We study the problem of finding statistically distinct plans for stochastic planning and task assignment problems such as online multi-robot pickup and delivery (MRPD) when facing multiple competing objectives. In many real-world settings robot fleets do not only need to fulfil delivery requests, but also have to consider auxiliary objectives such as energy efficiency or avoiding human-centered work spaces. We pose MRPD as a multi-objective optimization problem where the goal is to find MRPD policies that yield different trade-offs between given objectives. There are two main challenges: 1) MRPD is computationally hard, which limits the number of trade-offs that can reasonably be computed, and 2) due to the random task arrivals, one needs to consider statistical variance of the objective values in addition to the average. We present an adaptive sampling algorithm that finds a set of policies which i) are approximately optimal, ii) approximate the set of all optimal solutions, and iii) are statistically distinguishable. We prove completeness and adapt a state-of-the-art MRPD solver to the multi-objective setting for three example objectives. In a series of simulation experiments we demonstrate the advantages of the proposed method compared to baseline approaches and show its robustness in a sensitivity analysis. The approach is general and could be adapted to other multi-objective task assignment and planning problems under uncertainty.

翻译：我们研究在面临多个相互冲突目标时，针对随机规划与任务分配问题（例如在线多机器人取送货问题，MRPD）寻找统计显著规划方案的问题。在许多实际场景中，机器人车队不仅需要完成配送请求，还需考虑辅助目标（如能源效率或避让人工密集工作区）。我们将MRPD建模为多目标优化问题，其目标是寻找能在给定目标之间取得不同权衡的MRPD策略。存在两大挑战：1）MRPD的计算复杂度高，限制了可合理计算的权衡方案数量；2）由于任务随机到达，除均值外还需考虑目标值的统计方差。我们提出一种自适应采样算法，该算法能够找到满足以下条件的策略集：i）近似最优，ii）逼近所有最优解的空间，iii）具有统计可区分性。我们证明了算法的完备性，并针对三个示例目标将当前最优的MRPD求解器适配至多目标场景。通过一系列仿真实验，我们展示了该方法相较于基线方法的优势，并通过敏感性分析验证其鲁棒性。该算法具有通用性，可推广至不确定性条件下的其他多目标任务分配与规划问题。