An adaptive non-linear constraint control of mobile manipulators

• We offer the solution of constraint position control problem of mobile manipulators.
• It is subject to state equality and/or inequality constraints.
• Kinematics and dynamics of mobile manipulators are parametric uncertain.
• We propose a class of asymptotically stable controllers to solve this control task.

This paper addresses the problem of position control of mobile manipulators operating in the task space with state constraints. Motivated in part by the energy shaping and damping injection methodology, we first propose a class of non-linear model-based constraint task space regulators which, by the fulfilment of a reasonable condition, are shown both to be asymptotically stable and to provide an optimal solution at the desired end-effector location. This methodology is then generalized to a class of both parametrically uncertain kinematic and dynamic equations of the mobile manipulators. The position control problem in the presence of kinematic and dynamic uncertainties and (unknown) environment (obstacles) is solved herein based on the Lyapunov stability theory, the exterior penalty function approach and by using the sensory feed-back of the end-effector and the sensors, in which the mobile manipulator is equipped. Novel adaptive laws, extending the capability of the classic algorithms to deal with both holonomic and nonholonomic kinematic uncertainties and obstacles, are proposed.