Two-stage constrained control of mobile manipulators

This work offers the solution at the control feed back level of a complex mobile manipulator task. It comprises the following stages: attaining the desired trajectory to be tracked (end goal task) with zero platform velocity and then tracking this trajectory by the end-effector. These stages are subject to state equality and/or inequality constraints, suitably transformed into control dependent ones. Based on the Lyapunov stability theory, a class of asymptotically stable controllers fulfilling the above constraints and generating a singularity and collision free mobile manipulator trajectory with zero platform velocity and (instantaneous) minimal holonomic energy is proposed. The problem of singularity and collision avoidance enforcement is solved here based on an exterior penalty function approach which results in continuous and bounded mobile manipulator controls even near boundaries of obstacles. The numerical simulation results carried out for a mobile manipulator consisting of a nonholonomic differentially steered wheeled mobile robot and a holonomic manipulator of two revolute kinematic pairs, operating both in a two-dimensional unconstrained task space and task space including the obstacles, illustrate the performance of the proposed controllers.