arxiv_robotics 90% Match Research Paper Robotics Engineers,Control Engineers,AI Researchers,Multi-Agent Systems Researchers 3 weeks ago

Distributed 3D Source Seeking via SO(3) Geometric Control of Robot Swarms

robotics › navigation

📄 Abstract

Abstract: This paper presents a geometric control framework on the Lie group SO(3) for 3D source-seeking by robots with first-order attitude dynamics and constant translational speed. By working directly on SO(3), the approach avoids Euler-angle singularities and quaternion ambiguities, providing a unique, intrinsic representation of orientation. We design a proportional feed-forward controller that ensures exponential alignment of each agent to an estimated ascending direction toward a 3D scalar field source. The controller adapts to bounded unknown variations and preserves well-posed swarm formations. Numerical simulations demonstrate the effectiveness of the method, with all code provided open source for reproducibility.

Key Contributions

Presents a geometric control framework on the SO(3) Lie group for 3D source-seeking by robot swarms with first-order attitude dynamics. It avoids singularity issues by working directly on SO(3) and uses a proportional feed-forward controller for exponential alignment towards a source, adapting to bounded variations and preserving formations.

Business Value

Enables efficient and robust deployment of robot swarms for tasks like environmental sensing, search operations, and distributed exploration in complex 3D spaces.

Paper Metadata

Innovation Type

Geometric Control Framework

Deployment Feasibility

Moderate. Requires robots with attitude control capabilities and a well-defined scalar field to track. Simulation effectiveness needs real-world validation.

Limitations Addressed

Euler-angle singularities and quaternion ambiguities in 3D orientation control, and the challenge of coordinated source seeking in dynamic environments for robot swarms.

Performance Gains

Ensures exponential convergence to the source and stable swarm formations in 3D environments, overcoming common control issues.

View Code on GitHub

Technical Tags

Geometric ControlSO(3) Lie Group3D Source SeekingRobot SwarmsAttitude DynamicsTranslational SpeedEuler-Angle SingularitiesQuaternion AmbiguitiesProportional Feed-Forward ControllerScalar Field SourceSwarm Formations

Research Topics

RoboticsMulti-Agent SystemsControl TheoryGeometric MechanicsOptimization

Methods & Architectures

Geometric Control on Lie Groups (SO(3))Proportional Feed-Forward ControlState Estimation (implicit)

Applications & Tasks

Environmental Monitoring Search and Rescue Robotics Distributed Systems Source LocalizationCooperative NavigationDistributed Control3D Path Planning 3D Source SeekingCoordinated Swarm MovementMaintaining Formations

Related Fields

Control SystemsMulti-Robot SystemsDifferential GeometryOptimization

Keywords

robot swarmssource seekinggeometric controlSO(3)Lie group3D navigationattitude controlformation controldistributed systemsmulti-agent roboticsfeed-forward control

Academic Context

#Robotics#Multi-Agent Systems#Control Theory#Geometric Mechanics#Optimization

Commercial Potential

Potential Products

Cooperative Navigation Software for Robot SwarmsDistributed Sensing Platforms

Target Industries

RoboticsEnvironmental MonitoringSearch and RescueAgricultureDefense

Use Case Examples

Swarm of drones searching for a chemical leak sourceUnderwater robots coordinating to map a contaminated areaRobots exploring unknown 3D environments to find specific targets

Competitive Edge

Offers a mathematically rigorous and robust geometric control approach for 3D swarm source seeking, overcoming limitations of traditional methods related to orientation representation.

Market Opportunity

Growing market for multi-robot systems and autonomous exploration.

Revenue Models

Licensing of control softwareintegration services for swarm robotics platforms.

Resource Requirements

Compute Needs

Low to moderate for onboard computation.

Data Requirements

Requires a simulated or real-world environment with a detectable scalar field.

Deployment Constraints

Requires robots capable of precise attitude control, reliable communication within the swarm, and a detectable source signal.

Scalability

The framework is designed for scalability to large robot swarms.

Production Readiness

Maturity Level

Simulation-based Research

Time to Market

3-5 years for specialized applications.

Licensing

Open Source

Patent Potential

Moderate for the novel control algorithms and swarm coordination strategies.

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