Trajectory planning of multiple manipulators

In the paper, a global method of redundancy resolution has been proposed to solve the task of trajectories planning for multiple manipulators operating in a common workspace. The task of manipulators is to follow, via end-effectors, the geometric paths given in a task space. A final time of the task performance is not fixed. The control constraints and state inequality constraints resulting from collision avoidance are taken into account. This task has been solved based on the calculus of variations. A computer example involving two planar redundant manipulators of three revolute kinematics pairs is presented.