Observer design for position and velocity bias estimation from a single direction output
French Direction Générale de l’Armement (Technical Directorate)（法国国家军备总局）；I3S UNS-CNRS（尼斯-索菲亚-安蒂波利斯大学与法国国家科学研究中心联合研究所）；School of Engineering, Australian National University（澳大利亚国立大学工程学院）；INRIA（法国国家信息与自动化研究所）
Florent Le Bras, Tarek Hamel, Robert Mahony, Claude Samson
This paper addresses the problem of estimating the position of an object moving in $R^n$ from direction and velocity measurements. After addressing observability issues associated with this problem, a nonlinear observer is designed so as to encompass the case where the measured velocity is corrupted by a constant bias. Global exponential convergence of the estimation error is proved under a condition of persistent excitation upon the direction measurements. Simulation results illustrate the performance of the observer.
We consider the distributed $H_\infty$ estimation problem with an additional requirement of resilience to biasing attacks. An attack scenario is considered where an adversary misappropriates some of the observer nodes and injects biasing signals into observer dynamics. The paper proposes a procedure for the derivation of a distributed observer which endows each node with an attack detector which also functions as an attack compensating feedback controller for the main observer. Connecting these controlled observers into a network results in a distributed observer whose nodes produce unbiased r…
Successful navigation of a rigid-body traveling with six degrees of freedom (6 DoF) requires accurate estimation of attitude , position, and linear velocity. The true navigation dynamics are highly nonlinear and are modeled on the matrix Lie group of SE2(3). This paper presents novel geometric nonlinear continuous stochastic navigation observers on SE2(3) capturing the true nonlinearity of the problem. The proposed observers combines IMU and landmark measurements. It efficiently handles the IMU measurement noise. The proposed observers are guaranteed to be almost semi-globally uniformly ultima…
A geometric nonlinear observer algorithm for Simultaneous Localization and Mapping (SLAM) developed on the Lie group of \mathbb{SLAM}_{n}\left(3\right) is proposed. The presented novel solution estimates the vehicle's pose (i.e. attitude and position) with respect to landmarks simultaneously positioning the reference features in the global frame. The proposed estimator on manifold is characterized by predefined measures of transient and steady-state performance. Dynamically reducing boundaries guide the error function of the system to reduce asymptotically to the origin from its starting posit…
We propose globally exponentially convergent continuous observers for invariant kinematic systems on finite-dimensional matrix Lie groups. Such an observer estimates, from measurements of landmarks, vectors and biased velocity, both the system state and the unknown constant bias in velocity measurement, where the state belongs to the state-space Lie group and the velocity to the Lie algebra of the Lie group. The main technique is to embed a given system defined on a matrix Lie group into Euclidean space and build observers in the Euclidean space. The theory is illustrated with the special Eucl…
The rigid-body attitude tracking using vector and biased gyro measurements with unknown inertia matrix is studied in this note. First, a gyro-bias observer with global exponential stability is designed. Then, an attitude tracking controller based on this observer is devised, ensuring almost global asymptotic stability and almost semiglobal exponential stability. A separation property of the combined observer-controller is proved. Lastly, an adaptive attitude tracking controller relying on a modified gyro-bias observer and with no over-parametrization is developed to deal with the unknown inert…
A globally exponentially stable position observer for interior permanent magnet synchronous motors
ITMO University（圣彼得堡信息、光学和机械大学）；The University of Sydney（悉尼大学）；University of Belgrade（贝尔格莱德大学）；Pohang University of Science and Technology (POSTECH)（韩国科学技术院）
This work presents a contracting hierarchical observer that fuses position and orientation measurements with an IMU to generate smooth position, linear velocity, orientation, and IMU bias estimates that are guaranteed to converge to their true values. The proposed approach is composed of two contracting observers. The first is a quaternion-based orientation observer that also estimates gyroscope bias. The output of the orientation observer serves as an input for another contracting observer that estimates position, linear velocity, and accelerometer bias thus forming a hierarchy. We show that …
Navigation solutions suitable for cases when both autonomous robot's pose (\textit{i.e}., attitude and position) and its environment are unknown are in great demand. Simultaneous Localization and Mapping (SLAM) fulfills this need by concurrently mapping the environment and observing robot's pose with respect to the map. This work proposes a nonlinear observer for SLAM posed on the manifold of the Lie group of $\mathbb{SLAM}_{n}\left(3\right)$, characterized by systematic convergence, and designed to mimic the nonlinear motion dynamics of the true SLAM problem. The system error is constrained t…
The ever increasing need for performance results in increasingly rigorous demands on throughput and positioning accuracy of high-precision motion systems, which often suffer from position dependent effects that originate from relative actuation and sensing of the moving-body. Due to the highly stiff mechanical design, such systems are typically controlled using rigid body control design approaches. Nonetheless, the presence of position dependent flexible dynamics severely limits attainable position tracking performance. This paper presents two extensions of the conventional rigid body control …
This paper deals with the problem of full state estimation for vehicles navigating in a three dimensional space. We assume that the vehicle is equipped with an Inertial Measurement Unit (IMU) providing body-frame measurements of the angular velocity, the specific force, and the Earth's magnetic field. Moreover, we consider available sensors that provide partial or full information about the position of the vehicle. Examples of such sensors are those which provide full position measurements (e.g., GPS), range measurements (e.g., Ultra-Wide Band (UWB) sensors), inertial-frame bearing measurement…
In this work we solve the position-aided 3D navigation problem using a nonlinear estimation scheme. More precisely, we propose a nonlinear observer to estimate the full state of the vehicle (position, velocity, orientation and gyro bias) from IMU and position measurements. The proposed observer does not introduce additional auxiliary states and is shown to guarantee semi-global exponential stability without any assumption on the acceleration of the vehicle. The performance of the observer is shown, through simulation, to overcome the state-of-the-art approach that assumes negligible accelerati…
The position and the orientation of a rigid body object pushed by a robot on a planar surface are extremely difficult to predict. In this paper, the prediction problem is formulated as a disturbance observer design problem. The disturbance observer provides accurate estimation of the total sum of model errors and external disturbances acting on the object. From the estimation results, it is revealed that there is a strong linear relationship between the applied force or torque and the estimated disturbances. The proposed prediction algorithm has two phases: the identification & the prediction.…
Synchronous Observer Design for Landmark-Inertial SLAM with Magnetometer and Intermittent GNSS Measurements
Centre for Systems and Control, Indian Institute of Technology Bombay（印度理工学院孟买分校系统与控制中心）；School of Aerospace, Mechanical and Mechatronic Engineering (AMME), Faculty of Engineering, University of Sydney（悉尼大学工程学院航空航天、机械与机电工程系）
Detection and Mitigation of Biasing Attacks on Distributed Estimation Networks
The University of Melbourne（墨尔本大学）；University of New South Wales at the Australian Defence Force Academy（新南威尔士大学澳大利亚国防军学院）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
In this paper we consider estimating the system parameters and designing stable observer for unknown noisy linear time-invariant (LTI) systems. We propose a Support Vector Regression (SVR) based estimator to provide adjustable asymmetric error interval for estimations. This estimator is capable to trade-off bias-variance of the estimation error by tuning parameter $γ> 0$ in the loss function. This method enjoys the same sample complexity of $\mathcal{O}(1/\sqrt{N})$ as the Ordinary Least Square (OLS) based methods but achieves a $\mathcal{O}(1/(γ+1))$ smaller variance. Then, a stable observer …
For a class of uncertain systems with large-error sensing, the low-order stable signal corrector and observer are presented for signal correction and uncertainty estimation according to completely decoupling estimation. The signal corrector can reject the large error in global position sensing, and system uncertainty can be estimated by the observer, even the existence of stochastic non-Gaussian noise. The corrector and observer are applied to a UAV navigation and control for large-error corrections in position/attitude angle and the uncertainties estimation in the UAV flight dynamics. The con…
In this work, we present a mixed sensorless strategy for Permanent Magnets Synchronous Machines, combining a torque/current controller and an observer for position, speed, flux and stator resistance. The proposed co-design is motivated by the need of an appropriate signal injection technique, in order to guarantee full state observability. Neither the typical constant or slowly-varying speed assumptions, nor a priori mechanical model information are used in the observer design. Instead, the rotor speed is modeled as an unknown input disturbance with constant (unknown) sign and uniformly non-ze…
Nonlinear Deterministic Observer for Inertial Navigation using Ultra-wideband and IMU Sensor Fusion
Carleton University（卡尔顿大学）；The Hong Kong Polytechnic University（香港理工大学）；Georgia Institute of Technology（佐治亚理工学院）；Bowling Green State University（鲍灵格林州立大学）
The University of Sydney（悉尼大学）；DJI Innovation Inc.（大疆创新有限公司）
The design of a globally convergent position observer for feature points from visual information is a challenging problem, especially for the case with only inertial measurements and without assumptions of uniform observability, which remained open for a long time. We give a solution to the problem in this paper assuming that only the bearing of a feature point, and biased linear acceleration and rotational velocity of a robot -- all in the body-fixed frame -- are available. Further, in contrast to existing related results, we do not need the value of the gravitational constant either. The pro…
The process of simultaneously mapping the environment in three dimensional (3D) space and localizing a moving vehicle's pose (orientation and position) is termed Simultaneous Localization and Mapping (SLAM). SLAM is a core task in robotics applications. In the SLAM problem, each of the vehicle's pose and the environment are assumed to be completely unknown. This paper takes the conventional SLAM design as a basis and proposes a novel approach that ensures fast adaptation of the nonlinear observer for SLAM. Due to the fact that the true SLAM problem is nonlinear and is modeled on the Lie group …
Western University（韦仕敦大学）；Lakehead University（湖首大学）
This paper considers the problem of attitude, position and linear velocity estimation for rigid body systems relying on landmark measurements. We propose two hybrid nonlinear observers on the matrix Lie group $SE_2(3)$, leading to global exponential stability. The first observer relies on fixed gains, while the second one uses variable gains depending on the solution of a continuous Riccati equation (CRE). These observers are then extended to handle biased angular velocity measurements. Both simulation and experimental results are presented to illustrate the performance of the proposed observe…
A robust nonlinear stochastic observer for simultaneous localization and mapping (SLAM) is proposed using the available uncertain measurements of angular velocity, translational velocity, and features. The proposed observer is posed on the Lie Group of $\mathbb{SLAM}_{n}\left(3\right)$ to mimic the true stochastic SLAM dynamics. The proposed approach considers the velocity measurements to be attached with an unknown bias and an unknown Gaussian noise. The proposed SLAM observer ensures that the closed loop error signals are semi-globally uniformly ultimately bounded. Simulation results demonst…
Pose, Velocity and Landmark Position Estimation Using IMU and Bearing Measurements
School of Artificial Intelligence and Automation, Huazhong University of Science and Technology（华中科技大学人工智能与自动化学院）；Department of Electrical Engineering, Lakehead University（湖首大学电气工程系）；Department of Electrical and Computer Engineering, Western University（西安大略大学电气与计算机工程系）
Cascaded Tightly-Coupled Observer Design for Single-Range-Aided Inertial Navigation
Department of Computer Science（计算机科学系）；Engineering, University of Quebec in Outaouais, Gatineau, QC, Canada（魁北克大学Outaouais工程学院，加蒂纳岛，QC，加拿大）；Department of Electrical and Computer Engineering（电气与计算机工程系）；Lakehead University（拉克头大学）
Western University（韦仕敦大学）；Lakehead University（湖首大学）
This paper considers the problem of simultaneous estimation of the attitude, position and linear velocity for vehicles navigating in a three-dimensional space. We propose two types of hybrid nonlinear observers using continuous angular velocity and linear acceleration measurements as well as intermittent landmark position measurements. The first type relies on a fixed-gain design approach based on an infinite-dimensional optimization, while the second one relies on a variable-gain design approach based on a continuous-discrete Riccati equation. For each case, we provide two different observers…
Western University（西安大略大学）；University of Quebec in Outaouais（魁北克大学乌塔韦校区）；Lakehead University（湖首大学）
This paper deals with the simultaneous estimation of the attitude, position and linear velocity for vision-aided inertial navigation systems. We propose a nonlinear observer on $SO(3)\times \mathbb{R}^{15}$ relying on body-frame acceleration, angular velocity and (stereo or monocular) bearing measurements of some landmarks that are constant and known in the inertial frame. Unlike the existing local Kalman-type observers, our proposed nonlinear observer guarantees almost global asymptotic stability and local exponential stability. A detailed uniform observability analysis has been conducted and…
Western University（韦仕敦大学）；Lakehead University（湖首大学）
The design of navigation observers able to simultaneously estimate the position, linear velocity and orientation of a vehicle in a three-dimensional space is crucial in many robotics and aerospace applications. This problem was mainly dealt with using the extended Kalman filter and its variants which proved to be instrumental in many practical applications. Although practically efficient, the lack of strong stability guarantees of these algorithms motivated the emergence of a new class of geometric navigation observers relying on Riemannian geometry tools, leading to provable strong stability …
