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.

翻译：本文提出了一种反应式导航方法，该方法采用经样条插值增强控制输入序列的模型预测路径积分（MPPI）控制和斯坦变分梯度下降（SVGD）。MPPI框架通过基于采样的方法确定最优控制输入序列，从而解决非线性优化问题。MPPI的有效性受采样噪声的显著影响。为了快速识别能够绕过大型和/或新检测障碍物的路径，必须采用高水平的采样噪声。然而，这种高噪声水平会导致控制输入序列产生剧烈波动，进而形成不光滑的轨迹。为缓解此问题，我们提出在MPPI过程中集成样条插值，使其能够在采用大量采样噪声的情况下生成光滑的控制输入序列。然而，标准的MPPI算法在处理多个最优或近似最优解的场景（例如存在多条可行避障路径的环境）时表现不佳，因其假设最优控制输入序列的分布可近似为高斯分布。为解决这一局限，我们在带样条插值的MPPI框架中引入SVGD进行扩展。SVGD基于最优传输算法，具有将样本聚集到最优解周围的独特能力。因此，我们的方法能够快速识别避障路径并保持控制输入序列的光滑性，从而实现鲁棒的反应式导航。通过在四旋翼飞行器仿真中的验证，所提方法展现出了优于现有基线技术的性能。