Human-Robot Cooperative Distribution Coupling for Hamiltonian-Constrained Social Navigation

Weizheng Wang, Chao Yu, Yu Wang, and Byung-Cheol Min

SMART Lab, Purdue University; Tsinghua University

To appear in ICRA 2025

Abstract

Current researches on social navigation still have struggled with the lack of energy-based system attribute explicit description and human-robot cooperative distribution coupling. This article formulates the Hamiltonian-constrained socially-aware robot navigation (SAN) task, concerning the port-Hamiltonian framework to describe the physical configurations and environmental dynamics of SAN. Moreover, we propose a novel social navigation framework, named NaviDIFF (Hamiltonian-constrained social robot Navigation DIFFuser), in which NaviDIFF not only explicitly maintains an explainable energy conservative closed-loop attribute on human-robot interaction (HRI) inference, but also addresses the uncertainty of human-robot cooperation and social-temporal dependencies of HRI by a diffused spatial-temporal transformer neural network. Subsequently, the Hamiltonian-constrained SAN features are parameterized to generate action from deep reinforcement learning policy. Eventually, offline reinforcement learning from human feedback framework is employed to tailor robot behaviors with respect to human preferences and social norms. NaviDIFF outperforms other baselines on both extensive simulation and real-world experiments.

Core Contributions of NaviDIFF

1. NaviDIFF captures the physical-informed human-robot interaction (HRI) features that adheres to the closed-loop system energy stability guarantee, leveraging the port-Hamiltonian maechansim (PH) [2].

2. NaviDIFF approximates HRI cooperative and competitive uncertainty via Diffusion network.

3. NaviDIFF encodes social norms and human preferences into social robot policy, using the offline RLHF fine-tuning procedure.

Architecture of NaviDIFF

NaviDIFF Architecture: NaviDIFF not only leverages the spatial-temporal transformer to represent Hamiltonian terms which constructs the HRI environmental dynamics and closed-loop stability guarantee, but also explores the cooperative uncertainty with a diffusion neural network. Apart from that, the offline RLHF framework and LLM are also employed in NaviDIFF.

The Insights of PH Mechanism for Social Robots

The Physical Model of Two Objectives Linked by a Spring

Physical Model: Let consider a physical model that two objectives such as blocks or cars are linked by a spring, as shown in following Yotube videos.

Physical-Informed Dynamics: The motion dynamics of this physical model can be not only displayed via video, but also described by the conservation of energy and momentum. Hence, we can infer the system future motion attributes based on the physical-informed features.

The Motion Dynamics of Physical Models

Physical Model: We formulate a typical physical model to describe the interaction among objectives or agents as rightside figures.

Physical-Informed Dynamics: We can capture the physical-informed features of such scenarios, in which the objectives or agents kinematic energy is converted to system potential energy with a part of dissipative energy due to the interaction.

The Motion Dynamics of Physical System Proof

Physical Model: Let's define above physical model with more details as follows:

Newton Mechanics Physical System Proof

Port-Hamiltonian Mechanics Physical System Formulation

Port-Hamiltonian Mechanics Physical System Proof

Human-Robot Cooperative Collision Avoidance Problem

Physical Model: Let simplify human-human interaction model and human-robot interaction model as above two objectives linked by a spring formulation, where objective present agent, and their cooperation or competition dynamics are denoted by the spring. Additionally, we introduce the Hamiltonian physical theory to describe their motion attributes, in which H denotes agent's kinematic energy and potential energy, and J & R presents the energy transformation or energy dissipation from the interactive procedure that the energy from objective's kinematic energy (agents' Hamiltonian energy) is positively or reversely converted into spring's potential energy (agents' interative or competitive energy). Eventually, the complex multiple agents' situation can be also simplified by multiple objectives linked by multiple springs.

Hamiltonian-Constrained Social Navigation Proof: The PH dynamics proof can be found in the methodology section of our paper [Paper].

Physical-Informed Insights: We formulate the PH-inspired insights that summarize the motion or interaction dynamics among agents in social robot navigation environment as followsing figures. The Hamiltonian item H(mean) presents system total energy, and R(mean) is the system dissipative energy item, and J(mean) denotes system mean interactive energy item. Furthermore, the group-wise agents conditions can be thought as the comprehensive coupling of pair-wise agents dynamics. Eventually, we can infer the robot policy that adheres to closed-loop PH system energy stability guarantee via the PH mechanism of social robot navigation.

Human-Robot Cooperative Uncertainty

Human-Robot Cooperative Distribution: We utilize the diffusion network to approximate PH-inspired human-robot cooperative distribution as following figures, where each agent is abstracted by a peak that is estimated by individual Hamiltonian energy item H(i), and their cooperative and competitive correlations are evaluated by energy function R(i, j) and J(i, j). Thus, socail robot can search the clear paths based on physical-informed diffusing distribution features.