Using the Bezier Curve and Particle Swarm Optimization in Trajectory Planning for Overhead Cranes to Suppress the Payloads’ Residual Swing

An overhead crane is an underactuated system, which leads to residual swing of the crane’s payload when the crane accelerates or decelerates. This paper proposes a trajectory planning approach which uses the Bezier curve and particle swarm optimizer (PSO-BC) to limit the residual swing of a payload. The dynamic equation for an overhead crane is discredited, and a five-order Bezier curve is generated as the trolley’s displacement. The trolley’s desired position is set as the last control point of the Bezier curve, which guarantees that the trolley reaches the desired position accurately. Various constraints, including restricting the swing angle, the allowable trolley velocity, and the allowable trolley acceleration, are then taken into consideration as the constraints. In order to make the trolley reach its desired position whilst suppressing the payload’s swing under the constraints, a particle swarm optimizer is used to determine the optimal control point positions of the Bezier curve. Finally, the PSO-BC simulation results are compared to some existing approaches and are presented to show the feasibility and robustness of the proposed PSO-BC method. The simulation results indicate that the trolley moved to the desired position accurately whilst the payload’s swing angle is kept to an allowable level.