Manipulability Optimization of Redundant Manipulators Using Dynamic Neural Networks

For solving the singularity problem arising in the control of manipulators, an efficient way is to maximize its manipulability. However, it is challenging to optimize manipulability effectively because it is a nonconvex function to the joint angles of a robotic arm. In addition, the involvement of an inversion operation in the expression of manipulability makes it even hard for timely optimization due to the intensively computational burden for matrix inversion. In this paper, we make progress on real-time manipulability optimization by establishing a dynamic neural network for recurrent calculation of manipulability-maximal control actions for redundant manipulators under physical constraints in an inverse-free manner. By expressing position tracking and matrix inversion as equality constraints, physical limits as inequality constraints, and velocity-level manipulability measure, which is affine to the joint velocities, as the objective function, the manipulability optimization scheme is further formulated as a constrained quadratic program. Then, a dynamic neural network with rigorously provable convergence is constructed to solve such a problem online. Computer simulations are conducted and show that, compared to the existing methods, the proposed scheme can raise the manipulability almost 40% on average, which substantiates the efficacy, accuracy, and superiority of the proposed manipulability optimization scheme.