Opinion-Driven Decision-Making for Multi-Robot Navigation through Narrow Corridors

TL;DR

This work tackles deadlock risk in multi-robot traversal through a narrow corridor under decentralized coordination. It introduces an opinion-driven framework based on Nonlinear Opinion Dynamics (NOD) that allows robots to infer others’ intentions from observed motions and to converge on a shared passing strategy, guided by a softmax-based strategy selection and implemented via a multi-robot path planner and MPC. To scale to larger robot teams, the authors propose a game reduction technique that limits the number of game players considered by each robot, framed within a generalized NOD model, and a conflict-based method to select those players. Through extensive simulations with 2–4 robots, the approach achieves high success rates, demonstrates robustness to initial conditions and biases, and shows substantial computational savings from game reduction, making decentralized social navigation through narrow corridors feasible in practice. The work lays a foundation for future human-robot and data-driven parameter-tuning extensions, including implicit signaling and experimental validation with human participants.

Abstract

We propose an opinion-driven navigation framework for multi-robot traversal through a narrow corridor. Our approach leverages a multi-agent decision-making model known as the Nonlinear Opinion Dynamics (NOD) to address the narrow corridor passage problem, formulated as a multi-robot navigation game. By integrating the NOD model with a multi-robot path planning algorithm, we demonstrate that the framework effectively reduces the likelihood of deadlocks during corridor traversal. To ensure scalability with an increasing number of robots, we introduce a game reduction technique that enables efficient coordination in larger groups. Extensive simulation studies are conducted to validate the effectiveness of the proposed approach.

Figures (5)

• Figure 1: An Illustration of the Multi-Robot Narrow Corridor Passage: Multiple strategies are defined for individual robots to adopt. Each strategy specifies the order in which the robots pass through the corridor. The proposed opinion-driven framework facilitates coordination by enabling all robots to converge on the same strategy through interactions.
• Figure 2: Framework Overview: The NOD model is designed to promote coordination during corridor navigation by aggregating incentives based on the estimated strategies of other robots, inferred from their observed motions and predicted paths provided by a multi-robot path planner. Using the updated opinion state generated by the NOD model, each robot decides on an appropriate navigation strategy. This decision is then executed through a multi-robot path planner and a motion controller, which guide the robot toward its destination.
• Figure 3: Heatmap plots illustrate the strategy selections in a two-robot scenario with two possible strategies -- $S_1:(1,2)$ and $S_2:(2,1)$. The initial condition $z_{i1} (0)$ varies within the range $[-10, 10]$, while $z_{i2}(0) = 0$ is fixed for both robots ($i \in \{1,2\}$). Plots (a) and (b) show the strategy selections based on the steady-state limit $\lim_{t \to \infty} x_{11}(t)$, which is identical to $\lim_{t \to \infty} x_{21}(t)$, for $u_i=1$ and $u_i = 10$, respectively. These results are averaged over multiple simulations and computed directly using \ref{['eq:opinion_dynamics_continous']} and \ref{['eq:strategy_selection_softmax']}. Plot (c) depicts the strategy selections of both robots averaged over multiple simulations using the opinion-driven navigation framework explained in §\ref{['sec:opinion_driven_framework']}, with $u_i=10$.
• Figure 4: Illustrations of various evaluation scenarios. The colored circles indicate the robots’ origins, while the X-marks in the same colors represent their corresponding destinations.
• Figure 5: Success rates of corridor navigation across different scenarios, each case is illustrated in Fig. \ref{['fig:configuration_table']}, and for varying numbers $|\mathcal{N}_i(t)|$ of game players. The success rate represents the percentage of simulation trials in which all robots successfully navigated through the corridor and reached their destinations.

Theorems & Definitions (1)

• Remark 1