Control-Based Solution to Inverse Kinematics for Mobile Manipulators Using Penalty Functions

This study offers the solution at the control feedback level to the inverse kinematics problem subject to state equality and inequality constraints for mobile manipulators. Based on the Lyapunov stability theory, a class of controllers generating the mobile manipulator trajectory whose attractor attained in a finite time, fulfills the above state constraints. The problem of both holonomic manipulability enforcement and collision avoidance is solved here based on an exterior penalty function approach which results in continuous mobile manipulator velocities near obstacles. The numerical simulation results carried out for a mobile manipulator consisting of a nonholonomic wheel and a holonomic manipulator of two revolute kinematic pairs, operating in both a constraint-free task space and task space including obstacles, illustrate the performance of the proposed controllers.