A Mangasarian-Soldov Function Based Neural Network for Constrained Control of Parallel and Serial Robots

Zeroing neural networks (ZNNs) are powerful alternatives to solving quadratic programming (QP) for constrained control of parallel and serial robots. A recent study showed that a ZNN solver designed based on a perturbed Fischer-Burmeister function (pFB-ZNN) achieves more satisfactory performance than other ZNN solvers. The pFB-ZNN solver suffers from manual tuning of an extra hyper-parameter and may encounter residual error peaks. To tackle the above issues, this paper proposes a new Mangasarian-Solodov function-based ZNN (MS-ZNN) solver. The MS-ZNN solver has no extra hyper-parameter to be tuned and it can eliminate residual error peaks appeared in the pFB-ZNN solver, ensuring a higher solution accuracy. Mathematically, this paper details the design and convergence analysis of the MS-ZNN solver, demonstrating its convergence in the sense of Lyapunov. Numerical studies are comparatively performed, verifying the effectiveness and superiority of the MS-ZNN solver. The MS-ZNN solver is then successfully applied to kinematic control of a parallel robot and a serial robot under joint constraints. Both simulative and experimental results demonstrate that the proposed MS-ZNN solver is applicable to constrained control of parallel and serial robots with joint-limit avoidance achieved.