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

M. H. Shavakh; B. Bidabad

doi:10.3934/naco.2021023

Article Contents

2022, Volume 12, Issue 3: 583-599. Doi: 10.3934/naco.2021023

This issue Previous Article A modified Liu-Storey-Conjugate descent hybrid projection method for convex constrained nonlinear equations and image restoration Next Article Consensus stability analysis for stochastic multi-agent systems with multiplicative measurement noises and Markovian switching topologies

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

M. H. Shavakh^1, and
B. Bidabad^1,2, ,

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

Received: January 31, 2021

Revised: May 31, 2021

Early access: June 2021

Published: September 2022

Abstract Full Text(HTML) Figure(11) / Table(5) Related Papers Cited by

Abstract

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.

Keywords:

Mathematics Subject Classification: Primary: 34H05, 49J15; Secondary: 90C34, 49M37.

Citation:

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Figure 1. The kinematic plan of the UAV in the absence of the wind

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Figure 2. The bank angle schema

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Figure 3. Optimal time control for the first scenario

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Figure 4. Optimal flight-path angle control for the first scenario

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Figure 5. Optimal bank angle control for the first scenario

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Figure 6. Optimal time control for the second scenario

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Figure 7. Optimal flight-path angle control for the second scenario

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Figure 8. Optimal bank angle control for the second scenario

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Figure 9. Optimal time control for $ \rho = 10 $ and $ \varepsilon = 1 $

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Figure 10. Optimal flight-path angle control for $ \rho = 10 $ and $ \varepsilon = 1 $

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Figure 11. Optimal bank angle control for $ \rho = 10 $ and $ \varepsilon = 1 $

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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

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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

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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

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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 $

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Table 5. System specification

System	CPU	RAM	MATLAB version
Windows10(64bit)	Intel(R) Corei(7) 1.8GH	12 GB	9.1.0.441655

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