Fast motion planning for a laboratory 3D gantry crane in the presence of obstacles

Abstract In this paper, a concept is presented for the fast motion planning of a 3D laboratory crane in a static environment with obstacles taking into account the dynamic constraints on the state variables and control inputs. The focus is set on the possibility of a fast (re)planning if the starting and/or target state is changing. The proposed concept consists of two parts: an offline trajectory planner to set up a database of collision-free, time optimal trajectories from the starting to the target space, with an average computing time of 0.17 s for one trajectory, and an online planner based on a constrained quadratic program, with an average computing time of 7 ms for one trajectory. Simulation results for a validated mathematical model demonstrate the feasibility of the proposed approach.