Real-time inverse kinematics of redundant manipulators using neural networks and quadratic programming: A Lyapunov-based approach

In this paper, an online adaptive strategy based on the Lyapunov stability theory is presented to solve the inverse kinematics of redundant manipulators. In the proposed approach, Radial Basis Function (RBF) Neural Networks (NNs) are employed to obtain the joint angles of the robot using the Cartesian coordinate of the end-effector. Quadratic Programming (QP) method is incorporated in the training algorithm of the NNs to satisfy the constraints of the problem such as the joint angle limits and obstacles in the workspace of the robot. For better initialization of the NNs' weights, fuzzy logic is employed. In this way, smaller errors for the initial position of the end-effector and feasibility of the joint angles can be obtained. The convergence of the NNs' weights and satisfaction of the constraints are guaranteed by employing an adaptive scheme that is based on the Lyapunov stability analysis and Kuhn-Tucker conditions, which is part of the QP to update the NNs' weights. In addition, obstacle avoidance is also considered in the proposed method. The simulations are carried out on the seven degrees-of-freedom PA-10 robot manipulator. The results show the effectiveness of the proposed approach in obtaining successful configurations of the robot while the solutions of the inverse kinematics are feasible. Moreover, a comparison with the recently reported methods in the literature shows advantages of the proposed method.