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.

中文翻译：

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关节限制下运动冗余机器人无穷范数关节速度最小化的一种新神经方法

通常，物理约束运动学冗余机器人的无穷范数关节速度最小化 (INVM) 可以表示为具有等式和不等式约束的时变线性规划 (TVLP)。归零神经网络 (ZNN) 是求解等式约束 TVLP 的一种有效神经方法。然而，对于不等式约束的 TVLP，现有的 ZNN 由于缺乏相关的衍生信息和无法处理不等式约束而变得无能为力。目前，文献中还没有能够实现冗余机器人在关节限制下的 INVM 的 ZNN。为了填补这一空白，本文首先介绍了一种经典的 INVM 方案。然后，提出并采用了一种新的联合极限处理技术，将 INVM 方案转换为具有完整导数信息的统一 TVLP。通过使用扰动的 Fisher–Burmeister 函数，TVLP 进一步转换为非线性方程。这些转换技术为成功设计有能力的 ZNN 奠定了基础。为了求解非线性方程和 TVLP，设计了一种新型连续时间 ZNN (CTZNN)，并使用外推的后向微分公式建立了其对应的离散时间 ZNN (DTZNN)。严格进行理论分析以证明神经方法的收敛性。通过比较 DTZNN 求解器和最先进的 (SOTA) 线性规划 (LP) 求解器进行数值研究。比较结果表明，DTZNN 消耗的计算时间最少，可以成为 SOTA 求解器的强大替代方案。DTZNN 和INVM 方案最终应用于控制两个运动冗余机器人。