Employing Stochastic Nonlinear Model Predictive Control (SNMPC) for real-time applications is challenging due to the complex task of propagating uncertainties through nonlinear systems. This difficulty becomes more pronounced in high-dimensional systems with extended prediction horizons, such as autonomous vehicles. To enhance closed-loop performance in and feasibility in SNMPCs, we introduce the concept of the Uncertainty Propagation Horizon (UPH). The UPH limits the time for uncertainty propagation through system dynamics, preventing trajectory divergence, optimizing feedback loop advantages, and reducing computational overhead. Our SNMPC approach utilizes Polynomial Chaos Expansion (PCE) to propagate uncertainties and incorporates nonlinear hard constraints on state expectations and nonlinear probabilistic constraints. We transform the probabilistic constraints into deterministic constraints by estimating the nonlinear constraints' expectation and variance. We then showcase our algorithm's effectiveness in real-time control of a high-dimensional, highly nonlinear system-the trajectory following of an autonomous passenger vehicle, modeled with a dynamic nonlinear single-track model. Experimental results demonstrate our approach's robust capability to follow an optimal racetrack trajectory at speeds of up to 37.5m/s while dealing with state estimation disturbances, achieving a minimum solving frequency of 97Hz. Additionally, our experiments illustrate that limiting the UPH renders previously infeasible SNMPC problems feasible, even when incorrect uncertainty assumptions or strong disturbances are present.

翻译：将随机非线性模型预测控制（SNMPC）应用于实时场景具有挑战性，这源于通过非线性系统传播不确定性的复杂任务。对于具有扩展预测时域的高维系统（如自动驾驶车辆），该困难尤为突出。为提升SNMPC的闭环性能与可行性，我们引入了不确定性传播时域（UPH）概念。UPH限制了通过系统动力学传播不确定性的时间，从而防止轨迹发散、优化反馈回路优势并降低计算开销。我们的SNMPC方法采用多项式混沌展开（PCE）传播不确定性，并包含对状态期望的非线性硬约束和非线性概率约束。通过估计非线性约束的期望与方差，我们将概率约束转化为确定性约束。随后，我们展示了算法在高维、高度非线性系统——基于动态非线性单轨模型建模的自动驾驶乘用车轨迹跟踪——中的实时控制有效性。实验结果表明，该方法能在处理状态估计干扰的情况下，以高达37.5米/秒的速度稳定跟踪最优赛道轨迹，并实现最低97Hz的求解频率。此外，实验揭示，即使存在错误的不确定性假设或强干扰，限制UPH可使先前不可行的SNMPC问题变得可行。