Синтез оптимальних траєкторій переміщення вантажу стріловим краном

The article discusses the problem of synthesising optimal trajectories for moving load with a tower crane in order to increase its productivity and safety. A dynamic model of the system has been developed, including the boom, trolley and load suspended on a flexible rope, taking into account the pendulum oscillations of the load. To determine the laws of motion of the boom and trolley that ensure the specified load trajectory, the inverse kinematic problem has been solved. An optimisation approach has been proposed, aimed at minimising the duration of load transportation while complying with kinematic and dynamic constraints, in particular the maximum speeds of the trolley and boom rotation. To ensure smooth movement and reduce dynamic loads, regularisation methods are used to reduce the amplitude of load oscillations and eliminate unwanted changes in the direction of movement of the mechanisms. The numerical solution of the optimisation problem was performed using a modified particle swarm optimisation method (VCT-PSO), which demonstrated its effectiveness in selecting the optimal trajectory parameters. The influence of regularisation and the length of the flexible suspension on the dynamic characteristics of the system, in particular the amplitude of oscillations, peak forces and moments, as well as the duration of movement, was analysed. The results show that the use of regularisation significantly reduces dynamic loads and increases motion stability, although it increases transport time. Shortening the suspension length reduces motion time but can lead to an increase in oscillation amplitude. A new tool for analysing system dynamics in terms of deviations and velocity differences is proposed, which provides a visual assessment of the oscillation process and confirms the fulfilment of boundary conditions. The results obtained can be used to improve tower crane control systems and increase their efficiency on construction sites.