Fault-Tolerant Multi-Modal Localization of Multi-Robots on Matrix Lie Groups

2025/05/01 by Zarei, Mahboubeh, Chhabra, Robin
#FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Group Theory (math.GR) #Robotics (cs.RO) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2505.00842

Abstract

Consistent localization of cooperative multi-robot systems during navigation presents substantial challenges. This paper proposes a fault-tolerant, multi-modal localization framework for multi-robot systems on matrix Lie groups. We introduce novel stochastic operations to perform composition, differencing, inversion, averaging, and fusion of correlated and non-correlated estimates on Lie groups, enabling pseudo-pose construction for filter updates. The method integrates a combination of proprioceptive and exteroceptive measurements from inertial, velocity, and pose (pseudo-pose) sensors on each robot in an Extended Kalman Filter (EKF) framework. The prediction step is conducted on the Lie group \mathbbSE₂(3) × ℝ³ × ℝ³, where each robot's pose, velocity, and inertial measurement biases are propagated. The proposed framework uses body velocity, relative pose measurements from fiducial markers, and inter-robot communication to provide scalable EKF update across the network on the Lie group \mathbbSE(3) × ℝ³. A fault detection module is implemented, allowing the integration of only reliable pseudo-pose measurements from fiducial markers. We demonstrate the effectiveness of the method through experiments with a network of wheeled mobile robots equipped with inertial measurement units, wheel odometry, and ArUco markers. The comparison results highlight the proposed method's real-time performance, superior efficiency, reliability, and scalability in multi-robot localization, making it well-suited for large-scale robotic systems.

Citations

• Equivalence of Left- and Right-Invariant Extended Kalman Filters on Matrix Lie Groups
• Distributed Invariant Kalman Filter for Object-level Multi-robot Pose SLAM
• Distributed Invariant Kalman Filter for Cooperative Localization using Matrix Lie Groups
• Multi-Robot Relative Pose Estimation in SE(2) with Observability Analysis: A Comparison of Extended Kalman Filtering and Robust Pose Graph Optimization
• Equivariant Symmetries for Inertial Navigation Systems
• Lie Algebraic Unscented Kalman Filter for Pose Estimation
• Characterizing the Uncertainty of Jointly Distributed Poses in the Lie\n Algebra
• Contact-Aided Invariant Extended Kalman Filtering for Robot State Estimation
• Exploiting Symmetries to Design EKFs with Consistency Properties for Navigation and SLAM
• A White-Noise-On-Jerk Motion Prior for Continuous-Time Trajectory Estimation on SE(3)
• On-board Range-based Relative Localization for Micro Aerial Vehicles in indoor Leader-Follower Flight
• The invariant extended Kalman filter as a stable observer
• Integrating Generic Sensor Fusion Algorithms with Sound State Representations through Encapsulation of Manifolds

Related

• Distributed Invariant Kalman Filter for Cooperative Localization using Matrix Lie Groups
• SaWa-ML: Structure-Aware Pose Correction and Weight Adaptation-Based Robust Multi-Robot Localization
• Multi-Robot Relative Pose Estimation in SE(2) with Observability Analysis: A Comparison of Extended Kalman Filtering and Robust Pose Graph Optimization
• Distributed Invariant Kalman Filter for Object-level Multi-robot Pose SLAM
• Degradation-Aware Cooperative Multi-Modal GNSS-Denied Localization Leveraging LiDAR-Based Robot Detections