[Paper Review] Risk-aware Resource Allocation for Multiple UAVs-UGVs Recharging Rendezvous

Ahmad Asghar, Guangyao Shi+5 more|arXiv (Cornell University)|Sep 13, 2022

UAV Applications and Optimization4 citations

TL;DR

This paper proposes a risk-aware resource allocation framework for coordinating multiple UAVs and UGVs in persistent monitoring missions, where UAVs must periodically rendezvous with UGVs for recharging due to stochastic energy consumption. It formulates the Risk-aware Recharging Rendezvous Problem (RRRP) as an Integer Linear Program (ILP) with matching and knapsack constraints, and introduces a bicriteria approximation algorithm that balances detour cost and failure probability, achieving near-optimal performance with significantly improved scalability over exact ILP solving.

ABSTRACT

We study a resource allocation problem for the cooperative aerial-ground vehicle routing application, in which multiple Unmanned Aerial Vehicles (UAVs) with limited battery capacity and multiple Unmanned Ground Vehicles (UGVs) that can also act as a mobile recharging stations need to jointly accomplish a mission such as persistently monitoring a set of points. Due to the limited battery capacity of the UAVs, they sometimes have to deviate from their task to rendezvous with the UGVs and get recharged. Each UGV can serve a limited number of UAVs at a time. In contrast to prior work on deterministic multi-robot scheduling, we consider the challenge imposed by the stochasticity of the energy consumption of the UAV. We are interested in finding the optimal recharging schedule of the UAVs such that the travel cost is minimized and the probability that no UAV runs out of charge within the planning horizon is greater than a user-defined tolerance. We formulate this problem ({Risk-aware Recharging Rendezvous Problem (RRRP))} as an Integer Linear Program (ILP), in which the matching constraint captures the resource availability constraints and the knapsack constraint captures the success probability constraints. We propose a bicriteria approximation algorithm to solve RRRP. We demonstrate the effectiveness of our formulation and algorithm in the context of one persistent monitoring mission.

Motivation & Objective

• To address the challenge of stochastic UAV energy consumption in long-term, cooperative UAV-UGV missions where battery depletion risks mission failure.
• To minimize total UAV detour cost while ensuring the probability of any UAV running out of charge remains below a user-defined tolerance.
• To develop a scalable coordination strategy that efficiently schedules recharging rendezvous between multiple UAVs and UGVs with limited recharging capacity.
• To balance task performance and risk tolerance in persistent monitoring scenarios where UAVs must deviate for recharging.

Proposed method

• Formulates the Risk-aware Recharging Rendezvous Problem (RRRP) as an Integer Linear Program (ILP) with matching constraints to model UGV recharging capacity and knapsack constraints to enforce failure probability bounds.
• Introduces a bicriteria approximation algorithm that provides theoretical performance guarantees by balancing detour cost and risk tolerance, exploiting structural properties of the problem.
• Employs Lagrangian relaxation-inspired techniques to decompose the problem and derive efficient solutions, avoiding the exponential scaling of prior exact methods.
• Uses a receding horizon approach to iteratively solve RRRP over finite horizons, improving adaptability and runtime performance.
• Employs ILP solvers (e.g., MATLAB’s intlinprog) as a baseline for comparison, validating the approximation algorithm’s performance and scalability.
• Employs simulation-based evaluation with metrics including mean time to failure, travel time overhead, and number of recharging detours to assess performance.

Experimental results

Research questions

• RQ1 How can UAV-UGV recharging schedules be optimized to minimize detour costs while ensuring a user-defined upper bound on the probability of UAV battery depletion?
• RQ2 What is the trade-off between task performance (e.g., travel time overhead) and risk tolerance in persistent monitoring missions with stochastic UAV energy consumption?
• RQ3 Can a bicriteria approximation algorithm achieve near-optimal performance with significantly improved runtime scalability compared to exact ILP solving?
• RQ4 How does the proposed algorithm compare to greedy baselines that trigger recharging at fixed battery thresholds (e.g., 30%, 40%, 50%) in terms of failure resilience and detour efficiency?

Key findings

• The proposed bicriteria approximation algorithm achieves solutions within 15% of the optimal ILP solution on average across various problem sizes, with performance improving as problem scale increases.
• For problem instances with up to 60,500 variables, the algorithm’s runtime was up to seven times faster than the ILP solver, demonstrating strong scalability.
• The algorithm outperformed ILP in travel time overhead despite ILP solving RRRP optimally for a given horizon, likely due to the receding horizon strategy enabling better adaptability.
• Compared to greedy baselines (Greedy-30, Greedy-40, Greedy-50), the proposed method achieved longer mean time before first failure and lower travel time overhead, indicating fewer unnecessary recharging detours.
• As risk tolerance decreased (i.e., stricter failure probability bounds), the mean time before first failure increased, and both travel time overhead and number of recharging detours rose, confirming the expected trade-off between safety and efficiency.
• The average number of rendezvous per planning horizon was kept low, suggesting the algorithm avoids excessive recharging schedules while maintaining reliability.