Deep Stochastic Kinematic Models for Probabilistic Motion Forecasting in Traffic

TL;DR

This work tackles probabilistic motion forecasting for traffic by injecting differentiable kinematic priors derived from the bicycle model into Gaussian-M Mixture predictions. It introduces four formulations that propagate per-timestep kinematic distributions (velocity, acceleration, speed-heading, and acceleration-steering) through time via Euler integration, with linearized approximations to keep computations tractable. The method yields analytical variance propagation and an explicit error bound for the linearizations, delivering improvements on the Waymo Motion Dataset, particularly in data-scarce or noisy scenarios, and showing robustness across formulations. The approach requires minimal overhead and is compatible with SOTA architectures, with future directions including autoregressive extensions and transfer learning between domains.

Abstract

In trajectory forecasting tasks for traffic, future output trajectories can be computed by advancing the ego vehicle's state with predicted actions according to a kinematics model. By unrolling predicted trajectories via time integration and models of kinematic dynamics, predicted trajectories should not only be kinematically feasible but also relate uncertainty from one timestep to the next. While current works in probabilistic prediction do incorporate kinematic priors for mean trajectory prediction, _variance_ is often left as a learnable parameter, despite uncertainty in one time step being inextricably tied to uncertainty in the previous time step. In this paper, we show simple and differentiable analytical approximations describing the relationship between variance at one timestep and that at the next with the kinematic bicycle model. In our results, we find that encoding the relationship between variance across timesteps works especially well in unoptimal settings, such as with small or noisy datasets. We observe up to a 50% performance boost in partial dataset settings and up to an 8% performance boost in large-scale learning compared to previous kinematic prediction methods on SOTA trajectory forecasting architectures out-of-the-box, with no fine-tuning.

Figures (4)

• Figure 1: Motivating example for probabilistic kinematic priors. In real-world traffic, vehicles have a constrained range of behaviors. For instance, it is not possible for a vehicle to move side to side directly, and driving in reverse is highly unlikely. Without kinematic priors, neural networks may search the space of all trajectories, possible or impossible. Without accounting for analytical variances in trajectories as in previous work, the range of possible future trajectories may also be unrealistic.
• Figure 2: Qualitative example. We visualize an example of the mean trajectory of the highest-scored Gaussian from the results of Table \ref{['tb:1p_waymo']}. Standard deviations are visualized as ellipses at each second into the future, and ground truth trajectories are drawn in green. Our method (blue) not only predicts a smoother, less jagged mean trajectory but also provides a more realistic spread of trajectories into the future. The baseline method (red) shows uneven speeds (ellipses are at uneven intervals) in addition to uncertainty extending far beyond the road boundaries.
• Figure 3: Linear approximation of position distributions via kinematic priors.
• Figure 4: Average Displacement Error (ADE) across training across each method and formulation in the small dataset setting. Learning with stochastic kinematic priors aids with faster learning. Compared to the baseline (blue), all models employing kinematic priors converge much more quickly. Formulation 4 (brown) converges most quickly.