Adaptive Prescribed Performance Control of Robotic Manipulators with Velocity Constraints and Arbitrary Initial Joint Positions

A novel adaptive prescribed performance control method for the n-DOF robotic manipulators is proposed in this paper. Firstly, a normalization constraining function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$g$</tex> is designed for state transformation and constructing a new system model. The risk of singularity problems can be reduced by adjusting the parameters of function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$g$</tex>. Then, an adaptive prescribed performance controller is developed based on the constructed system model, which allows the initial joint positions of the manipulator to be arbitrary, and can guarantee that the tracking error reaches the desired accuracy within the preset time <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$T_{P}$</tex>. Meanwhile, different velocity constraints can be individually imposed on each joint. In addition, an adaptive law is designed to estimate the lumped uncertainty in the system and compensate for its negative influence, which improves the control performance. Finally, the effectiveness of the proposed method is verified by simulations and experiments on a 4-DOF manipulator.