Abstract
Accurate real-time information about an ongoing wildfire event is important for realizing effective and safe wildfire fighting. This paper is intended to solve the problem of guiding Unmanned Air Vehicles (UAVs) equipped with onboard cameras to monitor dynamic wildfire boundaries. According to whether the prior knowledge of the wildfire boundary is available or not, we propose a model-based vector field and a model-free vector field for UAV guidance. By describing the wildfire boundary with a zero level set function, the propagation of the wildfire boundary is modeled with the Hamilton-Jacobi equation. If the prior knowledge of the boundary is available, the typical radial basis function thin-plate spline is adopted to approximate the wildfire boundary and predicts its propagation. Then a 3D analytical vector field is constructed for an implicit function representing the wildfire boundary. If only partial observation of the wildfire boundary within the UAV’s field of view is available, the horizontal error between the UAV and its sensed segment of wildfire boundary and the vertical error between the UAV and the desired altitude are utilized to construct a 3D distance error based vector field, directly. To guide the UAV to converge to and patrol along the advancing wildfire boundary, the complex nonlinear dynamics of the UAV is exploited with differential flatness and incorporated with the above mentioned vector fields to design a nonlinear geometric controller. Computer simulations have been conducted to evaluate the performance of the proposed 3D vector field based controllers with both synthetic and real data, and simulation results demonstrate that the proposed algorithms can be effective methods to monitor the advancing wildfire boundaries.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Adams, M.A., Shadmanroodposhti, M., Neumann, M.: Causes and consequences of eastern australia’s 2019–20 season of mega-fires: a broader perspective. Global Change Bio. 26(7), 3756–3758 (2020)
Lizundia-Loiola, J., Lucrecia Pettinari, M., Chuvieco, E.: Temporal anomalies in burned area trends: satellite estimations of the amazonian 2019 fire crisis. Remote Sens. 12(1), 151 (2020)
Adámek, M., Jankovská, Z., Hadincová, V., Kula, E., Wild, J.: Drivers of forest fire occurrence in the cultural landscape of central europe. Landsc. Ecol. 33(11), 2031–2045 (2018)
Dios, J.R.M.-D., Arrue, B.C., Ollero, A., Merino, L., Gómez-Rodríguez, F.: Computer vision techniques for forest fire perception. Image Vis. Comput. 26(4), 550–562 (2008)
Feng, L., Katupitiya, J.: Accurate detection of occluded wildfire boundary. Fire Technol. 58 (3), 1789–1813 (2022)
Stanton, N.A., Chambers, P.R.G., Piggott, J.: Situational awareness and safety. Safety Sci. 39(3), 189–204 (2001)
Yuan, C., Zhang, Y., Liu, Z.: A survey on technologies for automatic forest fire monitoring, detection, and fighting using unmanned aerial vehicles and remote sensing techniques. Can. J. Forest Res. 45(7), 783–792 (2015)
Twidwell, D., Allen, C.R., Detweiler, C., Higgins, J., Laney, C., Elbaum, S.: Smokey comes of age: unmanned aerial systems for fire management. Front. Ecol. Environ. 14(6), 333–339 (2016)
Bailon-Ruiz, R., Lacroix, S.: Wildfire remote sensing with uavs: a review from the autonomy point of view. In: 2020 International conference on unmanned aircraft systems (ICUAS), pp. 412–420. IEEE (2020)
Bertozzi, A.L., Kemp, M., Marthaler, D.: Determining environmental boundaries: asynchronous communication and physical scales. In: Cooperative control, pp. 25–42. Springer (2005)
Susca, S., Bullo, F., Martinez, S.: Monitoring environmental boundaries with a robotic sensor network. IEEE Trans. Control Syst. Technol. 16(2), 288–296 (2008)
Cassandras, C.G., Ding, X.C., Lin, X.: An optimal control approach for the persistent monitoring problem. In: 2011 50th IEEE conference on decision and control and european control conference, pp. 2907–2912. IEEE (2011)
Lan, X., Schwager, M.: Planning periodic persistent monitoring trajectories for sensing robots in gaussian random fields. In: 2013 IEEE international conference on robotics and automation, pp. 2415–2420. IEEE (2013)
Smith, R.N., Schwager, M., Smith, S.L., Jones, B.H., Rus, D., Sukhatme, G.S.: Persistent ocean monitoring with underwater gliders: adapting sampling resolution. J. Field Robot. 28(5), 714–741 (2011)
Smith, S.L., Rus, D.: Multi-robot monitoring in dynamic environments with guaranteed currency of observations. In: 49th IEEE conference on decision and control (CDC), pp. 514–521. IEEE (2010)
Richards, G.D.: An elliptical growth model of forest fire fronts and its numerical solution. Int. J. Numeric. Methods Eng. 30(6), 1163–1179 (1990)
Balažovjech, M., Mikula, K.: A higher order scheme for a tangentially stabilized plane curve shortening flow with a driving force. SIAM J. Sci. Comput. 33(5), 2277–2294 (2011)
Dziuk, G.: Discrete anisotropic curve shortening flow. SIAM J. Numer. Anal. 36(6), 1808–1830 (1999)
Hou, T.Y., Lowengrub, J.S., Shelley, M.J.: Removing the stiffness from interfacial flows with surface tension. J. Comput. Phys. 114(2), 312–338 (1994)
Ambroz, M., Balažovjech, M., Medl’a, M., Mikula, K.: Numerical modeling of wildland surface fire propagation by evolving surface curves. Adv. Comput. Math. 45(2), 1067–1103 (2019)
Osher, S., Fedkiw, R.: Level set methods and dynamic implicit surfaces, vol. 153. Springer Science & Business Media (2006)
Sethian, J.A.: Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science, vol. 3. Cambridge University Press (1999)
Kumar, M., Cohen, K., HomChaudhuri, B.: Cooperative control of multiple uninhabited aerial vehicles for monitoring and fighting wildfires. J. Aerospace Comput. Inf. Commun. 8(1), 1–16 (2011)
Osher, S., speed, J.A.S.: Fronts propagating with curvature-dependent: algorithms based on hamilton-jacobi formulations. J. Comput. Phys. 79(1), 12–49 (1988)
Sharma, B.R., Narasimha, K.S.V., Ramakrishnan, S., Kumar, M.: Distributed cyclic motion control of multiple uavs for wildfire monitoring. In: Dynamic systems and control conference, vol. 44182, pp. 401–407 (2010)
Sharma, B.R., Ramakrishnan, S., Kumar, M.: Perimeter tracking by multiple uavs based on a cyclic-pursuit algorithm. In: AIAA Infotech@ Aerospace (I@ A) Conference, p. 4663 (2013)
Pham, H.X., La, H.M., Feil-Seifer, D., Deans, M.: A distributed control framework for a team of unmanned aerial vehicles for dynamic wildfire tracking. In: 2017 IEEE/RSJ international conference on intelligent robots and systems (IROS), pp. 6648–6653. IEEE (2017)
Matveev, A.S., Teimoori, H., Savkin, A.V.: Method for tracking of environmental level sets by a unicycle-like vehicle. Automatica 48(9), 2252–2261 (2012)
Malisoff, M., Sizemore, R., Zhang, F.: Adaptive planar curve tracking control and robustness analysis under state constraints and unknown curvature. Automatica 75, 133–143 (2017)
Dong, F., You, K., Wang, J.: Coordinate-free isoline tracking in unknown 2-d scalar fields. In: 2020 IEEE/RSJ international conference on intelligent robots and systems (IROS), pp. 2496–2501. IEEE (2020)
Jin, Z., Bertozzi, A.L.: Environmental boundary tracking and estimation using multiple autonomous vehicles. In: 2007 46th IEEE conference on decision and control, pp. 4918–4923. IEEE (2007)
Li, S., Yi, G., Bingham, B.: Multi-robot cooperative control for monitoring and tracking dynamic plumes. In: 2014 IEEE International Conference on Robotics and Automation (ICRA), pp. 67–73. IEEE (2014)
Fahad, M., Saul, N., Yi, G., Bingham, B.: Robotic simulation of dynamic plume tracking by unmanned surface vessels. In: 2015 IEEE international conference on robotics and automation (ICRA), pp. 2654–2659. IEEE (2015)
Jiang, X., Li, S.: Plume front tracking in unknown environments by estimation and control. IEEE Trans. Industr. Inf. 15(2), 911–921 (2018)
Wang, J.-W., Yi, G., Fahad, M., Bingham, B.: Dynamic plume tracking by cooperative robots. IEEE/ASME Trans. Mechatronics 24(2), 609–620 (2019)
Menon, P.P., Edwards, C., Shtessel, Y.B., Ghose, D., Haywood, J.: Boundary tracking using a suboptimal sliding mode algorithm. In: 53rd IEEE conference on decision and control, pp. 5518–5523. IEEE, (2014)
Dong, F., You, K.: The isoline tracking in unknown scalar fields with concentration feedback. Automatica p. 109779 (2021)
Sujit, P.B., Saripalli, S., Sousa, J.B.: Unmanned aerial vehicle path following: a survey and analysis of algorithms for fixed-wing unmanned aerial vehicless. IEEE Control. Syst. Mag. 34(1), 42–59 (2014)
Wilhelm, J.P., Clem, G.: Vector field uav guidance for path following and obstacle avoidance with minimal deviation. J. Guid. Cont. Dynamics 42(8), 1848–1856 (2019)
Goncalves, V.M., Pimenta, L.C.A., Maia, C.A., Dutra, B.C.O., Pereira, G.A.S.: Vector fields for robot navigation along time-varying curves in n-dimensions. IEEE Trans. Robot. 26(4), 647–659 (2010)
Kapitanyuk, Y.A., Proskurnikov, A.V., Cao, M.: A guiding vector-field algorithm for path-following control of nonholonomic mobile robots. IEEE Trans. Control Syst. Technol. 26(4), 1372–1385 (2017)
Marthaler, D., Bertozzi, A.L.: Collective motion algorithms for determining environmental boundaries. In: In SIAM conference on applications of dynamical systems. Citeseer (2003)
Triandaf, I., Schwartz, I.B.: A collective motion algorithm for tracking time-dependent boundaries. Math. Comput. Simul. 70(4), 187–202 (2005)
Lim, S., Jung, W., Bang, H.: Vector field guidance for path following and arrival angle control. In: 2014 International Conference on Unmanned Aircraft Systems (ICUAS), pp. 329–338. IEEE (2014)
Nelson, D.R., Blake Barber, D., McLain, T.W., Beard, R.W.: Vector field path following for miniature air vehicles. IEEE Trans. Robot. 23(3), 519–529 (2007)
Goncalves, V.M., Pimenta, L.C.A., Maia, C.A., Pereira, G.A.S.: Artificial vector fields for robot convergence and circulation of time-varying curves in n-dimensional spaces. In: 2009 American control conference, pp. 2012–2017. IEEE (2009)
Marina, H.G.D., Kapitanyuk, Y.A., Bronz, M., Hattenberger, G., Cao, M.: Guidance algorithm for smooth trajectory tracking of a fixed wing uav flying in wind flows. In: 2017 IEEE international conference on robotics and automation (ICRA), pp. 5740–5745. IEEE (2017)
Fossen, T.I.: Guidance and Control of Ocean Vehicles. Wiley, University of Trondheim, Norway, Chichester, England, ISBN: 0471941131 Doctors thesis (1999)
Tsourdos, A., White, B., Shanmugavel, M.: Cooperative path planning of unmanned aerial vehicles, vol. 32. Wiley (2010)
Beard, R.W., McLain, T.W.: Small unmanned aircraft. Princeton University Press (2012)
Zhou, D., Schwager, M.: Vector field following for quadrotors using differential flatness. In: 2014 IEEE international conference on robotics and automation (ICRA), pp. 6567–6572. IEEE (2014)
Goodarzi, F., Lee, D., Lee, T.: Geometric nonlinear pid control of a quadrotor uav on SE(3). In: 2013 European control conference (ECC), pp. 3845–3850. IEEE (2013)
Alaimo, A., Artale, V., Milazzo, C., Ricciardello, A., Trefiletti, L.: Mathematical modeling and control of a hexacopter. In: 2013 International conference on unmanned aircraft systems (ICUAS), pp. 1043–1050. IEEE (2013)
Lee, T., Leok, M., McClamroch, N.H.: Geometric tracking control of a quadrotor uav on SE (3). In: 49th IEEE conference on decision and control (CDC), pp. 5420–5425. IEEE (2010)
Mallet, V., Keyes, D.E., Fendell, F.E.: Modeling wildland fire propagation with level set methods. Comput. Math. Appl. 57(7), 1089–1101 (2009)
Alessandri, A., Bagnerini, P., Gaggero, M., Mantelli, L.: Parameter estimation of fire propagation models using level set methods. Appl. Math. Model. 92, 731–747 (2021)
Peng, D., Merriman, B., Osher, S., Zhao, H., Kang, M.: A pde-based fast local level set method. J. Comput. Phys. 155(2), 410–438 (1999)
Wei, P., Li, Z., Li, X., Wang, M.Y.: An 88-line matlab code for the parameterized level set method based topology optimization using radial basis functions. Struct. Multidiscip. Optim. 58(2), 831–849 (2018)
Kapitanyuk, A.Y., Chepinsky, S.A.: Control of mobile robot following a piecewise-smooth path. Gyroscopy Navigation 4(4), 198–203 (2013)
Michel, A.N., Hou, L., Liu, D.: Stability of dynamical systems. Springer (2008)
Nieuwstadt, M.J.V., Murray, R.M.: Real-time trajectory generation for differentially flat systems. Int. J. Robust Nonlinear Control: IFAC-Affil. J. 8(11), 995–1020 (1998)
Mellinger, D., Kumar, V.: Minimum snap trajectory generation and Control for quadrotors. In: 2011 IEEE international conference on robotics and automation, pp. 2520–2525. IEEE (2011)
Funding
Open Access funding enabled and organized by CAUL and its Member Institutions. The authors did not receive support from any organization for the submitted work.
Author information
Authors and Affiliations
Contributions
Licheng Feng contributes to the algorithm design, simulation and paper writing. Jay Katupitiya contributes to the simulation and paper writing.
Corresponding author
Ethics declarations
Ethics Approval
Research does not involve Human Participants and/or Animals
Consent for Publication
Yes
Consent to Participate
Yes
Conflict of Interests
The authors declare no conflicts of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Feng, L., Katupitiya, J. Vector Field based Control of Quadrotor UAVs for Wildfire Boundary Monitoring. J Intell Robot Syst 106, 27 (2022). https://doi.org/10.1007/s10846-022-01731-z
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10846-022-01731-z