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Distributed Model Predictive Control for Heterogeneous Platoons with Affine Spacing Policies and Arbitrary Communication Topologies

Michael H. Shaham, Taskin Padir

TL;DR

The paper develops a distributed model predictive control approach for heterogeneous vehicle platoons with affine spacing policies and arbitrary communication topologies, requiring each vehicle to communicate with a preceding vehicle. It proves a Lyapunov-based sufficient condition on the spacing weights that guarantees asymptotic stability and validates the method through large-scale simulations and hardware experiments, demonstrating scalability and practical viability. The DMPC uses terminal constraints and neighborhood information exchange to ensure convergence to leader-relative trajectories without requiring prior knowledge of the lead velocity. By extending prior work to broader topologies and CTH spacing, the work advances robust and scalable platooning for real-world networks.

Abstract

This paper presents a distributed model predictive control (DMPC) algorithm for a heterogeneous platoon using arbitrary communication topologies, provided each vehicle can communicate with a preceding vehicle in the platoon. The proposed DMPC algorithm can accommodate any spacing policy that is affine in a vehicle's velocity, which includes constant distance or constant time headway spacing policies. By analyzing the total cost for the entire platoon, a sufficient condition is derived to ensure platoon asymptotic stability. Simulation experiments with a platoon of 50 vehicles and hardware experiments with a platoon of four 1/10th-scale vehicles validate the algorithm and compare performance under different spacing policies and communication topologies.

Distributed Model Predictive Control for Heterogeneous Platoons with Affine Spacing Policies and Arbitrary Communication Topologies

TL;DR

The paper develops a distributed model predictive control approach for heterogeneous vehicle platoons with affine spacing policies and arbitrary communication topologies, requiring each vehicle to communicate with a preceding vehicle. It proves a Lyapunov-based sufficient condition on the spacing weights that guarantees asymptotic stability and validates the method through large-scale simulations and hardware experiments, demonstrating scalability and practical viability. The DMPC uses terminal constraints and neighborhood information exchange to ensure convergence to leader-relative trajectories without requiring prior knowledge of the lead velocity. By extending prior work to broader topologies and CTH spacing, the work advances robust and scalable platooning for real-world networks.

Abstract

This paper presents a distributed model predictive control (DMPC) algorithm for a heterogeneous platoon using arbitrary communication topologies, provided each vehicle can communicate with a preceding vehicle in the platoon. The proposed DMPC algorithm can accommodate any spacing policy that is affine in a vehicle's velocity, which includes constant distance or constant time headway spacing policies. By analyzing the total cost for the entire platoon, a sufficient condition is derived to ensure platoon asymptotic stability. Simulation experiments with a platoon of 50 vehicles and hardware experiments with a platoon of four 1/10th-scale vehicles validate the algorithm and compare performance under different spacing policies and communication topologies.
Paper Structure (15 sections, 5 theorems, 46 equations, 4 figures, 1 table, 1 algorithm)

This paper contains 15 sections, 5 theorems, 46 equations, 4 figures, 1 table, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. PLATOON MODELING
  3. Vehicle Dynamics
  4. Communication Topology
  5. Platooning Control Objective
  6. THE DISTRIBUTED MODEL PREDICTIVE CONTROL ALGORITHM
  7. STABILITY ANALYSIS
  8. Terminal Constraint Analysis
  9. Analysis of the Local Cost Function
  10. Analysis of the Sum of Local Cost Functions
  11. A Sufficient Condition for Platoon Asymptotic Stability
  12. EXPERIMENTS
  13. Simulation Experiments
  14. Hardware Experiments
  15. CONCLUSIONS

Key Result

Lemma 1

Suppose $A \in \mathbb R^{n \times n}$ and $B \in \mathbb R^{m \times m}$ have eigenvalues $\lambda_1, \ldots, \lambda_n$ and $\mu_1, \ldots, \mu_m$, respectively. Then the eigenvalues of $A \otimes B$ (the Kronecker product of $A$ and $B$) are given by

Figures (4)

  • Figure 1: Platoon velocity trajectory and spacing errors for the virtual leader and 6 of the followers from the $N = 50$ vehicles when using a CTH and CDH spacing policy.
  • Figure 2: Box plots depicting the spread of the worst errors for each vehicle in the platoon (not including the first vehicle). The notation "quad" indicates the weighted squared two norm formulation in the cost.
  • Figure 3: Four F1Tenth vehicles in a $4\,$m $\times$$8\,$m oval racetrack.
  • Figure 4: Results from two hardware experiments with four F1Tenth vehicles using CTH (left) and CDH (right) under a PF communication topology with the $\ell_1$ norm in the cost function.

Theorems & Definitions (13)

  • Lemma 1: horn_johnson_1985
  • Theorem 1
  • proof
  • Remark 1
  • Theorem 2
  • proof
  • Remark 2
  • Theorem 3
  • proof
  • Theorem 4
  • ...and 3 more