50 research outputs found

    An Equivariant Observer Design for Visual Localisation and Mapping

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    This paper builds on recent work on Simultaneous Localisation and Mapping (SLAM) in the non-linear observer community, by framing the visual localisation and mapping problem as a continuous-time equivariant observer design problem on the symmetry group of a kinematic system. The state-space is a quotient of the robot pose expressed on SE(3) and multiple copies of real projective space, used to represent both points in space and bearings in a single unified framework. An observer with decoupled Riccati-gains for each landmark is derived and we show that its error system is almost globally asymptotically stable and exponentially stable in-the-large.Comment: 12 pages, 2 figures, published in 2019 IEEE CD

    A Global Asymptotic Convergent Observer for SLAM

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    This paper examines the global convergence problem of SLAM algorithms, an issue that faces topological obstructions. This is because the state-space of attitude dynamics is defined on a non-contractible manifold: the special orthogonal group of order three SO(3). Therefore, this paper presents a novel, gradient-based hybrid observer to overcome these topological obstacles. The Lyapunov stability theorem is used to prove the globally asymptotic convergence of the proposed algorithm. Finally, comparative analyses of two simulations were conducted to evaluate the performance of the proposed scheme and to demonstrate the superiority of the proposed hybrid observer to a smooth observer.Comment: 7 pages, 8 figures, conferenc

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

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    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.Comment: to be published in Robotics and Automation Letter

    Equivariant Filter (EqF): A General Filter Design for Systems on Homogeneous Spaces

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    The kinematics of many mechanical systems encountered in robotics and other fields, such as single-bearing attitude estimation and SLAM, are naturally posed on homogeneous spaces: That is, their state lies in a smooth manifold equipped with a transitive Lie-group symmetry. This paper shows that any system posed in a homogeneous space can be extended to a larger system that is equivariant under a symmetry action. The equivariant structure of the system is exploited to propose a novel new filter, the Equivariant Filter (EqF), based on linearisation of global error dynamics derived from the symmetry action. The EqF is applied to an example of estimating the positions of stationary landmarks relative to a moving monocular camera that is intractable for previously proposed symmetry based filter design methodologie

    PEBO-SLAM: Observer design for visual inertial SLAM with convergence guarantees

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    This paper introduces a new linear parameterization to the problem of visual inertial simultaneous localization and mapping (VI-SLAM) -- without any approximation -- for the case only using information from a single monocular camera and an inertial measurement unit. In this problem set, the system state evolves on the nonlinear manifold SE(3)×R3nSE(3)\times \mathbb{R}^{3n}, on which we design dynamic extensions carefully to generate invariant foliations, such that the problem can be reformulated into online \emph{constant parameter} identification, then interestingly with linear regression models obtained. It demonstrates that VI-SLAM can be translated into a linear least squares problem, in the deterministic sense, \emph{globally} and \emph{exactly}. Based on this observation, we propose a novel SLAM observer, following the recently established parameter estimation-based observer (PEBO) methodology. A notable merit is that the proposed observer enjoys almost global asymptotic stability, requiring neither persistency of excitation nor uniform complete observability, which, however, are widely adopted in most existing works with provable stability but can hardly be assured in many practical scenarios

    Sensor-based formation control using a generalised rigidity framework and passivity techniques

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    The research in this thesis addresses the subject of sensor-based formation control for a network of autonomous agents. The task of formation control involves the stabilisation of the agents to a desired set of relative states, with the possible additional objective of manoeuvring the agents while maintaining this formation. Although the formation control challenge has been widely studied in the literature, many existing control strategies are based on full state information, and give little consideration to the sensor modalities available for the task. The focus of this thesis lies in the use of a generic arrangement of partial state measurements as can commonly be acquired by onboard sensors; for example, time-of-flight sensors can be used to measure the distances between vehicles, and onboard cameras can provide the bearing from one vehicle to each of the others. Particular aspects of the problem that are addressed in this thesis include (i) ways of modelling the formation control task, (ii) methods of analysing the system's behaviour, and (iii) the design of a formation control scheme based on generic arrangements of sensors that provide only partial position information. A key contribution in this thesis is a generalisation of the classical notion of rigidity, which considers the use of distance constraints between agents in R^2 or R^3 to specify a rigid body (or formation). This enables the concept of rigidity to be applied to agent networks involving a variety of (possibly non-Euclidean) state-spaces, with a generic set of state constraints that may, for example, include bearings between agents as well as distances. I demonstrate that this framework is very well-suited for modelling a wide variety of formation control problems (addressing goal (i) above), and I extend several fundamental results from classical rigidity theory in order to provide significant insight for system analysis (addressing goal (ii) above). To design a formation control scheme that uses generic partial position measurements (addressing goal (iii) above), I employ a modular passivity-based approach that is developed using the bondgraph modelling formalism. I illustrate how adaptive compensation can be incorporated into this design approach in order to account for the unknown position information that is not available from the onboard sensors. Although formation control is the subject of this thesis, it should be noted that the rigidity-based and passivity-based frameworks developed here are quite general and may be applied to a wide range of other problems
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