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

• 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.

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

 Citation: • • 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

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

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

Table 4.  Effects of $\psi_0$

 $\psi_0$ Time-optimal Average of Average of bank angle flight-path angle $1.0471(60^o)$ $14.1934$ $0.5006$ $0.61267$ $1.5707(90^o)$ $15.0414$ $0.5564$ $0.6398$ $0(0^o)$ $14.9590$ $0.5519$ $0.6353$ $-0.5235(-30^o)$ $16.2968$ $0.5841$ $0.6984$ $-1.0471(-60^o)$ $16.7622$ $0.59112$ $0.7003$

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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