Motion constraint satisfaction by means of closed form solution for redundant robot arms

Generation of flexible goal directed movement describes the key skill of autonomous articulated robots. Critical points are still the acknowledgement of reaching and grasping task while satisfying static and dynamically changing constraints given by the environment or caused by the human operator in a collaborative situation. This means that the motion planning dynamics has to incorporate multiple contributions of different qualities which should be formulated in constraint specific reference frames and then transformed into the frame of joint velocities. Whereby the handling of the contribution to motion planning is determined by the solution of the inverse kinematics problem. In this work a closed form solution for the inverse kinematics problem for an eight degree of freedom arm is presented. The geometrical properties of the multi redundant arm and the resulting free parameter which determine it´s null space motion are utilized to satisfy constraints of the desired motion. We implement this system on an eight DoF redundant manipulator and show its feasibility in a simulation.