  In this paper, a sampling-based trajectory planning algorithm for a
laboratory-scale 3D gantry crane in an environment with static obstacles and
subject to bounds on the velocity and acceleration of the gantry crane system
is presented. The focus is on developing a fast motion planning algorithm for
differentially flat systems, where intermediate results can be stored and
reused for further tasks, such as replanning. The proposed approach is based on
the informed optimal rapidly exploring random tree algorithm (informed RRT*),
which is utilized to build trajectory trees that are reused for replanning when
the start and/or target states change. In contrast to state-of-the-art
approaches, the proposed motion planning algorithm incorporates a linear
quadratic minimum time (LQTM) local planner. Thus, dynamic properties such as
time optimality and the smoothness of the trajectory are directly considered in
the proposed algorithm. Moreover, by integrating the branch-and-bound method to
perform the pruning process on the trajectory tree, the proposed algorithm can
eliminate points in the tree that do not contribute to finding better
solutions. This helps to curb memory consumption and reduce the computational
complexity during motion (re)planning. Simulation results for a validated
mathematical model of a 3D gantry crane show the feasibility of the proposed
approach.
