Attitude Error Research Articles

On Covariance Switch-Based Invariant Extended Kalman Filter for Multi-Source Fusion

The good estimation consistency of Invariant Extended Kalman Filter (InEKF) is mainly attributed to its excellent trajectory-independent property. However, when the InEKF is applied to multi-source inertial-based navigation that coexists left-invariant and right-invariant observations, the observation matrix would be unavoidably trajectory-dependent and might lead to the degradation of estimation performance. This paper for the first time performs theoretical analyses on the covariance switch between the left error and the right error in multi-source inertial-based navigation. Furthermore, detailed realizations of the covariance switch-based InEKF are formulated in this work, which are lacked in previous works. Numerical simulations and experiments demonstrate that the covariance switch significantly reduces the attitude errors during the transient phase in contrast with the original method using the incompatible error definition.

Adaptive predefined-time precise anti-unwinding attitude control for a spacecraft with inertia uncertainty

This paper proposes an adaptive predefined-time accurate anti-unwinding attitude controller for a spacecraft with uncertain inertia. The novelty of the proposed algorithm lies in that the spacecraft attitude error is regulated to exact zero after a predefined settling time, which is an explicit parameter in the control algorithm. A time mapping function containing the predefined settling time is introduced, thus transforming the time scale of the original attitude control system. Then a composite barrier Lyapunov function is constructed to avoid the unwinding phenomenon in the attitude control process, and an adaptive backstepping attitude controller is designed based on the attitude system in the new time scale. The stability analysis of the attitude system is carried out based on LaSalle-Yoshizawa theorem, and it is proved that the attitude quaternion and angular rate can converge to zero accurately within the desired predefined time without using the spacecraft inertia information. Numerical simulation results show the effectiveness and superiority of the proposed controller.

Analysis of Alignment Accuracy due to Velocity/Attitude Error of Master Inertial Navigation System in Velocity/Attitude Matching Transfer Alignment

This paper theoretically analyzes the effect of the velocity and attitude errors of Master Inertial Navigation System(MINS) on the accuracy of Slave Inertial Navigation System(SINS) transfer alignment in velocity and attitude matching, and validates the analysis through simulation. Theoretical analysis involves deriving a new state equation that considers the velocity and attitude errors of MINS from the state equation of the transfer alignment filter, and deriving the state estimation equation of the Kalman filter based on this. The analysis confirms that MINS's velocity and attitude errors induce the same level of velocity and attitude errors in SINS. A reference inertial navigation system model is added to the simulation model, and the transfer alignment accuracy is analyzed by comparing the navigation information of MINS and SINS with the reference inertial navigation system. It is confirmed that the accuracy analysis results through simulation are consistent with the theoretically analyzed results, and through this, the validity of the theoretically analysis in this paper is verified. The research findings indicate that when performing transfer alignment using MINS, which is likely to be operated for prolonged periods in pure inertial navigation mode, the navigation errors of MINS are transferred to SINS. This implies that initial correction navigation is necessary to be considered for SINS

Adaptive IMU error correction algorithm for dual-antenna GNSS/IMU integrated vehicle attitude determination

Abstract The attitude of a vehicle can be largely determined by integrating the global navigation satellite system (GNSS) and inertial measurement unit (IMU) in land-based applications. However, traditional dual-antenna GNSS/IMU integrated systems are susceptible to signal reflection, diffraction, and even interruption, leading to reduced accuracy and reliability in challenging environments. To address this issue, this paper proposes an adaptive IMU error correction algorithm for dual-antenna GNSS/IMU integrated vehicle attitude determination. First, we propose an IMU-aided baseline length constraint model to support the ambiguity resolution (AR) process. This model incorporates accurate prior information from the IMU, improving the success rate of AR within the dual-antenna GNSS/IMU integrated system. Second, we present an adaptive IMU error correction mechanism based on long short-term memory (LSTM) and particle swarm optimization (PSO) to assist in vehicle attitude determination and mitigate attitude error drift of the lMU during GNSS outages. Field test results verified that, compared to two other candidate algorithms, the proposed algorithm improves accuracy in roll, pitch, and yaw by 19.23%, 30.56%, and 67.12%, respectively, and by 12.50%, 10.71%, and 38.39% respectively. Moreover, in two distinct scenarios where GNSS is blocked for 120 seconds, the proposed algorithm still provides accurate and stable attitude information for vehicle navigation, with the accuracy of roll, pitch, and yaw kept within 0.08 degrees.

Geometric Attitude Tracking Control for Rigid Body Based on a Novel Attitude Error Dynamic Model on SO(3)

Geometric Attitude Tracking Control for Rigid Body Based on a Novel Attitude Error Dynamic Model on SO(3)

Magneto-inductive positioning network based on magnetic energy density

The magneto-inductive positioning system (MPS) is considered a promising solution for realizing accurate positioning in challenging environments, particularly to support the development of emerging technologies. However, obtaining the position of magnetic beacons increases the system’s complexity and the sensor’s attitude error lowers the positioning performance. To solve the above problems, this paper proposes an improved magneto-inductive positioning network system (MPNS) based on magnetic energy density (MED). An orientation model without the sensor’s attitude is derived from MED. An incrementally deployed magneto-inductive positioning network is developed with the orientation model, which reduces the system complexity. An advanced resampling method of particle filter is employed in the MPNS to improve the positioning accuracy. The realized system displays the max error of no more than 0.13 m for the static target . The performance of MPNS that tracks moving targets is examined with simulation. The results exhibit that 99% of tracking errors are less than 0.25 m.

Trajectory Tracking Control of Unmanned Vehicles via Front-Wheel Driving

Automated Guided Vehicles (AGVs) are the fastest commercially available application of unmanned driving technology, and the research significance of unmanned vehicle technology remains substantial. This paper investigates the driving mode of AGVs and proposes a method to extend the kinematic model of center-driven unmanned vehicles to front-wheel drive. This change in driving force enables unmanned vehicles to achieve faster tracking and higher consistency, solving the problems of long tracking time and insufficient accuracy in complex environments and reducing production costs. By analyzing the posture relationship of the unmanned vehicle system during movement, we established a posture error system to analyze the trajectory tracking problem. Utilizing Lyapunov stability theory and the concept of backstepping, we designed a control scheme that uses linear velocity and heading angular velocity as variables for the posture error system. This control scheme aims to stabilize the system and achieve synchronized trajectory tracking control of the unmanned vehicle. The impact of control parameters in the controller on tracking performance is also discussed. The final experimental simulation results show that the system error stabilizes, and the unmanned vehicle accurately follows the predetermined trajectory, verifying the feasibility of our proposed method and control scheme.

An Algorithm for Strapdown Airborne Gravity Disturbance Vector Measurement Based on High-Precision Navigation and EGM2008.

Attitude errors, accelerometer bias, the gravity disturbance vector, and their coupling are the primary factors obstructing strapdown airborne vector gravimetry. This paper takes the geocentric inertial frame as a reference and solves the kinematic equations of its motion and its errors of the body frame and local geographic frame in the Lie group, respectively; the attitude accuracy is improved through a high-precision navigation algorithm. The constant accelerometer bias is estimated through Kalman filtering and is deducted from the accelerometer output to eliminate its influence. Based on the EGM2008 model, the low-frequency components of the gravity disturbance vector are corrected. The gravity disturbance vectors after model data fusion were low-pass filtered to obtain the ultimate results. This method was applied to flight experimental data in the South China Sea, and a gravity anomaly accuracy of better than 0.5 mGal, a northward gravity disturbance accuracy of 0.85 mGal, and an eastward gravity disturbance accuracy of 4.0 mGal were obtained, with a spatial resolution of approximately 4.8 km.

Indoor altitude estimation assisted by inertial compensation and online floor modeling

Abstract Indoor pedestrian altitude information plays a key role in such applications as emergency relief and military reconnaissance. However, height errors of inertial positioning grow without boundary because of the altitude channel divergence of the Strap-down Inertial Navigation System (SINS). This article proposes a new vertical location method based on the foot-mounted Inertial Measurement Unit (IMU) and online floor modeling. First, the number of stairs at each step is calculated after the height of each step is corrected by the error compensation model. Second, the prior height is estimated by utilizing the number of stairs and the stair height. Then, the key point library related to the floor is built online. Finally, the error correction of the vertical displacement is carried out by matching the prior height with the key point library. The gait classification shows that the accuracy based on the error compensation model can reach up to 99%. Moreover, the maximum attitude error is less than 1 m and the accumulated vertical positioning errors are eliminated completely when a pedestrian walks up and down inside a multi-story building, and all these have verified accuracy and robustness of vertical indoor positioning.

Locomotion trajectory optimization for quadruped robots with kinematic parameter calibration and compensation

It is significant to improve the locomotion trajectory accuracy of a quadruped robot for more applications. A compensation approach with kinematic parameter calibration is proposed to enhance the trajectory accuracy. The motion equation of the foot ends in coordinated gait is given. The related kinematic error model is deduced. The model for identifying the joint parameter errors is implemented via the trajectory error in the Z-direction. The trunk trajectory accuracy enhancement is facilitated by compensating the joint parameter error with joint angles as tuning variables. The performance of the methodology is validated in the simulation system by predetermining ten random sets of joint variable errors. The results indicate that both the trajectory and the attitude accuracy of the calibrated robot can be significantly improved. In practical experiments, it is shown that an error reduction rate of 80% in positional deviation and 58% in attitude error can be achieved.

Controller design and remote piloting training module development for unmanned cropped delta reflex wing configuration

In this study, a cost-effective high-fidelity six-degree of freedom module augmented with an onboard controller is developed. The unmanned aerial vehicle (UAV) under consideration is a wing-alone configuration with a cropped delta planform and reflex airfoil cross-section designed to perform manoeuvres at high angles of attack. The six-degree of freedom dynamics for the aforementioned configuration is developed based on Newtonian mechanics incorporating linear and nonlinear aerodynamic models to expand flight simulations in corresponding regimes. Aerodynamic stability and control parameters for the simulations are obtained from full-scale wind tunnel measurements and flight tests. It is observed that the linear aerodynamic model is valid in angle of attack (α) domain −5°≤α≤10°, followed by nonlinearity up to α≈21°, post which lift coefficient remains almost constant with angle of attack till 45°. The simulation model is validated with the corresponding flight data obtained from flight tests. A user-friendly graphical interface with real-time animation of UAV has been developed for the aforementioned configuration by integrating MATLAB and Flightgear environment with real-time control input from the hardware to enable the pilot for visual and tactile feedback, respectively. A controller based on total energy control is designed for velocity and altitude hold modes, while an attitude hold controller is designed for pitch and roll angle tracking to enable controller-in-the-loop remote piloting simulations. In order to enhance practical applicability, the designed module has been tested under various simulated wind conditions. It is noticed from the results that the steady-state error in attitude remains below 2% with a maximum overshoot of 5° from reference. The total energy controller achieves a zero steady-state error with a maximum overshoot of 2 m/s for velocity and 6 m for altitude, respectively. The developed module enhances remote piloting training, flight response assessment, and control algorithm testing for cropped delta planform UAVs.

Low-cost dual-antenna GNSS-based heading and pitch angles estimation considering baseline length constraint

This contribution presents a vehicular heading and pitch angles estimation method based on the dual-antenna GNSS scheme, the baseline length is investigated as a priori nonlinear constraint to improve the estimation accuracy. The coordinates of the formed moving baseline are estimated first, the baseline length is exploited to enhance the ambiguity resolution process, and then its corresponding attitude angles are determined. The capability and reliability of the proposed algorithm are assessed by a real car-borne experiment with off-the-shelf, low-cost GNSS receivers. The driving trajectory contains both stationary periods and dynamic situations under the open sky and dense community environments. The experimental results show that, compared to the classical method that does not consider the baseline length constraint, the accuracy improvements of the proposed method on attitude angles range from 16.7% to 84.0% in different observation conditions, and the attitude errors of ambiguity fixed solutions are dominantly less than 5°.

Distributed avoidance-accommodating flexible performance approach for adaptive formation tracking of underactuated surface vehicles against moving obstacles

A novel strategy for formation tracking of multiple uncertain underactuated surface vehicles is introduced in this study, to maintain the prescribed formation performance in the presence of moving obstacles with unknown velocities. Unlike the existing methods for prescribed formation performance control, our key contribution is the development of distributed avoidance-accommodating flexible performance functions (FPFs). These functions prevent deviation from the prescribed performance bounds while navigating around moving obstacles, considering input saturation and model uncertainties. We design local adaptive formation controllers by using distributed posture errors and avoidance-accommodating FPFs. Auxiliary signals that facilitate adjustment of the posture errors and performance functions during obstacle avoidance are derived using a recursive design that ensures Lyapunov stability. Additionally, command filters for virtual control laws are redesigned as saturation-compensating filters to solve the input saturation problem. Consequently, the proposed controller ensures the prescribed distributed formation performance, even in scenarios involving moving obstacles and input saturation, a capability lacking in conventional prescribed performance-based formation controllers, which can become unstable in such scenarios. The theoretical findings of this study are validated through comparative simulations.

Optimization of acquisition patterns for establishing inter CubeSat optical communications

As commercially available CubeSats with up to six standardized units cannot achieve the precision required for an instantaneous establishment of a low-divergence optical inter-satellite link, search patterns are used to scan the remaining field of uncertainty. This analysis optimizes the simultaneously executed search pattern combinations of the two laser communication terminals involved. Based on a Monte Carlo simulation, the perturbations on these links are investigated, and the corresponding key performance parameters such as mean acquisition time and success rate are calculated. The results are penalized by the hardware specifications, including actuator and sensor bandwidths, given by their design. Residual attitude error components imply a significant influence on the acquisition process and are therefore presented within this work. The pattern pairs are fed through an automated optimization algorithm to tune and analyze them. In this particular scenario of two CubeISL models, the mean duration for a first detected acquisition hit is within a pattern period of 3.2 s for the best performing pairs spiral-rose and lissajous-rose. Assuming an uncertainty field of ±0.2deg due to limited attitude knowledge, success rates between 82.3% and 99.9% are achieved.

Pose Selection Based on a Hybrid Observation Index for Robotic Accuracy Improvement

The problem of the insufficient accuracy performance of industrial robots in high-precision manufacturing is addressed in this paper. Firstly, a kinematic error model based on an M-DH model was presented. Secondly, a hybrid observability index O6 was proposed to select the optimal poses for parameter identification. O6 is the combination of O1 and O3. The optimal poses were obtained by using the IOOPS algorithm. Thirdly, the fitness function for parameter identification was established, and the Levenberg–Marquardt (LM) algorithm was applied for the accurate identification of kinematic parameter errors. Finally, several experiments were conducted to evaluate the performance of the proposed hybrid observability index O6. The average position error and average attitude error of Staubli TX60 robot were reduced by 89% and 49%. The results show that the proposed hybrid observability index O6 has great stability and effectiveness for robot calibration.

Dual-Model Derailment Detection Algorithm Based on Variational Bayesian Kalman Filtering.

A derailment detection algorithm for railway freight cars based on micro inertial measurement units was designed to address the complex issue of the disassembly and assembly of derailment braking devices. Firstly, a horizontal attitude measurement model for freight cars was established, and attitude measurement algorithms based on gyroscopes and accelerometers were introduced. Subsequently, a high-precision attitude measurement algorithm based on variational Bayesian Kalman filtering was proposed, which used acceleration information as the observation data to correct attitude errors. In order to improve the accuracy of derailment detection, a dual-model instantaneous attitude difference measurement technique was further proposed. In order to verify the effectiveness of the algorithm, offline data from simulation experiments and in-vehicle experiments were used to validate the proposed algorithm. The results showed that the proposed algorithm can effectively improve the measurement accuracy of horizontal attitude changes, reducing the error by 89% compared to pure inertial attitude calculation, laying a technical foundation for improving the accuracy of derailment detection.

Fast inspection of flange faces of welded tubes using photogrammetry and auxiliary measuring tools

The attitudes (including positions and orientations) of flange faces on a multi-branch welded tube are critical to tube installation quality. However, it lacks appropriate approach for flange attitudes inspection. Given the inspection requirements, a novel Auxiliary Measuring Tool (AMT) is designed. A photogrammetry-based approach is put forward to inspect the attitude errors of the flange faces with the aid of the AMT. The specifically designed AMT can achieve flange face centering through a three-jaw chuck structure and establish in-plane rotation by employing a slider to locate the reference bolt hole. An ingenious calibration method is proposed to establish the AMT coordinate frame (ACF) and obtain the marker points’ coordinates in ACF. With the calibrated AMTs attached to each flange, the flange attitude error can be efficiently evaluated by simply capturing a set of images of the tube. Experiments on two welded tubes demonstrate the high performance of the proposed method.

Appointed time control for flexible satellite with active vibration suppression

This work addresses the problem of achieving precise appointed time attitude control and rapid active vibration suppression in flexible satellites. Firstly, an appointed time piecewise sliding mode controller is developed to ensure the convergence of attitude error to the vicinity of the origin at the appointed time. The convergence time can be predetermined using a parameter. Secondly, a modal observer is introduced to estimate the vibrations in the flexible elastic modal, and a predefined-time active vibration suppression controller is designed to mitigate the elastic vibrations in flexible solar panels. The stability of both controllers is proven using the Lyapunov theory. Finally, simulations are conducted to validate the proposed control strategy. Through comparison with two predefined time controllers, it is evident that the proposed controller achieves more precise convergence time, smoother attitude variations, and minimal magnitude of control inputs.

The Kinematic Models of the SINS and Its Errors on the SE(3) Group in the Earth-Centered Inertial Coordinate System.

In this paper, the kinematic models of the Strapdown Inertial Navigation System (SINS) and its errors on the SE(3) group in the Earth-Centered Inertial frame (ECI) are established. On the one hand, with the ECI frame being regarded as the reference, based on the joint representation of attitude and velocity on the SE(3) group, the dynamic of the local geographic coordinate system (n-frame) and the body coordinate system (b-frame) evolve on the differentiable manifold, respectively, and the high-order expansion of the Baker-Campbell-Haussdorff equation compensates for the non-commutative motion errors stimulated by strong maneuverability. On the other hand, the kinematics of the left- and right-invariant errors of the n-frame and the b-frame on the SE(3) group are separately derived, where the errors of the b-frame completely depend on inertial sensor errors, while the errors of the n-frame rely on position errors and velocity errors. In this way, the errors brought by the inconsistency of the reference coordinate system are tackled, and a novel attitude error definition is introduced to separate and decouple the factors affecting the dynamic of the n-frame errors and the b-frame errors for better attitude estimation. Through a turntable experiment and a car-mounted field experiment, the effectiveness of the proposed kinematic models in estimating attitude has been verified, with a remarkable improvement in yaw angle accuracy in the case of large initial misalignment angles, and the models developed have better robustness compared to the traditional SE(3) group-based model.

Geometric Error-Based Multi-Source Error Identification and Compensation Strategy for Five-Axis Side Milling

Based on a multi-source error model, this paper discusses the principle of error element identification and uses the mirror bias method to compensate the geometric errors of a process system. Firstly, a nine-line measurement method to determine the geometric error of the linear feed axes of machine tools is introduced, and the geometric error identification model based on the “nine-line method” is established. Then, using a ballbar mounted in the axial, tangential, and radial directions of the machine, the geometric error elements of the rotation axis are identified by three simple measurements in each direction. Subsequently, for the more common flat vise clamping workpiece in actual production, the workpiece position error is identified by using the traditional process of dimensional chain, and the workpiece attitude error is identified by fitting the angle between the positioning plane and the horizontal plane by the least squares method. Finally, based on the tool position points and tool axis vectors obtained from the multi-source error model, the error compensation value is solved using inverse machine tool kinematics to offset the machining error by mirroring the error value of the same size, and based on the “S-shaped specimen” to compensate the processing experiments, after compensation, the processing error is reduced by 30~45%, verifying the effectiveness of the compensation method.