scholarly journals Observer design for a single mast stacker crane

2021 ◽  
Vol 69 (9) ◽  
pp. 806-816
Author(s):  
Lukas Ecker ◽  
Tobias Malzer ◽  
Arne Wahrburg ◽  
Markus Schöberl
Keyword(s):  
Kalman Filter ◽  
Ritz Method ◽  
Observer Design ◽  
Measurement Unit ◽  
Dimensional System ◽  
Observer Error ◽  
Infinite Dimensional ◽  
Measurement Results ◽  
Automated Warehouses ◽  
Error System

Abstract This contribution is concerned with the design of observers for a single mast stacker crane, which is used, e. g., for storage and removal of loads in automated warehouses. As the mast of such stacker cranes is typically a lightweight construction, the system under consideration is described by ordinary as well as partial differential equations, i. e., the system exhibits a mixed finite-/infinite-dimensional character. We will present two different observer designs, an Extended Kalman Filter based on a finite-dimensional system approximation, using the Rayleigh-Ritz method and an approach exploiting the port-Hamiltonian system representation for the mixed finite-/infinite-dimensional scenario where in particular the observer-error system should be formulated in the port-Hamiltonian framework. The mixed-dimensional observer and the Kalman Filter are employed to estimate the deflection of the beam based on signals acquired by an inertial measurement unit at the beam tip. Such an approach considerably simplifies mechatronic integration as it renders strain-gauges at the base of the mast obsolete. Finally, measurement results demonstrate the capability of these approaches for monitoring and vibration-rejection purposes.

scholarly journals Kalman Filter untuk Mengurangi Derau Sensor Accelerometer pada IMU Guna Estimasi Jarak

AVITEC ◽  
2020 ◽  
Vol 2 (2) ◽  
Author(s):  
Muhammad Ari Roma Wicaksono ◽  
Freddy Kurniawan ◽  
Lasmadi Lasmadi
Keyword(s):  
Kalman Filter ◽  
Measurement Errors ◽  
System Modeling ◽  
Measurement Unit ◽  
Accelerometer Sensor ◽  
Matrix Operations ◽  
Threshold Algorithm ◽  
Average Accuracy ◽  
Measurement Results ◽  
Kalman Filter Algorithm

This study aims to develop a Kalman filter algorithm in order to reduce the accelerometer sensor noise as effectively as possible. The accelerometer sensor is one part of the Inertial Measurement Unit (IMU) used to find the displacement distance of an object. The method used is modeling the system to model the accelerometer system to form mathematical equations. Then the state space method is used to change the system modeling to the form of matrix operations so that the process of the data calculating to the Kalman Filter algorithm is not too difficult. It also uses the threshold algorithm to detect the sensor's condition at rest. The present study had good results, which of the four experiments obtained with an average accuracy of 93%. The threshold algorithm successfully reduces measurement errors when the sensor is at rest or static so that the measurement results more accurate. The developed algorithm can also detect the sensor to move forward or backward.

scholarly journals Contact-aided invariant extended Kalman filtering for robot state estimation

2020 ◽  
Vol 39 (4) ◽  
pp. 402-430 ◽  
Author(s):  
Ross Hartley ◽  
Maani Ghaffari ◽  
Ryan M Eustice ◽  
Jessy W Grizzle
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Domain Of Attraction ◽  
Observer Design ◽  
Measurement Unit ◽  
State Variables ◽  
Extended Kalman Filtering ◽  
Contact Points ◽  
Error Dynamics ◽  
Log Linear

Legged robots require knowledge of pose and velocity in order to maintain stability and execute walking paths. Current solutions either rely on vision data, which is susceptible to environmental and lighting conditions, or fusion of kinematic and contact data with measurements from an inertial measurement unit (IMU). In this work, we develop a contact-aided invariant extended Kalman filter (InEKF) using the theory of Lie groups and invariant observer design. This filter combines contact-inertial dynamics with forward kinematic corrections to estimate pose and velocity along with all current contact points. We show that the error dynamics follows a log-linear autonomous differential equation with several important consequences: (a) the observable state variables can be rendered convergent with a domain of attraction that is independent of the system’s trajectory; (b) unlike the standard EKF, neither the linearized error dynamics nor the linearized observation model depend on the current state estimate, which (c) leads to improved convergence properties and (d) a local observability matrix that is consistent with the underlying nonlinear system. Furthermore, we demonstrate how to include IMU biases, add/remove contacts, and formulate both world-centric and robo-centric versions. We compare the convergence of the proposed InEKF with the commonly used quaternion-based extended Kalman filter (EKF) through both simulations and experiments on a Cassie-series bipedal robot. Filter accuracy is analyzed using motion capture, while a LiDAR mapping experiment provides a practical use case. Overall, the developed contact-aided InEKF provides better performance in comparison with the quaternion-based EKF as a result of exploiting symmetries present in system.

A SIMPLE OBSERVER OF THE HYPERCHAOTIC RÖSSLER SYSTEM

2010 ◽  
Vol 24 (22) ◽  
pp. 4325-4331
Author(s):  
XING-YUAN WANG ◽  
JUN-MEI SONG
Keyword(s):  
Dynamical System ◽  
Time Domain ◽  
Global Exponential Stability ◽  
Observer Design ◽  
The Other ◽  
State Observation ◽  
Rossler System ◽  
Error System ◽  
Rössler System ◽  
The Time Domain

This paper studies the hyperchaotic Rössler system and the state observation problem of such a system being investigated. Based on the time-domain approach, a simple observer for the hyperchaotic Rössler system is proposed to guarantee the global exponential stability of the resulting error system. The scheme is easy to implement and different from the other observer design that it does not need to transmit all signals of the dynamical system. It is proved theoretically, and numerical simulations show the effectiveness of the scheme finally.

An Improved and Efficient Algorithm for SINS/GPS/Doppler Integrated Navigation Systems

2012 ◽  
Vol 245 ◽  
pp. 323-329 ◽  
Author(s):  
Muhammad Ushaq ◽  
Jian Cheng Fang
Keyword(s):  
Kalman Filter ◽  
Navigation System ◽  
Inertial Navigation System ◽  
Inertial Sensor ◽  
Inertial Navigation ◽  
Measurement Unit ◽  
Navigation Systems ◽  
Integrated Navigation ◽  
Efficient Manner ◽  
Position Errors

Inertial navigation systems exhibit position errors that tend to grow with time in an unbounded mode. This degradation is due, in part, to errors in the initialization of the inertial measurement unit and inertial sensor imperfections such as accelerometer biases and gyroscope drifts. Mitigation to this growth and bounding the errors is to update the inertial navigation system periodically with external position (and/or velocity, attitude) fixes. The synergistic effect is obtained through external measurements updating the inertial navigation system using Kalman filter algorithm. It is a natural requirement that the inertial data and data from the external aids be combined in an optimal and efficient manner. In this paper an efficient method for integration of Strapdown Inertia Navigation System (SINS), Global Positioning System (GPS) and Doppler radar is presented using a centralized linear Kalman filter by treating vector measurements with uncorrelated errors as scalars. Two main advantages have been obtained with this improved scheme. First is the reduced computation time as the number of arithmetic computation required for processing a vector as successive scalar measurements is significantly less than the corresponding number of operations for vector measurement processing. Second advantage is the improved numerical accuracy as avoiding matrix inversion in the implementation of covariance equations improves the robustness of the covariance computations against round off errors.

The Description of a Distributed Parameter Process through a Finite Discrete Dimensional System

2014 ◽  
Vol 657 ◽  
pp. 874-878
Author(s):  
Sever Şerban ◽  
Doina Corina Şerban
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Industrial Process ◽  
Time Discretization ◽  
Distributed Parameter ◽  
Geometrical Parameters ◽  
Dimensional System ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Distributed Parameters

This article analyses the process of warming a metal by using a walking beam furnace. This process is meant to offer the technologist objective information that may allow him to produce eventual modifications of the temperature references from the furnaces zones. Thus making the metals temperature at the furnaces exit to have an imposed distribution, within precise limits, according to the technological requests. This industrial process has a geometrical parameters distribution, more precisely it can be described through a partial differential equation, by being attached to dynamic infinite dimensional systems (or with distributed parameters). Using a procedure called geometric-time discretization (in the condition of the solutions convergence), we have managed to obtain a representation under the form of a finite discrete dimensional linear system for a process with distributed parameters.

scholarly journals Integration of GPS, Monocular Vision, and High Definition (HD) Map for Accurate Vehicle Localization

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3270 ◽  
Author(s):  
Hao Cai ◽  
Zhaozheng Hu ◽  
Gang Huang ◽  
Dunyao Zhu ◽  
Xiaocong Su
Keyword(s):  
Kalman Filter ◽  
Low Cost ◽  
Kinematic Model ◽  
Intelligent Vehicles ◽  
Monocular Vision ◽  
Measurement Unit ◽  
High Definition ◽  
Position Information ◽  
Vehicle Localization ◽  
Lateral Distance

Self-localization is a crucial task for intelligent vehicles. Existing localization methods usually require high-cost IMU (Inertial Measurement Unit) or expensive LiDAR sensors (e.g., Velodyne HDL-64E). In this paper, we propose a low-cost yet accurate localization solution by using a custom-level GPS receiver and a low-cost camera with the support of HD map. Unlike existing HD map-based methods, which usually requires unique landmarks within the sensed range, the proposed method utilizes common lane lines for vehicle localization by using Kalman filter to fuse the GPS, monocular vision, and HD map for more accurate vehicle localization. In the Kalman filter framework, the observations consist of two parts. One is the raw GPS coordinate. The other is the lateral distance between the vehicle and the lane, which is computed from the monocular camera. The HD map plays the role of providing reference position information and correlating the local lateral distance from the vision and the GPS coordinates so as to formulate a linear Kalman filter. In the prediction step, we propose using a data-driven motion model rather than a Kinematic model, which is more adaptive and flexible. The proposed method has been tested with both simulation data and real data collected in the field. The results demonstrate that the localization errors from the proposed method are less than half or even one-third of the original GPS positioning errors by using low cost sensors with HD map support. Experimental results also demonstrate that the integration of the proposed method into existing ones can greatly enhance the localization results.

Attitude Determination by Integration of Multi-Sensors Based on Federated Kalman Filter

2014 ◽  
Vol 602-605 ◽  
pp. 2958-2961
Author(s):  
Tao Lai ◽  
Guang Long Wang ◽  
Wen Jie Zhu ◽  
Feng Qi Gao
Keyword(s):  
Kalman Filter ◽  
Inertial Measurement Unit ◽  
Attitude Determination ◽  
Angular Rate ◽  
General Structure ◽  
Test System ◽  
Measurement Unit ◽  
Storage Test ◽  
Inertial Measurement ◽  
Federated Kalman Filter

Micro inertial measurement unit integration storage test system is a typical multi-sensor information fusion system consists of microsensors. The Federated Kalman filter is applied to micro inertial measurement unit integration storage test system. The general structure and characteristics of Federated Kalman filter is expounded. The four-order Runge-Kutta method based on quaternion differential equation was used to dispose the output angular rate data from gyroscope, and the recurrence expressions was established too. The control system based ARM Cortex-M4 master-slave structure is adopted in this paper. The result shown that the dimensionality reduced algorithm significantly reduces implementation complexity of the method and the amount computation. The filtering effect and real-time performance have much increased than traditionally method.

scholarly journals A Robust and Adaptive Complementary Kalman Filter Based on Mahalanobis Distance for Ultra Wideband/Inertial Measurement Unit Fusion Positioning

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3435 ◽  
Author(s):  
Xin Li ◽  
Yan Wang ◽  
Kourosh Khoshelham
Keyword(s):  
Kalman Filter ◽  
Mahalanobis Distance ◽  
Inertial Measurement Unit ◽  
Least Squares Method ◽  
Ultra Wideband ◽  
Measurement Unit ◽  
Observation Error ◽  
System State ◽  
Inertial Measurement ◽  
The Impact

Ultra wideband (UWB) has been a popular technology for indoor positioning due to its high accuracy. However, in many indoor application scenarios UWB measurements are influenced by outliers under non-line of sight (NLOS) conditions. To detect and eliminate outlying UWB observations, we propose a UWB/Inertial Measurement Unit (UWB/IMU) fusion filter based on a Complementary Kalman Filter to track the errors of position, velocity and direction. By using the least squares method, the positioning residual of the UWB observation is calculated, the robustness factor of the observation is determined, and an observation weight is dynamically set. When the robustness factor does not exceed a pre-defined threshold, the observed value is considered trusted, and adaptive filtering is used to track the system state, while the abnormity of system state, which might be caused by IMU data exceptions or unreasonable noise settings, is detected by using Mahalanobis distance from the observation to the prior distribution. When the robustness factor exceeds the threshold, the observed value is considered abnormal, and robust filtering is used, whereby the impact of UWB data exceptions on the positioning results is reduced by exploiting Mahalanobis distance. Experimental results show that the observation error can be effectively estimated, and the proposed algorithm can achieve an improved positioning accuracy when affected by outlying system states of different quantity as well as outlying observations of different proportion.

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