To address the Jacobian matrix approximation error, which usually exists in the iterative solving process of the classic singular robust inverse method, the correction coefficient α is introduced, and the improved singular robust inverse method is the result. On this basis, the constant improved singular robust method and the intelligent improved singular robust inverse method are proposed. In addition, a new scheme, combining particle swarm optimization and artificial neural network training, is applied to obtain real-time parameters. The stability of the proposed methods is verified according to the Lyapunov stability criteria, and the effectiveness is verified in the application examples of spatial linear and curve trajectories with a seven-axis manipulator. The simulation results show that the improved singular robust inverse method has better optimization performance and stability. In the allowable range, the terminal error is smallest, and there is no lasting oscillation or large amplitude. The least singular value is largest, and the joint angular velocity is smallest, exactly as expected. The derivative of the Lyapunov function is negative definite. Comparing the two extended methods, the constant improved singular robust method performs better in terms of joint angular velocity and least singular value optimization, and the intelligent improved singular robust inverse method can achieve a smaller terminal error. There is little difference between their overall optimization effects. However, the adaptability of the real-time parameters makes the intelligent improved singular robust inverse method the first choice for kinematic control of redundant serial manipulators.
Smooth Analysis of the Condition Number and the Least Singular Value
