Two new families of cluster Cohn and Markov-monodromy matrices for generalized Markov cluster algebras are introduced, fully classified, and made explicit via weighted fence posets whose order ideals expand cluster variables.
Socially-Aware Robot Navigation Enhanced by Bidirectional Natural Language Conversations Using Large Language Models
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abstract
Robot navigation is crucial across various domains, yet traditional methods focus on efficiency and obstacle avoidance, often overlooking human behavior in shared spaces. With the rise of service robots, socially aware navigation has gained prominence. However, existing approaches primarily predict pedestrian movements or issue alerts, lacking true human-robot interaction. We introduce Hybrid Soft Actor-Critic with Large Language Model (HSAC-LLM), a novel framework for socially aware navigation. By integrating deep reinforcement learning with large language models, HSAC-LLM enables bidirectional natural language interactions, predicting both continuous and discrete navigation actions. When potential collisions arise, the robot proactively communicates with pedestrians to determine avoidance strategies. Experiments in 2D simulation, Gazebo, and real-world environments demonstrate that HSAC-LLM outperforms state-of-the-art DRL methods in interaction, navigation, and obstacle avoidance. This paradigm advances effective human-robot interactions in dynamic settings. Videos are available at https://hsacllm.github.io/.
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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations
Two new families of cluster Cohn and Markov-monodromy matrices for generalized Markov cluster algebras are introduced, fully classified, and made explicit via weighted fence posets whose order ideals expand cluster variables.