Controlling walking biped robots is a challenging problem due to its complex and uncertain dynamics. In order to tackle this, we propose a sliding mode controller based on a dynamic model which was obtained using the conformal geometric algebra approach (CGA). The CGA framework permits us to use lines, points, and other geometric entities, to obtain the Lagrange equations of the system. The references for the joints of the robot were bio-inspired in the kinematics of a walking human body. The first and second derivatives of the reference signal were obtained through an exact robust differentiator based on high order sliding modes. The performance of the proposed control scheme is illustrated through simulation.

The kinematics of a robotic manipulator defines the geometric relationships between its elements. The synthesis of the kinematical model for this type of robots is presented in this work using the Conformal Geometric Algebra approach. Moreover, two error feedback controllers, one for the position tracking problem and another for the orientation tracking problem, are developed using the same framework. The stability analysis is obtained for both controllers, and their application to a robotic system, composed of a serial manipulator of 5 DOF and a robotic head of 2 DOF, is presented via simulation.

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.