Stochastic Nonlinear Model Predictive Control of a 3-DoF Suspended Cable-Driven Parallel Robot

This research paper focuses on the implementation of stochastic nonlinear model predictive control (SNMPC) to a suspended cable-driven parallel robot with three degrees of freedom. Cable robots are nonlinear systems which are exposed to measurement noises and uncertainties such as unmeasured disturbances, parametric uncertainties, and state estimation errors. Thus, nonlinear control, which has sufficient robustness, is required. Furthermore, an optimization procedure must be employed to consider the main challenge in cable robots, which is maintaining positive tension in cables. Although model predictive control has intrinsic robustness to small uncertainties, robust nonlinear model predictive control (RNMPC) and SNMPC are proposed for preserving sufficient robustness. RNMPC allows worst-case scenario analysis but can be so conservative in a way that leads to the infeasible control problem. However, probabilistic constraints of SNMPC enhance the balance between performance and constraints, reducing worst-case conservatism. According to this feature, in this paper, the proposed SNMPC uses an unscented Kalman filter to fulfill deterministic constraints on cable tension and probabilistic constraints on output errors for position tracking in cable robots. The simulation compares the tracking performance and stability of SNMPC with those of the NMPC approach. The results indicate a higher effectiveness in tracking for SNMPC and stability in the case of considerable measurement noises while NMPC is shown to be unstable.