Simulation of Aircraft Flight Track by BéZier and B-spline Curve
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摘要: 为克服用运动方程生成航迹曲线时无法控制曲线形状的缺陷,根据民航飞机遵循计划航路点飞行的特 点,提出了利用B湨Zier曲线和B 样条曲线生成飞机航迹的方法.用直线段距离和逼近B湨Zier曲线和开放均匀 B 样条曲线的长度近似计算航迹曲线长度,根据飞行计划中航路点位置的相互关系和飞机实时飞行的速度、位 置等,生成B湨Zier曲线飞行航迹控制点后得到航迹曲线,此外,B 样条曲线则不需要生成新控制点就能产生合理 的航迹曲线;利用相应的B湨Zier曲线或开放均匀B 样条曲线插值公式计算出下一个航迹点位置.仿真结果表 明:用本文两种方法计算出的航迹与真实航迹相符;与运动方程方法相比,具有能生成多种形状航迹曲线的优 势;在18个航路点条件下,用B湨Zier曲线模拟航迹的计算时间为0.13s,满足实时性要求.Abstract: To overcome the limitations of motion equation which can not control the curve shape of aircraft tracks, a method of track simulation by Bézier and B-spline curves was proposed since the civil aircrafts have regular flying rules and its motion follows the beacons in flight plan defined before flight. In this method, lengths of the Bézier and open uniform B-spline curves are approximated by sum of line segments subdivided from the curves; then, Bézier control points of the track curve are calculated with the beacon positions in flight plan and the real-time status such as flying speed, position, etc. of the aircraft. The B-spline method needs not to create new control points for generation of aircraft flight track curve because it can create a rational track curve using beacons. Furthermore, the position of the next point in flight track is calculated by the interpolation equation of Bézier or B-spline curve. The simulation result shows that the Bézier and B-spline track curve are basically the same as the real track curve. The proposed methods are superior to the method of motion equation, for it can create all kinds of track curves. Under the condition of 18 beacons, the calculating time of the Bézier method is 0.13 s and can satisfy the real-time requirement.
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Key words:
- flight track simulation /
- air traffic control /
- BéZier curve /
- B-splines
期刊类型引用(3)
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