安全自动驾驶概率密度函数的预测和最优反馈控制
Prediction and Optimal Feedback Steering of Probability Density Functions for Safe Automated Driving
摘要：
我们提出了一个随机预测控制框架，以促进自动驾驶的安全性，通过直接控制的联合状态概率密度函数（PDF）的车辆动力学通过随机级状态反馈。为了说明的主要思想，我们专注于多车道高速公路驾驶的情况下，虽然所提出的框架可以适应其他情况。计算管道由PDF预测层和PDF控制层组成。预测层对自我和非自我车辆的随机状态进行滚动时域非参数预测，从而得出自我的安全目标PDF。后者是基于预测的碰撞概率，并促进概率安全的自我。PDF控制层设计了一个反馈，该反馈在满足端点PDF约束的同时，最佳地操纵受控制的自我动力学约束的联合状态PDF。我们的PDF预测层的计算利用受控Liouville PDE的结构来演化联合PDF值，而不是凭经验近似PDF。PDF控制层的计算利用了车辆动力学中的微分平坦结构。我们利用最佳质量传输和薛定谔桥的最新理论和算法进展。数值模拟说明了所提出的框架的有效性。
英文摘要：
We propose a stochastic prediction-control framework to promote safety in automated driving by directly controlling the joint state probability density functions (PDFs) subject to the vehicle dynamics via trajectory-level state feedback. To illustrate the main ideas, we focus on a multi-lane highway driving scenario although the proposed framework can be adapted to other contexts. The computational pipeline consists of a PDF prediction layer, followed by a PDF control layer. The prediction layer performs moving horizon nonparametric forecasts for the ego and the non-ego vehicles' stochastic states, and thereby derives safe target PDF for the ego. The latter is based on the forecasted collision probabilities, and promotes the probabilistic safety for the ego. The PDF control layer designs a feedback that optimally steers the joint state PDF subject to the controlled ego dynamics while satisfying the endpoint PDF constraints. Our computation for the PDF prediction layer leverages the structure of the controlled Liouville PDE to evolve the joint PDF values, as opposed to empirically approximating the PDFs. Our computation for the PDF control layer leverages the differential flatness structure in vehicle dynamics. We harness recent theoretical and algorithmic advances in optimal mass transport, and the Schrödinger bridge. The numerical simulations illustrate the efficacy of the proposed framework.
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