Energy-efficient control of double pendulum crane via QP trajectory planning and optimized LQR

Abstract

Controlling cranes with double pendulum dynamics is a complex task due to their nonlinear, underactuated behavior and susceptibility to external disturbances. Traditional control methods often fall short in achieving both energy efficiency and robust trajectory tracking. In this paper, we propose a hybrid control framework that combines a quadratic programming (QP)-based trajectory planner with a linear quadratic regulator (LQR) for disturbance rejection. To enhance controller performance, the LQR weighting matrices are automatically optimized using genetic algorithm (GA) and particle swarm optimization (PSO). The integration of optimal trajectory generation and feedback stabilization provides both efficiency and robustness. Extensive simulations are conducted under disturbance-free and disturbed operating conditions, benchmarking the proposed QP+LQR(GA/PSO) schemes against the standalone QP trajectory planner, a direct set point LQR baseline without trajectory planning, manually tuned QP+LQR, and an enhanced coupling tracking method. Under conditions without disturbances, the QP trajectory planner reduces energy consumption by 72.8% and 7.3% compared with the LQR controller operating without a planned reference trajectory and the enhanced coupling method, respectively. Under disturbances, QP+LQR(PSO) provides the best overall performance, with lower viscous dissipation and smaller pendulum oscillations than QP+LQR(GA). Both optimized schemes maintain bounded responses and outperform manual tuning. Practical implementation aspects are further discussed, highlighting the potential of combining model-based optimization and intelligent tuning for advanced crane control systems.