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Adaptive Ergodic Search with Energy-Aware Scheduling for Persistent Multi-Robot Missions

Kaleb Ben Naveed, Devansh R. Agrawal, Rahul Kumar, Dimitra Panagou

TL;DR

The paper tackles persistent multi-robot missions under spatiotemporal uncertainty by integrating adaptive ergodic search with an energy-aware, fail-safe scheduling framework. It introduces a clarity-based Target Information Spatial Distribution (TISD) to steer ergodic exploration in stochastic environments and a centralized online scheduler, RmeSch, to coordinate a shared mobile charging station while enforcing safety gaps and energy constraints. The proposed genTISD, mEclares planning, and RmeSch come with formal feasibility guarantees and robustness to central node failures, and are validated through hardware experiments with heterogeneous aerial robots and a mobile charger. This work enables scalable, energy-conscious, persistent exploration with nonlinear dynamics, offering practical impact for long-duration missions in dynamic domains. Overall, the framework advances persistent autonomy by marrying information-theoretic guidance with rigorous energy-aware coordination in multi-robot teams.

Abstract

Autonomous robots are increasingly deployed for long-term information-gathering tasks, which pose two key challenges: planning informative trajectories in environments that evolve across space and time, and ensuring persistent operation under energy constraints. This paper presents a unified framework, mEclares, that addresses both challenges through adaptive ergodic search and energy-aware scheduling in multi-robot systems. Our contributions are two-fold: (1) we model real-world variability using stochastic spatiotemporal environments, where the underlying information evolves unpredictably due to process uncertainty. To guide exploration, we construct a target information spatial distribution (TISD) based on clarity, a metric that captures the decay of information in the absence of observations and highlights regions of high uncertainty; and (2) we introduce Robustmesch (Rmesch), an online scheduling method that enables persistent operation by coordinating rechargeable robots sharing a single mobile charging station. Unlike prior work, our approach avoids reliance on preplanned schedules, static or dedicated charging stations, and simplified robot dynamics. Instead, the scheduler supports general nonlinear models, accounts for uncertainty in the estimated position of the charging station, and handles central node failures. The proposed framework is validated through real-world hardware experiments, and feasibility guarantees are provided under specific assumptions.

Adaptive Ergodic Search with Energy-Aware Scheduling for Persistent Multi-Robot Missions

TL;DR

The paper tackles persistent multi-robot missions under spatiotemporal uncertainty by integrating adaptive ergodic search with an energy-aware, fail-safe scheduling framework. It introduces a clarity-based Target Information Spatial Distribution (TISD) to steer ergodic exploration in stochastic environments and a centralized online scheduler, RmeSch, to coordinate a shared mobile charging station while enforcing safety gaps and energy constraints. The proposed genTISD, mEclares planning, and RmeSch come with formal feasibility guarantees and robustness to central node failures, and are validated through hardware experiments with heterogeneous aerial robots and a mobile charger. This work enables scalable, energy-conscious, persistent exploration with nonlinear dynamics, offering practical impact for long-duration missions in dynamic domains. Overall, the framework advances persistent autonomy by marrying information-theoretic guidance with rigorous energy-aware coordination in multi-robot teams.

Abstract

Autonomous robots are increasingly deployed for long-term information-gathering tasks, which pose two key challenges: planning informative trajectories in environments that evolve across space and time, and ensuring persistent operation under energy constraints. This paper presents a unified framework, mEclares, that addresses both challenges through adaptive ergodic search and energy-aware scheduling in multi-robot systems. Our contributions are two-fold: (1) we model real-world variability using stochastic spatiotemporal environments, where the underlying information evolves unpredictably due to process uncertainty. To guide exploration, we construct a target information spatial distribution (TISD) based on clarity, a metric that captures the decay of information in the absence of observations and highlights regions of high uncertainty; and (2) we introduce Robustmesch (Rmesch), an online scheduling method that enables persistent operation by coordinating rechargeable robots sharing a single mobile charging station. Unlike prior work, our approach avoids reliance on preplanned schedules, static or dedicated charging stations, and simplified robot dynamics. Instead, the scheduler supports general nonlinear models, accounts for uncertainty in the estimated position of the charging station, and handles central node failures. The proposed framework is validated through real-world hardware experiments, and feasibility guarantees are provided under specific assumptions.
Paper Structure (50 sections, 2 theorems, 51 equations, 9 figures, 2 tables, 6 algorithms)

This paper contains 50 sections, 2 theorems, 51 equations, 9 figures, 2 tables, 6 algorithms.

Table of Contents

  1. Introduction
  2. Adaptive Informative Path Planning
  3. Task Persistence in Multi-Agent Systems
  4. Contributions
  5. Preliminaries
  6. Notation
  7. System Description
  8. Ergodic Search
  9. Clarity
  10. Problem Formulation
  11. Multi-robot Clarity Dynamics
  12. Environment Specification
  13. Problem Statement
  14. Clarity-based Objective functional
  15. Minimum Energy and Mutually Exclusive Charging Constraints
  16. ...and 35 more sections

Key Result

Lemma 1

At iteration $j = 0$, given the sorted list of remaining flight times $\{T_{F,0}^{1'}, T_{F,0}^{2'}, \dots\}$ where $T_{F,0}^{1'}$ is the minimum remaining flight time, the maximum number of robots that can be safely supported by the mission while satisfying all gap flags is where $T_R$ is the time a rechargeable robot takes to reach the charging station, $T_E$ is the iteration interval, and $T_\

Figures (9)

  • Figure 1: meSch: The block diagram shows the complete proposed framework mEclares.
  • Figure 2: The supported communication architecture of the system.
  • Figure 3: This figure illustrates the generation of candidate trajectories at time $t_j$. All the candidate trajectories terminate at the rendezvous point $x^{rp}_j$ at time $t^i_{j,C}$.
  • Figure 4: The figure shows the behavior of the algorithm when the central node fails.
  • Figure 5: Demonstration of mEclares through a case study: the rechargeable quadrotors track ergodic trajectories that are replanned every 30 seconds, while the mobile charging rover follows the geometric center of the nominal ergodic trajectories of all rechargeable robots.
  • ...and 4 more figures

Theorems & Definitions (9)

  • Definition 1
  • Lemma 1
  • proof
  • Theorem 1
  • proof
  • Remark 1
  • Remark 2
  • proof
  • proof