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A Semi-decentralized and Variational-Equilibrium-Based Trajectory Planner for Connected and Autonomous Vehicles

Zhengqin Liu, Jinlong Lei, Peng Yi

TL;DR

A semi-decentralized planner is proposed for the vehicles to seek VE-based fair trajectories, which can significantly improve computational efficiency through parallel computing among CAVs and enhance the safety of planned trajectories by ensuring equilibrium concordance among CAVs.

Abstract

This paper designs a novel trajectory planning approach to resolve the computational efficiency and safety problems in uncoordinated methods by exploiting vehicle-to-everything (V2X) technology. The trajectory planning for connected and autonomous vehicles (CAVs) is formulated as a game with coupled safety constraints. We then define interaction-fair trajectories and prove that they correspond to the variational equilibrium (VE) of this game. We propose a semi-decentralized planner for the vehicles to seek VE-based fair trajectories, which can significantly improve computational efficiency through parallel computing among CAVs and enhance the safety of planned trajectories by ensuring equilibrium concordance among CAVs. Finally, experimental results show the advantages of the approach, including fast computation speed, high scalability, equilibrium concordance, and safety.

A Semi-decentralized and Variational-Equilibrium-Based Trajectory Planner for Connected and Autonomous Vehicles

TL;DR

A semi-decentralized planner is proposed for the vehicles to seek VE-based fair trajectories, which can significantly improve computational efficiency through parallel computing among CAVs and enhance the safety of planned trajectories by ensuring equilibrium concordance among CAVs.

Abstract

This paper designs a novel trajectory planning approach to resolve the computational efficiency and safety problems in uncoordinated methods by exploiting vehicle-to-everything (V2X) technology. The trajectory planning for connected and autonomous vehicles (CAVs) is formulated as a game with coupled safety constraints. We then define interaction-fair trajectories and prove that they correspond to the variational equilibrium (VE) of this game. We propose a semi-decentralized planner for the vehicles to seek VE-based fair trajectories, which can significantly improve computational efficiency through parallel computing among CAVs and enhance the safety of planned trajectories by ensuring equilibrium concordance among CAVs. Finally, experimental results show the advantages of the approach, including fast computation speed, high scalability, equilibrium concordance, and safety.

Paper Structure

This paper contains 10 sections, 6 theorems, 7 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Traffic Scenario and Trajectory Planning Problem
  4. Detailed Modeling of Trajectory Planning Problem
  5. Solution Concept and Its Fairness
  6. Algorithm
  7. Experimental Results
  8. Experimental Setting
  9. Evaluation and Analysis
  10. Conclusion

Key Result

Lemma 1

If $s^*$ is the GNE of Problem de:abstract_game, then $\forall i\in \mathcal{N}$, there exists a Lagrange multiplier vector $\lambda_i^*$, such that where $\mathcal{N}_{S_i}$ represents the normal cone of the set $S_i$, and the gradient operator $\nabla$ follows the denominator layout.

Figures (2)

  • Figure 1: The illustration of the problem setting. (a) The traffic scenario and the trajectory planning problem. (b) The interaction graph of CAVs. (c) The communication topology of CAVs and the RSU.
  • Figure 3: The experimental scenario and the situation setup. The solid rectangles marked in the legend represent the area covered by the random initial positions of each CAV.

Theorems & Definitions (8)

  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Theorem 1
  • proof
  • Definition 1
  • Theorem 2
  • Theorem 3