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 Conformal 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.
The principal objective of the paper is to show the importance of the Hamiltonian in control theory. Instead of using the Lagrangian formulation of electromechanical or robotic systems, our work is focused on robot dynamics by its Hamiltonian. Using the iterative Newton–Euler, we generate the local Hamiltonians and the derivative of the moments at each joint of the robot manipulator. Thus, we can apply decentralized controllers at each joint. We compare and discuss the efficiency of the controllers. We show that the performance of the sliding modes controller is more robust than that of the PD or Bang–Bang controllers.
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