Robust optimal constrained control of fully-constrained cable-driven parallel robots based on GSDRE

This paper addresses constrained robust optimal control of Cable-Driven Parallel Robots (CDPRs) in detail. In the CDPRs, cables should remain in tension for all movements. Based on this fact, considering tension constraints, a robust optimal control scheme is presented for the cable robots in this study. To develop the idea, at first, the general nonlinear dynamic model of the CDPR is converted to a State-Dependent Coefficient (SDC) linear structure. In this model, uncertainties of the cable robot are included as a vector in the SDC linear structure. Next, a constrained robust optimal control algorithm is proposed based on Hamilton-Jacobi-Bellman (HJB) equations and Karush-Kuhn-Tucker (KKT) conditions using the state-dependent coefficient parameterization form. The proposed control scheme is formed based on the Generalized State-Dependent Riccati Equation (GSDRE), and a new equation is created to counteract with disturbances and uncertainty of the CDPR model. Finally, the stability of the closed-loop system is proved using Lyapunov's second method. Simulation results show the effectiveness of the proposed control algorithm in terms of tracking and coping with the uncertainties and external disturbances.