This invention relates to an underactuated bridge crane
trajectory planning method based on a two-
point boundary value problem, belonging to the field of
automation control technology. The method first constructs a complete nonlinear dynamic model considering the trolley displacement, hook swing angle, and load swing angle, and sets
engineering constraints such as the trolley's
maximum displacement, velocity, and acceleration. Then, the
trajectory planning problem is transformed into a two-
point boundary value problem, solved using numerical analysis methods, generating a unified reference trajectory for trolley positioning, hook swing, and load swing cancellation. This is then combined with an extended-state
linear quadratic regulator to form a feedforward-feedback
composite controller, achieving precise tracking of the planned trajectory. This invention eliminates the need for
linearization of the swing angle, fully considers the actual positional constraints of the trolley, and effectively solves the
strong coupling problem between trolley positioning and double-swing swing cancellation through precise nonlinear
trajectory planning, improving the positioning accuracy,
operational stability, and work efficiency of the bridge crane
system.