Collision avoiding continuation method for the inverse kinematics of redundant manipulators

An iterative solution method for the inverse kinematics (IK) of redundant serial manipulators (SM) is proposed that circumvents collision of manipulator and obstacles. Artificial potential fields are assigned to possibly colliding objects. A predictor-perturbation-corrector (PPC) algorithm accomplishes the IK while the manipulator´s end-effector (EE) is tracing a prescribed path. The predictor step achieves geometric tracking of the target EE configuration. An intermediate perturbation step adjusts the manipulator posture away from obstacles. A succeeding corrector step amends the perturbed configuration in accordance with the target EE configuration. The gradients of the artificial potential fields that are tangential to the self motion manifold of the manipulator are considered for perturbation. At each time step the three PPC steps are applied iteratively. The number of necessary PPC steps depends on the required distance to the obstacles. The algorithm is applicable for off-line planing and in real time implementations. It can be extended straight forward to parallel manipulators. Special attention is given to object modelling using artificial potentials functions. Results are shown for a planar 5R and a spatial 10R manipulator.