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. Note to Practitioners—Robotic arms are widely used in collaborative robots, industrial robots and embodied intelligence. However, these scenarios always have multi-stage, multi-type and time-limited motion accuracy requirements, which are difficult to meet with conventional methods. Moreover, such nonlinear systems are easily affected by uncertainties such as modeluncertainty, external disturbances, and electronic noise. In addition, existing control strategies are difficult to provide engineers with a visual comprehensive optimization and trade-off criteria between control cost and system performance. This paper is dedicated to developing a fuzzy optimal adaptive time-limited control based on model reconstruction to simultaneously address the above limitations. 1) Engineers reconstruct the model based on the principle of homeomorphic mapping and the designed transformation function. Then the multi-stage accuracy requirements are set as inequality constraint boundaries; 2) Motion control is performed based on the proposed leakage adaptive control method. Leakage parameters avoid overcompensation, and high-order terms avoid additional control costs. 3) Based on the description of uncertainty by fuzzy sets, the optimal parameters are solved according to the optimization strategy. The trade-off criteria between performance and cost depend on the trade-off factors. The importance is visualized, so the optimization is intelligent. All the above steps use basic operations and are in analytical form. In future research, multi-parameter optimization strategies will be designed to comprehensively improve system performance.