A Fast and Close-to-Optimal Receding Horizon Control for Trajectory Generation in Dynamic Environments

Abstract

This paper presents a new approach for the optimal trajectory planning of nonlinear systems in a dynamic environment. Given the start and end goals with an objective function, the problem is to find an optimal trajectory from start to end that minimizes the objective while taking into account the changes in the environment. One of the main challenges here is that the optimal control sequence needs to be computed in a limited amount of time and needs to be adapted on-the-fly. The control method presented in this work has two stages: the first-order gradient algorithm is used at the beginning to compute an initial guess of the control sequence that satisfies the constraints but is not yet optimal; then, sequential action control is used to optimize only the portion of the control sequence that will be applied on the system in the next iteration. This helps to reduce the computational effort while still being optimal with regard to the objective; thus, the proposed approach is more applicable for online computation as well as dealing with dynamic environments. We also show that under mild conditions, the proposed controller is asymptotically stable. Different simulated results demonstrate the capability of the controller in terms of solving various tracking problems for different systems under the existence of dynamic obstacles. The proposed method is also compared to the related indirect optimal control approach and sequential action control in terms of cost and computation time to evaluate the improvement of the proposed method.