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PRO-SPECT: Probabilistically Safe Scalable Planning for Energy-Aware Coordinated UAV-UGV Teams in Stochastic Environments

Roger Fowler, Cahit Ikbal Er, Benjamin Johnsenberg, Yasin Yazicioglu

Abstract

We consider energy-aware planning for an unmanned aerial vehicle (UAV) and unmanned ground vehicle (UGV) team operating in a stochastic environment. The UAV must visit a set of air points in minimum time while respecting energy constraints, relying on the UGV as a mobile charging station. Unlike prior work that assumed deterministic travel times or used fixed robustness margins, we model travel times as random variables and bound the probability of failure (energy depletion) across the entire mission to a user-specified risk level. We formulate the problem as a Mixed-Integer Program and propose PRO-SPECT, a polynomial-time algorithm that generates risk-bounded plans. The algorithm supports both offline planning and online re-planning, enabling the team to adapt to disturbances while preserving the risk bound. We provide theoretical results on solution feasibility and time complexity. We also demonstrate the performance of our method via numerical comparisons and simulations.

PRO-SPECT: Probabilistically Safe Scalable Planning for Energy-Aware Coordinated UAV-UGV Teams in Stochastic Environments

Abstract

We consider energy-aware planning for an unmanned aerial vehicle (UAV) and unmanned ground vehicle (UGV) team operating in a stochastic environment. The UAV must visit a set of air points in minimum time while respecting energy constraints, relying on the UGV as a mobile charging station. Unlike prior work that assumed deterministic travel times or used fixed robustness margins, we model travel times as random variables and bound the probability of failure (energy depletion) across the entire mission to a user-specified risk level. We formulate the problem as a Mixed-Integer Program and propose PRO-SPECT, a polynomial-time algorithm that generates risk-bounded plans. The algorithm supports both offline planning and online re-planning, enabling the team to adapt to disturbances while preserving the risk bound. We provide theoretical results on solution feasibility and time complexity. We also demonstrate the performance of our method via numerical comparisons and simulations.

Paper Structure

This paper contains 26 sections, 1 theorem, 22 equations, 3 figures, 9 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Proposed Solution
  4. Environmental Model
  5. Probabilistic Constraint Evaluation
  6. Tour Construction
  7. Dynamic Program
  8. Offline Planning
  9. Online Re-planning
  10. Re-planning Between Tours
  11. Re-planning During a Tour
  12. Proposed Algorithm
  13. Numerical Evaluations
  14. Scalability
  15. Validation of Probabilistic Constraints
  16. ...and 11 more sections

Key Result

Theorem 1

Algorithm alg:offline_planning returns a feasible solution to eq:problem, with worst-case time complexity $O(\tilde{n}^5)$. $\blacktriangleleft$$\blacktriangleleft$

Figures (3)

  • Figure C1: Offline plan generated by PRO-SPECT : (a) $\mathcal{P}_{\text{UAV}}$; (b) TSP solution for $\mathcal{S}$ with $x_{0}$ (lower left) and $x_\text{f}$ (upper right); (c) tour construction via dynamic programming with UGV path (gray) and UAV tours (blue).
  • Figure E1: Simulation setup. (a) UAV-UGV team in the simulated environment. (b) Simulated wind field applied to the UAV, with arrow direction and magnitude indicating local wind velocity.
  • Figure E2: Mission plan in the simulations with online re-planning. \ref{['fig:plan0']} at mission start, \ref{['fig:plan1']} partway through second tour, and \ref{['fig:plan2']} at mission end

Theorems & Definitions (2)

  • Theorem 1
  • proof