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Factor Graph-Based Planning as Inference for Autonomous Vehicle Racing

Salman Bari, Xiagong Wang, Ahmad Schoha Haidari, Dirk Wollherr

TL;DR

This study explores the utilization of factor graphs in modeling the autonomous racecar planning problem, presenting an alternate perspective to the traditional optimizationbased formulation with superior performance for cumulative curvature and average speed across the racetrack.

Abstract

Factor graph, as a bipartite graphical model, offers a structured representation by revealing local connections among graph nodes. This study explores the utilization of factor graphs in modeling the autonomous racecar planning problem, presenting an alternate perspective to the traditional optimization-based formulation. We model the planning problem as a probabilistic inference over a factor graph, with factor nodes capturing the joint distribution of motion objectives. By leveraging the duality between optimization and inference, a fast solution to the maximum a posteriori estimation of the factor graph is obtained via least-squares optimization. The localized design thinking inherent in this formulation ensures that motion objectives depend on a small subset of variables. We exploit the locality feature of the factor graph structure to integrate the minimum curvature path and local planning computations into a unified algorithm. This diverges from the conventional separation of global and local planning modules, where curvature minimization occurs at the global level. The evaluation of the proposed framework demonstrated superior performance for cumulative curvature and average speed across the racetrack. Furthermore, the results highlight the computational efficiency of our approach. While acknowledging the structural design advantages and computational efficiency of the proposed methodology, we also address its limitations and outline potential directions for future research.

Factor Graph-Based Planning as Inference for Autonomous Vehicle Racing

TL;DR

This study explores the utilization of factor graphs in modeling the autonomous racecar planning problem, presenting an alternate perspective to the traditional optimizationbased formulation with superior performance for cumulative curvature and average speed across the racetrack.

Abstract

Factor graph, as a bipartite graphical model, offers a structured representation by revealing local connections among graph nodes. This study explores the utilization of factor graphs in modeling the autonomous racecar planning problem, presenting an alternate perspective to the traditional optimization-based formulation. We model the planning problem as a probabilistic inference over a factor graph, with factor nodes capturing the joint distribution of motion objectives. By leveraging the duality between optimization and inference, a fast solution to the maximum a posteriori estimation of the factor graph is obtained via least-squares optimization. The localized design thinking inherent in this formulation ensures that motion objectives depend on a small subset of variables. We exploit the locality feature of the factor graph structure to integrate the minimum curvature path and local planning computations into a unified algorithm. This diverges from the conventional separation of global and local planning modules, where curvature minimization occurs at the global level. The evaluation of the proposed framework demonstrated superior performance for cumulative curvature and average speed across the racetrack. Furthermore, the results highlight the computational efficiency of our approach. While acknowledging the structural design advantages and computational efficiency of the proposed methodology, we also address its limitations and outline potential directions for future research.
Paper Structure (16 sections, 1 theorem, 25 equations, 13 figures, 6 tables, 1 algorithm)

This paper contains 16 sections, 1 theorem, 25 equations, 13 figures, 6 tables, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. RELATED WORK
  3. PRELIMINARIES and BACKGROUND
  4. FACTOR GRAPH FOR PLANNING AS INFERENCE
  5. VEHICLE MODEL
  6. PROBLEM STATEMENT AND APPROACH
  7. METHODOLOGY
  8. FORMULATION OF FACTOR NODES
  9. FACTORIZATION OF PRIOR
  10. FACTORIZATION OF LIKELIHOOD
  11. EVALUATION
  12. IMPLEMENTATION DETAILS
  13. RESULTS FOR 1:43 SCALED CAR
  14. RESULTS FOR FULL-SCALE CAR
  15. DISCUSSION
  16. ...and 1 more sections

Key Result

Proposition 1

For a racecar moving along a non-degenerate arc parameterized by centerline $\bm{p}$, minimizing the tangential rotation angle $\Delta \Psi_{i}$ between two consecutive waypoints $\bm{p}_{i}$ and $\bm{p}_{i+1}$ will result in reduced cumulative curvature $k$. Therefore, the minimum curvature plannin

Figures (13)

  • Figure 1: The schematic drawing of the vehicle model with mass $m$. $l_f$ and $l_b$ depict the distance from the CoG to the front and rear wheels. The vectors in red illustrate the forces between the tire and the road, while $v_x$ and $v_y$ denote velocity components, and $\alpha_{f}$ and $\alpha_{b}$ represent slip angles.
  • Figure 2: Overall methodology of the proposed framework. The offline phase includes computations conducted prior to the initiation of the race. The online phase involves trajectory generation.
  • Figure 3: Architecture of the factor graph for autonomous racecar planning. Note that the factor nodes are affixed to the state and control components, presented in the form of variable nodes emphasizing the local connections among them.
  • Figure 4: Representation of vectors formed among $\bm{p}_{i}$, $\bm{p}_{i+1}$, and $\bm{p}_{i+2}$ for the minimum curvature factor $f_{i}^{curv}$.
  • Figure 5: The trajectory generated by the proposed algorithm in case of 1:43 scaled car for one lap on Track-I.
  • ...and 8 more figures

Theorems & Definitions (5)

  • Remark 1
  • Remark 2
  • Proposition 1
  • Proof 1
  • Remark 3