Large Position Errors Research Articles

Low-Cost Automation for Gravity Compensation of Robotic Arm

During the Industry 4.0 era, the open source-based robotic arms control applications have been developed, in which the control algorithms apply for movement precision in the trajectory tracking paths based on direct or reverse kinematics. Therefore, small errors in the joint positions can summarize in large position errors of the end-effector in the industrial activities. Besides the change of the end-effector position for a given variation of the set-point in manipulator joint positions depends on the manipulator configuration. This research proposes a control based on Proportional Derivative (PD) Control with gravity compensation to show the robustness of this control scheme in the robotic arm’s industrial applications. The control algorithm is developed using a low-cost board like Raspberry Pi (RPI) where the Robot Operating System (ROS) is installed. The novelty of this approach is the development of new functions in ROS to make the PD control with gravity compensation in low-cost systems. This platform brings a fast exchange of information between the Kuka™ youBot robotic arm and a graphical user’s interface that allows a transparent interaction between them.

A compact ocean bottom electromagnetic receiver and seismometer

Abstract. Joint marine electromagnetic (EM) and seismic interpretations are widely used for offshore gas hydrate and petroleum exploration to produce improved estimates of lithology and fluids and to decrease the risk of low gas saturation. However, joint data acquisition is not commonly employed. Current marine EM data acquisition depends on an ocean bottom electromagnetic receiver (OBEM), and current seismic exploration methods use seismometers. Joint simultaneous data acquisition can decrease costs and improve efficiency, but conventional independent data receivers have several drawbacks, including a large size, high costs, position errors, and low operational efficiencies. To address these limitations, we developed a compact ocean bottom electromagnetic receiver and seismometer (OBEMS). Based on existing ocean bottom E-field receiver (OBE) specifications, including low noise levels, low power consumption, and low time drift errors, we integrated two induction coils for the magnetic sensor and a three-axis omnidirectional geophone for the seismic sensor to assemble an ultra-short baseline (USBL) transponder as the position sensor, which improved position accuracy and operational efficiency while reducing field data acquisition costs. The resulting OBEMS has a noise level of 0.1 nV m−1 rt−1 (Hz) at 1 Hz in the E-field, 0.1 pT rt−1 (Hz) at 1 Hz in the B-field, and a 30 d battery lifetime. This device also supports a Wi-Fi interface for the configuration of data acquisition parameters and data download. Offshore acquisition was performed to evaluate the system's field performance during offshore gas hydrate exploration. The OBEMS operated effectively throughout the operation and field testing. Therefore, the OBEMS can function as a low-cost, compact, and highly efficient joint data acquisition method.

Field-Based Assist-as-Needed Control Schemes for Rehabilitation Robots

This article presents assistive control schemes for rehabilitation robots. The objective was to develop control strategies to follow a predefined path by maximizing the active participation of impaired subjects during training sessions. For this purpose, the path following task was defined in the velocity domain by constructing a desired velocity field around the path, and two different controllers were designed, which adjust the intervention of the robot according to the performance of the users, delivering an assist-as-needed (AAN) feature with adequate timing freedom. First, we developed an impedance controller for velocity tracking, which gains the AAN property by means of modulating the target impedance. Second, we designed a velocity tracking controller, which adjusts its contribution, in an AAN way, by monitoring the tracking error. Utilizing force sensors, the first method does not require a compliant robotic system, while the second approach does not need force sensors but provides its best AAN performance whenever the system is compliant. The controllers were featured by a force field component to avoid large position errors. The performance of the controllers was evaluated through experimental tests performed on a planar upper-limb training robot.

A Method to Realize Low Velocity Movability and Eliminate Friction Induced Noise in Piezoelectric Ultrasonic Motors

In a piezoelectric ultrasonic motor (USM) or resonance drive type piezoelectric motor (RPM), movement is generated between a vibrator (stator) and a slider (rotor). Since the microscopic vibrations on a stator are transferred to a slider through friction interaction, the movement of a slider has a nonlinear characteristic due to the nature of the friction force. This nonlinear behavior causes large position errors due to the occurrence of discontinuous stick-slip movements and unpleasant audible noise, especially at a low velocity drive. This friction induced acoustic sound is magnified at low velocities as the natural frequency of the mechanical system of a piezoelectric motor with mass and the holding and prestress spring forces are dependent on the closed loop motion controller. This article addresses the abovementioned issues. First, a mechanical model, which considers the nature of movements in a resonance drive type piezoelectric motor, was established. The model could suitably define the friction induced forced vibration and noise source. Second, a new driving method for resonance drive type piezoelectric motors was proposed, in which the piezoelectric vibrator was excited using two driving sources at two different frequencies. The difference between the two excitation frequencies was synchronized to the servo sampling frequency of the digital control unit. Finally, the performance of the proposed driving method was compared with those of the conventional driving methods. It was noted that in addition to the realization of silent and smooth low velocity movements, the positioning error for the linear movements between the desired and actual positions decreased to less than 10 nm for velocities ranging from 1 to 0.001 mm/s.

Robotic Assembly of Rounded Parts With and Without Threads

This letter addresses the assembly of rounded parts with and without threads, which is considered as the backbone of several types of assembly, and proposes novel human-inspired strategies for the hole-in-peg and nut-in-screw assemblies. These strategies employ force/torque (F/T) measurements provided by a F/T sensor and consist of two phases, namely adjustment and alignment. The proposed solution is based on quasi-static models and on the concept of attractive region in environment, and it is implemented using active force control on a velocity-controlled manipulator to avoid damages in the manipulator or in the environment. The experiments using mechanical parts with narrow tolerances show a high success rate and performance, where relatively large position and orientation errors are dynamically eliminated.

A Method of On-Site Describing the Positional Relation between Two Horizontal Parallel Surfaces and Two Vertical Parallel Surfaces

The position error of two parallel surfaces is generally constrained by parallelism. However, as a range of change, it cannot represent the positional relation between two parallel surfaces. Large-scale equipment such as machine tools are complex and difficult to move. It is also an engineering problem to perform field measurements on it. To this end, a method of describing the positional relation between two horizontal parallel surfaces and two vertical parallel surfaces on-site is proposed in this paper, which is a novel kind of position error, enriching the form of parallel surface position error, and solves the inconvenience problem of large equipment position error measurement. The measurement mechanisms are designed, and the measurement principle is given. Firstly, the combined projection waveform of the measured surface can be obtained by the geometric relationship between the measurement mechanism and the measured surface. Secondly, an algorithm is studied to process the obtained waveform, and the combined projection curve of the measured surface is acquired. Then, under the condition of considering the shape contours of the two surfaces, an algorithm is developed to acquire the calculated shape contour of the measured surface. According to the difference between the calculated surface shape contour and the known shape contour of the measured surface, the positional relation of the two surfaces can be determined. Meanwhile, the mathematical models of algorithms are established, and the measurement experiments are carried out, and the algorithms are verified by the mutual measurement method of the two surfaces. The results show that this method can accurately obtain the positional relation of two horizontal parallel surfaces and two vertical parallel surfaces.

Bias Compensation Model for Sensor Orientation Under Weak Conditions

The high-precision geometric positioning of satellite images is the basis for the geometric processing of remote-sensing images and acquisition of various geospatial information. It is an important premise for the wide application of high-resolution remote-sensing satellite images. To correct systematic biases in rational function models (RFMs), many compensation methods for system errors inherent of RFMs have been proposed. Thus far, the bias compensation model (BCM) is the most widely accepted method under rigorous conditions, namely narrow camera field, small off-nadir angle, and small attitude error. However, research studies on the compensation effect of the BCM under weak conditions (wide camera field, large off-nadir angle, or large attitude error) are still lacking, and some researchers commented that the BCM is inapplicable under weak conditions in the absence of experiments. This letter analyzes the effect of position and attitude errors on orientation accuracy in the image space. An experiment was conducted using data from the Gaofen-1 (GF-1) wide-field-view-4 (WFV-4) sensor to compare the proposed analysis with the traditional analysis, and the results obtained using the BCM under weak conditions were found to be consistent with our analysis rather than the traditional analysis. This confirms that the BCM can also be used under weak conditions.

Adaptive UT-H∞ Filter for SINS’ Transfer Alignment Under Uncertain Disturbances

Accurate and rapid transfer alignment with large attitude errors under uncertain disturbances is crucial for the strapdown inertial navigation system (SINS). This paper proposes an adaptive UT-Hoc filter which combines UKF technology and a Hoc filter to increase the robustness of the nonlinear transfer alignment system. By focusing on the time-varying and the uncertain external disturbances, the robustness factor of the adaptive UT-H∞ filter can be adaptively adjusted to balance the robustness and filtering accuracy of the dynamic system. Then, the nonlinear error propagation model of the transfer alignment is established in detail, and the velocity plus attitude matrix measurement model is used to improve the performance of transfer alignment. Moreover, the sensor error compensation model is established to calibrate and compensate for the sensor errors of the gyros and accelerometers online during transfer alignment. The vehicle transfer alignment experiments show that the proposed adaptive UT-Hoc filter can significantly improve the transfer alignment accuracy and the pure inertial navigation accuracy compared with the existing filtering methods under uncertain disturbances.

Spatial Coordinates Correction Based on Multi-Sensor Low-Altitude Remote Sensing Image Registration for Monitoring Forest Dynamics

Tree species diversity plays a significant role in our ecosystem. In order to monitor forest dynamics, hyperspectral remote sensing equipped on a small unmanned aerial vehicle (UAV) is commonly applied, such as individual tree detection and classification. However, low resolution, positioning errors and the imaging perspective of small UAV affected by wind speed/direction, complex terrain, battery capacity, aircraft posture, flying height and other human factors result in relatively large positional errors (i.e., GPS errors) in such hyperspectral images, and the precise forest dynamics monitoring is limited, especially in spatial analysis. In order to reduce the positional errors of hyperspectral images captured from a small UAV and provide a precise forest dynamics monitoring, we present a novel spatial coordinates correction approach by registering low-altitude UAV visible light and hyperspectral images. The proposed method first employs visible light images and ground control points to stitch a geographic coordinate system as our groundtruth. Hyperspectral images (UHI) are then registered onto the stitched visible light image (UVI) via a novel image registration method. Finally, spatial coordinates of the registered hyperspectral images are updated by using the aforementioned groundtruth. Extensive experiments on image registration and spatial coordinates correction demonstrate the favorable performance of our method. Compared against four state-of-the-art registration methods, our method shows the best registration performance, and the positional errors of hyperspectral images are significantly reduced. Such accuracy is considered very high in this research.

A Novel Polar Rapid Transfer Alignment for Shipborne SINS Under Arbitrary Misalignments

The traditional polar rapid transfer alignment (RTA) are generally modeled under small angle misalignment assumption. Those linearized and nonlinear polar RTA error models presented, so far, are not capable of accurately representing the nonlinear properties of the system where the all-orientation large attitude errors happen between the master and slave strap-down inertial navigation systems (SINS). It cannot satisfy the accuracy for the SINS initialization and has a singularity in computation. In this article, the misalignment quaternion in the grid frame was selected as the state and observation. An innovative polar RTA algorithm using the quaternion matching and the augmented unscented Kalman filter (UKF) was then proposed to estimate all-orientation large attitude misalignments in polar regions. Furthermore, the associated error propagation equations were redesigned in the grid frame and with compensations for the lever-arm effect. The augmented UKF model was further adjusted to apply. Simulation and semi-physical experiment results demonstrated that the performance of the innovative polar RTA algorithm proposed here outperformed those via traditional polar RTA techniques, especially with 3-axis large-angle misalignments, and was even robust with the disturbance of lever-arm effect aggravated by the harsh polar environment.

GPS: User Position Calculation Including Advanced Troposphere Delay Modeling

Objective of this project is to analyze and mitigate troposphere delays induced in GPS signals, which can result in very large position errors while estimating user position. The standard models currently present do not take into account all the various set of parameters or elements of the troposphere that can cause a significant delay. This project also includes study of troposphere propagation delays that improve the understanding of GPS signal propagation through the troposphere during irregular conditions. This characteristic is very important as it can play crucial role in real time surveying, navigation, precision farming and positioning for emergency services. Due to the tropical nature of the Indian climate the troposphere delay can be observed significantly in India sub-continent. In order to accurately estimate delay troposphere in real time conditions is taken into account, which are provided by the Indian meteorological department, by their automatic weather surveillance systems. GPS data for stations in India is obtained from CORS data for Bangalore, from where we obtain the observation and navigation files used in the calculations. Obtained data is processed and run through various algorithms like least squares satellite position calculation, error mitigation and ray tracing algorithms to mitigate troposphere and better estimate user position. Apart from these algorithms this project also includes a study on various concepts/formulas that help in using the forecasted real time data to be used in snell’s law to estimate delay as part of ray tracing techniques. All the code development in this project is done using MATLAB by math works and GUI is developed for an easier interface. For analysis purposes the data is analyzed with and without the advanced mitigation techniques to show the improvement in position estimation using advanced troposphere mitigation techniques.

An Assistive Control Strategy for Rehabilitation Robots Using Velocity Field and Force Field.

In this paper, we address the problem of assist-as-needed (AAN) control of rehabilitation robots. The objective is to develop a path tracking control scheme with the minimized intervention of the robot to gain active participation of impaired subjects while avoiding large position errors. We achieve these properties by constructing a velocity field encoding the desired path, and by considering a force field around the path. In particular, the proposed controller includes a normal force term to keep the robot position arbitrarily close to the path, and also contains velocity tracking components, which adaptively adjust the contribution of the controller by monitoring the tracking error. As a result, we gain the AAN property with adequate freedom in the timing of movement, which is a key factor in reducing the robot intervention. The performance of the controller is examined on a lower-limb robotic exoskeleton in following the gait pattern.

Compounded Calibration Based on FNN and Attitude Estimation Method Using Intelligent Filtering for Low Cost MEMS Sensor Application

Micro electro mechanical system (MEMS) inertial sensors have advantages, including small size and low power consumption. The performances of Micro Inertial measurement unit (IMU), which is composed of MEMS inertial sensors, degrade, and error, will become larger in high dynamic environment. In order to solve the problem, a novel combined calibration method for compensating the deterministic error of MEMS sensors is proposed. Considering the rotation of different sensitive axes in high dynamic and low dynamic environment, the compounded calibration based on fuzzy neural network (FNN) is adopted to identify the coupling coefficients to eliminate the adverse coupling effects between different rotation axes. Furthermore, the self-developed Micro IMU and magnetometer are applied in attitude estimation system. Considering the large attitude error occurred in most cases, the approach utilizing the estimation of error quaternion vector could avoid the calculation error due to inaccurate modeling in the skew symmetric matrix that comprises attitude error vector components. The intelligent Kalman filter (IKF) based on complexity state equation of error quaternion is designed to improve the performance by adjusting the parameters of filter on line. The experimental results show that the proposed approach could have a higher level of stability and accuracy in comparison to other attitude estimation algorithms.

다중 자기센서를 이용한 실내 자기 지도 기반 보행자 위치 검출 정확도 향상 알고리즘

This research proposes a indoor magnetic map matching algorithm that improves the position accuracy by employing multiple magnetic sensors and probabilistic candidate weighting function. Since the magnetic field is easily distorted by the surrounding environment, the distorted magnetic field can be used for position mapping, and multiple sensor configuration is useful to improve mapping accuracy. Nevertheless, the position error is likely to increase because the external magnetic disturbances have repeated pattern in indoor environment and several points have similar magnetic field distortion characteristics. Those errors cause large position error, which reduces the accuracy of the position detection. In order to solve this problem, we propose a method to reduce the error using multiple sensors and likelihood boundaries that uses human walking characteristics. Also, to reduce the maximum position error, we propose an algorithm that weights according to their importance. We performed indoor walking tests to evaluate the performance of the algorithm and analyzed the position detection error rate and maximum distance error. From the results we can confirm that the accuracy of position detection is greatly improved.

Robust Four-Channel Teleoperation Through Hybrid Damping-Stiffness Adjustment

This paper presents three strategies that adjust the coordination damping and stiffness of four-channel teleoperators to maintain the teleoperation stable regardless of time-varying delays in the transmission of operator and environment forces between the master and slave robots. A first strategy employs hybrid control terms that depend on position errors and local velocities. Thus, the hybrid terms simultaneously and dynamically regulate the master–slave coupling and the local damping injections. They increase the robustness of the system to perturbations caused by delayed transmission of operator and environment forces, but are singular at zero velocities. A second strategy injects additional damping around zero velocities, according to the master–slave position error. The additional damping makes the hybrid term nonsingular and eliminates chattering at zero velocities. However, it cannot synchronize the master and slave robots in the presence of large position error. This problem is addressed by a third strategy, which reduces the order of the position error in the hybrid term to guarantee the dominance of the Proportional term in coordination. Then, the two robots can be synchronized from arbitrarily large position errors. Lyapunov stability analysis and hardware-in-the-loop experimental results verify and compare these three proposed hybrid approaches.

Empirical analysis and modeling of Argos Doppler location errors in Romania.

BackgroundAdvances in wildlife tracking technology have allowed researchers to understand the spatial ecology of many terrestrial and aquatic animal species. Argos Doppler is a technology that is widely used for wildlife tracking owing to the small size and low weight of the Argos transmitters. This allows them to be fitted to small-bodied species. The longer lifespan of the Argos units in comparison to units outfitted with miniaturized global positioning system (GPS) technology has also recommended their use. In practice, large Argos location errors often occur due to communication conditions such as transmitter settings, local environment, and the behavior of the tracked individual.MethodsConsidering the geographic specificity of errors and the lack of benchmark studies in Eastern Europe, the research objectives were: (1) to evaluate the accuracy of Argos Doppler technology under various environmental conditions in Romania, (2) to investigate the effectiveness of straightforward destructive filters for improving Argos Doppler data quality, and (3) to provide guidelines for processing Argos Doppler wildlife monitoring data. The errors associated with Argos locations in four geographic locations in Romania were assessed during static, low-speed and high-speed tests. The effectiveness of the Douglas Argos distance angle filter algorithm was then evaluated to ascertain its effect on the minimization of localization errors.ResultsArgos locations received in the tests had larger associated horizontal errors than those indicated by the operator of the Argos system, including under ideal reception conditions. Positional errors were similar to those obtained in other studies outside of Europe. The errors were anisotropic, with larger longitudinal errors for the vast majority of the data. Errors were mostly related to speed of the Argos transmitter at the time of reception, but other factors such as topographical conditions and orientation of antenna at the time of the transmission also contributed to receiving low-quality data. The Douglas Argos filter successfully excluded the largest errors while retaining a large amount of data when the threshold was set to the local scale (two km).DiscussionFilter selection requires knowledge about the movement patterns and behavior of the species of interest, and the parametrization of the selected filter typically requires a trial and error approach. Selecting the proper filter reduces the errors while retaining a large amount of data. However, the post-processed data typically includes large positional errors; thus, we recommend incorporating Argos error metrics (e.g., error ellipse) or use complex modeling approaches when working with filtered data.

DVL-Aided SINS In-Motion Alignment Filter Based on a Novel Nonlinear Attitude Error Model

A novel nonlinear attitude error model based on square root cubature information filter (SR-CIF) is proposed aiming to speed up the convergence rate of DVL-aided strapdown inertial navigation system (SINS) in-motion initial alignment for autonomous underwater vehicle (AUV) when both large initial heading error and large initial level attitude errors exist The new nonlinear attitude error model and measurement model are applicable for initial alignment after a short-time coarse alignment with large attitude errors exist. The SR-CIF embeds the whole iterative process into the data structure framework of the information filtering, replacing the covariance matrix in the square root cubature Kalman filter (SR-CKF) with an information matrix which simplifies the filter initialization. The square root technology ensures the symmetry and positive definiteness of the information matrix with enhanced stability of the filter. The simulation and experimental results indicate that the proposed DVL-aided alignment filter is effective with large initial attitude errors. The rate of convergence and estimation accuracy of the SR-CIF is higher than that of the conventional SR-CKF with large attitude misalignments.

Investigation of Vehicle Positioning by Infrared Signal-Direction Discrimination for Short-Range Vehicle-to-Vehicle Communications

A method to locate the position of the target vehicle with the aid of infrared signal-direction discrimination for short-range vehicle-to-vehicle communications is proposed in this paper. With the use of two one-dimensional (1-D) signal-direction discriminators mounted on a vehicle with a lateral separation between them to measure the coming directions of the signal emitted from another target vehicle, the position of the target vehicle relative to this detecting vehicle can be located by triangulation. The aforementioned 1-D signal-direction discriminator is composed of two planar receiving modules forming a specific geometric structure, which leads to different responsivities of these individual receiving modules for a signal incident from a definite direction. The coming direction of the signal is determined by comparing the signal strengths received by these individual receiving modules. With a proposed hardware and software implementation, the position of the target vehicle can be accurately determined within a longitudinal range of 50 m. Owing to the restriction of the width of the vehicle, the separation of the signal-direction discriminators mounted on the vehicle cannot exceed 1.8 m. This leads to the consequence that in the remote region any small inaccuracy of the measured signal directions may cause very large position error. However, our measured results reveal a specific characteristic of the distribution of the measured positions for the target vehicle at a definite location. This allows us to design deliberate statistical algorithms to accurately extract the position of the target vehicle in the remote region. Using the simplest statistical algorithm, we are able to locate the position of the target vehicle with acceptable accuracy within a longitudinal range of 80 m. In this paper, we show the feasibility and applicability of this method. Furthermore, improvement is foreseeable with more deliberate design of hardware and software.

Analysis of the Dosimetric and Geometrical Variations Caused by Irregular Breathing Patterns on Normal Helical CT and 4D CT Datasets for Lung Cancer SBRT Treatment

To analyze the dosimetric and geometrical variations due to irregular breathing patterns on normal helical CT and 4D CT datasets for lung cancer SBRT treatments. Regular and irregular motion models were created and imported into a dynamic thorax phantom for imaging, planning and does measurement 64-slice CT, 6-MV photon beams and a treatment planning system were used. The regular motion was a sine wave with longitudinal range of ±1.5 cm and period of 4 sec. The irregular motions were generated by extracting the RPM cycles of different degrees of amplitude or phase variations from patients. Two 20 mm diameter and soft-tissue equivalent semispherical target was embedded in a motion rod for use with the phantom. Helical CT for static target, and 4D CT for motion target in regular and all irregular motions were performed. Phase bin, maximum and average intensity projection (MIP, AIP) CTs were reconstructed to evaluate the target position and geometric distortion. Static plan, and the motion plans for different patterns with phase-based gating (interval of 30–70%) and non-gating treatment were generated using RaipArc and IMRT techniques. EBT3 film was used for dose measurement. Dose profile comparison and gamma analysis (±3%/1 mm criteria) were used to quantify the dose agreement between measurements and calculations. Compare with static CT, MIP images shown a slight higher HU (value of 50) in the target region. By contrast to MIP images with a homogeneous HU distribution in the target region, AIP images were with a much lower HU and with a shape of Gauss distribution (-780 to -350). Phase bin with 10 phases or 20 phases have similar geometrical shapes. Phase bin images with higher target motion velocity (phase 25% and 75%) have a significantly larger target center position errors (3.0 to 3.4 mm). The variations of target volume for static CT and regular motion phase bin CTs were within 2.5%, AIP and MIP CTs showed a volume reduction of -6.7% and -3.8%, respectively. For irregular motions, slightly differences (-6.2 to -7.7%) on ITV between AIP and MIP images (AIP/MIP) were found for gated plans, and had a larger differences (-12.3 to -15.2%) for non-gated plans. Dosimetric comparisons showed a high passing rate (>98.5%) for static plan in the target region, AIP and MIP gated plans have average passing rates of 92.2±5.3% and 85.8±8.9%, respectively. Non-gated plans have significantly lower and deviated passing rates, AIP and MIP plans were with passing rates of 43.6±20.8% and 66.7±36.4%, respectively (p < 0.05). Faster motion results in larger position errors in 4D CT image acquisition, and Irregular breathing motion leads to volume reduction for AIP images; therefore, plan CT should avoid using fast period CT, breath coaching should be used to maintain regular motion, and the ITV in AIP CT should be verified. For Irregular motions during treatment, phase-based gated plans have target doses more consistent with the plans than the non-gated plans.

Adaptive Second-Order Sliding-Mode Observer for PMSM Sensorless Control Considering VSI Nonlinearity

This paper proposes an adaptive super-twisting algorithm based sliding-mode observer (STA-SMO) for surface-mounted permanent magnet synchronous machine (PMSM) sensorless control, in which voltage source inverter (VSI) nonlinearity is taken into consideration. An adaptive algorithm for online tuning the sliding-mode coefficients of STA-SMO is proposed based on the existing stable conditions. Thus, position estimation error can be reduced by the proposed adaptive algorithm in wide-speed range. Furthermore, voltage distortion due to VSI nonlinearity is online compensated to improve the accuracy of PMSM model. Because mismatch between reference and actual voltage due to VSI nonlinearity may bring large rotor position and speed estimation error, especially in low-speed range where distorted voltages may become dominant compared to actual voltages. Thus, a STA-SMO with adaptive sliding-mode coefficients and accurate voltage value could be obtained. Finally, the effectiveness of the proposed adaptive STA-SMO with online VSI nonlinearity compensation is verified on a surface-mounted PMSM by experiments.