We present a path planning problem for a pursuing unmanned aerial vehicle (UAV) to intercept a target traveling on a circle. The target is cooperative, and its position, heading, and speed are precisely known. The pursuing UAV has nonholonomic motion constraints, and therefore the path traveled must satisfy the minimum turn radius constraints. We consider the class of Dubins paths as candidate solutions, and analyze the characteristics of the six modes of Dubins paths where the final position is restricted to lie on the target circle with heading in the tangential direction of the circle. For each Dubins mode, we derive the feasibility limits, discontinuities, and local extrema. Using this analysis the intercepting paths are found by a systematic bisection search in the feasible regions of each of the Dubins modes. We prove that the algorithm finds the optimal (shortest length) intercepting path if it is a Dubins path. If the shortest intercepting path is not a Dubins path for any given instance, the algorithm finds a tight lower bound and an upper bound to the optimal solution.

我们提出了一个追踪无人机 (UAV) 的路径规划问题，以拦截在圆周上行驶的目标。目标是合作的，它的位置、航向和速度是精确已知的。追击无人机具有非完整运动约束，因此行进路径必须满足最小转弯半径约束。我们将 Dubins 路径类作为候选解，分析了 Dubins 路径的六种模式的特征，其中最终位置被限制在目标圆上，航向为圆的切线方向。对于每个 Dubins 模式，我们推导出可行性极限、不连续性和局部极值。使用这种分析，通过在每个 Dubins 模式的可行区域中进行系统的二等分搜索来找到拦截路径。我们证明，如果是 Dubins 路径，该算法会找到最优（最短长度）截取路径。如果最短截取路径对于任何给定实例都不是 Dubins 路径，则该算法会找到最优解的严格下界和上界。