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Learning-based decentralized control with collision avoidance for multi-agent systems

Omayra Yago Nieto, Alexandre Anahory Simoes, Juan I. Giribet, Leonardo J. Colombo

TL;DR

The paper addresses robust, collision-free coordination of multiple agents evolving on the Lie group $SE(3)$ with partially unknown dynamics. It combines a nominal decentralized collision-avoidance controller based on a potential function with Gaussian Process regression to learn and compensate unknown disturbances, yielding probabilistic stability guarantees. Key contributions include integrating learning with decentralized navigation on $SE(3)$, deriving a Lyapunov-based bound on tracking error in probability, and demonstrating the approach via UAV simulations under wind and sensor disturbances. The work advances scalable, data-driven multi-agent control in 3D space, with practical implications for robotic swarms and collaborative tasks in uncertain environments.

Abstract

In this paper, we present a learning-based tracking controller based on Gaussian processes (GP) for collision avoidance of multi-agent systems where the agents evolve in the special Euclidean group in the space SE(3). In particular, we use GPs to estimate certain uncertainties that appear in the dynamics of the agents. The control algorithm is designed to learn and mitigate these uncertainties by using GPs as a learning-based model for the predictions. In particular, the presented approach guarantees that the tracking error remains bounded with high probability. We present some simulation results to show how the control algorithm is implemented.

Learning-based decentralized control with collision avoidance for multi-agent systems

TL;DR

The paper addresses robust, collision-free coordination of multiple agents evolving on the Lie group with partially unknown dynamics. It combines a nominal decentralized collision-avoidance controller based on a potential function with Gaussian Process regression to learn and compensate unknown disturbances, yielding probabilistic stability guarantees. Key contributions include integrating learning with decentralized navigation on , deriving a Lyapunov-based bound on tracking error in probability, and demonstrating the approach via UAV simulations under wind and sensor disturbances. The work advances scalable, data-driven multi-agent control in 3D space, with practical implications for robotic swarms and collaborative tasks in uncertain environments.

Abstract

In this paper, we present a learning-based tracking controller based on Gaussian processes (GP) for collision avoidance of multi-agent systems where the agents evolve in the special Euclidean group in the space SE(3). In particular, we use GPs to estimate certain uncertainties that appear in the dynamics of the agents. The control algorithm is designed to learn and mitigate these uncertainties by using GPs as a learning-based model for the predictions. In particular, the presented approach guarantees that the tracking error remains bounded with high probability. We present some simulation results to show how the control algorithm is implemented.

Paper Structure

This paper contains 12 sections, 3 theorems, 31 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Dynamics of agents evolving on $SE(3)$
  3. Background on Differential Geometry
  4. Modelling of agents on SE(3)
  5. Nominal control law for collision avoidance of agents on $SE(3)$
  6. Collision avoidance task
  7. Nominal Control Law
  8. Learning-based control with Gaussian processes
  9. Learning with Gaussian processes
  10. Control design
  11. Simulation results
  12. Conclusions and Future Work

Key Result

Theorem 1

The following decentralized feedback control law guarantees asymptotic convergence to $g_{di}$ for every agent $i$ and avoids possible collisions between them where, $\xi_i = g^{-1}_i(t) g_i(t)$, $K_i \in \mathbb{R}^+$, $F_d$ is a dissipative $(1,1)$-tensor, i.e., satisfying ${\langle\!\langle F_d \xi_i , \xi_i \rangle\!\rangle}_{\mathbb{I}_i}\leqslant 0$, $\theta_i(\xi_i, \frac{\partial \psi_i}{

Figures (9)

  • Figure 1: Block diagram of the proposed decentralized control law for each agent.
  • Figure 2: Spatial distribution of UAVs.
  • Figure 3: Trajectories of the seven UAVs in the formation. It can be observed how the vehicles evade each other during landing and takeoff.
  • Figure 4: UAV attitude, avoiding filming other vehicles. The vehicle starts from position $q_2$ and goes through all points during the first $70$ seconds.
  • Figure 5: UAV position avoiding collision with other vehicles. The vehicle is at $q_{6}$ after $40$ seconds, lands at $q_{7}$ at $49$ seconds and passes by $q_{1}$ after $58$ seconds.
  • ...and 4 more figures

Theorems & Definitions (11)

  • Remark 1
  • Theorem 1
  • proof
  • Remark 2
  • Remark 3
  • Lemma 1: adapted from srinivas2012information
  • proof
  • Remark 4
  • Theorem 2
  • proof
  • ...and 1 more