Modelling of UAV formation flight using 3D potential field
基于三维势场的无人机编队飞行建模

Tobias Paul a, Thomas R. Krogstad b, Jan Tommy Gravdahl b,*

a ESG Elektroniksystem- und Logistik GmbH, Fürstenfeldbruck, Germany
b Department of Engineering Cybernetics, Norwegian University of Science and Technology, O.S. Bragstads plass 2D, N-7033 Trondheim, Norway

abstract

In this paper, we present a solution for formation flight and formation reconfiguration of unmanned aerial vehicles (UAVs). Based on a virtual leader approach, combined with an extended local potential field, the method is universal applicable by driving the vehicle’s auto pilot. The solution is verified, using a group of UAVs based on a simplified small scale helicopter, which is simulated in MATLABTM/SimulinkTM. As necessary for helicopters, the potential field approach is realized in 3D including obstacle and collision avoidance. The collision avoidance strategy could be used separately for the sense and avoid problem.

在本文中，我们提出了无人机（UAV）的编队飞行和编队重构的解决方案。 基于虚拟领导者方法，结合扩展的局部势场，该方法通过驾驶的自动驾驶仪而普遍适用。 使用基于简化的小型直升机的一组无人机验证该解决方案，该直升机在MATLAB TM / SimulinkTM中模拟。 根据直升机的需要，势场方法以3D实现，包括障碍物和碰撞避免。 避碰策略可以单独用于感知和避免问题。

1. Introduction

The contribution of this paper is the presentation of a virtual leader formation approach combined with an extended version of the potential field solution presented in[1,2]. The approach is applied to a formation of helicopter UAVs presented in [3], providing obstacle and collision avoidance. The helicopters are of the traditional main rotor – tail rotor type. The algorithm supports flight with maximum vehicle speed and could be adopted easily to vehicles with different dynamics. To the authors knowledge, a potential field approach has not previously been applied on helicopter UAVs. However, a two dimensional approach for marine vehicles is presented in [1] while [2] presents a solution for tricycles.

本文的贡献是虚拟领导者编队方法的表现与[1,2]中提出的势场解决方案的扩展版本相结合。 该方法适用于[3]中提出的直升无人机的编队，提供障碍和碰撞避免。 直升机属于传统的主旋翼 - 尾桨式。 该算法支持具有最大机速的飞行，并且可以容易地用于具有不同动态的无人机。 据作者所知，势场方法以前没有应用于直升无人机。 然而，[1]中提出了一种用于船舶的二维方法，而[2]提出了三轮车的解决方案。

Modelling and control of formations of UAVs is a large and ever increasing field of research. Other formation flight approaches, focusing on fixed wing aircrafts, can be found in [4,5] or [7]. In [14], control of a formation of fixed winged aircraft taking off and landing on a ship is studied. Control of a formation of a piloted aircraft in formation with an UAV was reported in [6], while [15] report formation flight of three miniature jet aircraft.

无人机编队的建模和控制是一个庞大且不断增加的研究领域。 其他编队飞行方法，侧重于固定翼飞机，可以在[4,5]或[7]中找到。 在[14]中，研究了对在船上起降的固定翼飞机的编队的控制。 在[6]中报告了用无人机控制编队的飞行编队，而[15]报告了三架微型喷气式飞机的编队飞行。

UAVs are small size, light weight, able to operate autonomously and also be replaced at low cost. With these qualities, UAVs are interesting for industrial and military purposes. UAVs have been used for mapping of hot spots during forest fires [8] or agricultural and crop monitoring [9]. There is also a wide field of military applications. Applications are, among others, surveillance, reconnaissance, radio jamming, artillery acquisition, and target simulation. Formations of UAVs can distribute the equipment, necessary for a specific mission, to all vehicles in the swarm and offer a huge increase of performance and robustness compared to a single operating vehicle.

无人机体积小，重量轻，能够自主运行，并且可以低成本更换。 有了这些品质，无人机对工业和军事目的很有意义。 无人机已被用于森林火灾[8]或农业和作物监测[9]中的热点绘图。 还有广泛的军事应用领域。 应用包括监视，侦察，无线电干扰，火炮获取和目标模拟。 与单个操作相比，无人机的编队可以将特定任务所需的设备分配给群组中的所有无人机，并提供大幅提升的性能和稳健性。

The two main approaches for formation control are potential field and leader–follower. Combinations of those two approaches are often used to build and move formations because they are effective, robust and easy to handle [2,1].

编队控制的两种主要方法是势场法和领导者跟随者。 这两种方法的组合通常用于构建和移动编队，因为它们有效，稳健且易于处理[2,1]。

As UAVs, helicopters are of special interest. They are able to perform vertical take-offs and landings (VTOL) and to hover. Helicopters can operate from ships, undeveloped, or urban areas. Modeling and control of helicopters is challenging because of varying flight qualities and coupling of the dynamic equations. Nevertheless, in[10,11] one can find two nonlinear models for full scale helicopters. Especially small scale helicopter are interesting for UAV applications. They have a very high thrust to weight ratio and can perform extreme maneuvers. A complete and very detailed mathematical model of a small scale helicopter is presented by [12]. A classical control approach is based on a cascade controller, controlling attitude in the inner, lateral and longitudinal movement in the outer loop [3]. Other approaches are based on solving the state dependent Riccati equation [13] or neural networks [16].

作为无人机，直升机特别令人感兴趣。 他们能够执行垂直起飞和着陆（VTOL）并悬停。 直升机可以在船舶，未开发或城市地区运营。 由于飞行质量的变化和动力学方程的耦合，直升机的建模和控制具有挑战性。 然而，在[10,11]中，人们可以找到两种用于全尺寸直升机的非线性模型。 特别是小型直升机对无人机应用很有意义。 它们具有非常高的推重比，可以进行极端的操作。 [12]提出了一种完整且非常详细的小型直升机数学模型。 经典的控制方法基于级联控制器，控制外环内部，侧向和纵向运动的姿态[3]。 其他方法基于求解状态依赖的Riccati方程[13]或神经网络[16]。

3. Formation control

The approach presented in the following generates for each vehicle a potential field depending on swarm constellation, formation, desired, and actual position. It is a combination of virtual leader and potential field approach. A movement of the virtual leader results in a deflection from the desired position and causes the affected vehicles to correct their positions. The field is finally used for obstacle and collision avoidance. A specific position can be assigned to a specific vehicle in the formation. We give an overview of the system in Fig. 2. The advantage of this approach, compared to other approaches, is the application in three dimensions. In addition, a continuous field and thus a continuous trajectory for each vehicle is guaranteed, while providing obstacle and collision avoidance. The algorithm creates a vector which is used to guide the single vehicles. Finally, it guarantees acceleration to maximum vehicle speed.

下面给出的方法根据群星，编队，期望和实际位置为每个无人机形成势场。 它是虚拟领导者和势场法的结合。 虚拟引导件的运动导致从期望位置的偏转并且使受影响的无人机校正其位置。 该场最终用于避障和避碰。 可以将特定位置分配给编队中的特定无人机。 我们概述了图2中的系统。与其他方法相比，这种方法的优点是三维应用。 此外，保证了每个无人机的连续场和连续轨迹，同时提供障碍和碰撞避免。 该算法创建一个矢量，用于指导单个无人机。 最后，它保证加速到最大机速。