Alongside optimization-based planners, sampling-based approaches are often
used in trajectory planning for autonomous driving due to their simplicity.
Model predictive path integral control is a framework that builds upon
optimization principles while incorporating stochastic sampling of input
trajectories. This paper investigates several sampling approaches for
trajectory generation. In this context, normalizing flows originating from the
field of variational inference are considered for the generation of sampling
distributions, as they model transformations of simple to more complex
distributions. Accordingly, learning-based normalizing flow models are trained
for a more efficient exploration of the input domain for the task at hand. The
developed algorithm and the proposed sampling distributions are evaluated in
two simulation scenarios.

该研究探讨了基于采样的轨迹规划方法以及使用正则化流模型的采样分布生成，旨在提高自主驾驶中的路径生成效率。

自主驾驶中基于归一化流的模型预测轨迹规划的采样

Sampling for Model Predictive Trajectory Planning in Autonomous Driving  using Normalizing Flows

Sampling-based Model Predictive Control (MPC) has been a practical and
effective approach in many domains, notably model-based reinforcement learning,
thanks to its flexibility and parallelizability. Despite its appealing
empirical performance, the theoretical understanding, particularly in terms of
convergence analysis and hyperparameter tuning, remains absent. In this paper,
we characterize the convergence property of a widely used sampling-based MPC
method, Model Predictive Path Integral Control (MPPI). We show that MPPI enjoys
at least linear convergence rates when the optimization is quadratic, which
covers time-varying LQR systems. We then extend to more general nonlinear
systems. Our theoretical analysis directly leads to a novel sampling-based MPC
algorithm, CoVariance-Optimal MPC (CoVo-MPC) that optimally schedules the
sampling covariance to optimize the convergence rate. Empirically, CoVo-MPC
significantly outperforms standard MPPI by 43-54% in both simulations and
real-world quadrotor agile control tasks. Videos and Appendices are available
at https://lecar-lab.github.io/CoVO-MPC/.

Sampling-based Model Predictive Control (MPC) 在许多领域中具有实际和有效的方法，尤其是基于模型的强化学习，由于其灵活性和可并行化性。本文对一种广泛使用的基于采样的 MPC 方法，Model Predictive Path Integral Control (MPPI) 的收敛性进行了表征。理论分析直接导致了一种新颖的基于采样的 MPC 算法，CoVariance-Optimal MPC (CoVo-MPC)，它通过优化收敛速度来最优调度采样协方差。在模拟和实际的四旋翼敏捷控制任务中，CoVo-MPC 在性能上显著优于标准的 MPPI，提升了 43-54%。

CoVO-MPC：采样模型预测控制和最优协方差设计的理论分析

CoVO-MPC: Theoretical Analysis of Sampling-based MPC and Optimal  Covariance Design

Autonomous underwater vehicles (AUVs) play a crucial role in surveying marine
environments, carrying out underwater inspection tasks, and ocean exploration.
However, in order to ensure that the AUV is able to carry out its mission
successfully, a control system capable of adapting to changing environmental
conditions is required. Furthermore, to ensure the robotic platform's safe
operation, the onboard controller should be able to operate under certain
constraints. In this work, we investigate the feasibility of Model Predictive
Path Integral Control (MPPI) for the control of an AUV. We utilise a non-linear
model of the AUV to propagate the samples of the MPPI, which allow us to
compute the control action in real time. We provide a detailed evaluation of
the effect of the main hyperparameters on the performance of the MPPI
controller. Furthermore, we compared the performance of the proposed method
with a classical PID and Cascade PID approach, demonstrating the superiority of
our proposed controller. Finally, we present results where environmental
constraints are added and show how MPPI can handle them by simply incorporating
those constraints in the cost function.

自主水下航行器（AUV）在测量海洋环境、进行水下检查任务和海洋探索方面发挥着关键作用。本研究探讨了使用模型预测路径积分控制（MPPI）对 AUV 进行控制的可行性，并对主要超参数对 MPPI 控制器性能的影响进行了详细评估。同时，我们将所提出方法与经典的 PID 和级联 PID 方法进行了比较，证明了我们提出的控制器的优越性。最后，我们加入了环境约束并展示了 MPPI 如何通过将这些约束整合在成本函数中来处理它们。

利用模型预测路径积分控制增强 AUV 自主性

Enhancing AUV Autonomy With Model Predictive Path Integral Control

Safe autonomous vehicles must be able to predict and react to the drivers
around them. Previous control methods rely heavily on pre-computation and are
unable to react to dynamic events as they unfold in real-time. In this paper,
we extend Model Predictive Path Integral Control (MPPI) using differential game
theory and introduce Best-Response MPPI (BR-MPPI) for real-time multi-vehicle
interactions. Experimental results are presented using two AutoRally platforms
in a racing format with BR-MPPI competing against a skilled human driver at the
Georgia Tech Autonomous Racing Facility.

论文采用微分博弈论扩展了模型预测路径积分控制（MPPI），并引入最佳响应 MPPI（BR-MPPI）以应对实时多车交互，实验结果表明 BR-MPPI 在与熟练的人类驾驶员竞争的情况下能够在二个 AutoRally 平台的赛道上实现较好的效果。