As robots' manipulation capabilities improve for pick-and-place tasks (e.g., object packing, sorting, and kitting), methods focused on understanding human-acceptable object configurations remain limited expressively with regard to capturing spatial relationships important to humans. To advance robotic understanding of human rules for object arrangement, we introduce positionally-augmented RCC (PARCC), a formal logic framework based on region connection calculus (RCC) for describing the relative position of objects in space. Additionally, we introduce an inference algorithm for learning PARCC specifications via demonstrations. Finally, we present the results from a human study, which demonstrate our framework's ability to capture a human's intended specification and the benefits of learning from demonstration approaches over human-provided specifications.

When an AI system interacts with multiple users, it frequently needs to make allocation decisions. For instance, a virtual agent decides whom to pay attention to in a group, or a factory robot selects a worker to deliver a part.Demonstrating fairness in decision making is essential for such systems to be broadly accepted. We introduce a Multi-Armed Bandit algorithm with fairness constraints, where fairness is defined as a minimum rate at which a task or a resource is assigned to a user. The proposed algorithm uses contextual information about the users and the task and makes no assumptions on how the losses capturing the performance of different users are generated. We provide theoretical guarantees of performance and empirical results from simulation and an online user study. The results highlight the benefit of accounting for contexts in fair decision making, especially when users perform better at some contexts and worse at others.