Nonlinear Complementary Filter Research Articles

A Robust Observer with Gyroscopic Bias Correction for Rotational Dynamics

We propose an observer for rotational dynamics subject to directional and gyroscopic measurements, which simultaneously estimates the gyroscopic biases and attitude rates. We show uniform almost global asymptotic and local exponential stability of the resulting error dynamics, implying robustness against bounded disturbances. This robustness is quantified with respect to a popular nonlinear complementary filter in quantitative simulation studies, and we explore how the measurement noise propagates to the asymptotic errors as a function of tuning.

Guidance, Navigation and Control System for Multi-Robot Network in Monitoring and Inspection Operations

This work focuses on the challenges associated with autonomous robot guidance, navigation, and control in multi-robot systems. This study provides an affordable solution by utilizing a group of small unmanned ground vehicles and quadrotors that collaborate on monitoring and inspection missions. The proposed system utilizes a potential fields path planning algorithm to allow a robot to track a moving target while avoiding obstacles in a dynamic environment. To achieve the required performance and provide robust tracking against wind disturbances, a backstepping controller is used to solve the essential stability problem and ensure that each robot follows the specified path asymptotically. Furthermore, the performance is also compared with a proportional-integral-derivative (PID) controller to ensure the superiority of the control system. The system combines a low-cost inertial measurement unit (IMU), a GNSS receiver, and a barometer for UAVs to generate a navigation solution (position, velocity, and attitude estimations), which is then used in the guidance and control algorithms. A similar solution is used for UGVs by integrating the IMU, a GNSS receiver, and encoders. Non-linear complementary filters integrate the measurements in the navigation system to produce high bandwidth estimates of the state of each robotic platform. Experimental results of several scenarios are discussed to prove the effectiveness of the approach.

Sensor integration for real-time data acquisition in aerial surveillance

ABSTRACT The unmanned aerial vehicle (UAV) is one of the mobile robots which has grown rapidly in popularity in recent years. UAVs have been used in various activities to convey important information on the aerial transportation system. However, an application to get real-time information from UAVs remains a challenging task. Therefore, this paper presents an integration system to optimise the use of UAVs for aerial surveillance. The proposed system explains the design and implementation a UAV system which consists of on-board and ground stations. The on-board system has the function to send UAV flight data, send aerial images and carry items using a gripper which equipped with sensors to detect obstacles. The ground station has the function to control UAV flights, receive and display UAV flight data and aerial images, display the attitude of the UAV and send commands to move the camera and gripper. Flight controllers in this system use non-linear complementary filter on SO(3) to estimate the attitude of the UAV and proportional-integral (PI) controller to stabilise the UAV flight. By providing the real-time acquisition data of the UAV, we believe this system can be a useful tool for many implementations using UAV.

Nonlinear Complementary Filter for Attitude Estimation by Fusing Inertial Sensors and a Camera.

Using a standalone camera for pose estimation has been quite a standard task. However, the point correspondence-based algorithms require at least four feature points in the field of view. This paper considers the situation that there are only two feature points. Focusing on the attitude estimation, we propose to fuse a camera with low-cost inertial sensors based on a nonlinear complementary filter design. An implicit geometry measurement model is derived using two feature points in an image. This geometry measurement is fused with the angle rate measurement and vector measurement from inertial sensors using the proposed nonlinear complementary filter with only two parameters to be adjusted. The proposed nonlinear complementary filter is posed directly on the special orthogonal group SO(3). Based on the theory of nonlinear system stability analysis, the proposed filter ensures locally asymptotic stability. A quaternion-based discrete implementation of the filter is also given in this paper for computational efficiency. The proposed algorithm is validated using a smartphone with built-in inertial sensors and a rear camera. The experimental results indicate that the proposed algorithm outperforms all the compared counterparts in estimated accuracy and provides competitive computational complexity.

Real Time Estimation of the Pose of a Lower Limb Prosthesis from a Single Shank Mounted IMU.

The command of a microprocessor-controlled lower limb prosthesis classically relies on the gait mode recognition. Real time computation of the pose of the prosthesis (i.e., attitude and trajectory) is useful for the correct identification of these modes. In this paper, we present and evaluate an algorithm for the computation of the pose of a lower limb prosthesis, under the constraints of real time applications and limited computing resources. This algorithm uses a nonlinear complementary filter with a variable gain to estimate the attitude of the shank. The trajectory is then computed from the double integration of the accelerometer data corrected from the kinematics of a model of inverted pendulum rolling on a curved arc foot. The results of the proposed algorithm are evaluated against the optoelectronic measurements of walking trials of three people with transfemoral amputation. The root mean square error (RMSE) of the estimated attitude is around 3°, close to the Kalman-based algorithm results reported in similar conditions. The real time correction of the integration of the inertial measurement unit (IMU) acceleration decreases the trajectory error by a factor of 2.5 compared to its direct integration which will result in an improvement of the gait mode recognition.

Nonlinear robust control of a quadrotor helicopter with finite time convergence

In this paper, the control problem for a quadrotor helicopter which is subjected to modeling uncertainties and unknown external disturbance is investigated. A new nonlinear robust control strategy is proposed. First, a nonlinear complementary filter is developed to fuse the raw data from the onboard barometer and the accelerometer to decrease the negative effects from the noise associated with the low-cost onboard sensors Then the adaptive super-twisting methodology is combined with a backstepping method to formulate the nonlinear robust controller for the quadrotor’s attitude angles and the altitude position. Lyapunov based stability analysis shows that finite time convergence is ensured for the closed-loop operation of the quadrotor’s roll angle, pitch angle, row angle and the altitude position. Real-time flight experimental results, which are performed on a quadrotor flight testbed, are included to demonstrate the good control performance of the proposed control methodology.

Least square estimation-based adaptive complimentary filter for attitude estimation

Attitude estimation is one of the core fundamentals for navigation of unmanned vehicles and other robotic systems. With the advent of low cost and low accuracy micro-electro-mechanical systems (MEMS) based inertial sensors, these devices are used ubiquitously for all such commercial grade systems that need motion information. However, these sensors suffer from time-varying bias and noise parameters, which need to be compensated during system state estimation. Complementary filtering is one of such techniques that is used here for estimating attitude of a moving vehicle. However, the complementary filter structure is dependent on user fed gain parameters, KP and KI and needs a mechanism by which they can be obtained automatically. In this paper, an attempt has been made towards addressing this issue by applying least square estimation technique on the error obtained between estimated and measured attitude angles. The proposed algorithm simplifies the design of nonlinear complementary filter by computing the filter gains automatically. The experimental investigation has been carried out over several datasets, confirming the advantage of obtaining gain parameters automatically for the complementary filtering structure.

Sensor Fusion for Attitude Estimation and PID Control of Quadrotor UAV

This paper presents sensor fusion algorithm using nonlinear complementary filter (NCF) for attitude estimation and a proportional-integral-derivative (PID) controller for small-scale quadrotor unmanned aerial vehicle (UAV) stabilization. From inertial measurement unit (IMU) data, gyroscope as a main sensor is fused to another two sensors; accelerometer and magnetometer to correct drift error of gyroscope to obtain reliable attitude estimation. In this paper, the performance of NCF is implemented on real-time while applying PID controller for attitude stabilization of quadrotor UAV during hovering. Experimental results show the effectiveness of PID controller for quadrotor UAV stabilization during attitude control.

Design of autonomous smartphone based quadrotor and implementation of navigation and guidance systems,

This work discusses the design of a novel smartphone-based autopilot for quadrotor aerial platforms and the results of its flight tests. The proposed solution consists of two different layers, a low-level navigation and control layer and a high-level human-robot communication layer. The low-level navigation system uses nonlinear complementary filters for position, velocity and attitude estimation based on low-cost sensors. The structure of the filter allows a straightforward implementation without need of high performance signal processing. A nonlinear flight controller is used for the quadrotor stability and trajectory tracking. This controller demonstrates also the ability of the guidance system in the high-level layer to provide effective waypoint navigation capabilities for the quadrotor drone. The waypoints can be defined remotely using a human-robot interface that is able to receive commands and to send information to a human operator throughout a web-based social network, i.e. Twitter. The performances of the proposed solution are evaluated by means of flight tests and are compared to the results derived from a more traditional approach (i.e. PX4 controller) used for quadrotor tracking and control.

The Right Invariant Nonlinear Complementary Filter for Low Cost Attitude and Heading Estimation of Platforms

This paper presents a novel filter with low computational demand to address the problem of orientation estimation of a robotic platform. This is conventionally addressed by extended Kalman filtering (EKF) of measurements from a sensor suit which mainly includes accelerometers, gyroscopes, and a digital compass. Low cost robotic platforms demand simpler and computationally more efficient methods to address this filtering problem. Hence, nonlinear observers with constant gains have emerged to assume this role. The nonlinear complementary filter (NCF) is a popular choice in this domain which does not require covariance matrix propagation and associated computational overhead in its filtering algorithm. However, the gain tuning procedure of the complementary filter is not optimal, where it is often hand picked by trial and error. This process is counter intuitive to system noise based tuning capability offered by a stochastic filter like the Kalman filter. This paper proposes the right invariant formulation of the complementary filter, which preserves Kalman like system noise based gain tuning capability for the filter. The resulting filter exhibits efficient operation in elementary embedded hardware, intuitive system noise based gain tuning capability and accurate attitude estimation. The performance of the filter is validated using numerical simulations and by experimentally implementing the filter on an ARDrone 2.0 micro aerial vehicle (MAV) platform.

Multiple Model Adaptive Complementary Filter for Attitude Estimation

Attitude estimation plays a major role in the autonomy of unmanned aerial vehicles and requires fusion of different sensor measurements. This paper describes an adaptive estimation scheme in which the weight parameter for the complementary filter (CF) is varied over time. The adaptive mechanism proposed here is inspired from the multiple model adaptive estimation (MMAE) scheme used for varying noise parameters in the Kalman filter structure. In this paper, the linear complementary filters are used as elementary blocks in the MMAE structure and their weights are modified probabilistically to obtain an accurate orientation estimate. It avoids the problem of manual selection of weight factor for complementary filter and provides a robust orientation estimate against varying system dynamics. The proposed MMAE based adaptive CF scheme is modular in nature and is dependent on the residual error between estimated and the measured orientation angle. It is applied on the real world datasets logged from inertial sensors and the performance of MMAE based CF structure is found to work promisingly as compared to the non-linear complementary filter versions and the extended Kalman filter framework.

PSO Aided Adaptive Complementary Filter for Attitude Estimation

Attitude estimation is one of the core frame- works used for navigating an unmanned aerial vehicle from one place to the other. This paper presents an Euler-based non-linear complementary filter (CF) whose gain parameters are obtained using particle swarm optimization (PSO) technique. It relieves the user from feeding the KP and KI parameters manually and adjust these parameters automatically when the error between the attitude measured from accelerometer and the CF increases above a particular threshold. The measurement unit for this research consists of micro-electro-mechanical-systems (MEMS) based low cost tri-axial rate gyros, accelerometers and magnetometers, without resorting to global positioning system (GPS) data. The efficiency of the CF is experimentally investigated with the help of reference attitude and the raw sensor data obtained from commercial inertial measurement unit (IMU). Simulation results based on the test data show that the proposed PSO aided non-linear complementary filter (PNCF) can automatically obtain the required gain parameters and exhibits promising performance for attitude estimation.

A low-cost high-fidelity ultrasound simulator with the inertial tracking of the probe pose

The authors developed a versatile ultrasound simulator. The proposed system achieves the main features of a high-fidelity device exploiting low-cost rapid prototyping hardware. The hand-guided ultrasound simulator probe includes a RFID reader, a 9-DOF inertial sensor unit, consisting of an accelerometer, a magnetometer and a gyroscope, and a microcontroller that performs the real-time data acquisition, the processing and the transmission of the estimated pose information to the visualization system, so that the proper ultrasound view can be generated. Since the probe orientation is the main information involved in the pose reconstruction, this work presents and investigates several tracking methods for the probe orientation, exploiting a sensor fusion technique to filter the noisy measurements coming from inertial sensors. The performances of a Kalman filter, a nonlinear complementary filter and a quaternion-based filter as inertial trackers have been tested by means of a robot manipulator, in terms of readiness, accuracy and stability of the estimated orientation signal. The results show that the nonlinear complementary filter and the quaternion-based filter match all the application requirements (RMSE <3deg, variance <1deg2, and settling time <0.3s), and they involve a lower computational time with respect to the Kalman filter.

Nonlinear Observer for Tightly Integrated Inertial Navigation Aided by Pseudo-Range Measurements

A modular nonlinear observer for inertial navigation aided by pseudo-range measurements is designed and analyzed. The attitude observer is based on a recent nonlinear complementary filter that uses magnetometer and accelerometer vector measurements to correct the quaternion attitude estimate driven by gyro measurements, including gyro bias estimation. A tightly integrated translational motion observer is driven by accelerometer measurements, employs the attitude estimates, and makes corrections using the pseudo-range and range-rate measurements. It estimates position, range bias errors, velocity and specific force in an earth-fixed Cartesian coordinate frame, where the specific force estimate is used as a reference vector for the accelerometer measurements in the attitude observer. The exponential stability of the feedback interconnection of the two observers is analyzed and found to have a semiglobal region of attraction with respect to the attitude observer initialization and local region of attraction with respect to translational motion observer initialization. The latter is due to linearization of the range measurement equations that is underlying the selection of injection gains by solving a Riccati equation. In typical applications, the pseudo-range equations admit an explicit algebraic solution that can be easily computed and used to accurately initialize the position and velocity estimates. Hence, the limited region of attraction is not seen as a practical limitation of the approach for many applications. Advantages of the proposed nonlinear observer are low computational complexity and a solid theoretical foundation.

An Analysis System for Attitude Angles of Four-rotor Aircrafts

accurate attitude angles can make the control of four- rotor aircrafts more precise. Various filters have been adopted to get more precise attitude angles. However, so far there is no suitable analysis system to evaluate the performance of filters. In this paper, an analysis system has been designed which can get the realistic attitude angles directly and compare the processing results of filters so as to analyze the performance of filters. The hardware of the analysis system contains the main control module, data acquisition module and wireless communication module. And the software of the system which is designed by LabVIEW mainly includes displaying and saving module, analysis module and the front panel. An extended Kalman filter and an innovation-based extended Kalman filter are compared by the system and results show that the attitude angles got by the innovation-based extended Kalman filter are more accurate than the extended Kalman filter. better fusion effect than Kalman filter for the nonlinear characteristic (5). In the paper (6), Kalman filter combines 3- axis gyroscope and computed quaternion to determine pitch and roll angles. This algorithm is adequate for the real-time estimation of the orientation of a quadrotor. A nonlinear complementary filter that combines accelerometer output for low frequency was proposed by Euston (7). The results were provided with a real-world data set and the performance of the filter was evaluated against the output from a full GPS/INS (Global Position System/ Inertial Navigation System) that was available for the data set. The Four-rotor aircraft system is nonlinear system. At present, the most widely estimator used in the four-rotor aircraft is extended Kalman filter. In this paper, a simple and practical analysis system is designed of hardware and software. The system implements a hardware platform of real-time data measurement and transmission. The hardware contains the main controller design, the data acquisition module design and the wireless communication module design. The programs of the lower computer are written in the C++ language and the upper computer is designed by LabVIEW (8, 9). First, the attitude angles are measured by sensor MPU6050, and transmitted through the wireless communication module to the computer. Then these data are estimated accurately by the extended Kalman filter based on innovation and shown by the virtual oscilloscope. The system can provide more real and accurate data for the four-rotor aircrafts' control system and the interface of the system is real-time, high speed and intuitive.

An Attitude Estimation Algorithm for Mobile Robots Under Unknown Magnetic Disturbances

Attitude estimation is a crucial aspect for navigation and motion control of autonomous vehicles. This concept is particularly true in the case of unavailability of localization sensors when navigation and control rely on dead reckoning strategies; in this case, indeed, the orientation estimate is also used along with speed measurements to update the position estimate. Among the different approaches proposed in the literature, the de facto state of the art in this field is represented by nonlinear complementary filters: they fuse the measurements of angular rate obtained through gyroscopes, and a measurement of gravity and Earth's magnetic field vectors respectively obtained through accelerometers and magnetometers. This paper is focused on an attitude estimation strategy for autonomous underwater vehicles (AUV). The proposed novelty includes the identification of some critical issues that arise when AUV attitude estimation algorithms are applied in practice. They are mainly due to the use of low-accuracy low-cost microelectromechanical systems (MEMS) sensors and on different sources of magnetic disturbances. Some strategies to overcome the identified issues are proposed, including the integration of a single-axis fiber optic gyroscope (FOG) that ensures a considerable performance improvement with a moderate cost increase. The proposed strategies for detection of issues and sensor fusion have been experimentally tested and validated in a real application scenario estimating the attitude of an AUV performing a lawn mower path. The expected performance improvement is confirmed; the obtained results are described and analyzed in this paper.

A Novel Approach for Attitude Estimation Based on MEMS Inertial Sensors Using Nonlinear Complementary Filters

In this paper, a new method for attitude estimation using low-cost micro-electro-mechanical system (MEMS) inertial sensors is developed, in order to obtain accurate attitude parameters when other external sensors, such as the magnetometer and GPS, are limited in operation. The method is based on specific rotation of the inertial measurement unit, which is independent from rigid body motion. The problem of heading angles estimation using just inertial sensors without incorporating additional sensors is studied. An algorithm is developed by incorporating a nonlinear observer in order to fuse measurements from both the gyroscope and the accelerometers. The algorithm provides bias estimation of the gyroscope and better estimation results. Both numerical simulations and real experiments validate the effectiveness of the proposed method.

Single axis FOG aided attitude estimation algorithm for mobile robots

This paper is focused on an attitude estimation method for Autonomous Underwater Vehicles (AUVs). Data acquired by a commercial Micro-Electro-Mechanical Systems (MEMS) Inertial Measurement Unit (IMU), equipped with magnetometers, and a Fibre Optic Gyroscope (FOG) are fused to estimate the attitude of the vehicle. One of the most used attitude estimation filter, a Nonlinear Complementary Filter (NCF), is proposed as the basis of this work; then, some adaptations to the original formulation of the filter are illustrated to better suit it to the field of underwater robotics. The proposed improvements include the online tuning of the gains of the filter to cope with sensor disturbances and the employment of the data acquired by a FOG. In addition, a fast procedure for the calibration of a magnetometer is introduced to increase the reliability of its readings. The resulting filter is used to estimate the attitude of an AUV; the performance of the proposed solution is tested and evaluated, in particular when unpredictable magnetic disturbances are present, highlighting the improvements that the applied changes allow to achieve in the specific field of application.

Design of an ultrasound simulator with probe pose tracking and medical dataset processing and visualization

A high-fidelity, low-cost ultrasound simulator has been developed in order to improve the efficiency of ultrasound training, particularly in Focus Assessment by Sonography in Trauma (FAST). This examination is rapidly increasing its diffusion in Emergency Medicine, as it represents a quick tool for the detection of free fluids. The probe is the main component of the simulator as it provides the on-line tracking of its pose relative to the manikin representing the virtual patient. The proposed algorithm for the estimation of the probe orientation, a nonlinear complementary filter, is based on the fusion of information coming from inertial sensors. It is tested in static and dynamic conditions and its performances are compared with another traditional algorithm: the Kalman filter. Moreover, the software for the processing of medical dataset as images, videos and 3D volumes, has been developed in order to display the appropriate visualization on the simulator monitor. Finally, the simulator has been tested in a training session.

INS/GPS fusion architectures for unmanned aerial vehicles

Purpose– The purpose of this paper is to present fusion of inertial navigation system (INS) and global positioning system (GPS) for estimating position, velocities, attitude and heading of an unmanned aerial vehicle (UAV).Design/methodology/approach– A 15-state extended Kalman filter (EKF) and a split architecture consisting of six-state nonlinear complementary filter (NCF) and nine-state EKF are investigated in detail. In both these fusion architectures GPS and inertial measurement unit consisting of three axis accelerometers, three axis rate gyros and three axis magnetometer have been fused in open loop fashion (loosely coupled) to estimate the navigation states.Findings– These architectures have been implemented in MATLAB/SIMULINK environment and evaluated in closed loop guidance of Black-Kite MAV with software-in-the-loop-simulation (SILS) setup. Furthermore, both the algorithms are validated with flight test data obtained from on-board data logger using an off-the shelf autopilot board (Ardupilot Mega APM-2.5) on SLYBIRD UAV.Originality/value– The proposed architectures are of high value to accomplish INS/GPS fusion, which plays a vital role in autonomous guidance and navigation of an UAV.