Abstract
This paper presents a reactive navigation method that leverages a Model Predictive Path Integral (MPPI) control enhanced with spline interpolation for the control input sequence and Stein Variational Gradient Descent (SVGD). The MPPI framework addresses a nonlinear optimization problem by determining an optimal sequence of control inputs through a sampling-based approach. The efficacy of MPPI is significantly influenced by the sampling noise. To rapidly identify routes that circumvent large and/or newly detected obstacles, it is essential to employ high levels of sampling noise. However, such high noise levels result in jerky control input sequences, leading to non-smooth trajectories. To mitigate this issue, we propose the integration of spline interpolation within the MPPI process, enabling the generation of smooth control input sequences despite the utilization of substantial sampling noises. Nonetheless, the standard MPPI algorithm struggles in scenarios featuring multiple optimal or near-optimal solutions, such as environments with several viable obstacle avoidance paths, due to its assumption that the distribution over an optimal control input sequence can be closely approximated by a Gaussian distribution. To address this limitation, we extend our method by incorporating SVGD into the MPPI framework with spline interpolation. SVGD, rooted in the optimal transportation algorithm, possesses the unique ability to cluster samples around an optimal solution. Consequently, our approach facilitates robust reactive navigation by swiftly identifying obstacle avoidance paths while maintaining the smoothness of the control input sequences. The efficacy of our proposed method is validated on simulations with a quadrotor, demonstrating superior performance over existing baseline techniques.
Abstract (translated)
本文提出了一种反应式导航方法，该方法利用Model预测路径积分（MPPI）控制与平滑插值在控制输入序列和Stein变分梯度下降（SVGD）的增强。MPPI框架通过基于采样的方法确定最优的控制输入序列，从而解决非线性优化问题。MPPI的有效性在很大程度上受到采样噪声的影响。为了迅速识别绕过大型和/或新近发现的障碍物的路线，必须采用高水平的采样噪声。然而，这种高噪声水平会导致平滑控制输入序列，从而导致非平稳轨迹。为了减轻这个问题，我们将在MPPI过程中集成平滑插值，使得尽管使用了大量的采样噪声，仍然可以生成平滑的控制输入序列。然而，标准的MPPI算法在具有多个最优或近最优解决方案的环境中表现不佳，因为其假定最优控制输入序列的分布可以近似为高斯分布。为了解决这个问题，我们通过将SVGD集成到MPPI框架中并使用平滑插值来扩展我们的方法。SVGD，源于最优运输算法，具有将样本聚类在最优解周围的独特能力。因此，我们的方法通过迅速识别避障路径并保持控制输入序列的平滑性，促进了鲁棒的反应式导航。我们在四旋翼仿真中验证了所提出方法的有效性，表明其性能优于现有基线技术。
URL
https://arxiv.org/abs/2404.10395
