Model Reconstruction-Based Optimal Adaptive Prescribed Time Control for Multi-Stage Precision Robotic Arms: Inequality Constraints, Uncertainties, Disturbances

There are always multi-stage and multi-type precision requirements for robotic arms in industrial manufacturing. Due to uncertainties and disturbances, the tracking error is forced to exceed the time-varying precision boundary and the system is even broken. Therefore, an intelligent optimization framework of fuzzy adaptive prescribed time control for robotic arms with multi-stage precision is developed in this paper. Firstly, the multi-stage precision requirements are explained as time-varying piecewise inequality constraints of the tracking error. Based on homeomorphic mapping, a model reconstruction method is proposed by designing the transformation function to form a reconstructed system. Then, based on the constraint force analysis of the reconstructed system, a leaky adaptive prescribed time control method is proposed, which simultaneously handles uncertainties, disturbances and inequality constraints. The error convergence is achieved within a prescribed time by setting piecewise constraints. The overcompensation is avoided via the leaky-type adaptive law. The proposed method is proven to be uniformly bounded and uniformly ultimately bounded. Furthermore, an optimization strategy is designed based on fuzzy set theory to optimize system performance and control cost, forming a set of general trade-off rules. Finally, the effectiveness of the proposed method is verified. The results show that the time-varying piecewise inequality constraints are fully satisfied at low control cost.