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

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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 *x*–*y*–*z* reference frame be the reference frame at any point P on the rigid body and the *X*–*Y*–*Z* reference frame be the inertial reference frame at point *O*.

*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:

*X*–

*Y*–

*Z*reference frame, so (2) becomes

*x*–

*y*–

*z*reference frame and \( \omega \) denotes angular rate of the rigid body in the

*X*–

*Y*–

*Z*reference frame.

*P*\( \vec{v}_{p} = U_{p} {\mathbf{i}} + V_{p} {\mathbf{j}} + W_{p} {\mathbf{k}} \) in the

*x*–

*y*–

*z*reference frame.

*X*–

*Y*–

*Z*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).

*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

*P*in the

*x*–

*y*–

*z*reference frame as:

*x*–

*y*–

*z*axles, (10) expands to

## 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

*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.

*L*,

*D*and side force

*Y*in (13) as:

*L*,

*D*and

*Y*as a function of velocity (\( v \)), angle of attack (\( \alpha \)) and sideslip angle (\( \beta \)) as:

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.

*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.

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.

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

## 4 Route planning

### 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.

### 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

## 5 Simulation

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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