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Distributed Safe Learning and Planning for Multi-robot Systems

Zhenyuan Yuan, Minghui Zhu

TL;DR

This work tackles online multi-robot motion planning with general nonlinear dynamics subject to unknown disturbances. The authors propose dSLAP, a distributed Safe Learning And Planning framework that couples online disturbance learning via Gaussian process regression with set-valued model predictive control to guarantee safety while adapting plans online. Key contributions include a two-stage safety strategy (OCA/ICA) combined with discrete set-valued dynamics, probabilistic safety guarantees, and scalable distributed coordination with prioritized planning; extensive Monte Carlo simulations validate safety and performance. The framework enables robust, real-time navigation for teams of robots in uncertain environments and offers tunable trade-offs between exploration and goal-reaching.

Abstract

This paper considers the problem of online multi-robot motion planning with general nonlinear dynamics subject to unknown external disturbances. We propose dSLAP, a distributed safe learning and planning framework that allows the robots to safely navigate through the environments by coupling online learning and motion planning. Gaussian process regression is used to online learn the disturbances with uncertainty quantification. The planning algorithm ensures collision avoidance against the learning uncertainty and utilizes set-valued analysis to achieve fast adaptation in response to the newly learned models. A set-valued model predictive control problem is then formulated and solved to return a control policy that balances between actively exploring the unknown disturbances and reaching goal regions. Sufficient conditions are established to guarantee the safety of the robots in the absence of backup policy. Monte Carlo simulations are conducted for evaluation.

Distributed Safe Learning and Planning for Multi-robot Systems

TL;DR

This work tackles online multi-robot motion planning with general nonlinear dynamics subject to unknown disturbances. The authors propose dSLAP, a distributed Safe Learning And Planning framework that couples online disturbance learning via Gaussian process regression with set-valued model predictive control to guarantee safety while adapting plans online. Key contributions include a two-stage safety strategy (OCA/ICA) combined with discrete set-valued dynamics, probabilistic safety guarantees, and scalable distributed coordination with prioritized planning; extensive Monte Carlo simulations validate safety and performance. The framework enables robust, real-time navigation for teams of robots in uncertain environments and offers tunable trade-offs between exploration and goal-reaching.

Abstract

This paper considers the problem of online multi-robot motion planning with general nonlinear dynamics subject to unknown external disturbances. We propose dSLAP, a distributed safe learning and planning framework that allows the robots to safely navigate through the environments by coupling online learning and motion planning. Gaussian process regression is used to online learn the disturbances with uncertainty quantification. The planning algorithm ensures collision avoidance against the learning uncertainty and utilizes set-valued analysis to achieve fast adaptation in response to the newly learned models. A set-valued model predictive control problem is then formulated and solved to return a control policy that balances between actively exploring the unknown disturbances and reaching goal regions. Sufficient conditions are established to guarantee the safety of the robots in the absence of backup policy. Monte Carlo simulations are conducted for evaluation.
Paper Structure (21 sections, 18 theorems, 91 equations, 10 figures, 3 tables, 5 algorithms)

This paper contains 21 sections, 18 theorems, 91 equations, 10 figures, 3 tables, 5 algorithms.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Distributed safe learning and planning
  4. System learning
  5. Safe-state identification
  6. Active learning and real-time control (Algorithm \ref{['alg:active learning']})
  7. Performance guarantees
  8. Discussion
  9. Proof
  10. Concentration inequality of Gaussian process
  11. Set-valued approximation
  12. Proof of Theorem \ref{['thm: system safe']}
  13. Proof of Theorem \ref{['thm2: system safe']}
  14. Simulation
  15. Safe grid vs. safe region
  16. ...and 6 more sections

Key Result

Theorem III.2

(One-iteration safety). Suppose Assumptions assmp: model and assmp: ||g||_kappa hold. If $\mathcal{B}(x^{[i]}(k\xi), h_{p_{k-1}}) \cap\mathcal{X}^{[i]}_{safe, k-1}\neq \emptyset$ , $k\geqslant1$, for all $i\in\mathcal{V}$, then dSLAP renders $x_q^{[i]}(t)\in\mathcal{X}^{[i]}_F(x_q^{[\neg i]}(t))$ fo

Figures (10)

  • Figure 1: Implementation of dSLAP over one iteration
  • Figure 2: A graphical illustration of obstacle collision avoidance
  • Figure 3: A sample of wind fields and robot trajectories
  • Figure 4: Safe grid computed by dSLAP vs. actual safe region
  • Figure 5: Ablation study of dSLAP
  • ...and 5 more figures

Theorems & Definitions (19)

  • Theorem III.2
  • Theorem III.3
  • Lemma IV.1
  • Lemma IV.2
  • Lemma IV.3
  • Lemma IV.4
  • Lemma IV.5
  • Lemma IV.6
  • Lemma IV.7
  • Lemma IV.8
  • ...and 9 more