A Novel Neural Approach to Infinity-Norm Joint-Velocity Minimization of Kinematically Redundant Robots Under Joint Limits

Generally, the infinity-norm joint-velocity minimization (INVM) of physically constrained kinematically redundant robots can be formulated as time-variant linear programming (TVLP) with equality and inequality constraints. Zeroing neural network (ZNN) is an effective neural method for solving equality-constrained TVLP. For inequality-constrained TVLP, however, existing ZNNs become incompetent due to the lack of relevant derivative information and the inability to handle inequality constraints. Currently, there is no capable ZNN in the literature that has achieved the INVM of redundant robots under joint limits. To fill this gap, a classical INVM scheme is first introduced in this article. Then, a new joint-limit handling technique is proposed and employed to convert the INVM scheme into a unified TVLP with full derivative information. By using a perturbed Fisher–Burmeister function, the TVLP is further converted into a nonlinear equation. These conversion techniques lay a foundation for the success of designing a capable ZNN. To solve the nonlinear equation and the TVLP, a novel continuous-time ZNN (CTZNN) is designed and its corresponding discrete-time ZNN (DTZNN) is established using an extrapolated backward differentiation formula. Theoretical analysis is rigorously conducted to prove the convergence of the neural approach. Numerical studies are performed by comparing the DTZNN solver and the state-of-the-art (SOTA) linear programming (LP) solvers. Comparative results show that the DTZNN consumes the least computing time and can be a powerful alternative to the SOTA solvers. The DTZNN and the INVM scheme are finally applied to control two kinematically redundant robots. Both simulative and experimental results show that the robots successfully accomplish user-specified path-tracking tasks, verifying the effectiveness and practicability of the proposed neural approach and the INVM scheme equipped with the new joint-limit handling technique.