Optimal path planning including forces at the gripper

In recent years, a topological method has been established by several authors for the evaluation of time-optimal trajectories for manipulators with tree-like structures and without forces at the gripper, i.e. for free trajectories. In the following, we extend this method to the case of an arbitrary force vector at the robot's hand, which corresponds to some path in contact with a surface. Optimizing the actuator torques in such a way might be seen as a first step to controlling trajectories with regard to position, orientation, and forces in the presence of elasticity. Results of the method confirm the basic ideas of the topological solution.