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

Abstract

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.

Control of an underactuated double-pendulum overhead crane using improved model reference command shaping: Design, simulation and experiment

“…The particle 𝑖𝑖 in dimension 𝑗𝑗 for the searching optimisation process can also be defined as 𝑖𝑖 ∈ [1, 𝜌𝜌] and 𝑗𝑗 ∈ [1, 𝐷𝐷], where 𝜌𝜌 and 𝐷𝐷 were the entire population and they were high dimensional in a search space. Conceptually, the new particle velocity, 𝑉𝑉 𝑖𝑖𝑖𝑖 𝑘𝑘+1 , was adjusted, according to the 𝑋𝑋 𝑖𝑖𝑖𝑖 𝑘𝑘 , 𝑝𝑝𝑝𝑝𝑝𝑝𝑠𝑠𝑡𝑡 𝑖𝑖𝑖𝑖 , and 𝑔𝑔𝑝𝑝𝑝𝑝𝑠𝑠𝑡𝑡 𝑖𝑖 values, and the new particle position, 𝑋𝑋 𝑖𝑖𝑖𝑖 𝑘𝑘+1 , was updated based on 𝑋𝑋 𝑖𝑖𝑖𝑖 𝑘𝑘 and 𝑉𝑉 𝑖𝑖𝑖𝑖 𝑘𝑘+1 , as in [41][42][43]:…”

A smooth optimized input shaping method for two-dimensional crane systems using Bezier curves

“…Moreover, to make sure that the oscillation of the payload is suppressed at the final time of the trolley motion, the total energy of the payload at this time should be zero. The total energy of the payload is given (Liu and Cheng, 2018)…”

“…Combining the Bezier curve with the particle swarm optimization (PSO) method effectively controlled the movement of the trolley-load system (Jolly et al, 2009; Renny Simba et al, 2016; Wang et al, 2015). Liu and Cheng (2018) succeeded in suppressing the payload swing using a fifth-order Bezier curve that is generated as the trolley’s displacement. However, the displacement profile is constructed from several Bezier curve segments.…”

Error Compensation Trajectory Planning Method of Brake Disc Shaft Hole Assembly considering Robot Accumulated Error

“…In the research of trajectory optimization [15,16], researchers mainly focus on using various algorithms to optimize performance indicators such as time, energy consumption, and flatness [17][18][19]. Most of them use genetic algorithm (GA), ant colony algorithm (ACO), particle swarm algorithm (PSO) [20][21][22], etc., among intelligent algorithms in the group. Yang et al [23] build a system dynamics model based on the Lagrangian principle and uses the linear iteration method (ILP) to plan the optimal trajectory of the movement time.…”