We propose a Stochastic MPC (SMPC) formulation for path planning with autonomous vehicles in scenarios involving multiple agents with multi-modal predictions. The multi-modal predictions capture the uncertainty of urban driving in distinct modes/maneuvers (e.g., yield, keep speed) and driving trajectories (e.g., speed, turning radius), which are incorporated for multi-modal collision avoidance chance constraints for path planning. In the presence of multi-modal uncertainties, it is challenging to reliably compute feasible path planning solutions at real-time frequencies ($\geq$ 10 Hz). Our main technological contribution is a convex SMPC formulation that simultaneously (1) optimizes over parameterized feedback policies and (2) allocates risk levels for each mode of the prediction. The use of feedback policies and risk allocation enhances the feasibility and performance of the SMPC formulation against multi-modal predictions with large uncertainty. We evaluate our approach via simulations and road experiments with a full-scale vehicle interacting in closed-loop with virtual vehicles. We consider distinct, multi-modal driving scenarios: 1) Negotiating a traffic light and a fast, tailgating agent, 2) Executing an unprotected left turn at a traffic intersection, and 3) Changing lanes in the presence of multiple agents. For all of these scenarios, our approach reliably computes multi-modal solutions to the path-planning problem at real-time frequencies.

翻译：我们提出了一种用于自动驾驶路径规划的随机模型预测控制（SMPC）方法，适用于涉及具有多模态预测的多智能体场景。多模态预测通过不同的模式/驾驶行为（如让行、保持速度）和驾驶轨迹（如速度、转弯半径）捕捉城市驾驶的不确定性，并将其纳入路径规划的多模态碰撞避免机会约束中。在多模态不确定性存在的情况下，以实时频率（≥ 10 Hz）可靠地计算可行的路径规划解决方案具有挑战性。我们的主要技术贡献在于提出了一种凸SMPC公式，该公式同时（1）优化参数化反馈策略和（2）为每个预测模式分配风险水平。反馈策略和风险分配的使用增强了SMPC公式在应对具有大不确定性的多模态预测时的可行性和性能。我们通过仿真和与虚拟车辆进行闭环交互的全尺寸车辆道路实验评估了我们的方法。我们考虑了不同的多模态驾驶场景：1) 在红绿灯处与快速尾随智能体协商，2) 在交叉路口执行无保护左转，以及3) 存在多个智能体时变道。对于所有这些场景，我们的方法都能以实时频率可靠地计算出路径规划问题的多模态解决方案。