Orthogonal Manipulability Optimization for OMRM With Neural Networks and Nonconvex Constraints

Manipulability optimization is critical for avoiding singularities in an omnidirectional mobile redundant manipulator (OMRM), yet its intrinsic nonlinearity and nonconvexity introduce substantial computational challenges. Furthermore, the coupling between manipulability optimization and position error inevitably results in a theoretically nonzero error, thereby compromising control accuracy. To address these issues, this article proposes an orthogonal manipulability maximization optimization under non-convex constraints (OMMONC) scheme, which decouples position error and manipulability through an orthogonal projection matrix. It drives the position error to theoretically converge to zero, while simultaneously reducing the risk of singular postures in motion control. To generate smooth control signals, a non-convex recurrent neural network (NCRNN) is developed, which realizes real-time computation of the OMMONC scheme via an inverse-free solution, thereby mitigating lag-induced errors and enhancing computational efficiency. The proposed OMMONC scheme is theoretically proven to decouple position error and manipulability, and the convergence of the NCRNN model is also demonstrated. Numerical simulations, comparative results and platform experiments verify the validity and superiority of the proposed scheme and model.