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Control of Vehicle Platoons with Collision Avoidance Using Noncooperative Differential Games

Hossein B. Jond

TL;DR

This work models predecessor‑following vehicle platoons as a noncooperative differential game, deriving a closed‑form open‑loop Nash equilibrium for the collision‑free case under linearized, homogeneous dynamics. To address collision avoidance, it introduces an estimated Nash strategy that augments the PI with a safety term and relies on terminal/state‑trajectory estimates to compute implementable controls. Simulations show that the collision‑free strategy achieves the desired platoon with clear convergence, while the estimated Nash approach successfully enforces collision avoidance and accelerates platoon formation. The results suggest a practical framework for self‑interested automated vehicles to achieve coordinated platooning with safety guarantees, motivating extensions to richer topologies and stability analyses.

Abstract

This paper considers a differential game approach to the predecessor-following vehicle platoon control problem without and with collision avoidance. In this approach, each vehicle tries to minimize the performance index (PI) of its control objective, which is reaching consensual velocity with the predecessor vehicle while maintaining a small inter-vehicle distance from it. Two differential games were formulated. The differential game problem for platoon control without collision avoidance is solved for the open-loop Nash equilibrium and its associated state trajectories. The second differential game problem for platoon control with collision avoidance has a non-quadratic PI, which poses a greater challenge to obtaining its open-loop Nash equilibrium. Since the exact solution is unavailable, we propose an estimated Nash strategy approach that is greatly simplified for implementation. An illustrative example of a vehicle platoon control problem was solved under both the without and with collision avoidance scenarios. The results showed the effectiveness of the models and their solutions for both scenarios.

Control of Vehicle Platoons with Collision Avoidance Using Noncooperative Differential Games

TL;DR

This work models predecessor‑following vehicle platoons as a noncooperative differential game, deriving a closed‑form open‑loop Nash equilibrium for the collision‑free case under linearized, homogeneous dynamics. To address collision avoidance, it introduces an estimated Nash strategy that augments the PI with a safety term and relies on terminal/state‑trajectory estimates to compute implementable controls. Simulations show that the collision‑free strategy achieves the desired platoon with clear convergence, while the estimated Nash approach successfully enforces collision avoidance and accelerates platoon formation. The results suggest a practical framework for self‑interested automated vehicles to achieve coordinated platooning with safety guarantees, motivating extensions to richer topologies and stability analyses.

Abstract

This paper considers a differential game approach to the predecessor-following vehicle platoon control problem without and with collision avoidance. In this approach, each vehicle tries to minimize the performance index (PI) of its control objective, which is reaching consensual velocity with the predecessor vehicle while maintaining a small inter-vehicle distance from it. Two differential games were formulated. The differential game problem for platoon control without collision avoidance is solved for the open-loop Nash equilibrium and its associated state trajectories. The second differential game problem for platoon control with collision avoidance has a non-quadratic PI, which poses a greater challenge to obtaining its open-loop Nash equilibrium. Since the exact solution is unavailable, we propose an estimated Nash strategy approach that is greatly simplified for implementation. An illustrative example of a vehicle platoon control problem was solved under both the without and with collision avoidance scenarios. The results showed the effectiveness of the models and their solutions for both scenarios.
Paper Structure (6 sections, 2 theorems, 35 equations, 4 figures)

This paper contains 6 sections, 2 theorems, 35 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Differential Game Formulation
  3. Open-Loop Nash Equilibrium
  4. Collision Avoidance Estimated Nash Strategy
  5. Simulation Results
  6. Conclusions

Key Result

Theorem 1

Consider a platoon of vehicles with the feedback linearized dynamics (eq:dynamics) and PIs (eq:cost). The platoon control problem as a noncooperative differential game admits a unique open-loop Nash equilibrium given by where The state trajectories associated with the equilibrium actions are given by where

Figures (4)

  • Figure 1: A homogeneous vehicle platoon with predecessor-following topology. The corresponding information topology shows that each follower vehicle has the information of only its predecessor vehicle.
  • Figure 2: Time histories of positions, velocities, accelerations, and control inputs of vehicles in the platoon control problem without collision avoidance. A collision between the lead vehicle and vehicle 1 is unavoidable.
  • Figure 3: Time histories of positions, velocities, accelerations, and control inputs of vehicles in the platoon control problem with collision avoidance. All following vehicles pursue collision-free trajectories.
  • Figure 4: Time histories of the scalar function $f(\mathrm{e}^{tA}y_i(0))$.

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Theorem 2
  • proof