Modeling and control of a humanoid arm using Conformal Geometric Algebra and sliding modes

The geometric relationships between the elements of a humanoid robot manipulator are defined by the kinematics of the robot. The synthesis of the kinematical model for this type of robots is presented in this work using the Conformal Geometric Algebra framework. Moreover, two controllers are developed, one for the position tracking problem using a error feedback controller and another using sliding modes for the position tracking problem in precense of perturbations. The stability analysis is carried out for both controllers, and their application to a humanoid robot arm, composed of 5 DOF is presented. By proposing the error feedback and Lyapunov functions in terms of geometric algebra, we are opening a new venue of research in control of manipulators which involves the use of geometric primitives like lines, circles, planes and spheres.