This paper introduces a method to solve the crane motion trajectory control problem. A dynamic model is proposed based on the Udwadia-Kalaba equation, which can be solved without extra parameters, such as the Lagrange multiplier. The motion trajectory of a crane is used as a constraint (referred to as trajectory tracking constraint). To satisfy the system trajectory, a method to calculate the driving conditions on the basis of the above conditions is proposed. A 2D plane dynamic model of a crane is established. Five stages of crane movement are obtained. Simulation is performed with Matlab. Simulation results simulation show that the Udwadia-Kalaba equation can be well applied to trajectory tracking control of cranes.
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