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Aerospace Systems

, Volume 1, Issue 2, pp 73–80 | Cite as

Research on route planning based on performance constraints for UAS in battlefield

  • Bowen LiuEmail author
Review
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Abstract

The application area and the scope of tasks of unmanned aerial system (UAS) are becoming increasingly wider, while the complexity and danger of the working environment are also increasing. When implemented in modern battlefields or complicated circumstances, various dangers which UAS is confronted with would prevent UAS from continuing its mission smoothly. An increase in failure rate is usually inevitable alongside with the perfection of UAS’s performance. In this paper, a modified modeling method for UAS is proposed to solve route planning problems in battlefields or complicated circumstances, and an improved modeling method of performance constraints is established based on analysis of UAS’s physical constraints. And based on the aforesaid research, new design of UAS’s each flight segment is proposed to meet the requirements for different missions. The simulation results show that such design makes the UAS capable to continue its mission.

Keywords

Unmanned aerial system Route planning Simulation model Performance constraints 

1 Introduction

With the development of information technology and intelligent control technology, the modern battlefield is characterized by information, intelligence and unmanned. The application area and the scope of tasks of unmanned aerial system (UAS) are becoming increasingly wider, while the complexity and danger of the working environment are also increasing. When implemented in a dangerous environment, various dangers which UAS is confronted with would prevent UAS from continuing its mission smoothly.

An increase in failure rate is usually inevitable alongside with the perfection of UAS’s performance. At present, unmanned combat aerial vehicle with command of the air (UCAV-CA) and high-altitude long-endurance UAV have become the focus of the aviation industry. These aircrafts use the fly-by-wire flight control systems, which are highly complex and costly. During UAS’s mission, there will be some unexpected situations, such as aircraft fault, enemy attack, and mission information changes. It may cause huge losses if the aircraft malfunctioned or is damaged and fails to take timely measures. The route needs to be re-planned in order to make UAS complete the task.

Research on aircraft fault-tolerant control methods has been carried out in China since the 1980s [1]. Deng Jianhua and Liu Xiaoxiong from Northwestern Polytechnical University carried out the design of robust flight control system based on direct adaptive control, fault-tolerant control algorithm based on multi-model adaptive control, and research on flight control system reconstruction method based on adaptive neural network. Chen Zongji and Zhang Pingren from Beijing University of Aeronautics and Astronautics carried out research on self-repairing flight control system based on quantitative feedback theory, research on flight control law reconstruction technology based on pseudo-inverse method, and hybrid fault-tolerant control technology combined with active fault tolerance and passive fault-tolerant control [2].

The insufficient research on the route planning problem of faulted UAS has not been given a specific solution, especially the route planning of UAS after asymmetric damage [3]. In the previous research, the threat avoidance problem was often paid more attention and the consideration of UAS’s physical performance and the limitation of the guiding system were ignored [4, 5]. Therefore, it is necessary to conduct more in-depth research and discussion in this regard.

2 UAV model

When UAV is damaged in the mission, the UAV’s center of mass will change. This section uses Newton’s Laws to develop the general equations of motion referenced to an arbitrary point on the rigid body. With these equations, it is possible to get the motion model of UAV after encountering the damage [6].

Let the xyz reference frame be the reference frame at any point P on the rigid body and the XYZ reference frame be the inertial reference frame at point O.

According to the Newton’s laws of motion, the equation of rigid body shows as follows:
$$ \sum F = \sum {m_{i} (\ddot{\vec{r}}_{i} )}_{XYZ} = m(\ddot{\vec{r}})_{XYZ} , $$
(1)
where \( \vec{r}_{i} \) is the vector from point O to \( m_{i} \), and \( m_{i} \) denote the mass of a particle on the rigid body. Let \( \vec{\rho }_{i} \) denote the vector from point P to \( m_{i} \) and \( \vec{r}_{P} \) denote the vector from point O to P. So we can get the equation as:
$$ \vec{r}_{i} = \vec{\rho }_{i} + \vec{r}_{P} . $$
(2)
Then, we take the second derivative of (2) with respect to XYZ reference frame, so (2) becomes
$$ \begin{aligned} (\ddot{\vec{r}}_{i} )_{XYZ} & = \dot{\vec{v}}_{P} + \omega \times \vec{v}_{P} + \ddot{\vec{\rho }}_{i} + \dot{\omega } \times \vec{\rho }_{i} \\ & \quad + 2 \cdot \left( {\omega \times \dot{\vec{\rho }}_{i} } \right) + \omega \times \left( {\omega \times \vec{\rho }_{i} } \right), \\ \end{aligned} $$
(3)
where \( \vec{v}_{p} \) stands for \( \left( {\dot{\vec{r}}_{p} } \right)_{XYZ} \) in xyz reference frame and \( \omega \) denotes angular rate of the rigid body in the XYZ reference frame.
Therefore, \( \sum F \) can be expressed by
$$ \begin{aligned} \sum F & = \sum {m_{i} \left( \begin{aligned} \dot{\vec{v}}_{p} + \omega \times \vec{v}_{p} + \ddot{\vec{\rho }}_{i} + \dot{\omega } \times \vec{\rho }_{i} \hfill \\ + 2 \cdot \left( {\omega \times \dot{\vec{\rho }}_{i} } \right) + \omega \times \left( {\omega \times \vec{\rho }_{i} } \right) \hfill \\ \end{aligned} \right)} \\ \sum F \, & = m\left( {\dot{\vec{v}}_{p} + \omega \times \vec{v}_{p} } \right) + m\ddot{\bar{\rho }} + 2 \cdot \left( {\omega \times m\dot{\bar{\rho }}} \right) \\ & \quad + \, \dot{\omega } \times m\bar{\rho } + \omega \times \left( {\omega \times m\bar{\rho }} \right). \\ \end{aligned} $$
(4)
Because the UAV is rigid. \( \ddot{\bar{\rho }} = \dot{\bar{\rho }} = 0 \), and (4) becomes
$$ \begin{aligned} \sum F & = m\left( {\dot{\vec{v}}_{p} + \omega \times \vec{v}_{p} } \right) + \dot{\omega } \times m\bar{\rho } \\ & \quad + \omega \times \left( {\omega \times m\bar{\rho }} \right). \\ \end{aligned} $$
(5)
Here, we can get UAV’s force equation as:
$$ \begin{aligned} \sum {F_{X} } & = m\left( \begin{aligned} \dot{U}_{p} + QW_{p} - RV_{p} - \left( {Q^{2} + R^{2} } \right)\Delta x \hfill \\ + \left( {QP - \dot{R}} \right)\Delta y + \left( {RP + \dot{Q}} \right)\Delta z + g\sin \theta \hfill \\ \end{aligned} \right) \\ \sum {F_{Y} } & = m\left( \begin{aligned} \dot{V}_{p} + RU_{p} - PW_{p} + \left( {PQ + \dot{R}} \right)\Delta x \hfill \\ - \left( {P^{2} + R^{2} } \right)\Delta y + \left( {QR - \dot{P}} \right)\Delta z - g\cos \theta \sin \phi \hfill \\ \end{aligned} \right) \\ \sum {F_{Z} } & = m\left( \begin{aligned} \dot{W}_{p} + PV_{p} - QU_{p} + \left( {PR - \dot{Q}} \right)\Delta x \hfill \\ + \left( {QR + \dot{P}} \right)\Delta y - \left( {P^{2} + Q^{2} } \right)\Delta z - g\cos \theta \cos \phi \hfill \\ \end{aligned} \right), \\ \end{aligned} $$
(6)
where the angular velocity \( \omega = P{\mathbf{i}} + Q{\mathbf{j}} + R{\mathbf{k}} \), position of the center of mass \( \vec{\rho } = \Delta x{\mathbf{i}} + \Delta y{\mathbf{j}} + \Delta z{\mathbf{k}} \), and the velocity at point P \( \vec{v}_{p} = U_{p} {\mathbf{i}} + V_{p} {\mathbf{j}} + W_{p} {\mathbf{k}} \) in the xyz reference frame.
Then, we will consider the moment equation of UAV. Let \( \vec{v}_{i} \) denote the velocity at point \( m_{i} \) in the XYZ reference frame. The absolute angular momentum of the rigid body with respect to point P can be expressed by (7), and the first derivative of (7) is (8).
$$ H_{P} = \sum {\left( {\rho_{i} \times m_{i} \vec{v}_{i} } \right)} , $$
(7)
$$ \begin{aligned}&\left( {\dot{H}_{p} } \right)_{XYZ} = \sum {\left( {\left( {\dot{\vec{\rho }}_{i} } \right)_{XYZ} \times m_{i} \vec{v}_{i} } \right)} \nonumber \\ &\quad + {\sum {\left( {\vec{\rho }_{i} \times m_{i} \left( {\dot{\vec{v}}_{i} } \right)_{XYZ} } \right)} } .\end{aligned} $$
(8)
Consider the momentum about point P, and it has \( \sum {M_{p} } = \sum {\left( {\rho_{i} \times m_{i} \left( {\ddot{r}_{i} } \right)_{XYZ} } \right)} \), so that (8) can be described by
$$ \sum {M_{p} } = \left( {\dot{H}_{p} } \right)_{XYZ} + \left( {\dot{\vec{r}}_{p} } \right)_{XYZ} \times \sum {m_{i} \vec{v}_{i} } . $$
(9)
Using a method similar to that of the moment equation, we can describe (9) with respect to point P in the xyz reference frame as:
$$ \begin{aligned} \sum {M_{p} } & = \omega \times I\omega + I\dot{\omega } + m\bar{\rho } \times \dot{\vec{v}}_{p} + m\omega \\ & \quad \times \left( {\bar{\rho } \times v_{p} } \right) + m\vec{v}_{p} \times \left( {\omega \times \bar{\rho }} \right) - m\bar{\rho } \times g. \\ \end{aligned} $$
(10)
Decompose the above equation on the xyz axles, (10) expands to
$$ \begin{aligned} \sum {M_{{p_{x} }} } & = I_{xx} \dot{P} - I_{xy} \dot{Q} - I_{xz} \dot{R} + I_{xy} PR - I_{xz} PQ \\ & \quad + \left( {I_{zz} - I_{yy} } \right)QR + \left( {R^{2} - Q^{2} } \right)I_{yz} \\ & \quad + m\left( \begin{aligned} \left( {PV_{p} - QU_{p} + \dot{W}_{p} - g\cos \theta \cos \phi } \right)\Delta y \hfill \\ \left( { + PW_{p} - RU_{p} - \dot{V}_{p} + g\cos \theta \sin \phi } \right)\Delta z \hfill \\ \end{aligned} \right) \\ \sum {M_{{p_{y} }} } & = - I_{xy} \dot{P} + I_{yy} \dot{Q} - I_{yz} \dot{R} + I_{yz} PQ - I_{xy} QR \\ & \quad + \left( {I_{xx} - I_{zz} } \right)PR + \left( {P^{2} - R^{2} } \right)I_{xz} \\ & \quad + m\left( \begin{aligned} \left( {QU_{p} - PV_{p} - \dot{W}_{p} + g\cos \theta \cos \phi } \right)\Delta x \hfill \\ \left( { + QW_{p} - RV_{p} - \dot{U}_{p} + g\sin \theta } \right)\Delta z \hfill \\ \end{aligned} \right) \\ \sum {M_{{p_{z} }} } & = - I_{xz} \dot{P} - I_{yz} \dot{Q} + I_{zz} \dot{R} + I_{xz} QR - I_{yz} PR \\ & \quad + \left( {I_{yy} - I_{xx} } \right)PQ + \left( {Q^{2} - P^{2} } \right)I_{xy} \\ & \quad + m\left( \begin{aligned} \left( {RU_{p} - PW_{p} + \dot{V}_{p} - g\cos \theta \cos \phi } \right)\Delta x \hfill \\ \left( { + RV_{p} - QW_{p} - \dot{U}_{p} - g\sin \theta } \right)\Delta y \hfill \\ \end{aligned} \right). \\ \end{aligned} $$
(11)
Combining (6) and (11), it gives the equation of motion for UAV after the change of center of mass. We can rewrite it in matrix notation as:
$$\left[ {\begin{array}{*{20}c} {\dot{V}_{p} } \\ {\dot{\omega }} \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {mI_{3} } & { - D_{x} } \\ {D_{x} } & I \\ \end{array} } \right]^{ - 1} \left[ \begin{aligned} \left[ {\begin{array}{*{20}c} {\sum F } \\ {\sum {M_{p} } } \\ \end{array} } \right] - \hfill \\ \left[ {\begin{array}{*{20}c} {m\varOmega_{x} } & { - \varOmega_{x} D_{x} } \\ {\varOmega_{x} D_{x} } & {\varOmega_{x} I - V_{x} D_{x} } \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {V_{p} } \\ \omega \\ \end{array} } \right] \hfill \\ \end{aligned} \right],$$
(12)
where \( D_{x} = \left[ {\begin{array}{*{20}c} 0 & { - m\Delta z} & {m\Delta y} \\ {m\Delta z} & 0 & { - m\Delta z} \\ { - m\Delta y} & {m\Delta z} & 0 \\ \end{array} } \right] \) stands for the offset matrix of center of mass,\( \varOmega_{x} = \left[ {\begin{array}{*{20}c} 0 & { - R} & Q \\ R & 0 & { - P} \\ { - Q} & P & 0 \\ \end{array} } \right] \) stands for the matrix of angular velocity,\( V_{x} = \left[ {\begin{array}{*{20}c} 0 & { - W_{A} } & {V_{A} } \\ {W_{A} } & 0 & { - U_{A} } \\ { - V_{A} } & {U_{A} } & 0 \\ \end{array} } \right] \) stands for the matrix of velocity,\( I = \left[ {\begin{array}{*{20}c} {I_{xx} } & { - I_{xy} } & { - I_{xz} } \\ { - I_{xy} } & {I_{yy} } & { - I_{yz} } \\ { - I_{xz} } & { - I_{yz} } & {I_{zz} } \\ \end{array} } \right] \) stands for the matrix of moment inertia.

3 Performance constraints

In this section, we study the performance constraints of UAV. The aircraft cannot maintain its state if the designed route does not meet the aircraft’s physical performance constraints.

3.1 Longitudinal performance evaluation

Consider the force analysis in Fig. 1. Let T denote thrust in axis \( O_{b} x_{b} \) of aircraft-body coordinate frame. Let L denote lift perpendicular to plane \( O_{a} x_{a} y_{a} \) of velocity coordinate frame. Let D denote drag in the opposite direction of velocity.
Fig. 1

Forces on UAV in the climb

We can obtain the following equation in the path coordinate frame according to the force analysis of UAV:
$$ S_{a \to k} \left[ \begin{aligned} - D \\ 0 \\ - L \\ \end{aligned} \right] + S_{b \to k} \left[ \begin{aligned} T \hfill \\ Y \hfill \\ 0 \hfill \\ \end{aligned} \right] + S_{g \to k} \left[ \begin{aligned} 0 \hfill \\ 0 \hfill \\ G \hfill \\ \end{aligned} \right] = m\frac{{{\text{d}}v}}{{{\text{d}}t}} = 0, $$
(13)
where \( S_{a \to k} \) denotes the transfer matrix from wind coordinate frame to path coordinate frame, \( S_{b \to k} \) denotes the transfer matrix from aircraft-body coordinate frame to path coordinate frame, and \( S_{g \to k} \) denotes the transfer matrix from earth-surface inertial reference frame to path coordinate frame.
We can rewrite L, D and side force Y in (13) as:
$$ \left\{ \begin{aligned} L & = C_{Lw} QS_{w} + C_{Lb} QS_{b} + C_{Lv} QS_{v} = C_{L} QS \\ & = C_{L} \left( {\frac{1}{2}\rho v^{2} } \right)S \\ D & = \left( {C_{D0} + C_{Dt} } \right)QS = C_{D} QS \\ & = \frac{1}{2}\left( {C_{D0} + C_{Dt} } \right)\rho v^{2} S \\ Y & = C_{Y} \left( {\frac{1}{2}\rho v^{2} } \right)S = \frac{1}{2}\left( \begin{aligned} C_{Y\beta } \beta + C_{{Y\delta_{r} }} \delta_{r} \hfill \\ + C_{Yp} p + C_{Yr} r \hfill \\ \end{aligned} \right)\rho v^{2} S, \\ \end{aligned} \right. $$
(14)
where \( C_{Lw} ,C_{Lb} ,C_{Lv} \) denote lift coefficient due to wing, body and tail, \( S_{w} ,S_{b} ,S_{v} \) denote reference area of wing, body and tail, \( C_{D0} ,C_{Dt} \) denote drag coefficient due to zero-lift and lift, and \( C_{Y\beta } ,C_{{Y\delta_{r} }} ,C_{Yp} ,C_{Yr} \) denote side force coefficient due to sideslip angle, rudder, roll rate and yaw rate.
Since the angular rate is 0 when aircraft is in steady-state flight and the comparatively smaller coefficient is ignored, we can describe L, D and Y as a function of velocity (\( v \)), angle of attack (\( \alpha \)) and sideslip angle (\( \beta \)) as:
$$ \begin{aligned} L = f_{L} \left( {v,\alpha ,\beta } \right) \hfill \\ D = f_{D} \left( {v,\alpha ,\beta } \right) \hfill \\ Y = f_{Y} \left( {v,\alpha ,\beta } \right) \hfill \\ \end{aligned} . $$
(15)
Substituting (13) into (15), the relationship between angle of attack (\( \alpha \)), flight path angle (\( \gamma \)), bank angle (\( \mu \)) with velocity (\( v \)) can be expressed as:
$$ \alpha = f_{\alpha } \left( v \right), \, \gamma = f_{\gamma } \left( v \right), \, \mu = f_{\mu } \left( v \right) . $$
(16)
That is, for each value of the velocity, a set of values of \( \alpha \), \( \gamma \) and \( \mu \) can be obtained correspondingly. In this paper, the rate of change in altitude (\( \dot{H} \)) is considered to describe the ability of UAV in the longitudinal direction. Consider Fig. 1 and (16), \( \dot{H} \) is expressed as follows:
$$ \dot{H} = v\sin \gamma = v\sin \left( {f_{\gamma } \left( v \right)} \right). $$
(17)

Thus, \( \dot{H} \) is expressed as a function with only one variable. Therefore, \( \dot{H} \) will change with the change of velocity and get a maximum value \( \dot{H}_{{\rm max} } \) with the effective range of velocity.

Consider the situations of stalled or drag slows UAV, the relations can be listed as:
$$ \left\{ \begin{aligned} & - D + T\cos \alpha \cos \beta + Y\sin \beta - G\sin \gamma \ge 0 \\ & - L\cos \mu - T\left( {\sin \mu \cos \alpha \sin \beta + \cos \mu \sin \alpha } \right) \\ & + Y\sin \mu \cos \beta + G\cos \gamma \le 0. \\ \end{aligned} \right. $$
(18)
And the effective range of velocity is easily obtained with
$$ \begin{aligned} v & \ge \sqrt {\frac{{2\left( {G\cos \gamma - T\left( {\sin \mu \cos \alpha \sin \beta + \cos \mu \sin \alpha } \right)} \right)}}{{\rho S\left( {C_{L} cos\mu - C_{Y} sin\mu \cos \beta } \right)}}} , \\ v & \le \sqrt {\frac{{2\left( {T\cos \alpha \cos \beta - G\sin \gamma } \right)}}{{\rho S\left( {C_{D} - C_{Y} \sin \beta } \right)}}} . \\ \end{aligned} $$
(19)
Consider again the force analysis in Fig. 2. Compared to Fig. 1, only the directions of T, L and D have changed as flight path angle has changed. So that the formula from (13) to (19) still applies to descent stage. The difference is the minimum rate of change of altitude (\( \dot{H}_{\hbox{min} } \)) that needs to be obtained with the effective range of velocity.
Fig. 2

Forces on UAV in the descent

Also, the results of relations between (18) and (19) can be referred to in the process of determining the effective velocity.

3.2 Lateral performance evaluation

In this paper, the maximum roll angle (\( \phi_{{\rm max} } \)) and the time required to reach \( \phi_{{\rm max} } \) (\( \tau_{\text{roll}} \)) are chosen to evaluate lateral performance of UAV in emergency. And on this basis, the minimum turning radius of left and right sides can be obtained.

It may cause changes in the rolling performance of UAV when it is damaged in the battlefield. Let \( \delta_{0} \) denote the aileron’s new degree to trim the damaged UAV. Let \( \delta_{a,r{\rm max} } \) and \( \delta_{a,l{\rm max} } \) denote the maximum number of degrees that the right and left aileron can reach. Therefore, the maximum roll angle can be solved by the linear relationship between the roll rate and the degrees of aileron relative to the trim point.

Using the moment Eq. (10), the dynamic equation of angular rate can be obtained as follows:
$$ \dot{\omega } = I^{ - 1} \left( \begin{aligned} & M - \omega \times I\omega - m\bar{\rho } \times \dot{\vec{v}} - m\omega \times \left( {\bar{\rho } \times \vec{v}} \right) \\ & \quad - m\vec{v} \times \left( {\omega \times \bar{\rho }} \right) + m\bar{\rho } \times g \\ \end{aligned} \right), $$
(20)
where \( I \) denote inertial matrix in aircraft-body coordinate frame. The aircraft is stable in a range before the turning, so the velocity is nearly a constant, and the derivative of the velocity in (20) is zero. Equation (20) can be rewritten as:
$$\begin{aligned}& \left[ {\begin{array}{*{20}c} {\dot{p}} \\ {\dot{q}} \\ {\dot{r}} \\ \end{array} } \right] = I^{ - 1} \left( {\left[ {\begin{array}{*{20}c} L \\ M \\ N \\ \end{array} } \right]^{b} - \omega \times I\omega - m\omega \times \left( {\bar{\rho } \times \vec{v}} \right)} \right.\\ &\left. {- m\vec{v} \times \left( {\omega \times \bar{\rho }} \right) + m\bar{\rho } \times g} \right.\bigg).\end{aligned} $$
(21)
Consider the equation of rolling moment
$$ \begin{aligned} {\vec{L}} & = {\vec{L}}\left( {\delta_{a} } \right) + {\vec{L}}\left( {\delta_{r} } \right) + {\vec{L}}\left( p \right) + {\vec{L}}\left( r \right) \\ & = \left( {C_{{l\delta_{a} }} \Delta \delta_{a} + C_{{l\delta_{r} }} \delta_{r} + C_{lp} p + C_{lr} r} \right)QS_{w} b, \\ \end{aligned} $$
(22)
the time required for the roll angle to increase from the trim point to the maximum is very short, and the aircraft has no time to change in the longitudinal direction. The derivative of roll rate can be rewritten as:
$$ \dot{p} = - \left( {v^{2} c_{1} + vc_{2} } \right)p + v^{2} c_{3} \Delta \delta_{a} , $$
(23)
where \( c_{1} = - {{\rho SbC_{lp} } \mathord{\left/ {\vphantom {{\rho SbC_{lp} } {2I_{xx} }}} \right. \kern-0pt} {2I_{xx} }} \), \( c_{2} = {{m\Delta y} \mathord{\left/ {\vphantom {{m\Delta y} {I_{xx} }}} \right. \kern-0pt} {I_{xx} }} \) and \( c_{3} = {{\rho SbC_{{l\delta_{a} }} } \mathord{\left/ {\vphantom {{\rho SbC_{{l\delta_{a} }} } {2I_{xx} }}} \right. \kern-0pt} {2I_{xx} }}. \) Solving the differential equation in (23), we can get the following results:
$$ p = \frac{{v^{2} c_{3} }}{{v^{2} c_{1} + vc_{2} }}\Delta \delta_{a} \left( {1 - {\text{e}}^{{ - \left( {v^{2} c_{1} + vc_{2} } \right)t}} } \right), $$
(24)
which represents the first-order response after inputting a step signal to the roll rate. Set the ratio of the maximum roll rate of UAV to the left and right sides as \( R_{p} \), and we can obtain the relationship
$$ \begin{aligned}\frac{{\left| {\phi_{{{\text{left}}{\rm max} }} } \right|}}{{\left| {\phi_{{{\text{right}}{\rm max} }} } \right|}} & = \frac{{\left| {p_{{{\text{left}}{\rm max} }} } \right|}}{{\left| {p_{{{\text{right}}{\rm max} }} } \right|}} = \frac{{\left| {\left( {\Delta \delta_{{a,{\text{leftbank}}}} } \right)_{{\rm max} } } \right|}}{{\left| {\left( {\Delta \delta_{{a,{\text{rightbank}}}} } \right)_{{\rm max} } } \right|}}\\ & = \frac{{\left| {\delta_{0} - \delta_{a,r{\rm max} } } \right|}}{{\left| {\delta_{0} - \delta_{a,l{\rm max} } } \right|}} = R_{p} . \end{aligned} $$
(25)
In order to compare the tuning performance of UAV intuitively, we can calculate the minimum turning radius. Combined with force analysis when UAV turns and Eq. (13),
$$ \left\{ \begin{aligned} R = \frac{{mv^{2} }}{{L\sin \mu - T\sin \phi \cos \theta + Y\left( {\cos^{2} \phi - \sin \theta \sin^{2} \phi } \right)}}, \hfill \\ G + Y\cos \theta \sin \phi - L\cos \mu - T\sin \theta = 0. \hfill \\ \end{aligned} \right. $$
(26)
which equals to
$$ \begin{aligned} R_{{{\text{left}},{\rm min} }} = \frac{{mv^{2} }}{\begin{aligned} L\sin \mu - T\sin \phi_{{{\text{left}}{\rm max} }} \cos \theta \hfill \\ + Y\left( {\cos^{2} \phi_{{{\text{left}}{\rm max} }} - \sin \theta \sin^{2} \phi_{{{\text{left}}{\rm max} }} } \right) \hfill \\ \end{aligned} } \hfill \\ R_{{{\text{right}},{\rm min} }} = \frac{{mv^{2} }}{\begin{aligned} L\sin \mu - T\sin \phi_{{{\text{right}}{\rm max} }} \cos \theta \hfill \\ + Y\left( {\cos^{2} \phi_{{{\text{right}}{\rm max} }} - \sin \theta \sin^{2} \phi_{{{\text{right}}{\rm max} }} } \right) \hfill \\ \end{aligned} } \hfill \\ \end{aligned} $$
(27)
Let \( \tau_{\text{roll,left}} \) and \( \tau_{\text{roll,right}} \) denote the required time of roll angle from trim point to \( \phi_{{{\text{left}}{\rm max} }} \) and \( \phi_{{{\text{right}}{\rm max} }} \). Ignoring the transient change in roll rate, the expression is as follows:
$$ \tau_{\text{roll,left}} = \frac{{\phi_{{{\text{left}}{\rm max} }} }}{{p_{{{\text{left}}{\rm max} }} }}, \, \tau_{\text{roll,right}} = \frac{{\phi_{{{\text{right}}{\rm max} }} }}{{p_{{{\text{right}}{\rm max} }} }}, $$
(28)
where \( p_{{{\text{left}}{\rm max} }} ,p_{{{\text{right}}{\rm max} }} \) denote the maximum roll rate when rolling left or right.
According to Eq. (24), \( p_{{{\text{left}}{\rm max} }} ,p_{{{\text{right}}{\rm max} }} \) are expressed as:
$$ \left\{ \begin{aligned} p_{{s,{\text{left}}{\rm max} }} & = \frac{{v^{2} c_{3} }}{{v^{2} c_{1} + vc_{2} }}\left( {\Delta \delta_{{a,{\text{leftbank}}}} } \right)_{{\rm max} } \\ p_{{s,{\text{right}}{\rm max} }} & = \frac{{v^{2} c_{3} }}{{v^{2} c_{1} + vc_{2} }}\left( {\Delta \delta_{{a,{\text{rightbank}}}} } \right)_{{\rm max} } . \\ \end{aligned} \right. $$
(29)

The UAV’s physical performance constraints can be evaluated by the combination of (17), (25), (27) and (28).

4 Route planning

This paper proposes a route planning system for UAV. The system works with performance database, mission planning system, meteorological data processing systems and onboard sensor systems. And this system consists of three modules: track prediction and planning, track analysis and segment guiding (Fig. 3).
Fig. 3

Route planning system

4.1 Track prediction and planning

This module takes constraints such as time, velocity and position as inputs. UAV optimized flight plan based on its own physical performance constraints and other information. And an ETA-window of a certain waypoint or a location-window at a certain point in time was generated by this module; the window will be sent to the task decision module. Task re-planning is performed by the task decision module based on this information.

The track prediction process under this architecture can be divided into two steps. The first step is to calculate the speed, altitude, fuel consumption and ETA information of each waypoint according to the flight plan; the second step is to compare the predicted information with the UAV’s performance. If the constraints are not met, the predictions need to be repeated. The process is shown in Fig. 4.
Fig. 4

Flowchart of track prediction

4.2 Track analysis

The track analysis module decomposes the track generated by the track planning module into horizontal reference track and vertical reference track and converts the segment type and time constraint into the space and time information required by the flight guidance module. The horizontal reference track consists of a straight line segment and a curved line segment that takes into account the speed of UAV. The vertical reference track uses the distance as an independent variable to generate a vertical profile of height and velocity.

4.3 Segment guiding

The segment guiding module solves the horizontal error, the vertical error and the time error according to the analyzed route information, the meteorological data and the current state of UAV [7], and calculates the desired track angle, roll angle, descent rate, desired velocity and so on, which are sent to the flight control system or automatic throttle system to guide UAV. At the same time, the segment guiding module judges the switching logic of the segment or control mode according to the state of UAV (Fig. 5).
Fig. 5

Switching flowchart of segment and model

5 Simulation

The System Tool Kit (STK) software was used to simulate the route planning of UAV in this paper. We build the UAV’s models before and after asymmetric damage in Matlab/Simulink. The interface module of STK/Connect provides an external interface for data transmission with the UAV model in Matlab, ensuring real-time status of UAV’s position, speed and other conditions [8]. At the same time, the radar and communication model simulated by RD/Com module in STK can simulate the time-sensitive targets and threat sources in the battlefield which can trigger the switching of UAV’s model. After setting the initial task target, the simulation results are shown in Fig. 6. The green route in the figure is the route for the target Scan_Target planned by UAV based on the initial information, and the red area is the search range of the enemy early warning radar.
Fig. 6

Initial simulation scenario

Adding a new target and its radar sensor information at a certain time, as shown in Fig. 7, the darker the color, the greater the threat of the air defense radar to UAV. After receiving the suppression, UAV plans its own route according to the task assignment and remaining performance. The execution process is shown in Fig. 8.
Fig. 7

Simulation scenario of enemy targets

Fig. 8

Simulation scenario of route planning

The STK/Access module can be used to calculate the statue of UAV flying over the enemy radar and output it in the form of a graph. Figure 9a, b provides an access summary report between UAV and Radars. Figure 9c, d provides an azimuth-elevation-range analysis report for radars that in charge of electronic interference. The figures show that damaged UAV can re-plan routes through threats from radars. And the duration of UAV detected by Radar1 is less than the duration of Radar2, the absolute value of elevation angle of UAV and Radar1 is less than the angle of UAV and Radar2, which means that UAV can improve its reliability of route planning.
Fig. 9

Calculation result of access module

The calculation results quantitatively analyze the whole simulation process, which reflects the effect of UAV’s route planning decision to a certain extent.

6 Conclusion

When UAV is in an uncertain battlefield, there are space–time constraints such as complex terrain and time-sensitive targets to limit the effect of UAV’s task. This paper studies the performance constraints of UAV itself under the above complex conditions. And the architecture of UAV’s track prediction and flight guidance was designed. The STK simulation software is used to demonstrate the situation in which UAV performs the entire task under this architecture and analyzes the route planned by UAV.

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Copyright information

© Shanghai Jiao Tong University 2018

Authors and Affiliations

  1. 1.Key Laboratory of Science and Technology on Avionics Integration TechnologiesShanghaiChina
  2. 2.China Aeronautical Radio Electronics Research InstituteShanghaiChina

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