[Paper Review] Semi-centralized control for multi-robot formation and theoretical lower bound

Shuo Wan, Jiaxun Lu+2 more|arXiv (Cornell University)|Sep 12, 2017

Distributed Control Multi-Agent Systems3 references3 citations

TL;DR

This paper proposes a semi-centralized control framework for multi-robot formation that optimizes robot-to-position assignment using the Hungarian algorithm to minimize total moving distance. It derives a theoretical lower bound on formation bias using information-theoretic methods, enabling system design guidance, and validates the approach through simulations showing bias reduction with increased measurements, lower variance, and higher quantization rates.

ABSTRACT

Multi-robot formation control enables robots to cooperate as a working group in completing complex tasks, which has been widely used in both civilian and military scenarios. Before moving to reach a given formation, each robot should choose a position from the formation so that the whole system cost is minimized. To solve the problem, we formulate an optimization problem in terms of the total moving distance and give a solution by the Hungarian method. To analyze the deviation of the achieved formation from the ideal one, we obtain the lower bound of formation bias with respect to system's parameters based on notions in information theory. As an extension, we discuss methods of transformation between different formations. Some theoretical results are obtained to give a guidance of the system design.

Motivation & Objective

• To address the robot position assignment problem in multi-robot formation control, minimizing total moving distance.
• To quantify the deviation of the achieved formation from the ideal one, defined as formation bias.
• To derive a theoretical lower bound on formation bias using information theory to guide system parameter selection.
• To investigate formation transformation between different configurations with optimal center selection.
• To validate the theoretical bounds and system behavior through simulations under varying system parameters.

Proposed method

• Formulates the robot-to-position assignment as an assignment problem and solves it using the Hungarian algorithm to minimize total moving distance.
• Employs a leader-follower control strategy where each robot autonomously reaches its assigned position based on relative measurements.
• Defines formation bias as the deviation between the achieved and ideal formation, modeled using relative position measurements.
• Applies information-theoretic tools to derive a lower bound on formation bias using mutual information and Bayes risk estimation.
• Uses least squares fitting to model simulation data and compares it with the theoretical lower bound.
• Optimizes new formation center selection during transformation using the same assignment and control framework.

Experimental results

Research questions

• RQ1 How can robot-to-position assignment be optimized to minimize total moving distance in a multi-robot formation?
• RQ2 What is the theoretical minimum achievable formation bias under given system parameters?
• RQ3 How do measurement variance, number of measurements, and quantization rate affect formation bias?
• RQ4 What is the optimal strategy for transforming between different formations while maintaining low bias?
• RQ5 How well does the theoretical lower bound on formation bias match empirical simulation results?

Key findings

• The Hungarian method effectively minimizes total moving distance in robot-to-position assignment, ensuring optimal initial placement.
• Formation bias decreases with increasing number of measurements, as shown by simulation data and consistent with theoretical expectations.
• Higher measurement variance leads to increased formation bias, confirming the sensitivity of formation accuracy to measurement noise.
• Increased quantification rate reduces formation bias, with diminishing returns at higher rates, indicating a trade-off between resolution and performance.
• The theoretical lower bound derived using information theory consistently lies below the empirical simulation results, validating its role as a performance benchmark.
• The simulation results show strong agreement with theoretical trends, confirming the validity of the proposed lower bound for system design guidance.