object are expressed by a path parameter 's' which does not depend on the time 't' explicitly. Using this parameter 's', we express the position of the center of gravity and the attitude of the object as p(s) and /spl phi/(s), respectively. The joint path /spl theta//sub i/ of the i-th manipulator is also expressed by this parameter 's' and written as /spl theta//sub i/(s). A quantity /spl lambda/(s) which connects the time 't' and the path parameter 's' is introduced. /spl theta//sub i/(s) and /spl lambda/(s) are approximated by B-spline. Obstacles are artificially transferred to obtain initial collision free trajectories and gradually restored. Sub-optimal /spl theta//sub i/(s) and /spl lambda/(s) are determined by considering the boundary conditions of the start and goal points, the driving torque/force constraint of each joint of each manipulator and collision free condition. The proposed method is applied to a two-manipulator system. Numerical results show the effectiveness of the method.