Risk-aware Decision-making in Human-multi-robot Collaborative Search: A Regret Theory Approach

The expected value (EV) based optimization principle often used in engineering ignores risk-related human characteristics which are however important to human-robot interaction (HRI). The characteristics include risk-perception and risk-attitudes which can be called risk-awareness collectively. In this work, we study the effects of risk-awareness in a human-multi-robot collaborative search task. In such a task, the correctness of robotic visual detection is uncertain, but the robots can request human assistance. Assume there is only one human in the team, the requesting robots must be ordered into a sequence. To optimize the ordering, we propose to construct a risk-aware cost function with an extended version of regret theory (RTx). RTx is a decision theory modeling risk-awareness and is backed by neuroscientific and psychological evidences. We cast the optimal ordering into multi-option choice problems and use RTx to make human-like risk-aware decisions. This optimal ordering is combinatorial optimization with a nonlinear cost function which is generally difficult to solve. However, we prove the properties of RTx enable simplification of the optimal ordering to a sorting problem which has fast off-the-shelf solvers. The simplification has two parts. One part concerns with ordering a fixed number of robots optimally. The other concerns with selecting a not-yet-ordered sequence of robots with the optimal length. We examine the RTx-based ordering in simulation and show risk-aware decision-making is more advantageous than EV-based decision-making. The results indicate that risk-awareness renders improved performance of robotic decision-making for HRI and RTx is a tractable embodiment of risk-awareness.