Operational Space Formulation Under Joint Constraints

In this paper, the problem of including hard constraints in the stack of tasks for torque-controlled serial manipulators is treated. The classic potential field approach is studied and a novel implementation of it is proposed. This implementation reduces the kinetic energy in the proximity of joint limits. Furthermore, a novel approach is proposed in order to include not only joint positions but also joint velocities and acceleration limits. This approach is called "Saturation in Joint Space" (SJS). The algorithm proceeds by creating a task with the highest priority in a stack of tasks scheme. This high priority task saturates the acceleration of the joints that would exceed their motion limits. The methods are tested and compared in simulation for the KUKA LBR iiwa. The SJS approach presents smoother behaviour near to the joint limits, while a Cartesian trajectory is traced. Experiments are performed to test the efficiency of this method in a real environment and under interaction with a human. The on-line saturation of the joint acceleration generates a friendly behaviour with the human even when he pushes the robot towards its limits.