Model-free kinematic control of redundant manipulators with simultaneous joint-physical-limit and joint-angular-drift handling

Model-free tracking control methods have been developed for redundant robotic manipulators with unknown kinematic or dynamic models. However, most existing works have not considered the problems of joint physical limits and joint angular drift. Joint angular drift refers to the phenomenon that the joint angles of a redundant manipulator are different from their initial state when the end-effector of the manipulator returns to its initial position. Therefore, this article proposes a model-free scheme for the tracking control of redundant manipulators as well as the avoidance of joint physical limits and joint angular drift. The proposed method aims to overcome these challenges by formulating the inverse kinematics problem as a constrained optimization problem, which incorporates the avoidance of joint angular drift into the optimization objective and takes the joint physical limits as a constraint. At the same time, an online Jacobian estimator is designed to observe the state of the manipulator. Specifically, it can estimate the Jacobian matrix of a redundant manipulator in real-time during the operation by fully exploiting the sensory data, without knowing the analytic robot model. Then, the optimization problem is integrated with the Jacobian estimator and solved by a discrete-time algorithm. Theoretical analysis is conducted to prove the stability and convergence of the proposed method. Moreover, the efficacy, practicability and superiority of the proposed method are supported by simulations and experiments based on different redundant manipulators.