Accelerated Learning and Control of Robots with Uncertain Kinematics and Unknown Disturbances

This paper develops accelerated model-free robust adaptive control algorithms for unknown static maps which correspond to forward kinematics in robotics. The technique is based on the estimation of unknown Jacobian matrix by using a neural-network based approximation and use of monotonically increasing gain functions in the controller and update law. The introduced algorithms provide robustness against the unknown environmental disturbances and achieve asymptotic, exponential and prescribed-time reference trajectory tracking. The fixed-time stabilization in prescribed time is the strongest notion among them that allows user to predefine a terminal time irrespective of initial condition and system parameters. A formal stability analysis for each algorithm is presented and theoretical results are validated through numerical simulations conducted on a single-section three-actuator continuum robot.