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 φ(s), respectively. The joint path θ<sub>i</sub> of the i-th manipulator is also expressed by this parameter `s´ and written as θ_i(s). A quantity λ(s) which connects the time `t´ and the path parameter `s´ is introduced. θ_i(s) and λ(s) are approximated by B-spline. Obstacles are artificially transferred to obtain initial collision free trajectories and gradually restored. Sub-optimal θ_i(s) and λ(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