Exponential and robust position-constrained control of robot manipulators via diffeomorphisms

Mechanical systems subject to constraints play a essential role in the field of control engineering, profoundly influencing the design and performance of control strategies. Consequently, there is a compelling need to explore diverse control methods to effectively tackle the complex task of stabilizing nonlinear systems while ensuring the constraints are not violated. In this context, this paper proposes a design procedure for position-constrained controllers in robot manipulators. The solution relies on the construction of a diffeomorphism (a differentiable coordinate transformation) that maps all the trajectories of the constrained dynamics into an unconstrained one. The controller design is carried out in the unconstrained dynamics without dealing directly with the constraints. The proposed family of controllers employ an explicit control law which circumvents the need for additional time-consuming computation for feasibility and/or optimization. Moreover, the proposed controller is parametrized by a class of diffeomorphisms which can be selected by the designer. Exponential stability in constrained and unconstrained position states is achieved, in the certain case. For the uncertain case, the controller is augmented through sliding modes guaranteeing finite-time convergence towards the manifold and keeping the exponential convergence within the manifold dynamics. The approach is validated through experiments in an actual 2 DOF lightweight robot manipulator.