Newton–Euler modeling and Hamiltonians for robot control in the geometric algebra

Abstract

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.

Survey of New Applications of Geometric Algebra

“…To spread the information about GA, authors integrate new methods and models with standard approaches. Thus, the connection between GA and control on Lie groups is discussed by Jaroslav Hrdina et al in 108 and Eduardo Bayro-Corrochano et al in 109 show the importance of the Hamiltonian in control theory in terms of GA.…”

Phase-Space Modeling and Control of Robots in the Screw Theory Framework Using Geometric Algebra

“…In [10], geometric algebra is utilized to compute Hamiltonian mechanics and the Poisson bracket, where this work could be used in robotics. The authors in [11] illustrate the importance of Hamiltonians in robotics. The technique computes the dynamic equations using Newton-Euler and describes the local Hamiltonians in each joint to implement its law of control.…”