Geometric Tracking Control of a Three-Dimensional Revolute Joint Robot

This paper studies the tracking control of a three-dimensional revolute joint robot consisting of a rotating base and two rigid rotating links with bounded unstructured uncertainties to all three degrees of freedom. The configuration space of the system is considered as a direct product of three one-sphere (S-1) configuration spaces to provide a global formulation. Following a Lagrangian formulation, a nonlinear tracking control law is designed in terms of global coordinates. The proposed controller is mathematically proven to provide uniformly ultimately bounded stability, and simulations demonstrate its performance.