Abstract This paper presents a rapid (real time) solution to the minimum-time path planning problem for Dubins vehicles under environmental currents (wind or ocean currents). Real-time solutions are essential in time-critical situations (such as replanning under dynamically changing environments or tracking fast moving targets). Typically, Dubins problem requires to solve for six path types; however, due to the presence of currents, four of these path types require to solve the root-finding problem involving transcendental functions. Thus, the existing methods result in high computation times and their applicability for real-time applications is limited. In this regard, in order to obtain a real-time solution, this paper proposes a novel approach where only a subset of two Dubins path types ( L S L and R S R ) are used which have direct analytical solutions in the presence of currents. However, these two path types do not provide full reachability. We show that by extending the feasible range of circular arcs in the L S L and R S R path types from 2 π to 4 π : (1) full reachability of any goal pose is guaranteed, and (2) paths with lower time costs as compared to the corresponding 2 π -arc paths can be produced. Theoretical properties are rigorously established, supported by several examples, and evaluated in comparison to the Dubins solutions by extensive Monte-Carlo simulations.

中文翻译：

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环境流下 Dubins 车辆的快速路径规划

摘要 本文针对环境流（风或洋流）下的 Dubins 车辆的最小时间路径规划问题提出了一种快速（实时）解决方案。在时间紧迫的情况下（例如在动态变化的环境下重新规划或跟踪快速移动的目标），实时解决方案至关重要。通常，杜宾斯问题需要解决六种路径类型；然而，由于存在电流，其中四种路径类型需要解决涉及超越函数的求根问题。因此，现有方法导致高计算时间并且它们对实时应用的适用性是有限的。对此，为了获得实时解决方案，本文提出了一种新方法，其中仅使用两种 Dubins 路径类型（LSL 和 RSR）的子集，它们在存在电流的情况下具有直接解析解。但是，这两种路径类型不提供完全可达性。我们表明，通过将 LSL 和 RSR 路径类型中圆弧的可行范围从 2 π 扩展到 4 π：（1）保证任何目标姿势的完全可达性，以及（2）与可以产生相应的 2 π 弧路径。理论性质得到严格建立，得到几个例子的支持，并通过广泛的蒙特卡罗模拟与 Dubins 解决方案进行比较评估。我们表明，通过将 LSL 和 RSR 路径类型中圆弧的可行范围从 2 π 扩展到 4 π：（1）保证任何目标姿势的完全可达性，以及（2）与可以产生相应的 2 π 弧路径。理论性质得到严格建立，得到几个例子的支持，并通过广泛的蒙特卡罗模拟与 Dubins 解决方案进行比较评估。我们表明，通过将 LSL 和 RSR 路径类型中圆弧的可行范围从 2 π 扩展到 4 π：（1）保证任何目标姿势的完全可达性，以及（2）与可以产生相应的 2 π 弧路径。理论性质得到严格建立，得到几个例子的支持，并通过广泛的蒙特卡罗模拟与 Dubins 解决方案进行比较评估。