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An Equivariant Approach to Robust State Estimation for the ArduPilot Autopilot System

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An Equivariant Approach to Robust State Estimation for the A...

IEEE International Conference on robotics and Automation (ICRA)

作者： Alessandro Fornasier Yixiao Ge Pieter van Goor Martin Scheiber Andrew Tridgell Robert Mahony Stephan Weiss Control of Networked Systems Group University of Klagenfurt Austria System Theory and Robotics Lab Australian National University Australia

ISBN: (数字)9798350384574

ISBN: (纸本)9798350384581

The majority of commercial and open-source autopilot software for uncrewed aerial vehicles rely on the tried and tested extended Kalman filter (EKF) to provide the state estimation solution for the inertial navigation system (INS). While modern implementations achieve remarkable robustness, it is often due to the careful implementation of exception code for a multitude of corner cases along with significant skilled tuning effort. In this paper, we use the data wealth of the ArduPilot community to identify and highlight the most common real-world challenges in INS state estimation, including sensor self-calibration, robustness in static conditions, global navigation satellite system (GNSS) outliers and shifts, and robustness to faulty inertial measurement units (IMUs). We propose a novel equivariant filter (EqF) formulation for the INS solution that exploits a Semi-Direct-Bias symmetry group for multi-sensor fusion with self-calibration capabilities and incorporates equivariant velocity-type measurements. We augment the filter with a simple innovation-covariance inflation strategy that seamlessly handles GNSS outliers and shifts without requiring coding of a whole set of exception cases. We use real-world data from the Ardupilot community to demonstrate the performance of the proposed filter on known cases where existing filters fail without careful exception handling or case-specific tuning and benchmark against the ArduPilot’s EKF3, the most sophisticated EKF implementation currently available.

关键词： Global navigation satellite system Low-pass filters Inertial navigation Robot sensing systems Autonomous aerial vehicles Robustness Software

Equivariant IMU Preintegration with Biases: a Galilean group Approach

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arXiv 2024年

作者： Delama, Giulio Fornasier, Alessandro Mahony, Robert Weiss, Stephan Control of Networked Systems Group University of Klagenfurt Austria System Theory and Robotics Lab Australian National University Australia

This letter proposes a new approach for Inertial Measurement Unit (IMU) preintegration, a fundamental building block that can be leveraged in different optimization-based Inertial Navigation System (INS) localization solutions. Inspired by recent advances in equivariant theory applied to biased INSs, we derive a discrete-time formulation of the IMU preintegration on Gal(3) ⋈ gal(3), the left-trivialization of the tangent group of the Galilean group Gal(3). We define a novel preintegration error that geometrically couples the navigation states and the bias leading to lower linearization error. Our method improves in consistency compared to existing preintegration approaches which treat IMU biases as a separate state-space. Extensive validation against state-of-the-art methods, both in simulation and with real-world IMU data, implementation in the Lie++ library, and open-source code are provided. Copyright © 2024, The Authors. All rights reserved.

关键词： Inertial navigation systems

EXPLOITING EQUIVARIANCE IN THE DESIGN OF TRACKING controlLERS FOR EULER-POINCARE systems ON MATRIX LIE groupS

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arXiv 2024年

作者： Hampsey, Matthew Banavar, Ravi van Goor, Pieter Mahony, Robert Systems Theory and Robotics Group Australian National University ACT2601 Australia Interdisciplinary Programme in Systems and Control Engineering Indian Institute of Technology Bombay India

The trajectory tracking problem is a fundamental control task in the study of mechanical systems. A key construction in tracking control is the error or difference between an actual and desired trajectory. This construction also lies at the heart of observer design and recent advances in the study of equivariant systems have provided a template for global error construction that exploits the symmetry structure of a group action if such a structure exists. Hamiltonian systems are posed on the cotangent bundle of configuration space of a mechanical system and symmetries for the full cotangent bundle are not commonly used in geometric control theory. In this paper, we propose a group structure on the cotangent bundle of a Lie-group and leverage this to define momentum and configuration errors for trajectory tracking drawing on recent work on equivariant observer design. We show that this error definition leads to error dynamics that are themselves "Euler-Poincare like" and use these to derive simple, almost global trajectory tracking control for fully-actuated Euler-Poincare systems on a Lie-group state space. Copyright © 2024, The Authors. All rights reserved.

关键词： Lie groups

MSCEqF: A Multi State Constraint Equivariant Filter for Vision-aided Inertial Navigation

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arXiv 2023年

作者： Fornasier, Alessandro van Goor, Pieter Allak, Eren Mahony, Robert Weiss, Stephan The Control of Networked Systems Group University of Klagenfurt Austria The System Theory and Robotics Lab Australian National University Australia

This letter re-visits the problem of visual-inertial navigation system (VINS) and presents a novel filter design we dub the multi state constraint equivariant filter (MSCEqF, in analogy to the well known MSCKF). We define a symmetry group and corresponding group action that allow specifically the design of an equivariant filter for the problem of visual-inertial odometry (VIO) including IMU bias, and camera intrinsic and extrinsic calibration states. In contrast to state-of-the-art invariant extended Kalman filter (IEKF) approaches that simply tack IMU bias and other states onto the SE2(3) group, our filter builds upon a symmetry that properly includes all the states in the group structure. Thus, we achieve improved behavior, particularly when linearization points largely deviate from the truth (i.e., on transients upon state disturbances). Our approach is inherently consistent even during convergence phases from significant errors without the need for error uncertainty adaptation, observability constraint, or other consistency enforcing techniques. This leads to greatly improved estimator behavior for significant error and unexpected state changes during, e.g., long-duration missions. We evaluate our approach with a multitude of different experiments using three different prominent real-world datasets. Copyright © 2023, The Authors. All rights reserved.

关键词： Errors

Reprojection Methods for Koopman-Based Modelling and Prediction

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Reprojection Methods for Koopman-Based Modelling and Predict...

IEEE Conference on Decision and control

作者： Pieter Van Goor Robert Mahony Manuel Schaller Karl Worthmann Systems Theory and Robotics Group School of Engineering Australian National University Canberra Australia Optimization-based Control Group Institute of Mathematics Technische Universitat Ilmenau Ilmenau Germany

Extended Dynamic Mode Decomposition (eDMD) is a powerful tool to generate data-driven surrogate models for the prediction and control of nonlinear dynamical systems in the Koopman framework. In eDMD a compression of the lifted system dynamics on the space spanned by finitely many observables is computed, in which the original space is embedded as a low-dimensional manifold. While this manifold is invariant for the infinite-dimensional Koopman operator, this invariance is typically not preserved for its eDMD-based approximation. Hence, an additional (re-)projection step is often tacitly incorporated to improve the prediction capability. We propose a novel framework for consistent reprojectors respecting the underlying manifold structure. Further, we present a new geometric reprojector based on maximum-likelihood arguments, which significantly enhances the approximation accuracy and preserves known finite-data error bounds.

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Reprojection methods for Koopman-based modelling and prediction

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arXiv 2023年

作者： van Goor, Pieter Mahony, Robert Schaller, Manuel Worthmann, Karl Systems Theory and Robotics Group School of Engineering Australian National University Canberra Australia Optimization-based Control Group Institute of Mathematics Technische Universität Ilmenau Germany

关键词： Dynamic mode decomposition

Equivariant Symmetries for Inertial Navigation systems

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arXiv 2023年

作者： Fornasier, Alessandro Ge, Yixiao van Goor, Pieter Mahony, Robert Weiss, Stephan Control of Networked Systems Group University of Klagenfurt Austria System Theory and Robotics Lab Australian Centre for Robotic Vision Australian National University Australia

This paper investigates the problem of inertial navigation system (INS) filter design through the lens of symmetry. The extended Kalman filter (EKF) and its variants, have been the staple of INS filtering for 50 years;however, recent advances in inertial navigation systems have exploited matrix Lie group structure to design stochastic filters and state observers that have been shown to display superior performance compared to classical solutions. In this work, we consider the case where a vehicle has an inertial measurement unit (IMU) and a global navigation satellite system (GNSS) receiver. We show that all the modern variants of the EKF for these sensors can be interpreted as the recently proposed Equivariant Filter (EqF) design methodology applied to different choices of symmetry group for the INS problem. This leads us to propose two new symmetries for the INS problem that have not been considered in the prior literature, and provide a discussion of the relative strengths and weaknesses of all the different algorithms. We believe the collection of symmetries that we present here capture all the sensible choices of symmetry for this problem and sensor suite, and that the analysis provided is indicative of the relative real-world performance potential of the different algorithms. Copyright © 2023, The Authors. All rights reserved.

关键词： Inertial navigation systems

Equivariant filter design for inertial navigation systems with input measurement biases

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arXiv 2022年

作者： Fornasier, Alessandro Ng, Yonhon Mahony, Robert Weiss, Stephan Control of Networked Systems Group University of Klagenfurt Austria System Theory and Robotics Lab Australian National University Australia

Inertial Navigation systems (INS) are a key technology for autonomous vehicles applications. Recent advances in estimation and filter design for the INS problem have exploited geometry and symmetry to overcome limitations of the classical Extended Kalman Filter (EKF) approach that formed the mainstay of INS systems since the mid-twentieth century. The industry standard INS filter, the Multiplicative Extended Kalman Filter (MEKF), uses a geometric construction for attitude estimation coupled with classical Euclidean construction for position, velocity and bias estimation. The recent Invariant Extended Kalman Filter (IEKF) provides a geometric framework for the full navigation states, integrating attitude, position and velocity, but still uses the classical Euclidean construction to model the bias states. In this paper, we use the recently proposed Equivariant Filter (EqF) framework to derive a novel observer for biased inertial-based navigation in a fully geometric framework. The introduction of virtual velocity inputs with associated virtual bias leads to a full equivariant symmetry on the augmented system. The resulting filter performance is evaluated with both simulated and realworld data, and demonstrates increased robustness to a wide range of erroneous initial conditions, and improved accuracy when compared with the industry standard Multiplicative EKF (MEKF) approach. Copyright © 2022, The Authors. All rights reserved.

关键词： Inertial navigation systems

Overcoming Bias: Equivariant Filter Design for Biased Attitude Estimation with Online Calibration

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arXiv 2022年

作者： Fornasier, Alessandro Ng, Yonhon Brommer, Christian Böhm, Christoph Mahony, Robert Weiss, Stephan The Control of Networked Systems Group University of Klagenfurt Austria The System Theory and Robotics Lab Australian National University Australia

Stochastic filters for on-line state estimation are a core technology for autonomous systems. The performance of such filters is one of the key limiting factors to a system’s capability. Both asymptotic behavior (e.g., for regular operation) and transient response (e.g., for fast initialization and reset) of such filters are of crucial importance in guaranteeing robust operation of autonomous systems. This paper introduces a new generic formulation for a gyroscope aided attitude estimator using N direction measurements including both body-frame and reference-frame direction type measurements. The approach is based on an integrated state formulation that incorporates navigation, extrinsic calibration for all direction sensors, and gyroscope bias states in a single equivariant geometric structure. This newly proposed symmetry allows modular addition of different direction measurements and their extrinsic calibration while maintaining the ability to include bias states in the same symmetry. The subsequently proposed filter-based estimator using this symmetry noticeably improves the transient response, and the asymptotic bias and extrinsic calibration estimation compared to state-of-the-art approaches. The estimator is verified in statistically representative simulations and is tested in real-world experiments. Copyright © 2022, The Authors. All rights reserved.

关键词： Calibration