A Novel Fuzzy-Adaptive Extended Kalman Filter for Real-Time Attitude Estimation of Mobile Robots

Robust Attitude Estimation for Low-Dynamic Vehicles Based on MEMS-IMU and External Acceleration Compensation

Attitude determination based on a micro-electro-mechanical system inertial measurement unit (MEMS-IMU) has attracted extensive attention. The non-gravitational components of the MEMS-IMU have a significant effect on the accuracy of attitude estimation. To improve the attitude estimation of low-dynamic vehicles under uneven soil conditions or vibrations, a robust Kalman filter (RKF) was developed and tested in this paper, where the noise covariance was adaptively changed to compensate for the external acceleration of the vehicle. The state model for MEMS-IMU attitude estimation was initially constructed using a simplified direction cosine matrix. Subsequently, the variance of unmodeled external acceleration was estimated online based on filtering innovations of different window lengths, where the acceleration disturbance was addressed by tradeoffs in time-delay and prescribed computation cost. The effectiveness of the RKF was validated through experiments using a three-axis turntable, an automatic vehicle, and a tractor tillage test. The turntable experiment demonstrated that the angle result of the RKF was 0.051° in terms of root mean square error (RMSE), showing improvements of 65.5% and 29.2% over a conventional KF and MTi-300, respectively. The dynamic attitude estimation of the automatic vehicle showed that the RKF achieves smoother pitch angles than the KF when the vehicle passes over speed bumps at different speeds; the RMSE of pitch was reduced from 0.875° to 0.460° and presented a similar attitude trend to the MTi-300. The tractor tillage test indicated that the RMSE of plough pitch was improved from 0.493° with the KF to 0.259° with the RKF, an enhancement of approximately 47.5%, illustrating the superiority of the RKF in suppressing the external acceleration disturbances of IMU-based attitude estimation.

Crossing-Point Estimation in Human-Robot Navigation-Statistical Linearization versus Sigma-Point Transformation

Interactions between mobile robots and human operators in common areas require a high level of safety, especially in terms of trajectory planning, obstacle avoidance and mutual cooperation. In this connection, the crossings of planned trajectories and their uncertainty based on model fluctuations, system noise and sensor noise play an outstanding role. This paper discusses the calculation of the expected areas of interactions during human-robot navigation with respect to fuzzy and noisy information. The expected crossing points of the possible trajectories are nonlinearly associated with the positions and orientations of the robots and humans. The nonlinear transformation of a noisy system input, such as the directions of the motion of humans and robots, to a system output, the expected area of intersection of their trajectories, is performed by two methods: statistical linearization and the sigma-point transformation. For both approaches, fuzzy approximations are presented and the inverse problem is discussed where the input distribution parameters are computed from the given output distribution parameters.

A Customized Extended Kalman Filter for Removing the Impact of the Magnetometer's Measurements on Inclination Determination

Normally, a three-dimensional orientation determination algorithm that is used in a magnetic and inertial measurement unit calculates the inclination (including both the pitch and roll) of rigid bodies by fusing the measurements of the gyroscope, as well as the measurements of both the accelerometer and the magnetometer. The measurements of the magnetometer can be helpful in improving the inclination estimation accuracy; however, once the measurements of the magnetometer are disturbed by ferromagnetic materials, the inclination estimation accuracy could be significantly decreased. Hence, a better approach should be followed in terms of not employing the measurements of the magnetometer for inclination determination. In order to achieve this goal, the component of the measurement of the magnetometer that is used for the improvement of the inclination estimation accuracy, along with the measurement of the accelerometer at each sampling time instant, is abandoned. Consequently, the remaining component of the measurement of the magnetometer, which is perpendicular to the measurement of the accelerometer, is used for the azimuth determination. After applying this process, the extended Kalman filter (EKF) is proposed for the inclination and azimuth estimations. Through experiments, the EKF is compared with three algorithms that were recently proposed with the same objective as this work, and the extracted outcomes show that the EKF approach clearly outperforms these three algorithms.

A Novel Prediction Method of Transfer-Assisted Action Oriented to Individual Differences for the Excretion Care Robot

The excretion care robot's (ECR) accurate recognition of transfer-assisted actions is crucial during its usage. However, transfer action recognition is a challenging task, especially since the differentiation of actions seriously affects its recognition speed, robustness, and generalization ability. We propose a novel approach for transfer action recognition assisted by a bidirectional long- and short-term memory (Bi-LSTM) network combined with a multi-head attention mechanism. Firstly, we utilize posture sensors to detect human movements and establish a lightweight three-dimensional (3D) model of the lower limbs. In particular, we adopt a discrete extended Kalman filter (DEKF) to improve the accuracy and foresight of pose solving. Then, we construct an action prediction model that incorporates a fused Bi-LSTM with Multi-head attention (MHA Bi-LSTM). The MHA extracts key information related to differentiated movements from different dimensions and assigns varying weights. Utilizing the Bi-LSTM network effectively combines past and future information to enhance the prediction results of differentiated actions. Finally, comparisons were made by three subjects in the proposed method and with two other time series based neural network models. The reliability of the MHA Bi-LSTM method was verified. These experimental results show that the introduced MHA Bi-LSTM model has a higher accuracy in predicting posture sensor-based excretory care actions. Our method provides a promising approach for handling transfer-assisted action individual differentiation in excretion care tasks.

Cautious Bayesian Optimization: A Line Tracker Case Study

In this paper, a procedure for experimental optimization under safety constraints, to be denoted as constraint-aware Bayesian Optimization, is presented. The basic ingredients are a performance objective function and a constraint function; both of them will be modeled as Gaussian processes. We incorporate a prior model (transfer learning) used for the mean of the Gaussian processes, a semi-parametric Kernel, and acquisition function optimization under chance-constrained requirements. In this way, experimental fine-tuning of a performance objective under experiment-model mismatch can be safely carried out. The methodology is illustrated in a case study on a line-follower application in a CoppeliaSim environment.

Research on Gradient-Descent Extended Kalman Attitude Estimation Method for Low-Cost MARG

Aiming at the problem of the weak dynamic performance of the gradient descent method in the attitude and heading reference system, the susceptibility to the interference of accelerometers and magnetometers, and the complex calculation of the nonlinear Kalman Filter method, an extended Kalman filter suitable for a low-cost magnetic, angular rate, and gravity (MARG) sensor system is proposed. The method proposed in this paper is a combination of a two-stage gradient descent algorithm and the extended Kalman filter (GDEKF). First, the accelerometer and magnetometer are used to correct the attitude angle according to the two-stage gradient descent algorithm. The obtained attitude quaternion is combined with the gyroscope measurement value as the observation vector of EKF and the calculated attitude of the gyroscope and the bias of the gyroscope are corrected. The elimination of the bias of the gyroscope can further improve the stability of the attitude observation results. Finally, the MARG sensor system was designed for mathematical model simulation and hardware-in-the-loop simulation to verify the performance of the filter. The results show that compared with the gradient descent method, it has better anti-interference performance and dynamic performance, and better measurement accuracy than the extended Kalman filter.

Vortex signal model based Kalman filter of vortex signal processing method

To improve the performance of the vortex flowmeter, a vortex signal model based Kalman filter of the vortex signal processing method is proposed. According to the characteristics of the vortex signal, a linear vortex signal model is designed. Combining the fuzzy search and iterative algorithm, the Kalman filter algorithm is improved by analyzing the principle and key parameters of the Kalman filter algorithm. The proposed method is verified by simulation and real flow experiments and compared with other methods; the experimental results show that the proposed method has the advantages of adaptive filtering, better anti-interference ability, and faster filtering speed.

Perspectives of RealSense and ZED Depth Sensors for Robotic Vision Applications

This review paper presents an overview of depth cameras. Our goal is to describe the features and capabilities of the introduced depth sensors in order to determine their possibilities in robotic applications, focusing on objects that might appear in applications with high accuracy requirements. A series of experiments was conducted, and various depth measuring conditions were examined in order to compare the measurement results of all the depth cameras. Based on the results, all the examined depth sensors were appropriate for applications where obstacle avoidance and robot spatial orientation were required in coexistence with image vision algorithms. In robotic vision applications where high accuracy and precision were obligatory, the ZED depth sensors achieved better measurement results.

Sensorless Estimation Based on Neural Networks Trained with the Dynamic Response Points

In the present work, a neuronal dynamic response prediction system is shown to estimate the response of multiple systems remotely without sensors. For this, a set of Neural Networks and the response to the step of a stable system is used. Six basic characteristics of the dynamic response were extracted and used to calculate a Transfer Function equivalent to the dynamic model. A database with 1,500,000 data points was created to train the network system with the basic characteristics of the dynamic response and the Transfer Function that causes it. The contribution of this work lies in the use of Neural Network systems to estimate the behavior of any stable system, which has multiple advantages compared to typical linear regression techniques since, although the training process is offline, the estimation can perform in real time. The results show an average 2% MSE error for the set of networks. In addition, the system was tested with physical systems to observe the performance with practical examples, achieving a precise estimation of the output with an error of less than 1% for simulated systems and high performance in real signals with the typical noise associated due to the acquisition system.

Improved Attitude and Heading Accuracy with Double Quaternion Parameters Estimation and Magnetic Disturbance Rejection

The use of unmanned aerial vehicle (UAV) applications has grown rapidly over the past decade with the introduction of low-cost microelectromechanical system (MEMS)-based sensors that measure angular velocity, gravity, and magnetic field, which are important for an object orientation determination. However, the use of low-cost sensors has also been limited because their readings are easily distorted by unwanted internal and/or external noise signals such as environmental magnetic disturbance, which lead to errors in attitude and heading estimation results. In an extended Kalman filter (EKF) process, this study proposes a method for mitigating the effect of magnetic disturbance on attitude determination by using a double quaternion parameters for representation of orientation states, which decouples the magnetometer from attitude computation. Additionally, an online measurement error covariance matrix tuning system was implemented to reject the impact of magnetic disturbance on the heading estimation. Simulation and experimental tests were conducted to verify the performance of the proposed methods in resolving the magnetic noise effect on attitude and heading. The results showed that the proposed method performed better than complimentary, gradient descent, and single quaternion-based EKF.

Estimation of Transfer Function Coefficients for Second-Order Systems via Metaheuristic Algorithms

The present research develops the parametric estimation of a second-order transfer function in its standard form, employing metaheuristic algorithms. For the estimation, the step response with a known amplitude is used. The main contribution of this research is a general method for obtaining a second-order transfer function for any order stable systems via metaheuristic algorithms. Additionally, the Final Value Theorem is used as a restriction to improve the velocity search. The tests show three advantages in using the method proposed in this work concerning similar research and the exact estimation method. The first advantage is that using the Final Value Theorem accelerates the convergence of the metaheuristic algorithms, reducing the error by up to 10 times in the first iterations. The second advantage is that, unlike the analytical method, it is unnecessary to estimate the type of damping that the system has. Finally, the proposed method is adapted to systems of different orders, managing to calculate second-order transfer functions equivalent to higher and lower orders. Response signals to the step of systems of an electrical, mechanical and electromechanical nature were used. In addition, tests were carried out with simulated signals and real signals to observe the behavior of the proposed method. In all cases, transfer functions were obtained to estimate the behavior of the system in a precise way before changes in the input. In all tests, it was shown that the use of the Final Value Theorem presents advantages compared to the use of algorithms without restrictions. Finally, it was revealed that the Gray Wolf Algorithm has a better performance for parametric estimation compared to the Jaya algorithm with an error up to 50% lower.

Cascaded Complementary Filter Architecture for Sensor Fusion in Attitude Estimation

Attitude estimation is the process of computing the orientation angles of an object with respect to a fixed frame of reference. Gyroscope, accelerometer, and magnetometer are some of the fundamental sensors used in attitude estimation. The orientation angles computed from these sensors are combined using the sensor fusion methodologies to obtain accurate estimates. The complementary filter is one of the widely adopted techniques whose performance is highly dependent on the appropriate selection of its gain parameters. This paper presents a novel cascaded architecture of the complementary filter that employs a nonlinear and linear version of the complementary filter within one framework. The nonlinear version is used to correct the gyroscope bias, while the linear version estimates the attitude angle. The significant advantage of the proposed architecture is its independence of the filter parameters, thereby avoiding tuning the filter's gain parameters. The proposed architecture does not require any mathematical modeling of the system and is computationally inexpensive. The proposed methodology is applied to the real-world datasets, and the estimation results were found to be promising compared to the other state-of-the-art algorithms.

An Open-Source Test Environment for Effective Development of MARG-Based Algorithms

This paper presents an open-source environment for development, tuning, and performance evaluation of magnetic, angular rate, and gravity-based (MARG-based) filters, such as pose estimators and classification algorithms. The environment is available in both ROS/Gazebo and MATLAB/Simulink, and it contains a six-degrees of freedom (6 DOF) test bench, which simultaneously moves and rotates an MARG unit in the three-dimensional (3D) space. As the quality of MARG-based estimation becomes crucial in dynamic situations, the proposed test platform intends to simulate different accelerating and vibrating circumstances, along with realistic magnetic perturbation events. Moreover, the simultaneous acquisition of both the real pose states (ground truth) and raw sensor data is supported during these simulated system behaviors. As a result, the test environment executes the desired mixture of static and dynamic system conditions, and the provided database fosters the effective analysis of sensor fusion algorithms. The paper systematically describes the structure of the proposed test platform, from mechanical properties, over mathematical modeling and joint controller synthesis, to implementation results. Additionally, a case study is presented of the tuning of popular attitude estimation algorithms to highlight the advantages of the developed open-source environment.

Painting Path Planning for a Painting Robot with a RealSense Depth Sensor

The utilization of stereo cameras in robotic applications is presented in this paper. The use of a stereo depth sensor is a principal step in robotics applications, since it is the first step in sequences of robotic actions where the intent is to detect and extract windows and obstacles that are not meant to be painted from the surrounding wall. A RealSense D435 stereo camera was used for surface recording via a real-time, appearance-based (RTAB) mapping procedure, as well as to navigate the painting robot. Later, wall detection and the obstacle avoidance processes were performed using statistical filtering and a random sample consensus model (RANSAC) algorithm.

Inertial Sensors-Applications and Challenges in a Nutshell

This editorial provides a concise introduction to the methods and applications of inertial sensors. We briefly describe the main characteristics of inertial sensors and highlight the broad range of applications as well as the methodological challenges. Finally, for the reader’s guidance, we give a succinct overview of the papers included in this special issue.

Fast AHRS Filter for Accelerometer, Magnetometer, and Gyroscope Combination with Separated Sensor Corrections

A new predictor–corrector filter for attitude and heading reference systems (AHRS) using data from an orthogonal sensor combination of three accelerometers, three magnetometers and three gyroscopes is proposed. The filter uses the predictor—corrector structure, with prediction based on gyroscopes and independent correction steps for acceleration and magnetic field sensors. We propose two variants of the filter: (i) one using mathematical operations of special orthogonal group SO(3), that are accurate for nonlinear operations, for highest possible accuracy, and (ii) one using linearization of nonlinear operations for fast evaluation. Both approaches are quaternion-based filter realizations without redundant steps. The filters are compared to state of the art methods in this field on data recorded using low-cost microelectromechanical systems (MEMS) sensors with ground truth measured by the VICON optical system. Both filters achieved better accuracy than conventional methods at lower computational cost. The recorded data with ground truth reference and the source codes of both filters are publicly available.

Integrated Guidance and Control Using Model Predictive Control with Flight Path Angle Prediction against Pull-Up Maneuvering Target

Integrated guidance and control using model predictive control against a maneuvering target is proposed. Equations of motion for terminal homing are developed with the consideration of short-period dynamics as well as actuator dynamics of a missile. The convex optimization problem is solved considering inequality constraints that consist of acceleration and look angle limits. A discrete-time extended Kalman filter is used to estimate the position of the target with a look angle as a measurement. This is utilized to form a flight-path angle of the target, and polynomial fitting is applied for prediction. Numerical simulation including a Monte Carlo simulation is performed to verify the performance of the proposed algorithm.