arXiv subjects

Robert Mahony

Publications and source records attributed to Robert Mahony.

At least 55 records · Page 3Linked to original sources

arXiv2023

Constructive Equivariant Observer Design for Inertial Navigation

Inertial Navigation Systems (INS) are algorithms that fuse inertial measurements of angular velocity and specific acceleration with supplementary sensors including GNSS and magnetometers to estimate the position, velocity and attitude, or extended pose, of a vehicle. The industry-standard extended Kalman filter (EKF) does not come with strong stability or robustness guarantees and can be subject to catastrophic failure. This paper exploits a Lie group symmetry of the INS dynamics to propose the first nonlinear observer for INS with error dynamics that are almost-globally asymptotically and locally exponentially stable, independently of the chosen gains. The observer is aided only by a GNSS measurement of position. As expected, the convergence guarantee depends on persistence of excitation of the vehicle's specific acceleration in the inertial frame. Simulation results demonstrate the observer's performance and its ability to converge from extreme errors in the initial state estimates.

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arXiv2023

Tracking control on homogeneous spaces: the Equivariant Regulator (EqR)

Accurate tracking of planned trajectories in the presence of perturbations is an important problem in control and robotics. Symmetry is a fundamental mathematical feature of many dynamical systems and exploiting this property offers the potential of improved tracking performance. In this paper, we investigate the tracking problem for systems on homogeneous spaces, manifolds which admit symmetries with transitive group actions. We show that there is natural manner to lift any desired trajectory of such a system to a lifted trajectory on the symmetry group. This construction allows us to define a global tracking error and apply LQR design to obtain an approximately optimal control in a single coordinate chart. The resulting control is then applied to the original plant and shown to yield excellent tracking performance. We term the resulting design methodology the Equivariant Regulator (EqR). We provide an example system posed on a homogeneous space, derive the trajectory linearisation in error coordinates and demonstrate the effectiveness of EqR compared to standard approaches in simulation.

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arXiv2023

Reprojection methods for Koopman-based modelling and prediction

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.

math.DS↗

arXiv2023

GoferBot: A Visual Guided Human-Robot Collaborative Assembly System

The current transformation towards smart manufacturing has led to a growing demand for human-robot collaboration (HRC) in the manufacturing process. Perceiving and understanding the human co-worker's behaviour introduces challenges for collaborative robots to efficiently and effectively perform tasks in unstructured and dynamic environments. Integrating recent data-driven machine vision capabilities into HRC systems is a logical next step in addressing these challenges. However, in these cases, off-the-shelf components struggle due to generalisation limitations. Real-world evaluation is required in order to fully appreciate the maturity and robustness of these approaches. Furthermore, understanding the pure-vision aspects is a crucial first step before combining multiple modalities in order to understand the limitations. In this paper, we propose GoferBot, a novel vision-based semantic HRC system for a real-world assembly task. It is composed of a visual servoing module that reaches and grasps assembly parts in an unstructured multi-instance and dynamic environment, an action recognition module that performs human action prediction for implicit communication, and a visual handover module that uses the perceptual understanding of human behaviour to produce an intuitive and efficient collaborative assembly experience. GoferBot is a novel assembly system that seamlessly integrates all sub-modules by utilising implicit semantic information purely from visual perception.

cs.RO↗

arXiv2022

Exploiting Different Symmetries for Trajectory Tracking Control with Application to Quadrotors

High performance trajectory tracking control of quadrotor vehicles is an important challenge in aerial robotics. Symmetry is a fundamental property of physical systems and offers the potential to provide a tool to design high-performance control algorithms. We propose a design methodology that takes any given symmetry, linearises the associated error in a single set of coordinates, and uses LQR design to obtain a high performance control; an approach we term Equivariant Regulator design. We show that quadrotor vehicles admit several different symmetries: the direct product symmetry, the extended pose symmetry and the pose and velocity symmetry, and show that each symmetry can be used to define a global error. We compare the linearised systems via simulation and find that the extended pose and pose and velocity symmetries outperform the direct product symmetry in the presence of large disturbances. This suggests that choices of equivariant and group affine symmetries have improved linearisation error.

cs.RO↗

arXiv2022

Equivariant Filters are Equivariant

Observers for systems with Lie group symmetries are an active area of research that is seeing significant impact in a number of practical domains, including aerospace, robotics, and mechatronics. This paper builds on the theory of the recently proposed Equivariant Filter (EqF), which is a general observer design for systems on homogeneous spaces that takes advantage of symmetries to yield significant performance advantages. It is shown that the EqF error dynamics are invariant to transformation of the input signal and equivariant as a parametrised vector field. The main theorem shows that two EqF's with different choices of local coordinates and origins and with equivalent noise modelling yield identical performance. In other words, the EqF is intrinsic to the system equations and symmetry. This is verified in a simulation of a 2D robot localisation problem, which also shows how the ability to choose an origin for the EqF can yield practical performance advantages by mitigating floating point precision errors.

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arXiv2022

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

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.

cs.RO↗

arXiv2022

Equivariant Filter Design for Discrete-time systems

The kinematics of many nonlinear control systems, especially in the robotics field, admit a transitive Lie-group symmetry, which is useful in high performance observer design. The recently proposed equivariant filter (EqF) exploits equivariance to generate high performance filters for a wide range of real-world systems. However, existing work on the equivariant filter, and equivariance of control systems in general, is based on a continuous-time formulation. In this paper, we first present the equivariant structure of a discrete-time system. We then use this to propose a discrete-time version of the equivariant filter. A novelty of the approach is that the geometry of the symmetry group naturally appears as parallel transport in the reset step of the filter. Preliminary results for linear second order kinematics with separate bearing and range measurements indicate that the discrete EqF significantly outperforms both a discretized version of the continuous EqF and a classical discrete EKF.

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arXiv2022

Smart Visual Beacons with Asynchronous Optical Communications using Event Cameras

Event cameras are bio-inspired dynamic vision sensors that respond to changes in image intensity with a high temporal resolution, high dynamic range and low latency. These sensor characteristics are ideally suited to enable visual target tracking in concert with a broadcast visual communication channel for smart visual beacons with applications in distributed robotics. Visual beacons can be constructed by high-frequency modulation of Light Emitting Diodes (LEDs) such as vehicle headlights, Internet of Things (IoT) LEDs, smart building lights, etc., that are already present in many real-world scenarios. The high temporal resolution characteristic of the event cameras allows them to capture visual signals at far higher data rates compared to classical frame-based cameras. In this paper, we propose a novel smart visual beacon architecture with both LED modulation and event camera demodulation algorithms. We quantitatively evaluate the relationship between LED transmission rate, communication distance and the message transmission accuracy for the smart visual beacon communication system that we prototyped. The proposed method achieves up to 4 kbps in an indoor environment and lossless transmission over a distance of 100 meters, at a transmission rate of 500 bps, in full sunlight, demonstrating the potential of the technology in an outdoor environment.

cs.RO↗

arXiv2022

A Linear Comb Filter for Event Flicker Removal

Event cameras are bio-inspired sensors that capture per-pixel asynchronous intensity change rather than the synchronous absolute intensity frames captured by a classical camera sensor. Such cameras are ideal for robotics applications since they have high temporal resolution, high dynamic range and low latency. However, due to their high temporal resolution, event cameras are particularly sensitive to flicker such as from fluorescent or LED lights. During every cycle from bright to dark, pixels that image a flickering light source generate many events that provide little or no useful information for a robot, swamping the useful data in the scene. In this paper, we propose a novel linear filter to preprocess event data to remove unwanted flicker events from an event stream. The proposed algorithm achieves over 4.6 times relative improvement in the signal-to-noise ratio when compared to the raw event stream due to the effective removal of flicker from fluorescent lighting. Thus, it is ideally suited to robotics applications that operate in indoor settings or scenes illuminated by flickering light sources.

cs.CV↗

arXiv2022

An Asynchronous Kalman Filter for Hybrid Event Cameras

Event cameras are ideally suited to capture HDR visual information without blur but perform poorly on static or slowly changing scenes. Conversely, conventional image sensors measure absolute intensity of slowly changing scenes effectively but do poorly on high dynamic range or quickly changing scenes. In this paper, we present an event-based video reconstruction pipeline for High Dynamic Range (HDR) scenarios. The proposed algorithm includes a frame augmentation pre-processing step that deblurs and temporally interpolates frame data using events. The augmented frame and event data are then fused using a novel asynchronous Kalman filter under a unifying uncertainty model for both sensors. Our experimental results are evaluated on both publicly available datasets with challenging lighting conditions and fast motions and our new dataset with HDR reference. The proposed algorithm outperforms state-of-the-art methods in both absolute intensity error (48% reduction) and image similarity indexes (average 11% improvement).

cs.CV↗

arXiv2022

Stereo Hybrid Event-Frame (SHEF) Cameras for 3D Perception

Stereo camera systems play an important role in robotics applications to perceive the 3D world. However, conventional cameras have drawbacks such as low dynamic range, motion blur and latency due to the underlying frame-based mechanism. Event cameras address these limitations as they report the brightness changes of each pixel independently with a fine temporal resolution, but they are unable to acquire absolute intensity information directly. Although integrated hybrid event-frame sensors (eg., DAVIS) are available, the quality of data is compromised by coupling at the pixel level in the circuit fabrication of such cameras. This paper proposes a stereo hybrid event-frame (SHEF) camera system that offers a sensor modality with separate high-quality pure event and pure frame cameras, overcoming the limitations of each separate sensor and allowing for stereo depth estimation. We provide a SHEF dataset targeted at evaluating disparity estimation algorithms and introduce a stereo disparity estimation algorithm that uses edge information extracted from the event stream correlated with the edge detected in the frame data. Our disparity estimation outperforms the state-of-the-art stereo matching algorithm on the SHEF dataset.

cs.CV↗

arXiv2022

Observer Design for Nonlinear Systems with Equivariance

Equivariance is a common and natural property of many nonlinear control systems, especially those associated with models of mechatronic and navigation systems. Such systems admit a symmetry, associated with the equivariance, that provides structure enabling the design of robust and high performance observers. A key insight is to pose the observer state to lie in the symmetry group rather than on the system state space. This allows one to define a globally defined intrinsic equivariant error but poses a challenge in defining internal dynamics for the observer. By choosing an equivariant lift of the system dynamics for the observer internal model we show that the error dynamics have a particularly nice form. Applying the methodology of Extended Kalman Filtering (EKF) to the equivariant error state yields the Equivariant Filter (EqF). The geometry of the state-space manifold appears naturally as a curvature modification to the classical EKF Riccati equation. The equivariant filter exploits the symmetry and respects the geometry of an equivariant system model and yields high performance robust filters for a wide range of mechatronic and navigation systems.

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arXiv2022

Equivariant Filter Design for Inertial Navigation Systems with Input Measurement Biases

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 real-world 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.

cs.RO↗

arXiv2021

VDO-SLAM: A Visual Dynamic Object-aware SLAM System

Combining Simultaneous Localisation and Mapping (SLAM) estimation and dynamic scene modelling can highly benefit robot autonomy in dynamic environments. Robot path planning and obstacle avoidance tasks rely on accurate estimations of the motion of dynamic objects in the scene. This paper presents VDO-SLAM, a robust visual dynamic object-aware SLAM system that exploits semantic information to enable accurate motion estimation and tracking of dynamic rigid objects in the scene without any prior knowledge of the objects' shape or geometric models. The proposed approach identifies and tracks the dynamic objects and the static structure in the environment and integrates this information into a unified SLAM framework. This results in highly accurate estimates of the robot's trajectory and the full SE(3) motion of the objects as well as a spatiotemporal map of the environment. The system is able to extract linear velocity estimates from objects' SE(3) motion providing an important functionality for navigation in complex dynamic environments. We demonstrate the performance of the proposed system on a number of real indoor and outdoor datasets and the results show consistent and substantial improvements over the state-of-the-art algorithms. An open-source version of the source code is available.

cs.RO↗

arXiv2021

A Novel Passivity-Based Trajectory Tracking Control For Conservative Mechanical Systems

Most passivity based trajectory tracking algorithms for mechanical systems can only stabilise reference trajectories that have constant energy. This paper overcomes this limitation by deriving a single variable Hamiltonian model for the reference trajectory and solving along the constrained trajectory to obtain a reference potential. This potential is then used as the model to shape the energy of the true system such that its free solutions include the desired reference trajectory. The proposed trajectory tracking algorithm interconnects the reference and true systems through a virtual spring damper along with an outer-loop energy pump/damper that stabilises the desired energy level of the interconnected system, ensuring asymptotic tracking of the desired trajectory. The resulting algorithm is a fully energy based trajectory tracking control for non-stationary trajectories of conservative mechanical systems.

eess.SY↗

arXiv2021

Equivariant filter (EqF): A general filter design for systems on homogeneous spaces

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 methodologies.

eess.SY↗

arXiv2021

Equivariant Systems Theory and Observer Design for Second Order Kinematic Systems on Matrix Lie Groups

This paper presents the equivariant systems theory and observer design for second order kinematic systems on matrix Lie groups. The state of a second order kinematic system on a matrix Lie group is naturally posed on the tangent bundle of the group with the inputs lying in the tangent of the tangent bundle known as the double tangent bundle. We provide a simple parameterization of both the tangent bundle state space and the input space (the fiber space of the double tangent bundle) and then introduce a semi-direct product group and group actions onto both the state and input spaces. We show that with the proposed group actions the second order kinematics are equivariant. An equivariant lift of the kinematics onto the symmetry group is defined and used to design a nonlinear observer on the lifted state space using nonlinear constructive design techniques. A simple hovercraft simulation verifies the performance of our observer.

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