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Semantic Property Maps for Driving Applications

Marcus Greiff, Ray Zhang, Takeru Shirasawa, John Subosits

TL;DR

The paper presents Semantic Property Maps (SPMs) to online estimate spatially varying vehicle parameter likelihoods for predictive driving control by fusing camera-derived semantics with proprioceptive estimates. Using Dirichlet priors for semantic categories and Normal-Gamma priors for properties, the map is defined in road path coordinates and updated via Bayesian moment matching, ensuring differentiable moments in space. Projections from image space to path coordinates are achieved through inverse perspective mapping and a diffeomorphism, while sparse, finite-support kernels enable efficient, local updates. Numerical results with real driving data demonstrate convergence of the estimated semantic-property maps and improved horizon friction predictions compared to Kalman Filter and GP baselines, highlighting potential gains for planning and control in varying road conditions.

Abstract

We consider the problem of estimating the parameters of a vehicle dynamics model for predictive control in driving applications. Instead of solely using the instantaneous parameters estimated from the vehicle signals, we combine this with cameras and update a probabilistic map with parameter estimates and semantic information using Bayesian moment matching. Key to this approach is the map representation, which is constructed with conjugate priors to the measurement likelihoods and defined in the same path coordinates as the vehicle controller, such that the map can be externalized to provide a local representation of the parameter likelihoods that vary in space. The result is a spatial map of vehicle parameters adapted online to enhance the driving control system. We provide theoretical guarantees on the smoothness of relevant parameter likelihood statistics as a function of space, which is critical for their use in predictive control.

Semantic Property Maps for Driving Applications

TL;DR

The paper presents Semantic Property Maps (SPMs) to online estimate spatially varying vehicle parameter likelihoods for predictive driving control by fusing camera-derived semantics with proprioceptive estimates. Using Dirichlet priors for semantic categories and Normal-Gamma priors for properties, the map is defined in road path coordinates and updated via Bayesian moment matching, ensuring differentiable moments in space. Projections from image space to path coordinates are achieved through inverse perspective mapping and a diffeomorphism, while sparse, finite-support kernels enable efficient, local updates. Numerical results with real driving data demonstrate convergence of the estimated semantic-property maps and improved horizon friction predictions compared to Kalman Filter and GP baselines, highlighting potential gains for planning and control in varying road conditions.

Abstract

We consider the problem of estimating the parameters of a vehicle dynamics model for predictive control in driving applications. Instead of solely using the instantaneous parameters estimated from the vehicle signals, we combine this with cameras and update a probabilistic map with parameter estimates and semantic information using Bayesian moment matching. Key to this approach is the map representation, which is constructed with conjugate priors to the measurement likelihoods and defined in the same path coordinates as the vehicle controller, such that the map can be externalized to provide a local representation of the parameter likelihoods that vary in space. The result is a spatial map of vehicle parameters adapted online to enhance the driving control system. We provide theoretical guarantees on the smoothness of relevant parameter likelihood statistics as a function of space, which is critical for their use in predictive control.

Paper Structure

This paper contains 11 sections, 5 theorems, 15 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Contributions
  3. Preliminaries
  4. Semantic Property Maps
  5. Projections and Diffeomorphisms
  6. Sparse Kernels and Interpolated Likelihoods
  7. Categorical Updates with Semantic Information
  8. Gaussian Mixture Updates with Properties
  9. Continuity Properties
  10. Numerical Results
  11. Conclusions

Key Result

Lemma 1

If $\boldsymbol{g}\in\mathcal{C}^2([s_{\min},s_{\max}],\mathbb{R}^2_{\mathrm{BEV}})$ with maximum curvature less than $e_{\max}^{-1}$ and $\min_{|s-s^{\prime}|> \pi e_{\max}}\|\boldsymbol{g}(s)- \boldsymbol{g}(s^{\prime})\|_2 > 2 e_{\max}$, then a diffeomorphism $\phi$ exists with and $(x,y) = ([\boldsymbol{g}(s)]_1 + e[\boldsymbol{g}^{\prime}(s)]_2, [\boldsymbol{g}(s)]_2 - e[\boldsymbol{g}^{\pri

Figures (3)

  • Figure 1: The semantic property map performs Bayesian updates using visual information and vehicle parameter estimates.
  • Figure 2: KL-divergence in the moments of the likelihood of the true map and the estimated map as a function of distance traveled, with a 95% confidence interval.
  • Figure 3: Difference in the property estimate error along a planning horizon in front of the vehicle. Top: Local class likelihoods ahead of the vehicle and a prediction horizon $\mathcal{V}$, corresponding to one slice of the tensor in the externalization in Fig. \ref{['fig:method']}. Bottom: Predicted friction parameter along $\mathcal{V}$.

Theorems & Definitions (10)

  • Lemma 1
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Remark 1
  • Lemma 4
  • proof
  • Lemma 5
  • proof