collision-free control of mobile manipulators in a task space

this work offers the solution at the control feed-back level of the end-effector trajectory tracking problem for mobile manipulators subject to state equality and/or inequality constraints, suitably transformed into control dependent ones. based on the lyapunov stability theory, a class of controllers fulfilling the above constraints and generating a collision-free mobile manipulator trajectory with (instantaneous) minimal energy, is proposed. the problem of collision avoidance 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 non-holonomic unicycle 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.