Applications of potential fields and conformal geometric algebra for humanoid manipulation maneuvering

In this work we show the use of potential fields in conformal geometric algebra to assist the humanoid manipulation planning. Since the computational unit in conformal geometry algebra is the sphere, it appears natural to use the potential fields for computing navigation trajectories avoiding obstacles. Furthermore, by covering obstacles with convex hulls, one can obtain certain shapes which are amenable of being parameterized as spheres, thus this equivalent potential fields can be used so that the robot device can move around the irregular shapes of obstacle without increasing the computation complexity. In this paper we present this theory and show with simulations the effectiveness of the approach.