Solving Trajectory Optimization Problems in the Presence of Probabilistic Constraints

Stochastic Optimal Linear Control for Generalized Cost Functions With Time-Invariant Stochastic Parameters

This study presents the design of feedback controllers for generalized cost functions to deal with stochastic optimal control problems. Target linear systems contain time-invariant stochastic parameters that describe system uncertainty. The cost functions involve nonlinear mappings and polynomial forms of the system states and inputs to express various performance metrics. Unfortunately, these properties cause difficulties in solving the problems. Conventional methods, such as the principle of optimality, are not employed to solve such problems owing to the time-invariant parameters. As opposed to the well-known quadratic functions, handling the generalized cost functions is a complicated task. This study overcomes these challenges by deriving an explicit relation between the cost function and the linear feedback gain of a controller. The derived relation enables the feedback gain to be optimized via a gradient method. A theoretical analysis ensures the convergence of the proposed gradient method. A suboptimal feedback controller is obtained to solve the problem, even for the generalized cost. Furthermore, the controller guarantees robust stability of the feedback system even with the stochastic parameters. It is demonstrated that the proposed cost function can express an expectation of a quadratic cost, risk-sensitive cost, polynomial cost, and input-to-state gain. A numerical simulation shows the effectiveness of the proposed method.

Integrated Decision and Control: Toward Interpretable and Computationally Efficient Driving Intelligence

Decision and control are core functionalities of high-level automated vehicles. Current mainstream methods, such as functional decomposition and end-to-end reinforcement learning (RL), suffer high time complexity or poor interpretability and adaptability on real-world autonomous driving tasks. In this article, we present an interpretable and computationally efficient framework called integrated decision and control (IDC) for automated vehicles, which decomposes the driving task into static path planning and dynamic optimal tracking that are structured hierarchically. First, the static path planning generates several candidate paths only considering static traffic elements. Then, the dynamic optimal tracking is designed to track the optimal path while considering the dynamic obstacles. To that end, we formulate a constrained optimal control problem (OCP) for each candidate path, optimize them separately, and follow the one with the best tracking performance. To unload the heavy online computation, we propose a model-based RL algorithm that can be served as an approximate-constrained OCP solver. Specifically, the OCPs for all paths are considered together to construct a single complete RL problem and then solved offline in the form of value and policy networks for real-time online path selecting and tracking, respectively. We verify our framework in both simulations and the real world. Results show that compared with baseline methods, IDC has an order of magnitude higher online computing efficiency, as well as better driving performance, including traffic efficiency and safety. In addition, it yields great interpretability and adaptability among different driving scenarios and tasks.

Fast Trajectory Generation and Asteroid Sequence Selection in Multispacecraft for Multiasteroid Exploration

As an increasing number of asteroids are being discovered, detecting them using limited propulsion resources and time has become an urgent problem in the aerospace field. However, there is no universal fast asteroid sequence selection method that finds the trajectories for multiple low-thrust spacecraft for detecting a large number of asteroids. Furthermore, the calculation efficiency of the traditional trajectory optimization method is low, and it requires a large number of iterations. Therefore, this study combines Monte Carlo tree search (MCTS) with spacecraft trajectory optimization. A fast MCTS pruning algorithm is proposed, which can quickly complete asteroid sequence selection and trajectory generation for multispacecraft exploration of multiple asteroids. By combining the Bezier shape-based (SB) method and MCTS, this study realizes the fast search of the exploration sequence and the efficient optimization of the continuous transfer trajectories. In the simulation example, compared with the traversal algorithm, the MCTS pruning algorithm obtained the global optimal detection sequence of the search tree in a very short time. Under the same conditions, the Bezier SB method obtained the transfer trajectory with a better performance index faster than the finite Fourier series SB method. Performances of the proposed method are illustrated through a complex asteroid multiflyby mission design.