Manipulator control with superquadric artificial potential functions: theory and experiments

A potential function based on superquadrics is presented that closely models a large class of object shapes. This potential function also prevents the creation of local minima when it is added to spherically symmetric attractive wells. Two compatible forms of the superquadric potential function are introduced: one for obstacle avoidance, and another for obstacle approach. The avoidance and approach potentials are implemented in simulations. In these simulations the end effector of the manipulator experiences an attractive force from a global spherical well, while the end effector and each of the links experience repulsive forces from all of the objects. The authors have also experimentally implemented the avoidance potentials on the CMU DDARM II system. The results demonstrate successful obstacle avoidance and approach, and exhibit an improvement over existing schemes