Decentralized Rigidity Maintenance Control with Range Measurements for Multi-Robot Systems (1309.0535v3)

Abstract: This work proposes a fully decentralized strategy for maintaining the formation rigidity of a multi-robot system using only range measurements, while still allowing the graph topology to change freely over time. In this direction, a first contribution of this work is an extension of rigidity theory to weighted frameworks and the rigidity eigenvalue, which when positive ensures the infinitesimal rigidity of the framework. We then propose a distributed algorithm for estimating a common relative position reference frame amongst a team of robots with only range measurements in addition to one agent endowed with the capability of measuring the bearing to two other agents. This first estimation step is embedded into a subsequent distributed algorithm for estimating the rigidity eigenvalue associated with the weighted framework. The estimate of the rigidity eigenvalue is finally used to generate a local control action for each agent that both maintains the rigidity property and enforces additional con- straints such as collision avoidance and sensing/communication range limits and occlusions. As an additional feature of our approach, the communication and sensing links among the robots are also left free to change over time while preserving rigidity of the whole framework. The proposed scheme is then experimentally validated with a robotic testbed consisting of 6 quadrotor UAVs operating in a cluttered environment.

• The paper presents a decentralized control scheme enabling multi-robot systems to maintain formation rigidity using only range measurements, particularly useful in environments without GPS.
• A distributed algorithm is introduced for estimating a common relative position reference frame and the rigidity eigenvalue from local information, allowing for decentralized control actions.
• The approach is robust to dynamic changes in the robot network's communication and sensing topology while ensuring the overall system's rigidity is maintained.

Decentralized Rigidity Maintenance Control with Range Measurements for Multi-Robot Systems

The paper discusses the development of a decentralized control scheme to maintain the formation rigidity of multi-robot systems using only range measurements. The primary focus is on retaining the rigidity property while allowing dynamic changes in the graph topology over time. This work is situated within the broader context of multi-robot coordination and the challenges encountered in environments where GPS data is unavailable, such as indoors, underwater, or in space.

Key Contributions and Innovations

1. Extension of Rigidity Theory: The authors provide an extension of traditional rigidity theory to incorporate weighted frameworks and introduce the concept of the rigidity eigenvalue. A positive rigidity eigenvalue ensures the infinitesimal rigidity of the framework.
2. Distributed Position Estimation: The paper proposes a distributed algorithm to estimate a common relative position reference frame among a team of robots. This estimation process relies solely on range measurements and one agent capable of measuring the bearing to two other agents. The ability to establish a common reference frame underpins the practical execution of decentralized control protocols in environments without a global reference frame.
3. Rigidity Eigenvalue Estimation and Control: Following the establishment of a common frame, the paper introduces a distributed algorithm to estimate the rigidity eigenvalue associated with the weighted framework. The process involves a modified power iteration method that allows for a fully distributed calculation using only local information.
4. Implementation of Local Control Actions: The estimated rigidity eigenvalue is then utilized to generate local control actions for each agent. These control actions maintain the rigidity property and enforce additional operational constraints such as collision avoidance and compliance with sensing/communication range limits.
5. Adaptive Graph Topology: An innovative aspect of this research is that the communication and sensing links among robots are allowed to change dynamically over time. Despite these changes, the approach ensures that the rigidity of the entire framework is maintained, facilitating robust operations in uncertain and dynamic environments.

Practical and Theoretical Implications

The decentralized control scheme presented in the paper has significant theoretical implications for the paper of distributed systems and rigidity theory. By extending rigidity to weighted frameworks and employing eigenvalue-based methods for analysis and control, this research broadens the theoretical toolkit available for addressing problems in networked robotics and beyond.

From a practical standpoint, the proposed methods have wide-ranging applications in fields requiring precise coordination of multiple robotic agents, such as search and rescue operations, autonomous monitoring, and environmental exploration. The ability to maintain formation rigidity without a common world-frame or extensive GPS infrastructure reduces deployment costs and expands the applicability of multi-robot systems to new domains.

Future Directions

While this research addresses several critical challenges in decentralized multi-robot control, it also opens avenues for further exploration. Future work could explore relaxing some assumptions, such as the initial requirement for an infinitesimally rigid configuration or the reliance on a special agent capable of bearing measurement. Additionally, extending the methods to scenarios with more complex constraints or incorporating machine learning techniques for enhanced adaptability could further refine and broaden the applicability of this decentralized control strategy.

In conclusion, the paper provides a robust framework for maintaining rigidity in multi-robot systems, overcoming challenges related to dynamic environments and limited sensing capabilities. The methodologies presented not only advance theoretical understanding but also offer practical strategies for the deployment of autonomous multi-robot teams in a variety of real-world scenarios.