[论文解读] Towards Efficient MPPI Trajectory Generation with Unscented Guidance: U-MPPI Control Strategy

Ihab S. Mohamed, Junhong Xu+2 more|arXiv (Cornell University)|Jun 21, 2023

Real-time simulation and control systemsEngineering被引用 3

一句话总结

本文提出U-MPPI，一种风险敏感、不确定性感知的MPPI扩展方法，利用无迹变换（Unscented Transform）传播系统状态的均值与协方差，实现更高效的轨迹采样并提升鲁棒性。相较于原始MPPI，该方法在复杂环境中的导航实现了无碰撞、平滑运动，并显著提升了定位精度。

ABSTRACT

The classical Model Predictive Path Integral (MPPI) control framework, while effective in many applications, lacks reliable safety features due to its reliance on a risk-neutral trajectory evaluation technique, which can present challenges for safety-critical applications such as autonomous driving. Furthermore, when the majority of MPPI sampled trajectories concentrate in high-cost regions, it may generate an infeasible control sequence. To address this challenge, we propose the U-MPPI control strategy, a novel methodology that can effectively manage system uncertainties while integrating a more efficient trajectory sampling strategy. The core concept is to leverage the Unscented Transform (UT) to propagate not only the mean but also the covariance of the system dynamics, going beyond the traditional MPPI method. As a result, it introduces a novel and more efficient trajectory sampling strategy, significantly enhancing state-space exploration and ultimately reducing the risk of being trapped in local minima. Furthermore, by leveraging the uncertainty information provided by UT, we incorporate a risk-sensitive cost function that explicitly accounts for risk or uncertainty throughout the trajectory evaluation process, resulting in a more resilient control system capable of handling uncertain conditions. By conducting extensive simulations of 2D aggressive autonomous navigation in both known and unknown cluttered environments, we verify the efficiency and robustness of our proposed U-MPPI control strategy compared to the baseline MPPI. We further validate the practicality of U-MPPI through real-world demonstrations in unknown cluttered environments, showcasing its superior ability to incorporate both the UT and local costmap into the optimization problem without introducing additional complexity.

研究动机与目标

• 解决风险中性MPPI缺乏安全保证的问题，避免在高成本区域产生不可行的控制序列。
• 通过无迹变换实现不确定性传播，提升状态空间探索能力，减少陷入局部极小值的风险。
• 提出一种风险敏感的成本函数，显式在轨迹评估中考虑不确定性。
• 通过结合无迹变换与局部代价图，提升运动平滑性与定位精度。
• 在仿真与真实场景中验证该方法在已知与未知复杂环境中的高速导航性能。

提出的方法

• 在每个时间步应用无迹变换（UT）传播状态向量的均值与协方差，替代MPPI中标准的高斯噪声采样。
• 通过在Mσ个批次中传播nσ = 2nx + 1个sigma点，生成M条采样轨迹，实现比随机噪声注入更智能、更高效的采样。
• 将系统状态协方差整合到轨迹评估过程中，引导采样向低不确定性、高概率区域集中。
• 构建一种风险敏感的成本函数，对高方差或高不确定性轨迹施加惩罚，提升在不确定条件下的鲁棒性。
• 将局部代价图与基于UT的不确定性传播相结合，在不增加计算复杂度的前提下引导轨迹优化。
• 采用GPU加速实现，确保每轮迭代执行时间低于33.33ms，满足实时性能要求。

Figure 1 : Our proposed sampling strategy, for a ground vehicle model, under the U-MPPI control strategy based on unscented transform; such a sampling strategy propagates both the mean $\bar{\mathbf{x}}_{k}$ (blue dots) and covariance $\mathbf{\Sigma}_{k}$ (gray ellipses) of the state vector at each

实验结果

研究问题

• RQ1 无迹变换能否提升基于MPPI的轨迹采样效率与状态空间探索能力？
• RQ2 在不确定性环境中，引入状态协方差传播对碰撞避免与鲁棒性有何影响？
• RQ3 风险敏感成本函数在不确定性条件下对MPPI的安全性与性能提升程度如何？
• RQ4 U-MPPI能否在提升运动平滑性与定位精度的同时保持实时性能？
• RQ5 在真实复杂环境中，U-MPPI相较于原始MPPI在成功率、碰撞避免与定位精度方面表现如何？

主要发现

• 在六次真实世界试验的复杂室内走廊环境中，U-MPPI实现零碰撞，而原始MPPI平均每轮试验发生一次碰撞。
• U-MPPI展现出显著更平滑的运动表现，累积线加速度（228.15 m/s³）与角加速度（263.02 rad/s³）均低于MPPI（257.75 m/s³ 与 306.91 rad/s³）。
• U-MPPI下定位精度提升，x方向误差降低至0.10 m（MPPI为0.38 m），y方向误差降低至-0.04 m（MPPI为0.30 m）。
• U-MPPI的航向误差更低（0.80°），相比MPPI的7.20°，表明其航向一致性更优。
• 尽管执行时间略有增加，U-MPPI仍保持实时性能（t_exec < 33.33 ms），满足在线控制可行性要求。
• LOAM位姿误差的可视化结果表明，由于控制输入更平滑，U-MPPI显著减少了累积定位漂移，尤其在最坏情况试验中表现更优。

Figure 2 : Schematic illustration of system dynamics propagation in MPPI for $M$ sampled trajectories over a finite time-horizon $N$ .