Minimal/canonical 1D vehicle platooning example illustrating asymmetry-induced stability under the VNAE framework.
This repository provides a minimal R implementation of a 1D vehicle platooning model inspired by the Victoria–Nash Asymmetric Equilibrium (VNAE) framework.
The example illustrates how asymmetric dissipation across agents induces global stability in a classical formation control problem.
For a chain of N vehicles, the dynamics are given by:
dx₁/dt = −θ₁ x₁
dxᵢ/dt = −[(xᵢ − xᵢ₋₁) − d] − θᵢ xᵢ, i = 2,…,N
where:
- xᵢ denotes the position of vehicle i,
- d is the desired inter-vehicle distance,
- θᵢ > 0 are agent-specific asymmetry parameters.
Despite heterogeneous dissipation, the formation converges to a stable configuration. Stability is not enforced by symmetry or fine-tuned gains, but emerges from asymmetry, consistent with the VNAE geometric perspective.
This example is intended as a minimal, software-level reference for control, multi-agent systems, and autonomous vehicle research.
Pereira, D. H. (2025). Riemannian Manifolds of Asymmetric Equilibria: The Victoria-Nash Geometry.