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Optimal planning for heterogeneous autonomous teams with precedence and compatibility constraints and its application on power grid inspection with Unmanned Aerial Vehicles

Antonio Sojo, Iván Maza, Aníbal Ollero

Abstract

In this paper we address the optimal planning of autonomous teams for general purpose tasks including a wide spectrum of situations: from project management of human teams to the coordination of an automated assembly lines, focusing in the automated inspection of power grids. There exist many methods for task planning. However, the vast majority of such methods are conceived for very specific problems or situations and are often based in certain assumptions and simplifications. Consider for example all the different algorithms developed to solve the Vehicle Routing Problem (VRP) for all the different vehicles and environment characteristics. This means that no robust general planning method exists and that a possible extension of any of them to a more general situation is often not a trivial task. To address this, we propose a new truly general method ultimately based on a generalization of the Traveling Salesman Problem (TSP). We call this new model the Heterogeneous Multi-worker Task Planning Problem (HMWTPP). It provides a natural framework to model many situations typical in task planning of all kinds. Task-Worker compatibility, precedence/order and time-windows constraints are already encoded into the HMWTPP while it can be easily extended to include weight capacity or battery per node constraints in an intuitive manner. Several classical TSP problems included in the TSPLIB library are solved for validation and performance analysis of HMWTPP showing a comparable numerical performance to that of existing models. In addition, a synthetic example modeling an automated assembly line is analyzed to prove the potential capabilities of the HMWTPP in real-life scenarios. Ultimately, we focus in the computation of the optimal plan of Unmanned Aerial Vehicles (UAVs) specifically in the context of automated inspection of electrical power grids.

Optimal planning for heterogeneous autonomous teams with precedence and compatibility constraints and its application on power grid inspection with Unmanned Aerial Vehicles

Abstract

In this paper we address the optimal planning of autonomous teams for general purpose tasks including a wide spectrum of situations: from project management of human teams to the coordination of an automated assembly lines, focusing in the automated inspection of power grids. There exist many methods for task planning. However, the vast majority of such methods are conceived for very specific problems or situations and are often based in certain assumptions and simplifications. Consider for example all the different algorithms developed to solve the Vehicle Routing Problem (VRP) for all the different vehicles and environment characteristics. This means that no robust general planning method exists and that a possible extension of any of them to a more general situation is often not a trivial task. To address this, we propose a new truly general method ultimately based on a generalization of the Traveling Salesman Problem (TSP). We call this new model the Heterogeneous Multi-worker Task Planning Problem (HMWTPP). It provides a natural framework to model many situations typical in task planning of all kinds. Task-Worker compatibility, precedence/order and time-windows constraints are already encoded into the HMWTPP while it can be easily extended to include weight capacity or battery per node constraints in an intuitive manner. Several classical TSP problems included in the TSPLIB library are solved for validation and performance analysis of HMWTPP showing a comparable numerical performance to that of existing models. In addition, a synthetic example modeling an automated assembly line is analyzed to prove the potential capabilities of the HMWTPP in real-life scenarios. Ultimately, we focus in the computation of the optimal plan of Unmanned Aerial Vehicles (UAVs) specifically in the context of automated inspection of electrical power grids.

Paper Structure

This paper contains 9 sections, 28 equations, 6 figures, 3 tables.

Table of Contents

  1. Introduction
  2. The HMWTPP formulation for optimal task planning problems
  3. Weighed directed multigraph representation
  4. Mixed-integer programming problem (MILP) representation
  5. Example I: Classical TSPs
  6. Example II: Guitar assembly line with 2 workers
  7. Power grid inspection
  8. Conclusion
  9. Acknowledgements

Figures (6)

  • Figure 1: Solution for the eil51 instance with two workers and 50 compatibility constraints
  • Figure 2: Solutions to the guitar assembly problem in both the incomplete case and the one that includes waiting points.
  • Figure 3: The two mainly used UAVs for real missions. Photos from gil-castilla2024
  • Figure 4: Typical routes for a DJI M300 (to the left) and a DeltaQuad Pro V2 (to the right)
  • Figure 5: The ground control station displaying the optimal planning for three DJI M300 UAVs inspecting 10 cable segments of a sample power grid near El Rocío, Spain obtained using the HMWTPP model.
  • ...and 1 more figures