针对桥式起重机欠驱动荷载在惯性力等作用下会产生残余摆动的问题，对起重机荷载的摆动进行相平面分析，提出抑制荷载残余摆动的起重小车运动轨迹规划。首先建立有阻尼摆动的起重机系统动力学模型，采用相平面分析法研究三种起重小车加速度曲线对荷载残余摆动的影响。构建李雅普诺夫函数从而设计起重机小车加速度曲线，得到基于荷载等效能量控制的起重小车动态运动轨迹。仿真结果表明：基于荷载等效能量控制的起重小车轨迹规划能有效减小荷载的摆动幅度，起重小车的运行加速度曲线更为平滑。当起重小车加速度与荷载摆动的方向相同时，起重小车的加速度越大，荷载等效能量减少的速度越快。当荷载初始摆角为0.087rad时，基于荷载等效能量运动轨迹规划的起重小车在7.9秒后使荷载摆动达到允许摆角范围内。

In view of the problem of an under actuated overhead crane’s payload swing caused by the inertia force, the trajectory planning of trolley was put forward to suppress the payload residual swing. The dynamic model of a crane system with damped oscillation was established, the method of phase plane analysis was used to study residual swing of the payload which are affected by the three different acceleration curves of the trolley. The Lyapunov function based on energy control method was used to dynamically design the acceleration curve of the trolley in real time. The simulation results show that the trajectory planning based on energy control method can effectively restrain the residual vibration of the overhead crane, and the acceleration curve of the trolley is smoother. When the trolley acceleration direction are same with the payload swing direction, the larger the trolley’s acceleration is, the faster the payload normalized energy decrease. The proposed control method can suppress the payload swing angle to the allowable value in 7.9s when the initial angle of payload is 0.087 rad.