A trajectory planning algorithm with path search for cooperative multiple manipulators

Proposes an algorithm to determine sub-optimal paths and trajectories for cooperative multiple manipulators which hold an object and transfer it from a given start point to a given goal point. The dynamic equations of manipulators and the object are expressed by a path parameter `s´ which is the length along the path and does not depend on the time `t´ explicitly. Using this parameter `s´, the authors express the position of the center of gravity and the attitude of the object as p(s) and φ(s), respectively. And 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. Suboptimal θ_i(s) and λ(s) are determined by considering the boundary conditions of both end points and the driving torque/force constraint of each joint of each manipulator. The proposed algorithm is applied to a two-manipulator system. Numerical results show the effectiveness of the algorithm