# Diverse Planning for UAV Control and Remote Sensing

^{*}

## Abstract

**:**

## 1. Introduction

- improve human–machine interface (HMI),
- increase UAV autonomy.

- [R]ealistically even the lightest onboard sensors would add some weight. The heavier the payload the less fuel can be added, which reduces flight duration.

## 2. Diverse Planning for Multi-UAV Coordination

- $y\in Y$ is a set of sensor types the UAVs can equip in form of particular sensors,
- $\overline{l}\in L$ is a set of target ground locations for sensing in form $\overline{l}=\langle {l}_{x},{l}_{y}\rangle $,
- $u\in U$ is a set of (identificators of) the UAVs carrying out the mission,
- $\langle \overline{l},y\rangle \in T$ is the set of the sensing tasks of the UAVs of sensor type y at target location $\overline{l}$ (the optimization criterion is to fulfill maximal number of these tasks),
- c is the number of sensor slots (identical for all UAVs),
- b is the maximal battery charge (identical for all UAVs), and
- p represents the battery penalty for one equipped sensor (identical for all UAVs).

#### 2.1. Why Is This Task Difficult?

#### 2.2. The Pseudo-Optimal Algorithm

#### 2.3. The Greedy Algorithm

Algorithm 1: GreedySolver $(\mathcal{M})$ – a greedy algorithm solving MUSPs. |

Algorithm 2: Greedy Orienteering Problem solver (with greedy sensors selection) of one UAV. |

## 3. Diverse Planning Based Algorithm

Algorithm 3: DivPlan—A MUSP solver based on diverse planning and constraint optimization. |

input : Problem $\mathcal{M}=\langle Y,L,U,T,c,b,p\rangle $output: Solution μ${\mu}^{\mathit{greedy}}\u27f5\mathtt{GreedySolver}(\mathcal{M})$; $\overline{\mu}\u27f5\mathtt{CreateDiverseTrajecotries}(\mathcal{M})\cup {\bigcup}_{u\in U}{\mu}^{\mathit{greedy}}(u)$; $\mu \u27f5\mathtt{COPSolver}(X\leftarrow U,\forall {X}_{i}\in X:{D}_{i}\leftarrow \overline{\mu},C,{f}_{\mathit{opt}},{\mu}^{\mathit{greedy}})$; // $\phantom{(}$UAVs U as COP variables X,// $\overline{\mu}$ as the COP domains ${D}_{i}$ for all variables,// constraints C forbidding selection of the same trajectory by two UAVs,// ${f}_{\mathit{opt}}$ maximizing the number of sensor tasks covered by the solution μ,// ${\mu}^{\mathit{greedy}}$ as the initial solution, and// returns μ assigning a value from ${D}_{i}$ for each ${X}_{i}$, i.e., trajectories to UAVs$\phantom{(}$return μ; |

`OptaPlanner`(http://www.optaplanner.org/) a popular Constraint Satisfaction and Optimization Solver.

`OptaPlanner`assigns a trajectory with a set of sensors $\langle \mathit{traj},\mathit{eqSensors}\rangle $ to each UAV optimizing the selection by ${f}_{\mathit{opt}}$. Such assignment solves the original MUSP problem. There is only one rule specifying the quality of the solution, i.e., how many sensor tasks are covered by this solution. The rule in form of optimization criterion follows

`OptaPlanner`. Note that the trajectory length is not being optimized by

`OptaPlanner`, only the number of covered tasks. For practical purposes, one of the very convenient features of

`OptaPlanner`is that it is an any-time algorithm and thus it produces better solutions as it is granted more computation time.

Algorithm 4: Creates a set of diverse trajectories. |

Algorithm 5: OptaPlanner rule (in the Drools syntax). |

rule ‘‘CoveredTasks’’when$task : SensorTask()not UavPlan(hasSensor($task.sensor), trajectory.isCovered($task.point))thenscoreHolder.addMediumConstraintMatch(kcontext, −1);end |

## 4. Complexity Analysis

#### 4.1. Pseudo-Optimal Algorithm

#### 4.2. Greedy Algorithm

#### 4.3. DivPlan Algorithm

`OptaPlanner`is an anytime algorithm and thus it is difficult to evaluate its time complexity, moreover there is too many variables to theoretically estimate its performance profile (for experimental evaluations refer to the following experimental section, particularly Figure 7). Nevertheless, we can evaluate the total size of the search space as

## 5. Experiments

#### 5.1. Comparison of the Multi-UAV Sensor Problem Solvers

#### 5.2. Real-World-Inspired Scenario

## 6. Conclusions and Future Work

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

MUSP | Multi-UAV Sensing Problem |

STRIPS | Stanford Research Institute Problem Solver |

TSP | Traveling Salesmen Problem |

KP | Knapsack Problem |

COP | Constraint Optimization Problem |

UAV | Unmanned Aerial Vehicle |

## Appendix A. Translation of MUPS to Planning Problem

- net-benefit selection of goals (selecting the maximal set of goal facts), and
- discretization of the continuous variables (locations, moving and battery charge).

#### Appendix A.1. Objects

- $\mathsf{Pos}$—possible positions of UAVs and sensing targets; each location (in form of its name) $\overline{l}\in L$ is a position, each intermediate interpolation step between two locations is a position as well,
- -
- $\mathsf{Base}$ (Pos subtype)—one of the positions is marked as a base, where the UAVs can equip sensors and where their plans have to begin and end,

- $\mathsf{Uav}$—objects representing the UAVs $u\in U$
- $\mathsf{Slot}$—each UAV has c sensor slots, the objects of type $\mathsf{Slot}$ represent such slots,
- $\mathsf{Type}$—types y of the sensor targets of the tasks defined as $y\in Y$ and
- $\mathsf{Level}$—number ${b}^{\prime}$ of possible levels of the UAV battery, the objects of the type $\mathsf{Level}$ represent particular charge of a UAV’s battery.

#### Appendix A.2. Predicates

- $\mathsf{at}(\mathsf{Uav},\mathsf{Pos})$—in which position a UAV is,
- $\mathsf{slotEmpty}(\mathsf{Uav},\mathsf{Slot})$—whether a slot a of a UAV is not equipped yet,
- $\mathsf{senseType}(\mathsf{Uav},\mathsf{Type})$—whether a UAV is able to sense a sensor type (by equipping appropriate sensor to one of its empty slots) and
- $\mathsf{battery}(\mathsf{Uav},\mathsf{Level})$—current level of the UAV’s battery.

- $\mathsf{batteryDec}(\mathsf{Level},\mathsf{Level})$—relates a battery level to its decremented value by one level (corresponds to depletion of the battery by one move action),
- $\mathsf{batteryEquipDec}(\mathsf{Level},\mathsf{Level})$—relates a battery level to its decremented value by ${p}^{\prime}$ (corresponds to depletion of the battery by equipping one sensor and models shorter reach by heavier UAV) and
- $\mathsf{adj}(\mathsf{Pos},\mathsf{Pos})$ - together with positions describes the movement graph (the move actions are allowed to move only between two adjacent positions).

- $\mathsf{task}(\mathsf{Pos},\mathsf{Type})$

**Example**

**A1.**

#### Operators

#### Appendix A.3. Initial State and Goal Conditions

**Figure A1.**Interpolation of moves between two locations longer than d by intermediate positions ${p}_{i}$. The figure (

**a**) shows additional positions ${p}_{1},\dots ,{p}_{n({\overline{l}}_{f},{\overline{l}}_{t})}$ between two locations ${\overline{l}}_{f},{\overline{l}}_{t}$ based on the distance between them and the distance granularity. The solid arrows denote possible $\mathsf{move}$ actions. Note that the locations ${\overline{l}}_{f},{\overline{l}}_{t}$ are described by $x,y$ coordinates in the MUSP $\mathcal{M}$, therefore the distance between them (denoted by dashed lines) is defined. On the other hand the positions (in the translated problem), which are either location names or interpolated positions are defined only by means of the objects of type $\mathsf{Pos}$; The figure (

**b**) shows interpolation in both directions between two locations ${\overline{l}}_{1},{\overline{l}}_{2}$. The superscripts distinguish direction from ${\overline{l}}_{1}$ to ${\overline{l}}_{2}$ and from ${\overline{l}}_{2}$ to ${\overline{l}}_{1}$.

**Example**

**A2.**

## References

- Villa, T.F.; Gonzalez, F.; Miljievic, B.; Ristovski, Z.D.; Morawska, L. An Overview of Small Unmanned Aerial Vehicles for Air Quality Measurements: Present Applications and Future Prospectives. Sensors
**2016**, 16, 1072. [Google Scholar] [CrossRef] [PubMed] - Norris, G. NOAA plans fleet of 40 UAVs to monitor climate changes. Flight Int.
**2004**, 166, 7. [Google Scholar] - Boccardo, P.; Chiabrando, F.; Dutto, F.; Tonolo, F.G.; Lingua, A. UAV Deployment Exercise for Mapping Purposes: Evaluation of Emergency Response Applications. Sensors
**2015**, 15, 15717–15737. [Google Scholar] [CrossRef] [PubMed] - Casbeer, D.W.; Beard, R.W.; McLain, T.W.; Li, S.M.; Mehra, R.K. Forest fire monitoring with multiple small UAVs. In Proceedings of the American Control Conference, Portland, OR, USA, 8–10 June 2005; pp. 3530–3535.
- Merino, L.; Caballero, F.; Martínez-de Dios, J.R.; Maza, I.; Ollero, A. An Unmanned Aircraft System for Automatic Forest Fire Monitoring and Measurement. J. Intell. Robot. Syst.
**2012**, 65, 533–548. [Google Scholar] [CrossRef] - Bruzzone, A.; Longo, F.; Massei, M.; Nicoletti, L.; Agresta, M.; di Matteo, R.; Maglione, G.L.; Murino, G.; Padovano, A. Disasters and Emergency Management in Chemical and Industrial Plants: Drones Simulation for Education and Training. In Modelling and Simulation for Autonomous Systems; Hodicky, J., Ed.; Springer International Publishing: Cham, Switzerland, 2016; pp. 301–308. [Google Scholar]
- Las Fargeas, J.; Kabamba, P.; Girard, A. Cooperative Surveillance and Pursuit Using Unmanned Aerial Vehicles and Unattended Ground Sensors. Sensors
**2015**, 15, 1365–1388. [Google Scholar] [CrossRef] [PubMed] - Gonzalez, L.F.; Montes, G.A.; Puig, E.; Johnson, S.; Mengersen, K.; Gaston, K.J. Unmanned Aerial Vehicles (UAVs) and Artificial Intelligence Revolutionizing Wildlife Monitoring and Conservation. Sensors
**2016**, 16, 97. [Google Scholar] [CrossRef] [PubMed] - Olivares-Mendez, M.A.; Fu, C.; Ludivig, P.; Bissyandé, T.F.; Kannan, S.; Zurad, M.; Annaiyan, A.; Voos, H.; Campoy, P. Towards an Autonomous Vision-Based Unmanned Aerial System against Wildlife Poachers. Sensors
**2015**, 15, 31362–31391. [Google Scholar] [CrossRef] [PubMed] - Tožička, J.; Šišlák, D.; Pěchouček, M. Diverse Planning for UAV Trajectories. In Agents and Artificial Intelligence; Springer: Berlin/Heidelberg, Germany, 2013; pp. 277–292. [Google Scholar]
- Tožička, J.; Šišlák, D.; Pěchouček, M. Planning of Diverse Trajectories. In Proceedings of the 2013 5th International Conference on Agents and Artificial Intelligence (ICAART), Barcelona, Spain, 15–18 February 2013; Volume 2, pp. 120–129.
- Tožička, J.; Šišlák, D.; Pěchouček, M. Planning of diverse trajectories for UAV control displays. In Proceedings of the International conference on Autonomous Agents and Multi-Agent Systems (AAMAS ’13), Saint Paul, MN, USA, 6–10 May 2013; pp. 1231–1232.
- Tožička, J.; Balata, J.; Mikovec, Z. Diverse trajectory planning for UAV control displays. In Proceedings of the International conference on Autonomous Agents and Multi-Agent Systems (AAMAS ’13), Saint Paul, MN, USA, 6–10 May 2013; pp. 1411–1412.
- Selecký, M.; Štolba, M.; Meiser, T.; Čáp, M.; Komenda, A.; Rollo, M.; Vokřínek, J.; Pěchouček, M. Deployment of Multi-agent Algorithms for Tactical Operations on UAV Hardware. In Proceedings of the 2013 International Conference on Autonomous Agents and Multi-agent Systems (AAMAS ’13), Saint Paul, MN, USA, 6–10 May 2013; pp. 1407–1408.
- Kumar, P.; Morawska, L.; Birmili, W.; Paasonen, P.; Hu, M.; Kulmala, M.; Harrison, R.M.; Norford, L.; Britter, R. Ultrafine particles in cities. Environ. Int.
**2014**, 66, 1–10. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Simpson, I.J.; Colman, J.J.; Swanson, A.L.; Bandy, A.R.; Thornton, D.C.; Blake, D.R.; Rowland, F.S. Aircraft measurements of dimethyl sulfide (DMS) using a whole air sampling technique. J. Atmos. Chem.
**2001**, 39, 191–213. [Google Scholar] [CrossRef] - Chwaleba, A.; Olejnik, A.; Rapacki, T.; Tuśnio, N. Analysis of capability of air pollution monitoring from an unmanned aircraft. Aviation
**2014**, 18, 13–19. [Google Scholar] [CrossRef] - Techy, L.; Schmale, D.G.; Woolsey, C.A. Coordinated aerobiological sampling of a plant pathogen in the lower atmosphere using two autonomous unmanned aerial vehicles. J. Field Robot.
**2010**, 27, 335–343. [Google Scholar] [CrossRef] - Avellar, G.S.C.; Pereira, G.A.S.; Pimenta, L.C.A.; Iscold, P. Multi-UAV Routing for Area Coverage and Remote Sensing with Minimum Time. Sensors
**2015**, 15, 27783–27803. [Google Scholar] [CrossRef] [PubMed] - Smith, K.W. Drone Technology: Benefits, Risks, and Legal Considerations. Seattle J. Environ. Law
**2015**, 5, 12. [Google Scholar] - Cork, L.; Clothier, R.; Gonzalez, L.F.; Walker, R. The Future of UAS: Standards, Regulations, and Operational Experiences [Workshop Report]. IEEE Aerosp. Electron. Syst. Mag.
**2007**, 22, 29–44. [Google Scholar] [CrossRef] [Green Version] - Vansteenwegen, P.; Souffriau, W.; Oudheusden, D.V. The orienteering problem: A survey. Eur. J. Oper. Res.
**2011**, 209, 1–10. [Google Scholar] [CrossRef] [Green Version] - Edelkamp, S.; Kissmann, P.; Torralba, A. BDDs Strike Back (in AI Planning). In Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligenc, Austin, TX, USA, 25–29 January 2015.
- Dechter, R. Constraint Processing; Morgan Kaufmann: San Francisco, CA, USA, 2003. [Google Scholar]
- Lloyd, S. Least squares quantization in PCM. IEEE Trans. Inf. Theory
**1982**, 28, 129–137. [Google Scholar] [CrossRef] - Nau, D.; Ghallab, M.; Traverso, P. Automated Planning: Theory & Practice; Morgan Kaufmann Publishers Inc.: San Francisco, CA, USA, 2004. [Google Scholar]
- Smith, D.E. Choosing Objectives in Over-Subscription Planning. In Proceedings of the Fourteenth International Conference on Automated Planning and Scheduling (ICAPS 2004), Whistler, BC, Canada, 3–7 June 2004; pp. 393–401.
- Bylander, T. The Computational Complexity of Propositional STRIPS Planning. Artif. Intell.
**1994**, 69, 165–204. [Google Scholar] [CrossRef]

**Figure 1.**Example of planning alternative trajectories of two unmanned aerial vehicles (UAVs) for a task of covering a set of waypoints (A–G). Two possible solutions are shown for both UAVs (solid and dashed lines).

**Figure 2.**Time and coverage of solved sensor tasks comparison of all methods. Time of DivPlan is time needed to find final solution (DivPlan was always granted 30 min timeout, but typically the final solution has been found within few seconds). Coverage of DivPlan and greedy is always counted for all the problems while for pseudo-optimal it is only over the solved problems. For size 9, the pseudo-optimal planner solved only approximately one fourth of the problem instances. These instances were solved by DivPlan and greedy algorithms with coverage 1 too.

**Figure 3.**Comparison of DivPlan solution with the optimal solution of “omnipotent UAV” covering the same sensor tasks. We can see that the DivPlan solution was in average at most three times longer even for the longest solutions of scenarios with several dozens of UAVs.

**Figure 4.**Number of created trajectories for different numbers of sensor tasks for UAVs with 3, 4, and 5 sensor slots. The number of trajectories is in log scale.

**Figure 6.**Planned trajectories for 20 UAVs tasked to monitor 3506 locations in Prague. Each location is required to be monitored by 3 different sensors giving 10,518 sensor tasks in total. DivPlan reached coverage of 64%.

**Figure 7.**How the coverage improves over time. Base (time 0) is greedy solution: coverage 57%. The time limit has been set to 10 min, but the best solution with coverage of 64% was found after 8.1 min.

**Table 1.**Decrease of the UAV range of flight based on the number of equipped sensors used in the Real-World-Inspired Scenario.

Number of Equipped Sensors | Range of Flight |
---|---|

1 | 83 km |

2 | 67 km |

3 | 50 km |

4 | 33 km |

5 | 17 km |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Tožička, J.; Komenda, A.
Diverse Planning for UAV Control and Remote Sensing. *Sensors* **2016**, *16*, 2199.
https://doi.org/10.3390/s16122199

**AMA Style**

Tožička J, Komenda A.
Diverse Planning for UAV Control and Remote Sensing. *Sensors*. 2016; 16(12):2199.
https://doi.org/10.3390/s16122199

**Chicago/Turabian Style**

Tožička, Jan, and Antonín Komenda.
2016. "Diverse Planning for UAV Control and Remote Sensing" *Sensors* 16, no. 12: 2199.
https://doi.org/10.3390/s16122199