Sampling-based trajectory (re)planning for differentially flat systems: Application to a 3D gantry crane

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