This paper considers the collaborative graph exploration problem in GPS-denied environments, where a group of robots are required to cover a graph environment while maintaining reliable pose estimations in collaborative simultaneous localization and mapping (SLAM). Considering both objectives presents challenges for multi-robot pathfinding, as it involves the expensive covariance inference for SLAM uncertainty evaluation, especially considering various combinations of robots' paths. To reduce the computational complexity, we propose an efficient two-stage strategy where exploration paths are first generated for quick coverage, and then enhanced by adding informative and distance-efficient loop-closing actions, called loop edges, along the paths for reliable pose estimation. We formulate the latter problem as a non-monotone submodular maximization problem by relating SLAM uncertainty with pose graph topology, which (1) facilitates more efficient evaluation of SLAM uncertainty than covariance inference, and (2) allows the application of approximation algorithms in submodular optimization to provide optimality guarantees. We further introduce the ordering heuristics to improve objective values while preserving the optimality bound. Simulation experiments over randomly generated graph environments verify the efficiency of our methods in finding paths for quick coverage and enhanced pose graph reliability, and benchmark the performance of the approximation algorithms and the greedy-based algorithm in the loop edge selection problem. Our implementations will be open-source at https://github.com/bairuofei/CGE.

翻译：本文研究在无GPS环境下的协同图探索问题，其中一组机器人需要在覆盖图环境的同时，在协同同步定位与建图（SLAM）中保持可靠的位姿估计。同时考虑这两个目标对多机器人路径规划提出了挑战，因为这涉及用于SLAM不确定性评估的高成本协方差推断，尤其是在考虑机器人路径的各种组合时。为降低计算复杂度，我们提出一种高效的两阶段策略：首先生成探索路径以实现快速覆盖，然后通过沿路径添加信息丰富且距离高效的闭环动作（称为环边）来增强路径，以实现可靠的位姿估计。我们通过将SLAM不确定性与位姿图拓扑相关联，将后一问题表述为非单调子模最大化问题，这（1）比协方差推断更高效地评估SLAM不确定性，且（2）允许应用子模优化中的近似算法以提供最优性保证。我们进一步引入排序启发式方法，在保持最优性界的同时提高目标函数值。在随机生成的图环境上的仿真实验验证了我们的方法在寻找快速覆盖路径和增强位姿图可靠性方面的效率，并对近似算法与基于贪心的算法在环边选择问题中的性能进行了基准测试。我们的实现将在 https://github.com/bairuofei/CGE 开源。