We introduce and study the Joint Task Assistance Planning problem which generalizes prior work on optimizing assistance in robotic collaboration. In this setting, two robots operate over predefined roadmaps, each represented as a graph corresponding to its configuration space. One robot, the task robot, must execute a timed mission, while the other, the assistance robot, provides sensor-based support that depends on their spatial relationship. The objective is to compute a path for both robots that maximizes the total duration of assistance given. Solving this problem is challenging due to the combinatorial explosion of possible path combinations together with the temporal nature of the problem (time needs to be accounted for as well). To address this, we propose a nested branch-and-bound framework that efficiently explores the space of robot paths in a hierarchical manner. We empirically evaluate our algorithm and demonstrate a speedup of up to two orders of magnitude when compared to a baseline approach.

翻译：本文提出并研究了联合任务辅助规划问题，该问题推广了先前关于机器人协作中辅助优化的研究。在此设定下，两个机器人在预定义的路线图上运行，每条路线图均表示为对应其配置空间的图。其中一个机器人（任务机器人）必须执行定时任务，而另一个机器人（辅助机器人）则提供基于传感器的支持，该支持取决于两者间的空间关系。目标是计算两条机器人的路径，以最大化给定辅助的总持续时间。由于可能路径组合的组合爆炸性以及问题的时间特性（还需考虑时间因素），解决该问题具有挑战性。为此，我们提出了一种嵌套分支定界框架，以分层方式高效探索机器人路径空间。我们通过实验评估了所提算法，并证明与基线方法相比，其速度提升可达两个数量级。