Predictive control of single pendulum cranes under actuated/underactuated state constraints: A higher-order fully actuated approach

The single pendulum crane (SPC), as a typical nonlinear underactuated system, presents challenges in directly implementing control and imposing constraints on underactuated states. To address these challenges, this paper proposes a predictive control method for the SPC system based on a high-order fully actuated (HOFA) system framework. Specifically, the underactuated SPC is converted into a HOFA system, and a disturbance observer is designed to estimate the uncertainty term. Then, a model predictive controller is designed to convert the control problem into a quadratic programming(QP) problem, which realizes the control of the SPC and the constraints on the actuated/underactuated states. Finally, we propose an online physics-informed preset-time solver that guarantees bounded-time convergence for the QP problem. In experiments, two types of SPC systems are considered, with payloads connected by a sling and by a rigid rod, respectively. This demonstrates the universality of the method proposed in this paper. Results show that the payload maximum swing angles of the two systems are reduced by 78.81% and 64.29% compared with PD-like control, 75.96% and 59.75% compared with partially linearized HOFA control, and 13.48% and 27.48% compared with linearized model predictive control, respectively. Moreover, the constraints on the actuated/underactuated states are achieved. Finally, cases involving system parameter uncertainties and external disturbances are also considered, and the proposed method still exhibits good control performance.