In this paper, we present a novel Reduced Robustified NMPC (R$^2$NMPC) algorithm that has the same complexity as an equivalent nominal NMPC while enhancing it with robustified constraints based on the dynamics of ellipsoidal uncertainty sets. This promises both a closed-loop- and constraint satisfaction performance equivalent to common Robustified NMPC approaches, while drastically reducing the computational complexity. The main idea lies in approximating the ellipsoidal uncertainty sets propagation over the prediction horizon with the system dynamics' sensitivities inferred from the last optimal control problem (OCP) solution, and similarly for the gradients to robustify the constraints. Thus, we do not require the decision variables related to the uncertainty propagation within the OCP, rendering it computationally tractable. Next, we illustrate the real-time control capabilities of our algorithm in handling a complex, high-dimensional, and highly nonlinear system, namely the trajectory following of an autonomous passenger vehicle modeled with a dynamic nonlinear single-track model. Our experimental findings, alongside a comparative assessment against other Robust NMPC approaches, affirm the robustness of our method in effectively tracking an optimal racetrack trajectory while satisfying the nonlinear constraints. This performance is achieved while fully utilizing the vehicle's interface limits, even at high speeds of up to 37.5m/s, and successfully managing state estimation disturbances. Remarkably, our approach maintains a mean solving frequency of 144Hz.

翻译：本文提出一种新型简化鲁棒NMPC（R$^2$NMPC）算法，其复杂度与等效标称NMPC相当，同时通过基于椭球不确定集动力学特性的鲁棒约束增强算法性能。该方法在显著降低计算复杂度的前提下，实现了与常见鲁棒NMPC方法相当的闭环性能与约束满足能力。核心思想在于利用上一最优控制问题（OCP）解中提取的系统动力学灵敏度，近似预测时域内的椭球不确定集传播过程，并类似地计算约束鲁棒化所需的梯度。因此，我们无需在OCP中引入与不确定性传播相关的决策变量，从而确保计算可行性。随后，我们展示了算法在处理复杂、高维且高度非线性系统时的实时控制能力——具体通过采用动态非线性单轨模型建模的自动驾驶乘用车轨迹跟踪任务进行验证。实验结果表明，与其它鲁棒NMPC方法相比，本方法在有效跟踪最优赛道轨迹的同时满足非线性约束，并展现出卓越鲁棒性。该性能在充分利用车辆接口极限（即使车速高达37.5m/s）并成功应对状态估计扰动的情况下实现，且算法平均求解频率达到144Hz。