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Over-the-Air Consensus-based Formation Control of Heterogeneous Agents: Communication-Rate and Geometry-Aware Convergence Guarantees

Michael Epp, Fabio Molinari, Jörg Raisch

TL;DR

This paper exploits the superposition property of the wireless channel to compute, at each receiver, normalized convex combinations of simultaneously broadcast neighbor signals, and derives a communication-rate based sufficient condition that guarantees convergence to a prescribed formation.

Abstract

This paper investigates the formation control problem of heterogeneous, autonomous agents that communicate over a wireless multiple access channel. Instead of avoiding interference through orthogonal node-to-node transmissions, we exploit the superposition property of the wireless channel to compute, at each receiver, normalized convex combinations of simultaneously broadcast neighbor signals. At every communication instant, agents update their reference positions from these aggregates, and track the references in continuous time between updates. The only assumption on the agent dynamics is that each agent tracks constant reference positions exponentially, which accommodates a broad class of platforms. Under this assumption, we analyze the resulting jump-flow system under time-varying communication graphs and unknown channel coefficients. We derive a communication-rate based sufficient condition that guarantees convergence to a prescribed formation. We then provide a geometry-aware refinement showing how favorable tracking transients can relax the required condition. Simulations with unicycle agents illustrate the theoretical results and demonstrate a substantial reduction in the number of required orthogonal transmissions compared to interference-avoiding node-to-node communication protocols.

Over-the-Air Consensus-based Formation Control of Heterogeneous Agents: Communication-Rate and Geometry-Aware Convergence Guarantees

TL;DR

This paper exploits the superposition property of the wireless channel to compute, at each receiver, normalized convex combinations of simultaneously broadcast neighbor signals, and derives a communication-rate based sufficient condition that guarantees convergence to a prescribed formation.

Abstract

This paper investigates the formation control problem of heterogeneous, autonomous agents that communicate over a wireless multiple access channel. Instead of avoiding interference through orthogonal node-to-node transmissions, we exploit the superposition property of the wireless channel to compute, at each receiver, normalized convex combinations of simultaneously broadcast neighbor signals. At every communication instant, agents update their reference positions from these aggregates, and track the references in continuous time between updates. The only assumption on the agent dynamics is that each agent tracks constant reference positions exponentially, which accommodates a broad class of platforms. Under this assumption, we analyze the resulting jump-flow system under time-varying communication graphs and unknown channel coefficients. We derive a communication-rate based sufficient condition that guarantees convergence to a prescribed formation. We then provide a geometry-aware refinement showing how favorable tracking transients can relax the required condition. Simulations with unicycle agents illustrate the theoretical results and demonstrate a substantial reduction in the number of required orthogonal transmissions compared to interference-avoiding node-to-node communication protocols.
Paper Structure (7 sections, 4 theorems, 63 equations, 2 figures)

This paper contains 7 sections, 4 theorems, 63 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Communication Model
  4. Control Strategy
  5. Convergence Analysis
  6. Simulation Results
  7. Conclusion

Key Result

Corollary 1

For all $k\in\mathbb{N}_0$, the matrix $H_k$, with $[H_k]_{ij}=h_{ij,k}$, is row-stochastic.

Figures (2)

  • Figure 1: Comparison of guaranteed end-of-interval regions. Under Assumption \ref{['as:expo_stable']}, this is for agent $i$, a ball centered at $r_{i,k^+}$ shown as the dashed circle. Assumption \ref{['as:expo_stable_relaxed']} relaxes the guaranteed end-of interval region to the entire blue shaded area. The yellow set is the guaranteed end-of-interval region under which Theorem \ref{['thm:relaxed']} formulates a sufficient consensus condition.
  • Figure 2: Evolution of the formation error for varying choices of $\mu$ and $T$.

Theorems & Definitions (10)

  • Remark
  • Definition 1: Wireless Multiple Access Channel
  • Corollary 1
  • Remark
  • Theorem 1
  • proof
  • Lemma 1
  • proof
  • Theorem 2
  • proof