Dubins车对运动目标的最小时间侧向拦截
Minimum-time lateral interception of a moving target by a Dubins car
AI总结：
本文研究Dubins车对沿已知轨迹运动目标的最小时间侧向拦截问题，通过三维可达集性质证明最优拦截点位于解析曲面上，并推导出10个代数方程以求解最优控制参数。
摘要：
本文提出了Dubins车对一个沿先验已知轨迹运动的目标进行侧向拦截的问题。该轨迹由平面位置的两个坐标和一个航向角给出，其中每一个都是时间的连续函数。在存在先验已知的时变风矢量场的情况下，为Dubins车构造最小时间轨迹的最优轨迹规划问题是本文所提问题的一个特例。利用Dubins车三维可达集的性质，证明了最优拦截点属于三维空间中一个解析描述曲面的一部分。该曲面的解析描述使得可以获得10个代数方程，用于计算实现最小时间侧向拦截的最优控制参数。这些方程通常是超越方程，并且可以针对目标运动的特定情形（例如静止目标、匀速直线运动目标）进行简化。最后，最优侧向拦截的一些特定情形验证了本文的推导，并强调了在一般情形下需要考虑全部10个代数方程的必要性。
英文摘要：
This paper presents the problem of lateral interception by a Dubins car of a target that moves along an a priori known trajectory. This trajectory is given by two coordinates of a planar location and one angle of a heading orientation, every one of them is a continuous function of time. The optimal trajectory planning problem of constructing minimum-time trajectories for a Dubins car in the presence of a priory known time-dependent wind vector field is a special case of the presented problem. Using the properties of the three-dimensional reachable set of a Dubins car, it is proved that the optimal interception point belongs to a part of an analytically described surface in the three-dimensional space. The analytical description of the surface makes it possible to obtain 10 algebraic equations for calculating parameters of the optimal control that implements the minimum-time lateral interception. These equations are generally transcendental and can be simplified for particular cases of target motion (e.g. resting target, straight-line uniform target motion). Finally, some particular cases of the optimal lateral interception validate developments of the paper and highlight the necessity to consider each of 10 algebraic equations in general case.
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