  Multi-robot task allocation (MRTA) problems involve optimizing the allocation
of robots to tasks. MRTA problems are known to be challenging when tasks
require multiple robots and the team is composed of heterogeneous robots. These
challenges are further exacerbated when we need to account for uncertainties
encountered in the real-world. In this work, we address coalition formation in
heterogeneous multi-robot teams with uncertain capabilities. We specifically
focus on tasks that require coalitions to collectively satisfy certain minimum
requirements. Existing approaches to uncertainty-aware task allocation either
maximize expected pay-off (risk-neutral approaches) or improve worst-case or
near-worst-case outcomes (risk-averse approaches). Within the context of our
problem, we demonstrate the inherent limitations of unilaterally ignoring or
avoiding risk and show that these approaches can in fact reduce the probability
of satisfying task requirements. Inspired by models that explain foraging
behaviors in animals, we develop a risk-adaptive approach to task allocation.
Our approach adaptively switches between risk-averse and risk-seeking behavior
in order to maximize the probability of satisfying task requirements.
Comprehensive numerical experiments conclusively demonstrate that our
risk-adaptive approach outperforms risk-neutral and risk-averse approaches. We
also demonstrate the effectiveness of our approach using a simulated
multi-robot emergency response scenario.
