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Recent work has considered trust-aware decision making for human-robotcollaboration (HRC) with a focus on model learning. In this paper, we areinterested in enabling the HRC system to complete complex tasks specified usingtemporal logic that involve human trust. Since human trust in robots is notobservable, we adopt the widely used partially observable Markov decisionprocess (POMDP) framework for modelling the interactions between humans androbots. To specify the desired behaviour, we propose to use syntacticallyco-safe linear distribution temporal logic (scLDTL), a logic that is definedover predicates of states as well as belief states of partially observablesystems. The incorporation of belief predicates in scLDTL enhances itsexpressiveness while simultaneously introducing added complexity. This alsopresents a new challenge as the belief predicates must be evaluated over thecontinuous (infinite) belief space. To address this challenge, we present analgorithm for solving the optimal policy synthesis problem. First, we enhancethe belief MDP (derived by reformulating the POMDP) with a probabilisticlabelling function. Then a product belief MDP is constructed between theprobabilistically labelled belief MDP and the automaton translation of thescLDTL formula. Finally, we show that the optimal policy can be obtained byleveraging existing point-based value iteration algorithms with essentialmodifications. Human subject experiments with 21 participants on a drivingsimulator demonstrate the effectiveness of the proposed approach.

Trust-Aware Motion Planning for Human-Robot Collaboration under Distribution Temporal Logic Specifications