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Coordinated Path Following of UAVs over Time-Varying Digraphs Connected in an Integral Sense

Hyungsoo Kang, Isaac Kaminer, Venanzio Cichella, Naira Hovakimyan

TL;DR

A new connectivity condition on the information flow between UAVs to achieve coordinated path following is presented, which shows that a distributed coordination controller ensures exponential convergence of the coordination error vector to a neighborhood of zero.

Abstract

This paper presents a new connectivity condition on the information flow between UAVs to achieve coordinated path following. The information flow is directional, so that the underlying communication network topology is represented by a time-varying digraph. We assume that this digraph is connected in an integral sense. This is a much more general assumption than the one currently used in the literature. Under this assumption, it is shown that a decentralized coordination controller ensures exponential convergence of the coordination error vector to a neighborhood of zero. The efficacy of the algorithm is confirmed with simulation results.

Coordinated Path Following of UAVs over Time-Varying Digraphs Connected in an Integral Sense

TL;DR

A new connectivity condition on the information flow between UAVs to achieve coordinated path following is presented, which shows that a distributed coordination controller ensures exponential convergence of the coordination error vector to a neighborhood of zero.

Abstract

This paper presents a new connectivity condition on the information flow between UAVs to achieve coordinated path following. The information flow is directional, so that the underlying communication network topology is represented by a time-varying digraph. We assume that this digraph is connected in an integral sense. This is a much more general assumption than the one currently used in the literature. Under this assumption, it is shown that a decentralized coordination controller ensures exponential convergence of the coordination error vector to a neighborhood of zero. The efficacy of the algorithm is confirmed with simulation results.
Paper Structure (9 sections, 3 theorems, 34 equations, 5 figures)

This paper contains 9 sections, 3 theorems, 34 equations, 5 figures.

Table of Contents

  1. INTRODUCTION
  2. PRELIMINARIES
  3. Graph Theory
  4. TIME-COORDINATED PATH-FOLLOWING FRAMEWORK
  5. Path Following of a Single UAV
  6. Time Coordination of Multiple UAVs
  7. DISTRIBUTED TIME-COORDINATION CONTROLLER : MAIN RESULT
  8. SIMULATION RESULTS
  9. CONCLUSION

Key Result

Lemma 1

Consider the following dynamics where $a$ and $b$ are the positive coordination control gains in dyn1. Under Assumption assum3 on $L(t)$, the components $x_i$'s of $x$ reach consensus exponentially where $k\triangleq\frac{1}{1-(\delta')^n}$ and $\lambda\triangleq-\frac{1}{nT}\ln(1-(\delta')^n)$ with $\delta'\triangleq \min\left\{1,\frac{a}{b}\delta\right\}e^{-(n-1)\frac{a}{b}T}$.

Figures (5)

  • Figure 1: Coordinated path-following of five quadrotor UAVs. Blue dots, the starting points of the desired trajectories, are on $y=0\,m$. Red dots, the end points, are on $y=150\,m$.
  • Figure 2: Inter-vehicle information flow with digraph topologies.
  • Figure 3: Convergence of the coordination errors $\gamma_i(t)-\gamma_j(t)$$(i<j)$ to zero.
  • Figure 4: Convergence of the coordination rate $\dot{\gamma}_i(t)$ to the desired mission rate $\dot{\gamma}_d(t)$.
  • Figure 5: Path-following errors

Theorems & Definitions (14)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5
  • Remark 6
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • ...and 4 more