Nonlinear MPC with embedded super-twisting sliding modes for robust control of elastic cable-driven parallel robots

Cable-Driven Parallel Robots (CDPRs) pose significant control challenges due to unilateral actuation, cable elasticity, nonlinear-coupling, and tension-feasibility constraints. Model Predictive Control (MPC) can handle such constraints, but its performance remains sensitive to modeling inaccuracies and computational complexity. Sliding Mode Control (SMC), on the other hand, provides robustness to disturbances and uncertainties but lacks constraint handling and induce chattering.This paper proposes a robust Nonlinear MPC (NMPC) framework for CDPRs in which super-twisting sliding mode dynamics are embedded into the prediction model. Rather than cascading or switching between predictive and robust controllers, the correction is introduced as an internal NMPC state. This allows the optimizer to anticipate model mismatches and elasticity effects while computing cable tensions satisfying non-negativity, magnitude, and smoothness constraints.Trajectory tracking is achieved through regulation of a sliding variable, avoiding model-dependent tracking terms in the cost function.The resulting NMPC unifies robustness and feasibility. Simulation results on a full-order model of an eight-cable 6-DoF CDPR demonstrate high-precision tracking, smooth tension profiles, strict feasibility, and absence of chattering, even under significant modeling errors, elastic effects, and aggressive motion profiles.