Receding Horizon Control of UAVs using Gradual Dense-Sparse Discretizations

In this paper we propose a way of increasing the efficiency of some direct Receding Horizon Control (RHC) schemes. The basic idea is to adapt the allocation of computational resources to how the iterative plans are used. By using Gradual Dense-Sparse discretizations (GDS), we make sure that the plans are detailed where they need to be, i.e., in the very near future, and less detailed further ahead. The gradual transition in discretization density reflects increased uncertainty and reduced need for detail near the end of the planning horizon. The proposed extension is natural, since the standard RHC approach already contains a computational asymmetry in terms of the coarse cost-to-go computations and the more detailed short horizon plans. Using GDS discretizations, we bring this asymmetry one step further, and let the short horizon plans themselves be detailed in the near term and more coarse in the long term. The rationale for different levels of detail is as follows. 1) Near future plans need to be implemented soon, while far future plans can be refined or revised later. 2) More accurate sensor information is available about the system and its surroundings in the near future, and detailed planning is only rational in low uncertainty situations. 3) It has been shown that reducing the node density in the later parts of fixed horizon optimal control problems gives a very small reduction in the solution quality of the first part of the trajectory. The reduced level of detail in the later parts of a plan can increase the efficiency of the RHC in two ways. If the discretization is made sparse by removing nodes, fewer computations are necessary, and if the discretization is made sparse by spreading the last nodes over a longer time-horizon, the performance will be improved.