Stable trajectory design for highly constrained environments using receding horizon control

This paper presents a new formulation of a stable receding horizon controller (RHC) for the minimum time trajectory optimization problem with a vehicle flying in a complex environment with obstacles and no-fly zones. The overall problem is formulated using Mixed-integer Linear Programming (MILP). The RHC uses a simple vehicle dynamics model in the near term and an approximate path model in the long term. This combination gives a good estimate of the cost-to-go and greatly reduces the computational effort required to design the complete trajectory, but discrepancies in the assumptions made in the two models can lead to infeasible solutions. This paper extends our previous RHC formulation to ensure that the on-line optimizations will always be feasible, while eliminating the binary variables associated with feasible turns. Novel pruning and graph-search algorithms are also integrated with the new MILP RHC, and these are shown to significantly reduce the computation time. A worst case analysis is performed to obtain an upper bound on the planning horizon, and the resulting controller is analytically shown to guarantee finite-time arrival at the goal.