Manipulator control with superquadric artificial potential functions: theory and experiments

Previous work in arti cial potentials has demonstrated the need for an obstacle avoidance potential that closely models the obstacle, yet does not generate local minima in the workspace of the manipulator. This paper presents a potential function based on superquadrics, which 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. We introduce two compatible forms of the superquadric potential function: one for obstacle avoidance, and another for obstacle approach. We have implemented the avoidance and approach potentials in simulations. In these simulations the end e ector of the manipulator experiences an attractive force from a global spherical well, while the end e ector and each of the links experience repulsive forces from all of the objects. We have also experimentally implemented the avoidance potentials on the CMU DDARM II. The results demonstrate successful obstacle avoidance and approach, and exhibit an improvement over existing potential schemes.