This work offers the solution at the control feed-back level of the accurate positioning in a finite time of the end-effector whose mobile manipulator is subject to control and complex state constraints (both holonomic singularity and collision avoidance). Based on the Lyapunov stability theory, a suitably defined extended task error and exterior penalty function approach, a class of simple non-linear controllers converging in a finite time, which fulfil control and state constraints, is proposed. The numerical simulation results carried out for a mobile manipulator consisting of a nonholonomic differentially steered wheeled mobile platform and a holonomic manipulator of two revolute kinematic pairs, operating both in a two-dimensional unconstrained work space and work space including the obstacles, illustrate performance of the proposed controllers.
Galicki, M. (2014). Constrained finite-time control of mobile manipulators. In Procedia Engineering (Vol. 96, pp. 111–125). Elsevier Ltd. https://doi.org/10.1016/j.proeng.2014.12.120