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Pedestrian Trajectory Prediction Using Dynamics-based Deep Learning

Honghui Wang, Weiming Zhi, Gustavo Batista, Rohitash Chandra

TL;DR

Pedestrian trajectory prediction faces explainability and constraint challenges in deep learning. The paper proposes Dynamics-based Deep Learning (DDL), which embeds an asymptotically stable dynamical system into a Transformer (STAR) to enforce convergence to a predicted goal and provide interpretable priors. Key components include a goal estimator using $\gamma$-soft-DTW and an expert repository with K-means endpoint estimation, a learnable positive-definite matrix $P(p_i(t))$ via the Transformer, and a goal-shift encoding; the dynamics are implemented as $v_i(t)=-P(p_i(t))\nabla_{p_i(t)}\Phi(p_i(t))$ with $\Phi(p_i(t))=\|p_i(t)-p_i^*\|_2$ and $P$ decomposed as $P=L L^T+\sigma I$. Experiments on ETH/UCY show improved ADE and FDE over baselines, demonstrating both accuracy gains and enhanced explainability through stability-based constraints, with practical impact for autonomous navigation systems.

Abstract

Pedestrian trajectory prediction plays an important role in autonomous driving systems and robotics. Recent work utilizing prominent deep learning models for pedestrian motion prediction makes limited a priori assumptions about human movements, resulting in a lack of explainability and explicit constraints enforced on predicted trajectories. We present a dynamics-based deep learning framework with a novel asymptotically stable dynamical system integrated into a Transformer-based model. We use an asymptotically stable dynamical system to model human goal-targeted motion by enforcing the human walking trajectory, which converges to a predicted goal position, and to provide the Transformer model with prior knowledge and explainability. Our framework features the Transformer model that works with a goal estimator and dynamical system to learn features from pedestrian motion history. The results show that our framework outperforms prominent models using five benchmark human motion datasets.

Pedestrian Trajectory Prediction Using Dynamics-based Deep Learning

TL;DR

Pedestrian trajectory prediction faces explainability and constraint challenges in deep learning. The paper proposes Dynamics-based Deep Learning (DDL), which embeds an asymptotically stable dynamical system into a Transformer (STAR) to enforce convergence to a predicted goal and provide interpretable priors. Key components include a goal estimator using -soft-DTW and an expert repository with K-means endpoint estimation, a learnable positive-definite matrix via the Transformer, and a goal-shift encoding; the dynamics are implemented as with and decomposed as . Experiments on ETH/UCY show improved ADE and FDE over baselines, demonstrating both accuracy gains and enhanced explainability through stability-based constraints, with practical impact for autonomous navigation systems.

Abstract

Pedestrian trajectory prediction plays an important role in autonomous driving systems and robotics. Recent work utilizing prominent deep learning models for pedestrian motion prediction makes limited a priori assumptions about human movements, resulting in a lack of explainability and explicit constraints enforced on predicted trajectories. We present a dynamics-based deep learning framework with a novel asymptotically stable dynamical system integrated into a Transformer-based model. We use an asymptotically stable dynamical system to model human goal-targeted motion by enforcing the human walking trajectory, which converges to a predicted goal position, and to provide the Transformer model with prior knowledge and explainability. Our framework features the Transformer model that works with a goal estimator and dynamical system to learn features from pedestrian motion history. The results show that our framework outperforms prominent models using five benchmark human motion datasets.
Paper Structure (22 sections, 15 equations, 4 figures, 2 tables)

This paper contains 22 sections, 15 equations, 4 figures, 2 tables.

Table of Contents

  1. INTRODUCTION
  2. Dynamics-based deep learning
  3. Problem formulation
  4. Framework
  5. Human goal-targeted motion representation
  6. Goal estimator
  7. $\gamma$-soft-DTW algorithm
  8. Expert repository
  9. Goal estimation by K-means clustering
  10. A novel asymptotically stable dynamical system
  11. Dynamics-based Trajectory Predictor
  12. Goal shift
  13. Training the novel asymptotically stable dynamical system
  14. Loss function
  15. Empirical Evaluation
  16. ...and 7 more sections

Figures (4)

  • Figure 1: Goal-driven pedestrian trajectories where the pedestrian arrives around a predetermined goal.
  • Figure 2: We train the Transformer-based model to estimate the positive-definite matrix to predict trajectories. The red line represents the past pedestrian trajectory, while the blue line represents the predicted pedestrian trajectory. The figure shows only a one-step prediction, and the prediction at $T_{obs+1}$ is added back to the past pedestrian trajectory for future steps that are predicted recurrently. The dotted box indicates the dynamics-based trajectory predictor.
  • Figure 3: Trajectory visualization of human goal-targeted walking. The dots represent observed trajectories, discrete lines represent predicted trajectories, and the continuous lines represent ground truth trajectories. The round dots represent ground truth endpoints, and the stars represent predicted endpoints. The arrow represents the velocity, and the length of the arrow indicates the speed.
  • Figure 4: Trajectory visualization in the case of collision avoidance. The dots represent observed trajectories, discrete lines represent predicted trajectories, and the continuous lines represent ground truth trajectories. The round dots represent ground truth endpoints, and the stars represent predicted endpoints.