• Previous Article
    Smoothing approximations for piecewise smooth functions: A probabilistic approach
  • NACO Home
  • This Issue
  • Next Article
    A modified extragradient algorithm for a certain class of split pseudo-monotone variational inequality problem
doi: 10.3934/naco.2021023
Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Online First articles via the “Online First” tab for the selected journal.

Time-optimal of fixed wing UAV aircraft with input and output constraints

1. 

Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Hafez av., Tehran, 15914 Iran

2. 

Institut de Mathematique de Toulouse, (IMT) Université Paul Sabatier, 118, route de Narbonne - F-31062 Toulouse, France

*Corresponding author: B. Bidabad; bidabad@aut.ac.ir; behroz.bidabad@math.univ-toulouse.fr

Received  February 2021 Revised  June 2021 Early access June 2021

The route prediction of unmanned aerial vehicles (UAVs) according to their missions is a strategic issue in the aviation field. In some particular missions, the UAV tasks are to start a movement from a defined point to a target reign in the shortest time. This paper proposes a practical method to find the guidance law of the fixed-wing UAV to achieve time-optimal considering the ambient wind. The unique features of this paper are that the environment includes the moving and fixed obstacles as the route constraints, and the fixed-wing UAVs have to keep a given distance from these obstacles. Also, we consider the specific kinematic equation of the fixed-wing UAV and limitations on the flight-path angle and bank-angles as other constraints. We suggest a method for controlling a fixed-wing UAV to get time-optimal using the re-scaling and parameterization techniques. These techniques are useful and effective in maximizing the performance of the gradient-based methods as a sequential quadratic programming method ($ SQP $) for numerical solutions. Then, all constraints of the time-optimal control problem are converted to a constraint using an exact penalty function. Due to being exact, finding the control variables and switching times is more accurate and faster. Finally, some numerical examples are simulated to explore the effectiveness of our proposed study in reality.

Citation: M. H. Shavakh, B. Bidabad. Time-optimal of fixed wing UAV aircraft with input and output constraints. Numerical Algebra, Control & Optimization, doi: 10.3934/naco.2021023
References:
[1]

T. AlladiV. Chamola and N. Kumar, A two-stage lightweight mutual authentication protocol for UAV surveillance networks, Computer Communications, 160 (2020), 81-90.   Google Scholar

[2]

J. Backer and D. Kirkpatrick, A complete approximation algorithm for shortest bounded-curvature paths, International Symposium on Algorithms and Computation, (2008), 628-643. doi: 10.1007/978-3-540-92182-0_56.  Google Scholar

[3]

S. Bandopadhyay, A. Rastogi and R. Juszczak, Review of Top-of-Canopy Sun-Induced Fluorescence (SIF) studies from ground, UAV, airborne to spaceborne observations, Sensors, 20 (2020), 1144. Google Scholar

[4]

J. BarraquandB. Langlois and J. C. Latombe, Numerical potential field techniques for robot path planning, IEEE Transactions on Systems, Man, and Cybernetics, 22 (1992), 224-241.  doi: 10.1109/21.148426.  Google Scholar

[5]

R. W. BeardJ. Ferrin and J. Humpherys, Fixed wing UAV path following in wind with input constraints, IEEE Transactions on Control Systems Technology, 22 (2014), 2103-2117.   Google Scholar

[6] R. W. Beard and T. W. McLain, Small Unmanned Aircraft, Theory and Practice, Princeton University Press, 2012.   Google Scholar
[7]

J. D. BoissonatA. Cérézo and K. Leblond, Shortest paths of bounded curvature in the plane, Journal of Intelligent and Robotic Systems, 11 (1994), 5-20.   Google Scholar

[8]

A. BrezoescuP. Castillo and R. Lozano, Wind estimation for accurate airplane path following applications, Journal of Intelligent and Robotic Systems, 73 (2014), 823-831.   Google Scholar

[9]

W. L. Chan, C. S. Lee and F. B. Hsiao, Real-time approaches to the estimation of local wind velocity for a fixed-wing unmanned air vehicle, Measurement Science and Technology, 22 (2011), 105203. Google Scholar

[10]

C. M. Cheng, P. H. Hsiao, H. T. Kung and D. Vlah, Maximizing throughput of UAV-relaying networks with the load-carry-and-deliver paradigm, IEEE Wireless Communications and Networking Conference, (2007), 4417-4424. Google Scholar

[11]

H. Chitsaz and S. M. LaValle, Time-optimal paths for a Dubins airplane, 46th IEEE Conference on Decision and Control, (2007), 2379-2384. Google Scholar

[12]

C. Citak, S. Ozgen and G. W. Weber, Mathematical modelling for wave drag optimization and design of high-speed aircrafts, In International Conference on Dynamics, Games and Science, Springer, (2014), 109-132. Google Scholar

[13]

M. CoombesT. FletcherW. H. Chen and C. Liu, Decomposition based mission planning for fixed wing UAVs surveying in wind, Journal of Field Robotics, 37 (2020), 440-465.   Google Scholar

[14]

L. E. Dubins, On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents, American Journal of Mathematics, 79 (1957), 497-516.  doi: 10.2307/2372560.  Google Scholar

[15]

M. FladelandM. SumichB. LobitzR. KolyerD. HerlthR. BertholdD. McKinnonL. MonfortonJ. Brass and G. Bland, The NASA SIERRA science demonstration programme and the role of small medium unmanned aircraft for earth science investigations, Geocarto International, 26 (2011), 157-163.   Google Scholar

[16]

A. Goli and B. Malmir, A covering tour approach for disaster relief locating and routing with fuzzy demand, International Journal of Intelligent Transportation Systems Research, 18 (2020), 140-152.   Google Scholar

[17]

V. M. GonalvesL. C. PimentaC. A. MaiaB. C. Dutra and G. A. Pereira, Vector fields for robot navigation along time-varying curves in $ n $-dimensions, IEEE Transactions on Robotics, 26 (2010), 647-659.   Google Scholar

[18]

Y. GottliebJ. G. Manathara and T. Shima, Multi-target motion planning amidst obstacles for autonomous aerial and ground vehicles, Journal of Intelligent and Robotic Systems, 90 (2018), 515-536.   Google Scholar

[19]

A. GurtnerD. G. GreerR. GlassockL. MejiasR. A. Walker and W. W. Boles, Investigation of fish-eye lenses for small-UAV aerial photography, IEEE Transactions on Geoscience and Remote Sensing, 47 (2009), 709-721.   Google Scholar

[20]

H. Heidari and M. Saska, Collision-free trajectory planning of multi-rotor UAVs in a wind condition based on modified potential field, Mechanism and Machine Theory, 156 (2021), 104140. Google Scholar

[21]

M. Heinkenschloss, Projected sequential quadratic programming methods, SIAM Journal on Optimization, 6 (1996), 373-417.  doi: 10.1137/0806022.  Google Scholar

[22]

E. R. Hunt Jr and C. S. Daughtry, What good are unmanned aircraft systems for agricultural remote sensing and precision agriculture?, International Journal of Remote Sensing, 39 (2018), 5345-5376.   Google Scholar

[23]

H. H. Johnson, An application of the maximum principle to the geometry of plane curves, Proceedings ofthe American Mathematical Society, 44 (1974), 432-435. doi: 10.2307/2040451.  Google Scholar

[24]

L. E. KavrakiP. SvestkaJ. C. Latombe and M. H. Overmars, Probabilistic roadmaps for path planning in high-dimensional configuration spaces, IEEE Transactions on Robotics and Automation, 12 (1996), 566-580.  doi: 10.1007/BFb0036074.  Google Scholar

[25]

Y. KimD. W. Gu and I. Postlethwaite, Real-time path planning with limited information for autonomous unmanned air vehicles, Automatica, 44 (2008), 696-712.  doi: 10.1016/j.automatica.2007.07.023.  Google Scholar

[26]

J. O. Kim and P. Khosla, Real-time obstacle avoidance using harmonic potential functions, IEEE Transactions on Robotics and Automation, 8 (1992), 338-349.   Google Scholar

[27]

J. C. Latombe, Introduction and overview, Robot Motion Planning, (1991), 1-57. Google Scholar

[28]

S. M. LaValle, Rapidly-exploring random trees: A new tool for path planning, Tech. Rep. TR 98-11, Computer Science Dept, Iowa State University, August, 1998. Google Scholar

[29]

H. W. J. LeeK. L. TeoL. S. Jennings and V. Rehbock, Control parametrization enhancing technique for time optimal control problems, Dynamic Systems and Applications, 6 (1997), 243-262.   Google Scholar

[30]

P. Lommel, M. W. McConley and N. Roy, Robust path planning in GPS-denied environments using the Gaussian augmented markov decision process, Navigation, 12 (2006), 1. Google Scholar

[31]

R. C. LoxtonK. L. Teo and V. Rehbock, Optimal control problems with multiple characteristic time points in the objective and constraints, Automatica, 44 (2008), 2923-2929.  doi: 10.1016/j.automatica.2008.04.011.  Google Scholar

[32]

A. MateseP. ToscanoS. F. Di GennaroL. GenesioF. P. VaccariJ. PrimicerioC. BelliA. ZaldeiR. Bianconi and B. Gioli, Intercomparison of UAV, aircraft and satellite remote sensing platforms for precision viticulture, Remote Sensing, 7 (2015), 2971-2990.   Google Scholar

[33]

T. McLainR. W. Beard and M. Owen, Implementing dubins airplane paths on fixed-wing UAVs, Contributed Chapter to the Handbook of Unmanned Aerial Vehicles, 68 (2014), 1677-1701.   Google Scholar

[34]

Z. MengC. Dang and X. Yang, On the smoothing of the square-root exact penalty function for inequality constrained optimization, Computational Optimization and Applications, 35 (2006), 375-398.  doi: 10.1007/s10589-006-8720-6.  Google Scholar

[35]

M. Moshref-JavadiA. Hemmati and M. Winkenbach, A truck and drones model for last-mile delivery: a mathematical model and heuristic approach, Applied Mathematical Modelling, 80 (2020), 290-318.  doi: 10.1016/j.apm.2019.11.020.  Google Scholar

[36]

L. D. Nguyen, K. K. Nguyen, A. Kortun and T. Q. Duong, Real-time deployment and resource allocation for distributed UAV systems in disaster relief, In 2019 IEEE 20th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), (2019), 1-5. Google Scholar

[37]

D. Popescu, F. Stoican, G. Stamatescu, L. Ichim and C. Dragana, Advanced UAVWSN system for intelligent monitoring in precision agriculture, Sensors, 20 (2020), 817. Google Scholar

[38]

A. Puri, A survey of unmanned aerial vehicles (UAV) for traffic surveillance, Department of Computer Science and Engineering, (2005), 1-29. Google Scholar

[39]

A. Puri, UAV for mapping low altitude photogrammetric survey, International Archives of Photogrammetry and Remote Sensing, 37 (2008), 1183-1186.   Google Scholar

[40]

D. S. Shalymov, O. N. Granichin, Z. Volkovich and G. W. Weber, Multi-agent control of airplane wing stability under the flexural torsion flutter, arXiv: 2012.04582. Google Scholar

[41]

M. H. Shavakh and B. Bidabad, The Generalization of zermelo's navigation problem with variable speed and limited acceleration, International Journal of Dynamics and Control, 2021. doi: 10.1007/s40435-021-00826-z.  Google Scholar

[42]

C. Tang, C. Zhu, X. Wei, H. Peng and Y. Wang, Integration of UAV and fog-enabled vehicle: application in post-disaster relief, 2019 IEEE 25th International Conference on Parallel and Distributed Systems (ICPADS), (2019), 548-555. Google Scholar

[43]

A. R. Teel, Global stabilization and restricted tracking for multiple integrators with bounded controls, Systems and Control Letters, 18 (1992), 165-171.  doi: 10.1016/0167-6911(92)90001-9.  Google Scholar

[44]

E. B. Tirkolaee, A. Goli, A. Faridnia, M. Soltani and G. W. Weber, Multi-objective optimization for the reliable pollution-routing problem with cross-dock selection using Pareto-based algorithms, Journal of Cleaner Production, 276 (2020), 122927. Google Scholar

[45]

E. B. Tirkolaee, A. Goli, G. W. Weber and K. Szwedzka, A novel formulation for the sustainable periodic waste collection arc-routing problem: A hybrid multi-objective optimization algorithm, 15th International Congress on Logistics and SCM Systems, (2020), 77-98. Google Scholar

[46]

P. TsiotrasD. Jung and E. Bakolas, Multiresolution Hierarchical path-planning for small UAVs using wavelet decompositions, Journal of Intelligent and Robotic Systems, 66 (2012), 505-522.   Google Scholar

[47]

A. C. WattsV. G. Ambrosia and E. A. Hinkley, Unmanned aircraft systems in remote sensing and scientific research: Classification and considerations of use, Remote Sensing, 4 (2012), 1671-1692.   Google Scholar

[48]

H. Xiang and L. Tian, Method for automatic georeferencing aerial remote sensing (RS) images from an unmanned aerial vehicle (UAV) platform, Biosystems Engineering, 108 (2011), 104-113.   Google Scholar

[49]

Z. XuD. Deng and K. Shimada, Autonomous UAV exploration of dynamic environments via incremental sampling and probabilistic roadmap, IEEE Robotics and Automation Letters, 6 (2021), 2729-2736.   Google Scholar

show all references

References:
[1]

T. AlladiV. Chamola and N. Kumar, A two-stage lightweight mutual authentication protocol for UAV surveillance networks, Computer Communications, 160 (2020), 81-90.   Google Scholar

[2]

J. Backer and D. Kirkpatrick, A complete approximation algorithm for shortest bounded-curvature paths, International Symposium on Algorithms and Computation, (2008), 628-643. doi: 10.1007/978-3-540-92182-0_56.  Google Scholar

[3]

S. Bandopadhyay, A. Rastogi and R. Juszczak, Review of Top-of-Canopy Sun-Induced Fluorescence (SIF) studies from ground, UAV, airborne to spaceborne observations, Sensors, 20 (2020), 1144. Google Scholar

[4]

J. BarraquandB. Langlois and J. C. Latombe, Numerical potential field techniques for robot path planning, IEEE Transactions on Systems, Man, and Cybernetics, 22 (1992), 224-241.  doi: 10.1109/21.148426.  Google Scholar

[5]

R. W. BeardJ. Ferrin and J. Humpherys, Fixed wing UAV path following in wind with input constraints, IEEE Transactions on Control Systems Technology, 22 (2014), 2103-2117.   Google Scholar

[6] R. W. Beard and T. W. McLain, Small Unmanned Aircraft, Theory and Practice, Princeton University Press, 2012.   Google Scholar
[7]

J. D. BoissonatA. Cérézo and K. Leblond, Shortest paths of bounded curvature in the plane, Journal of Intelligent and Robotic Systems, 11 (1994), 5-20.   Google Scholar

[8]

A. BrezoescuP. Castillo and R. Lozano, Wind estimation for accurate airplane path following applications, Journal of Intelligent and Robotic Systems, 73 (2014), 823-831.   Google Scholar

[9]

W. L. Chan, C. S. Lee and F. B. Hsiao, Real-time approaches to the estimation of local wind velocity for a fixed-wing unmanned air vehicle, Measurement Science and Technology, 22 (2011), 105203. Google Scholar

[10]

C. M. Cheng, P. H. Hsiao, H. T. Kung and D. Vlah, Maximizing throughput of UAV-relaying networks with the load-carry-and-deliver paradigm, IEEE Wireless Communications and Networking Conference, (2007), 4417-4424. Google Scholar

[11]

H. Chitsaz and S. M. LaValle, Time-optimal paths for a Dubins airplane, 46th IEEE Conference on Decision and Control, (2007), 2379-2384. Google Scholar

[12]

C. Citak, S. Ozgen and G. W. Weber, Mathematical modelling for wave drag optimization and design of high-speed aircrafts, In International Conference on Dynamics, Games and Science, Springer, (2014), 109-132. Google Scholar

[13]

M. CoombesT. FletcherW. H. Chen and C. Liu, Decomposition based mission planning for fixed wing UAVs surveying in wind, Journal of Field Robotics, 37 (2020), 440-465.   Google Scholar

[14]

L. E. Dubins, On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents, American Journal of Mathematics, 79 (1957), 497-516.  doi: 10.2307/2372560.  Google Scholar

[15]

M. FladelandM. SumichB. LobitzR. KolyerD. HerlthR. BertholdD. McKinnonL. MonfortonJ. Brass and G. Bland, The NASA SIERRA science demonstration programme and the role of small medium unmanned aircraft for earth science investigations, Geocarto International, 26 (2011), 157-163.   Google Scholar

[16]

A. Goli and B. Malmir, A covering tour approach for disaster relief locating and routing with fuzzy demand, International Journal of Intelligent Transportation Systems Research, 18 (2020), 140-152.   Google Scholar

[17]

V. M. GonalvesL. C. PimentaC. A. MaiaB. C. Dutra and G. A. Pereira, Vector fields for robot navigation along time-varying curves in $ n $-dimensions, IEEE Transactions on Robotics, 26 (2010), 647-659.   Google Scholar

[18]

Y. GottliebJ. G. Manathara and T. Shima, Multi-target motion planning amidst obstacles for autonomous aerial and ground vehicles, Journal of Intelligent and Robotic Systems, 90 (2018), 515-536.   Google Scholar

[19]

A. GurtnerD. G. GreerR. GlassockL. MejiasR. A. Walker and W. W. Boles, Investigation of fish-eye lenses for small-UAV aerial photography, IEEE Transactions on Geoscience and Remote Sensing, 47 (2009), 709-721.   Google Scholar

[20]

H. Heidari and M. Saska, Collision-free trajectory planning of multi-rotor UAVs in a wind condition based on modified potential field, Mechanism and Machine Theory, 156 (2021), 104140. Google Scholar

[21]

M. Heinkenschloss, Projected sequential quadratic programming methods, SIAM Journal on Optimization, 6 (1996), 373-417.  doi: 10.1137/0806022.  Google Scholar

[22]

E. R. Hunt Jr and C. S. Daughtry, What good are unmanned aircraft systems for agricultural remote sensing and precision agriculture?, International Journal of Remote Sensing, 39 (2018), 5345-5376.   Google Scholar

[23]

H. H. Johnson, An application of the maximum principle to the geometry of plane curves, Proceedings ofthe American Mathematical Society, 44 (1974), 432-435. doi: 10.2307/2040451.  Google Scholar

[24]

L. E. KavrakiP. SvestkaJ. C. Latombe and M. H. Overmars, Probabilistic roadmaps for path planning in high-dimensional configuration spaces, IEEE Transactions on Robotics and Automation, 12 (1996), 566-580.  doi: 10.1007/BFb0036074.  Google Scholar

[25]

Y. KimD. W. Gu and I. Postlethwaite, Real-time path planning with limited information for autonomous unmanned air vehicles, Automatica, 44 (2008), 696-712.  doi: 10.1016/j.automatica.2007.07.023.  Google Scholar

[26]

J. O. Kim and P. Khosla, Real-time obstacle avoidance using harmonic potential functions, IEEE Transactions on Robotics and Automation, 8 (1992), 338-349.   Google Scholar

[27]

J. C. Latombe, Introduction and overview, Robot Motion Planning, (1991), 1-57. Google Scholar

[28]

S. M. LaValle, Rapidly-exploring random trees: A new tool for path planning, Tech. Rep. TR 98-11, Computer Science Dept, Iowa State University, August, 1998. Google Scholar

[29]

H. W. J. LeeK. L. TeoL. S. Jennings and V. Rehbock, Control parametrization enhancing technique for time optimal control problems, Dynamic Systems and Applications, 6 (1997), 243-262.   Google Scholar

[30]

P. Lommel, M. W. McConley and N. Roy, Robust path planning in GPS-denied environments using the Gaussian augmented markov decision process, Navigation, 12 (2006), 1. Google Scholar

[31]

R. C. LoxtonK. L. Teo and V. Rehbock, Optimal control problems with multiple characteristic time points in the objective and constraints, Automatica, 44 (2008), 2923-2929.  doi: 10.1016/j.automatica.2008.04.011.  Google Scholar

[32]

A. MateseP. ToscanoS. F. Di GennaroL. GenesioF. P. VaccariJ. PrimicerioC. BelliA. ZaldeiR. Bianconi and B. Gioli, Intercomparison of UAV, aircraft and satellite remote sensing platforms for precision viticulture, Remote Sensing, 7 (2015), 2971-2990.   Google Scholar

[33]

T. McLainR. W. Beard and M. Owen, Implementing dubins airplane paths on fixed-wing UAVs, Contributed Chapter to the Handbook of Unmanned Aerial Vehicles, 68 (2014), 1677-1701.   Google Scholar

[34]

Z. MengC. Dang and X. Yang, On the smoothing of the square-root exact penalty function for inequality constrained optimization, Computational Optimization and Applications, 35 (2006), 375-398.  doi: 10.1007/s10589-006-8720-6.  Google Scholar

[35]

M. Moshref-JavadiA. Hemmati and M. Winkenbach, A truck and drones model for last-mile delivery: a mathematical model and heuristic approach, Applied Mathematical Modelling, 80 (2020), 290-318.  doi: 10.1016/j.apm.2019.11.020.  Google Scholar

[36]

L. D. Nguyen, K. K. Nguyen, A. Kortun and T. Q. Duong, Real-time deployment and resource allocation for distributed UAV systems in disaster relief, In 2019 IEEE 20th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), (2019), 1-5. Google Scholar

[37]

D. Popescu, F. Stoican, G. Stamatescu, L. Ichim and C. Dragana, Advanced UAVWSN system for intelligent monitoring in precision agriculture, Sensors, 20 (2020), 817. Google Scholar

[38]

A. Puri, A survey of unmanned aerial vehicles (UAV) for traffic surveillance, Department of Computer Science and Engineering, (2005), 1-29. Google Scholar

[39]

A. Puri, UAV for mapping low altitude photogrammetric survey, International Archives of Photogrammetry and Remote Sensing, 37 (2008), 1183-1186.   Google Scholar

[40]

D. S. Shalymov, O. N. Granichin, Z. Volkovich and G. W. Weber, Multi-agent control of airplane wing stability under the flexural torsion flutter, arXiv: 2012.04582. Google Scholar

[41]

M. H. Shavakh and B. Bidabad, The Generalization of zermelo's navigation problem with variable speed and limited acceleration, International Journal of Dynamics and Control, 2021. doi: 10.1007/s40435-021-00826-z.  Google Scholar

[42]

C. Tang, C. Zhu, X. Wei, H. Peng and Y. Wang, Integration of UAV and fog-enabled vehicle: application in post-disaster relief, 2019 IEEE 25th International Conference on Parallel and Distributed Systems (ICPADS), (2019), 548-555. Google Scholar

[43]

A. R. Teel, Global stabilization and restricted tracking for multiple integrators with bounded controls, Systems and Control Letters, 18 (1992), 165-171.  doi: 10.1016/0167-6911(92)90001-9.  Google Scholar

[44]

E. B. Tirkolaee, A. Goli, A. Faridnia, M. Soltani and G. W. Weber, Multi-objective optimization for the reliable pollution-routing problem with cross-dock selection using Pareto-based algorithms, Journal of Cleaner Production, 276 (2020), 122927. Google Scholar

[45]

E. B. Tirkolaee, A. Goli, G. W. Weber and K. Szwedzka, A novel formulation for the sustainable periodic waste collection arc-routing problem: A hybrid multi-objective optimization algorithm, 15th International Congress on Logistics and SCM Systems, (2020), 77-98. Google Scholar

[46]

P. TsiotrasD. Jung and E. Bakolas, Multiresolution Hierarchical path-planning for small UAVs using wavelet decompositions, Journal of Intelligent and Robotic Systems, 66 (2012), 505-522.   Google Scholar

[47]

A. C. WattsV. G. Ambrosia and E. A. Hinkley, Unmanned aircraft systems in remote sensing and scientific research: Classification and considerations of use, Remote Sensing, 4 (2012), 1671-1692.   Google Scholar

[48]

H. Xiang and L. Tian, Method for automatic georeferencing aerial remote sensing (RS) images from an unmanned aerial vehicle (UAV) platform, Biosystems Engineering, 108 (2011), 104-113.   Google Scholar

[49]

Z. XuD. Deng and K. Shimada, Autonomous UAV exploration of dynamic environments via incremental sampling and probabilistic roadmap, IEEE Robotics and Automation Letters, 6 (2021), 2729-2736.   Google Scholar

Figure 1.  The kinematic plan of the UAV in the absence of the wind
Figure 2.  The bank angle schema
Figure 3.  Optimal time control for the first scenario
Figure 4.  Optimal flight-path angle control for the first scenario
Figure 5.  Optimal bank angle control for the first scenario
Figure 6.  Optimal time control for the second scenario
Figure 7.  Optimal flight-path angle control for the second scenario
Figure 8.  Optimal bank angle control for the second scenario
Figure 9.  Optimal time control for $ \rho = 10 $ and $ \varepsilon = 1 $
Figure 10.  Optimal flight-path angle control for $ \rho = 10 $ and $ \varepsilon = 1 $
Figure 11.  Optimal bank angle control for $ \rho = 10 $ and $ \varepsilon = 1 $
Table 1.  Data of The Second Scenario
Variable Value
Time-optimal 14.7942 $ s $
Average of flight-path angle 0.6011
Average of bank-angle 0.5276
Variable Value
Time-optimal 14.7942 $ s $
Average of flight-path angle 0.6011
Average of bank-angle 0.5276
Table 2.  Data of The Second Scenario for $ \rho = 10 $ and $ \varepsilon = 1 $
Variable Value
Time-optimal 14.4583 $ s $
Average of flight-path angle 0.6001
Average of bank-angle 0.5157
Variable Value
Time-optimal 14.4583 $ s $
Average of flight-path angle 0.6001
Average of bank-angle 0.5157
Table 3.  Data of The Second Scenario for $ \rho = 10 $ and $ \varepsilon = 0.01 $
Variable Value
Time-optimal 14.4254 $ s $
Average of flight-path angle 0.6001
Average of bank-angle 0.5148
Variable Value
Time-optimal 14.4254 $ s $
Average of flight-path angle 0.6001
Average of bank-angle 0.5148
Table 4.  Effects of $ \psi_0 $
$ \psi_0 $ Time-optimal Average of Average of
bank angle flight-path angle
$ 1.0471(60^o) $ $ 14.1934 $ $ 0.5006 $ $ 0.61267 $
$ 1.5707(90^o) $ $ 15.0414 $ $ 0.5564 $ $ 0.6398 $
$ 0(0^o) $ $ 14.9590 $ $ 0.5519 $ $ 0.6353 $
$ -0.5235(-30^o) $ $ 16.2968 $ $ 0.5841 $ $ 0.6984 $
$ -1.0471(-60^o) $ $ 16.7622 $ $ 0.59112 $ $ 0.7003 $
$ \psi_0 $ Time-optimal Average of Average of
bank angle flight-path angle
$ 1.0471(60^o) $ $ 14.1934 $ $ 0.5006 $ $ 0.61267 $
$ 1.5707(90^o) $ $ 15.0414 $ $ 0.5564 $ $ 0.6398 $
$ 0(0^o) $ $ 14.9590 $ $ 0.5519 $ $ 0.6353 $
$ -0.5235(-30^o) $ $ 16.2968 $ $ 0.5841 $ $ 0.6984 $
$ -1.0471(-60^o) $ $ 16.7622 $ $ 0.59112 $ $ 0.7003 $
Table 5.  System specification
System CPU RAM MATLAB version
Windows10(64bit) Intel(R) Corei(7) 1.8GH 12 GB 9.1.0.441655
System CPU RAM MATLAB version
Windows10(64bit) Intel(R) Corei(7) 1.8GH 12 GB 9.1.0.441655
[1]

Changjun Yu, Kok Lay Teo, Liansheng Zhang, Yanqin Bai. A new exact penalty function method for continuous inequality constrained optimization problems. Journal of Industrial & Management Optimization, 2010, 6 (4) : 895-910. doi: 10.3934/jimo.2010.6.895

[2]

Giulia Cavagnari. Regularity results for a time-optimal control problem in the space of probability measures. Mathematical Control & Related Fields, 2017, 7 (2) : 213-233. doi: 10.3934/mcrf.2017007

[3]

Canghua Jiang, Zhiqiang Guo, Xin Li, Hai Wang, Ming Yu. An efficient adjoint computational method based on lifted IRK integrator and exact penalty function for optimal control problems involving continuous inequality constraints. Discrete & Continuous Dynamical Systems - S, 2020, 13 (6) : 1845-1865. doi: 10.3934/dcdss.2020109

[4]

Changjun Yu, Kok Lay Teo, Liansheng Zhang, Yanqin Bai. On a refinement of the convergence analysis for the new exact penalty function method for continuous inequality constrained optimization problem. Journal of Industrial & Management Optimization, 2012, 8 (2) : 485-491. doi: 10.3934/jimo.2012.8.485

[5]

Z.Y. Wu, H.W.J. Lee, F.S. Bai, L.S. Zhang. Quadratic smoothing approximation to $l_1$ exact penalty function in global optimization. Journal of Industrial & Management Optimization, 2005, 1 (4) : 533-547. doi: 10.3934/jimo.2005.1.533

[6]

Piotr Kopacz. A note on time-optimal paths on perturbed spheroid. Journal of Geometric Mechanics, 2018, 10 (2) : 139-172. doi: 10.3934/jgm.2018005

[7]

Cheng Ma, Xun Li, Ka-Fai Cedric Yiu, Yongjian Yang, Liansheng Zhang. On an exact penalty function method for semi-infinite programming problems. Journal of Industrial & Management Optimization, 2012, 8 (3) : 705-726. doi: 10.3934/jimo.2012.8.705

[8]

Ahmet Sahiner, Gulden Kapusuz, Nurullah Yilmaz. A new smoothing approach to exact penalty functions for inequality constrained optimization problems. Numerical Algebra, Control & Optimization, 2016, 6 (2) : 161-173. doi: 10.3934/naco.2016006

[9]

Lijuan Wang, Qishu Yan. Optimal control problem for exact synchronization of parabolic system. Mathematical Control & Related Fields, 2019, 9 (3) : 411-424. doi: 10.3934/mcrf.2019019

[10]

Junyuan Lin, Timothy A. Lucas. A particle swarm optimization model of emergency airplane evacuations with emotion. Networks & Heterogeneous Media, 2015, 10 (3) : 631-646. doi: 10.3934/nhm.2015.10.631

[11]

Nguyen Huy Chieu, Jen-Chih Yao. Subgradients of the optimal value function in a parametric discrete optimal control problem. Journal of Industrial & Management Optimization, 2010, 6 (2) : 401-410. doi: 10.3934/jimo.2010.6.401

[12]

Enkhbat Rentsen, J. Zhou, K. L. Teo. A global optimization approach to fractional optimal control. Journal of Industrial & Management Optimization, 2016, 12 (1) : 73-82. doi: 10.3934/jimo.2016.12.73

[13]

Changjun Yu, Shuxuan Su, Yanqin Bai. On the optimal control problems with characteristic time control constraints. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021021

[14]

Regina S. Burachik, C. Yalçın Kaya. An update rule and a convergence result for a penalty function method. Journal of Industrial & Management Optimization, 2007, 3 (2) : 381-398. doi: 10.3934/jimo.2007.3.381

[15]

Yibing Lv, Zhongping Wan. Linear bilevel multiobjective optimization problem: Penalty approach. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1213-1223. doi: 10.3934/jimo.2018092

[16]

Zhongwen Chen, Songqiang Qiu, Yujie Jiao. A penalty-free method for equality constrained optimization. Journal of Industrial & Management Optimization, 2013, 9 (2) : 391-409. doi: 10.3934/jimo.2013.9.391

[17]

Piermarco Cannarsa, Cristina Pignotti, Carlo Sinestrari. Semiconcavity for optimal control problems with exit time. Discrete & Continuous Dynamical Systems, 2000, 6 (4) : 975-997. doi: 10.3934/dcds.2000.6.975

[18]

Jérome Lohéac, Jean-François Scheid. Time optimal control for a nonholonomic system with state constraint. Mathematical Control & Related Fields, 2013, 3 (2) : 185-208. doi: 10.3934/mcrf.2013.3.185

[19]

Piermarco Cannarsa, Carlo Sinestrari. On a class of nonlinear time optimal control problems. Discrete & Continuous Dynamical Systems, 1995, 1 (2) : 285-300. doi: 10.3934/dcds.1995.1.285

[20]

Shaojun Lan, Yinghui Tang, Miaomiao Yu. System capacity optimization design and optimal threshold $N^{*}$ for a $GEO/G/1$ discrete-time queue with single server vacation and under the control of Min($N, V$)-policy. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1435-1464. doi: 10.3934/jimo.2016.12.1435

 Impact Factor: 

Metrics

  • PDF downloads (90)
  • HTML views (191)
  • Cited by (0)

Other articles
by authors

[Back to Top]