Real-time Optimal Planning and Model Predictive Control of a Multi-rotor with a Suspended Load

This paper presents planning and control algorithms for a multi-rotor with a suspended load. The suspended load cannot be controlled easily by the multi-rotor due to severe dynamic coupling between them. Difficulties are exacerbated by under-actuated, highly nonlinear nature of multi-rotor dynamics. Although many studies have been proposed to plan trajectories and control this system, there exist only a few reports on real-time trajectory generation. With this in mind, we propose a planning method which is capable of generating collision-free trajectories real-time and applicable to a high-dimensional nonlinear system. Using a differential flatness property, the system can be linearized entirely with elaborately chosen flat outputs. Convexification of non-convex constraints is carried out, and concave obstacle-avoidance constraints are converted to convex ones. After that, a convex optimization problem is solved to generate an optimal trajectory, but semi-feasible trajectory which considers only some parts of the initial state. We apply model predictive control with a sequential linear quadratic solver to compute a feasible collision-free trajectory and to control the system. Performance of the algorithm is validated by flight experiment.