Inverse-free control of a robotic manipulator in a task space

• A class of kinematic inverse-free nonlinear manipulator controllers is proposed.
• The control laws are shown to be asymptotically stable.
• Adaptive inverse-free controllers generating bounded controls are also offered.
• The numerical simulations confirm theoretical results.

This paper addresses the control problem in a task space of the redundant and/or non-redundant manipulators with both known and parametric unknown kinematics and dynamics. A computationally simple class of the inverse-free control algorithms is proposed for the end-effector trajectory tracking. These controllers use some suitably constructed non-singular matrix whose inverse estimates the product of the manipulator Jacobian by its transposition. Moreover, by introducing a suitably defined sliding vector and nonlinear errors of the parameters estimation, the new controllers generate bounded and continuous signals. Based on the Lyapunov stability theory, inverse-free control schemes proposed are shown to be asymptotically stable provided that some reasonable assumptions are fulfilled during the manipulator movement. The performance of the proposed control strategies is illustrated through computer simulations for a planar redundant manipulator of three revolute kinematic pairs which accomplishes trajectory tracking by the end-effector in a two-dimensional task space.