Fast trajectory planning and control of a lab-scale 3D gantry crane for a moving target in an environment with obstacles

In this work, the real-time optimal trajectory planning, together with a cascaded tracking controller, is presented for a three-dimensional (3D) gantry crane in an environment with static obstacles and a dynamically moving target considering dynamic constraints and control input limits. State-of-the-art trajectory optimization-based approaches require long computation times and cannot quickly respond to changes in the target state. The focus of this paper lies on a novel trajectory planning algorithm, which consists of two steps. First, an offline trajectory planner is implemented to compute a time-optimal, collision-free, and dynamically feasible trajectory database that connects all possible initial states of the gantry crane from a predefined starting subspace to the target states in a target subspace. Second, based on linear constrained quadratic programming, the online trajectory replanner makes use of this trajectory database to generate an optimal trajectory in real time that accounts for all changes in the target state. Additionally, a trajectory tracking controller is developed to take into account the dynamic constraints of the gantry crane and to compensate for possible model inaccuracies, disturbances, and other non-modeled effects. Both simulation and experimental results are presented to demonstrate the performance of the proposed trajectory (re)planning algorithm and the control concept.