In this paper, we study the problem of exploring an unknown Region Of Interest (ROI) with a team of aerial robots. The size and shape of the ROI are unknown to the robots. The objective is to find a tour for each robot such that each point in the ROI must be visible from the field-of-view of some robot along its tour. In conventional exploration using ground robots, the ROI boundary is typically also as an obstacle and robots are naturally constrained to the interior of this ROI. Instead, we study the case where aerial robots are not restricted to flying inside the ROI (and can fly over the boundary of the ROI). We propose a recursive depth-first search-based algorithm that yields a constant competitive ratio for the exploration problem. Our analysis also extends to the case where the ROI is translating, \eg, in the case of marine plumes. In the simpler version of the problem where the ROI is modeled as a 2D grid, the competitive ratio is $\frac{2(S_r+S_p)(R+\lfloor\log{R}\rfloor)}{(S_r-S_p)(1+\lfloor\log{R}\rfloor)}$ where $R$ is the number of robots, and $S_r$ and $S_p$ are the robot speed and the ROI speed, respectively. We also consider a more realistic scenario where the ROI shape is not restricted to grid cells but an arbitrary shape. We show our algorithm has $\frac{2(S_r+S_p)(18R+\lfloor\log{R}\rfloor)}{(S_r-S_p)(1+\lfloor\log{R}\rfloor)}$ competitive ratio under some conditions. We empirically verify our algorithm using simulations as well as a proof-of-concept experiment mapping a 2D ROI using an aerial robot with a downwards-facing camera.
翻译:在本文中, 我们研究与一组航空机器人一起探索未知区域( ROI) 的问题 。 机器人不知道 ROI 的大小和形状 。 我们的目标是为每个机器人找到一个循环的深度第一搜索算法, 使ROI 中的每一点在巡演期间都能够从某个机器人的实地观察中看到。 在使用地面机器人进行常规探索时, ROI 边界通常也是一个障碍, 并且机器人自然被限制在ROI 的内部。 相反, 我们研究的是, 空中机器人不受限制在ROI 内飞行( 并且可以飞过ROI 的边界 ) 的情况。 我们建议为勘探问题寻找一个连续的 深度第一搜索算法 。 我们的分析还延伸到ROI 正在翻译( eg) 的情况。 在将ROI 建为 2D 网格的更简单的问题中, 竞争比率是 $( sr_ sr_ r) roial_ robal_ a ( r_ slobal_ sal_ sal_ sal_ sal_ sal_ laudal_ sal_ sal_ sweal_ sal_ sl_ sl_ sl_ sl_ exal_ squotal_ sweal_ sweal_ sweal_ sweal_ sweal_ sweat) ( We) ( Wer_ sweal_ sweal_ we_ we_ sweal_ sweal_) a) (我们 r_ wer_ sweal_ sl_ sl_ sl_ real_ r_ sl_ sal_ real_ real_ real_ real_ real_ real_r_r_r_ real_)