Oscar Eleno Carbajal-Espinosa

Geometric techniques for the kinematic modeling and control of robotic manipulators

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.

Continuous and discrete time robust control for bipedal robot assuming minimal knowledge of the plant

In this paper, a control approach in continuous and discrete time, for the robust tracking of walking patterns in a bipedal robot, is proposed. A discrete time model of the robot is obtained using the symplectic Euler method, in order to define a comparison between the proposed continuous and discrete time controllers in presence of parametric variations. Two robust controllers are designed using the Sliding Mode approach, one is based on the discrete time model and the other one on the continuous time model of the bipedal robot. The performance and robustness with respect to external disturbances and parametric variations of the proposed controllers, are demonstrated via Lyapunov stability analysis and simulations. By means of a discrete event model, the switching logic is simulated to represent the switching in the walking phases of the robot.

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.

Inverse kinematics of a 3 DOF parallel manipulator: A conformal geometric algebra approach

In this paper we propose a method to solve the inverse kinematic of a 3 DOF parallel manipulator, best know as Stewart platform. Using the entities of the rotors and motors it is possible define an algorithm to find the joint values of each actuator that allow to reach the desired position and orientation of the manipulator, describing only one geometric solution for one arm of the platform and applying a rigig transformation to this solution in order to define the solution for the rest of the arms of the robot. Simulations and real time implementation of the algorithm were done to prove the effectiveness of the proposal.

Visual servoing and robust object manipulation using symmetries and Conformai Geometric Algebra

Object tracking and manipulation is an important process for many applications in robotics and computer vision. A novel 3D pose estimation of objects using reflectionally symmetry formulated in Conformai Geometric Algebra (CGA) is proposed in this work. The synthesis of the kinematics model for robots and a sliding mode controller using the CGA approach is described. Real time implementation results are presented for the pose estimation of object using a stereo vision system.

Robust tracking of bio-inspired references for a biped robot using geometric algebra and sliding modes

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.

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.