The Generalized Dubins Interval Problem (GDIP) stands to determine the minimal length path connecting two disk-shaped regions where the departure and terminal headings of Dubins vehicle are within the specified angle intervals. The GDIP is a generalization of the existing point-to-point planning problem for Dubins vehicle with a single heading angle per particular location that can be solved optimally using closed-form expression. For the GDIP, both the heading angles and locations need to be chosen from continuous sets which makes the problem challenging because of infinite possibilities how to connect the regions by Dubins path. We provide the optimal solution of the introduced GDIP based on detailed problem analysis. Moreover, we propose to employ the GDIP to provide the first tight lower bound for the Dubins Touring Regions Problem which stands to find the shortest curvature-constrained path through a set of regions in the prescribed order.

中文翻译：

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广义Dubins间隔问题的最佳解决方案：通过一组区域找到最短的曲率约束路径

广义杜宾斯区间问题（GDIP）用于确定连接两个盘形区域的最小长度路径，在该区域中，杜宾斯车辆的出发航向和终点航向在指定的角度间隔内。GDIP是Dubins车辆在每个特定位置具有单个航向角的现有点对点规划问题的概括，可以使用闭合形式的表达式最佳地解决该问题。对于GDIP，航向角和方位都需要从连续的集合中选择，这使该问题具有挑战性，因为如何通过Dubins路径连接区域具有无限的可能性。我们会根据详细的问题分析为引入的GDIP提供最佳解决方案。此外，