Coordinate-Invariant Modeling and Control of a Three-DOF Robot Manipulator

This article presents coordinate-free modeling and control law synthesis for a 3-DOF, revolute-joint robotic manipulator. Most conventional robot analysis and design methods still operate in a parametric framework, which makes all results in a sense local. In contrast to this, we introduce a coordinate-free representation of the robots kinematics on S-1 x S-1 x S-1, which allows to express the continuous-time dynamics in a global, structured form. In parallel to the continuous case, a discrete-time model based on the discrete mechanics approach and the approximation of the Lagrangian using the implicit midpoint rule is introduced in the form of a variational integrator. On the basis of the derived models, we cover geometric potential shaping and PD control in continuous and discrete time, where remarkably, the discrete control laws share the structure of their continuous-time counterparts. Numerical experiments illustrate the benefits of the discrete-time geometric approach for simulation and control. Copyright (C) 2021 The Authors.