Obstacle avoidance for a humanoid arm using conformal geometric algebra

In this work we show the use of conformal geometric algebra to assist the humanoid manipulation planning and obstacle avoidance. Adding the concept of potential fields to the geometric algebra framework we obtain a good approach to avoid 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.