Abstract The problem of optimal trajectory planning for a moving object with a nonuniform radiation pattern is considered and analytically solved as a variational problem. The object tries to evade detection by a search system consisting of a single sensor. Necessary and sufficient conditions for trajectory optimality are obtained. Analytical expressions for optimal trajectories, the velocity law, and the integral risk of detection on optimal trajectories are derived.

中文翻译：

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具有非均匀辐射模式的运动物体的轨迹最优条件

摘要 具有非均匀辐射方向图的运动目标的最优轨迹规划问题作为一个变分问题被考虑并解析解决。该对象试图逃避由单个传感器组成的搜索系统的检测。得到了轨迹最优的充要条件。推导出最优轨迹的解析表达式、速度定律和最优轨迹检测的积分风险。