在复杂环境不确定性下，实现安全轨迹规划的高效求解方法
Chance-Constrained Trajectory Planning with Multimodal Environmental Uncertainty
- 用高斯混合模型建模障碍物多模态不确定状态
- 提出紧致的概率约束近似，保证95%以上场景下不违规
- 适用于自动驾驶等对安全性要求高的系统
针对高斯混合模型（GMM）下的不确定性，本文研究安全轨迹规划问题。利用GMM建模障碍物状态的多模态行为，构建确定性线性系统与多面体障碍物下的混合整数锥形近似方法，解决概率约束轨迹规划问题。当通过有限样本估计GMM矩时，设计紧致的浓度界以保证所需置信水平下的概率约束。为控制违规程度，引入条件风险价值（CVaR）方法，并推导出已知与估计GMM矩下的可计算近似。在先进轨迹预测算法和自动驾驶数据集上验证了方法的有效性。
原文摘要 · Abstract (English)
We tackle safe trajectory planning under Gaussian mixture model (GMM) uncertainty. Specifically, we use a GMM to model the multimodal behaviors of obstacles' uncertain states. Then, we develop a mixed-integer conic approximation to the chance-constrained trajectory planning problem with deterministic linear systems and polyhedral obstacles. When the GMM moments are estimated via finite samples, we develop a tight concentration bound to ensure the chance constraint with a desired confidence. Moreover, to limit the amount of constraint violation, we develop a Conditional Value-at-Risk (CVaR) approach corresponding to the chance constraints and derive a tractable approximation for known and estimated GMM moments. We verify our methods with state-of-the-art trajectory prediction algorithms and autonomous driving datasets.
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