[Paper Review] MultiPath: Multiple Probabilistic Anchor Trajectory Hypotheses for Behavior Prediction

Yuning Chai, Benjamin Sapp+2 more|arXiv (Cornell University)|Oct 11, 2019

Anomaly Detection Techniques and Applications298 citations

TL;DR

MultiPath predicts a parametric distribution of future trajectories using a fixed set of anchor trajectories, yielding a Gaussian mixture over time and enabling efficient, multi-modal behavior forecasting for autonomous agents.

ABSTRACT

Predicting human behavior is a difficult and crucial task required for motion planning. It is challenging in large part due to the highly uncertain and multi-modal set of possible outcomes in real-world domains such as autonomous driving. Beyond single MAP trajectory prediction, obtaining an accurate probability distribution of the future is an area of active interest. We present MultiPath, which leverages a fixed set of future state-sequence anchors that correspond to modes of the trajectory distribution. At inference, our model predicts a discrete distribution over the anchors and, for each anchor, regresses offsets from anchor waypoints along with uncertainties, yielding a Gaussian mixture at each time step. Our model is efficient, requiring only one forward inference pass to obtain multi-modal future distributions, and the output is parametric, allowing compact communication and analytical probabilistic queries. We show on several datasets that our model achieves more accurate predictions, and compared to sampling baselines, does so with an order of magnitude fewer trajectories.

Motivation & Objective

• Address the inherent uncertainty and multi-modality in predicting future agent trajectories for motion planning.
• Propose a fixed anchor-based parameterization to obtain a compact, communicable distribution over futures.
• Enable efficient, one-pass inference to generate multi-modal trajectory hypotheses and their likelihoods.
• Learn anchor-conditional residuals and uncertainties to refine anchors in context-specific scenes.
• Demonstrate improved likelihoods and trajectory-set metrics across autonomous-driving and drone-based pedestrian datasets.

Proposed method

• Define a fixed set of K anchor trajectories as modes of the future trajectory distribution.
• Model intent uncertainty with a softmax over anchors π(a^k|x) generated by a neural network.
• Model control uncertainty as Gaussian distributions around each anchor state s_t^k with mean a_t^k + μ_t^k(x) and covariance Σ_t^k(x).
• Assume time-step conditional independence given an anchor to yield a Gaussian Mixture Model p(s|x) = Σ_k π(a^k|x) ∏_t φ(s_t|a^k,x).
• Obtain anchors a^k via a-priori clustering (k-means in a canonical frame) or uniform sampling to avoid mode collapse.
• Train by imitation learning to maximize the log-likelihood of ground-truth trajectories with hard anchor assignment (k^m) as in (3).
• At test time, output K MAP trajectories (one per anchor) with weights π(a^k|x) to form a weighted set of trajectories for evaluation.

Experimental results

Research questions

• RQ1 Can a fixed, multi-anchor basis capture the multi-modal nature of future agent trajectories?
• RQ2 Does a parametric Gaussian mixture over fixed anchors provide accurate likelihoods and compact trajectory samples compared to sampling-based methods?
• RQ3 How does anchor count K affect predictive likelihood and trajectory accuracy across driving and aerial datasets?
• RQ4 What is the impact of modeling scene-context dependent residuals μ_t^k and covariances Σ_t^k on prediction quality?

Key findings

• MultiPath achieves higher log-likelihood than unimodal baselines on autonomous driving data.
• With the same number of samples, MultiPath provides better coverage than sampling-based baselines by using weighted anchor MAP trajectories.
• On autonomous driving data, MultiPath μ achieves ADE 1.17±0.00 and minADE 5 0.58±0.00, while MultiPath μ,Σ achieves LL 4.37±0.00 and ADE 1.25±0.01.
• On Stanford Drone Dataset, MultiPath μ,Σ attains LL 3.06 and ADE 26.67 with minADE 5 not reported for that row, while MultiPath μ,Σ shows competitive FDE and minADE values.
• On CARLATown01/02, MultiPath μ,Σ yields minMSD 12 of 0.68 and 0.69 respectively, outperforming several baselines in that metric.
• Across datasets, MultiPath consistently outperforms linear, single-regression, and CVAE baselines on likelihood and top-k trajectory metrics.