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

TL;DR

The paper tackles autonomous driving trajectory planning by enhancing Model Predictive Path Integral control (MPPI) with learned sampling distributions. It introduces normalizing flow–based sampling to replace or augment simple Gaussian perturbations, enabling richer and more generalizable exploration across environments. Two NF-based schemes, NF-A2DOF and NF-AIL, generate training data from existing sampling methods and learn flexible input distributions that improve planning performance in static and moving traffic scenarios. Across two simulated driving setups, NF-based sampling consistently yields lower planning costs than baseline sampling methods, demonstrating the potential for generalizable, data-driven sampling in real-time trajectory optimization.

Abstract

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.

Figures (4)

• Figure 1: A scenario specific cost landscape is defined to determine the road related cost $c_4(X)$. Zero costs are assigned for the local path and the lateral offset $\boldsymbol{\tau}$ is penalized quadratically.
• Figure 2: For the traffic cost $c_5(X)$, the distance between ego and traffic vehicle is computed in the coordinate system of the traffic vehicle. Longitudinal and lateral distances can be scaled with ellipsoidal parameters.
• Figure 3: Loss curves for model training. When the test loss can no longer be decreased, the training is terminated.
• Figure 4: Spatial trajectories for the static traffic scenario with desired velocity $\upsilon_\mathrm{des}=6\frac{\mathrm{m}}{\mathrm{s}}$ and total duration $T_\mathrm{end}=45\, \mathrm{s}$.