Spline-Interpolated Model Predictive Path Integral Control with Stein Variational Inference for Reactive Navigation

TL;DR

The paper tackles reactive UAV navigation in unknown environments by enhancing Model Predictive Path Integral (MPPI) control with spline interpolation and Stein Variational Gradient Descent (SVGD). The proposed Sparse Control Points MPPI (SCP-MPPI) reduces the dimensionality of sampling by using sparse control points, then reconstructs full trajectories via spline interpolation, and refines samples with SVGD to better approximate the optimal distribution. Key contributions include integrating spline interpolation with a low-dimensional sampling strategy and applying SVGD to transport interpolated samples, enabling smooth and collision-free trajectories with as few as M=4 control points. Empirical results on quadrotor simulations demonstrate improved obstacle avoidance and smoother trajectories at reduced sample counts, albeit with higher computational overhead that can be mitigated by parallelization. This approach offers a practical route to robust, real-time reactive navigation in cluttered environments with limited computational budgets.

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.

Figures (4)

• Figure 1: A selected simulation result. The original MPPI's candidate paths (light green) are erratic due to the randomness of the injected Gaussian noise, leading to a jerky predicted path (green). To achieve a smoother solution, we employ spline interpolation in MPPI, which samples sparse control points and interpolates them using spline curves. This approach enables the generation of smoother candidate paths. However, some paths (light purple) collide with obstacles due to the scarcity of control points. To address this, we apply the SVGD method, enhancing MPPI with spline interpolation and SVGD, referred to as SCP-MPPI. This method improves the quality of collision-free interpolated samples (light blue). Consequently, SCP-MPPI is able to identify a smooth and collision-free solution (blue), even with sparse control points, resulting in improved computational efficiency.
• Figure 2: The overview of SCP-MPPI with and without the SVGD method. (A) Initially, SCP-MPPI sparsely samples control points (illustrated as light red points) and (B) employs spline curves to interpolate these points, creating control input sequences (shown as light red lines). (C) If SVGD is applied, the sparse control points are adjusted (depicted as light blue points), followed by (D) another round of spline interpolation (resulting in light blue lines). (E) The process culminates in determining the optimal action distribution and generating a reactive navigation path (represented by a blue line). While SCP-MPPI without SVGD can navigate around obstacles (indicated by a red line), incorporating SVGD enables SCP-MPPI to approximate the global optimum more closely, even when the initial distribution is not close to the optimal solution.
• Figure 3: Experimental environments. Each environment is filled with cylinders of a radius of 0.75 meters. The quadrotor departs from the orange circle and goes to the destination depicted by the blue circle.
• Figure : Sparse Control Points MPPI