提出精确凸化方法，让无人机在高噪声下仍能生成最优轨迹。
Exact and Approximate Convex Reformulation of Linear Stochastic Optimal Control with Chance Constraints
- 通过状态向量升维显式编码矩信息，精确处理多步线性随机约束。
- 对二次约束的凸近似比现有方法更紧致，降低保守性。
- 在四旋翼轨迹生成中验证，噪声容忍度提升一个数量级。
本文针对离散时间随机线性系统提出了等价的凸优化公式，适用于线性机会约束；对于二次机会约束，给出了紧致的凸松弛。通过将状态向量升维以显式编码矩信息，该方法可精确刻画多个时间步上状态与控制变量的线性机会约束，无保守性，显著提升可行性和最优性。针对二次机会约束，推导出严格比现有方法更小保守性的凸近似。在四旋翼最小加速度轨迹生成任务中进行了验证，结果表明，所提方法在噪声水平超出先前方法工作范围一个数量级时仍保持可行性，且实现成本降低。
原文摘要 · Abstract (English)
In this paper, we present an equivalent convex optimization formulation for discrete-time stochastic linear systems subject to linear chance constraints, alongside a tight convex relaxation for quadratic chance constraints. By lifting the state vector to encode moment information explicitly, the formulation captures linear chance constraints on states and controls across multiple time steps exactly, without conservatism, yielding strict improvements in both feasibility and optimality. For quadratic chance constraints, we derive convex approximations that are provably less conservative than existing methods. We validate the framework on minimum-snap trajectory generation for a quadrotor, demonstrating that the proposed approach remains feasible at noise levels an order of magnitude beyond the operating range of prior formulations.
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