Treatment of Extended Kalman Filter Implementations for the Gyroless Star Tracker

The literature since Apollo contains exhaustive material on attitude filtering, usually treating the problem of two sensors, a combination of state measuring and inertial devices. More recently, it has become popular for a sole attitude determination device to be considered. This is especially the case for a star tracker given its unbiased stellar measurement and recent improvements in optical sensor performance. The state device indirectly estimates the attitude rate using a known dynamic model. In estimation theory, two main attitude filtering approaches are classified, the additive and the multiplicative. Each refers to the nature of the quaternion update in the filter. In this article, these two techniques are implemented for the case of a sole star tracker, using simulated and real night sky image data. Both sets of results are presented and compared with each other, with a baseline established through a basic linear least square estimate. The state approach is more accurate and precise for measuring angular velocity than using the error-based filter. However, no discernible difference is observed between each technique for determining pointing. These results are important not only for sole device attitude determination systems, but also for space situational awareness object localisation, where attitude and rate estimate accuracy are highly important.

On the Solutions of Quaternion Difference Equations in Terms of Generalized Fibonacci-Type Numbers

The aim of this paper is to investigate the solution of the following difference equation zn+1=(pn)−1,n∈N0,N0=N∪0 where pn=a+bzn+czn−1zn with the parameters a, b, c and the initial values z−1,z0 are nonzero quaternions such that their solutions are associated with generalized Fibonacci-type numbers. Furthermore, we deal with the solutions to the following symmetric system of difference equations given by zn+1=(qn)−1,wn+1=(rn)−1,n∈N0 where qn=a+bwn+czn−1wn and rn=a+bzn+cwn−1zn. We provide the solution to the third-order quaternion linear difference equation in terms of the zeros of the characteristic polynomial associated with the linear difference equation.

Attitude Solving Algorithm and FPGA Implementation of Four-Rotor UAV Based on Improved Mahony Complementary Filter

With the development of modern industry, small UAVs have been widely used in agriculture, mapping, meteorology, and other fields. There is an increasing demand for the core attitude-solving algorithm of UAV flight control. In this paper, at first, a novel attitude solving algorithm is proposed by using quaternions to represent the attitude matrix and using Allan variance to analyze the gyroscope error and to quantify the trend of the error over time, so as to improve the traditional Mahony complementary filtering. Simulation results show that the six-axis data from the initial sensors (gyroscope and accelerometer) agree well with the measured nine-axis data with an extra magnetometer, which reduces the complexity of the system hardware. Second, based on the hardware platform, the six-axis data collected from MPU6050 are sent to FPGA for floating-point operation, transcendental function operation, and attitude solution module for processing through IIC communication, which effectively validates the attitude solution by using the proposed method. Finally, the proposed algorithm is applied to a practical scenario of a quadrotor UAV, and the test results show that the RMSE does not exceed 2° compared with the extended Kalman filter method. The proposed system simplifies the hardware but keeps the accuracy and speed of the solution, which may result in application in UAV flight control.

Optimal Trajectory Planning for Minimizing Base Disturbance of a Redundant Space Robot with IQPSO

With the development of aerospace technology, the practical application of a free-floating redundant space robot has become more and more popular. The problem of minimizing base disturbance has been paid attention among academic researchers. If the space robot moves, it would have an impact on the pose of a base. The interference on a base should be reduced, which was caused by the movements of the space robot. In the paper, the simplified model of a redundant space robot has been described, which consists of a base and a 7-joint manipulator. Using the nonholonomic redundancy features, the pose of the base has been optimized planning. First, a set of kinematic equations of the redundant space robot was founded. Second, the 5-order polynomial function could be used for the parametric 7 joints. Third, on the basis of the pose requirements, a fitness function was defined. At last, the proposed improved quantum particle swarm optimization (IQPSO) algorithm was presented. The proposed IQPSO algorithm not only searched the optimal value easily but also had a good robust performance. The advantages could be shown through the numerical experiments, compared with the quantum-behaved particle swarm optimization (QPSO) algorithm, particle swarm optimization (PSO) algorithm, and simulated annealing particle swarm (SAPSO) algorithm. Then, the proposed IQPSO algorithm was used to optimize the fitness function of trajectory planning. By the simulation results, it could be confirmed that the proposed IQPSO algorithm searched the global optimal solution not only easily but also smoothly, compared with the QPSO, PSO, and SAPSO algorithms. The proposed approach was suitable for planning an optimal trajectory.

Assembly of Compliant Structures with Autonomous Industrial Mobile Manipulators (AIMM) Using an End Effector with Active Deformation Compensation for the Assembly of Flaps

Composite structures in aeroplanes are often thin-walled and lightweight, resulting in significant compliance, which presents a handling and assembly challenge due to the associated part deformations. In order to counteract these deformations, the parts are held in their specified geometry using stiff and correspondingly heavy fixtures or jigs. Mobile industrial robots are very versatile and widely used in industrial volume production, but they are limited in their payload capacity. High-rate production of large aerospace modules requires highly automated flexible assembly processes. The approach presented in this paper is to combine mobile units with lightweight assembly jigs that have the capability of deformation compensation. The subject of the study is a high-rate assembly process for flap modules using an Autonomous Industrial Mobile Manipulator (AIMM) and a lightweight end effector. The end effector has a shape compensation function, implemented by an integrated Stewart platform, which enables the compensation of manufacturing tolerances as well as gravity effects. The compensation function is used in a closed loop and counteracts shape deviations by appropriate fixture shape adjustments. The paper reports on the conceptual design of the assembly scenario, the design of the end effector, its realization and the successful experimental demonstration at 1:1 scale.

Versatile Low-Cost Volumetric 3D Ultrasound Imaging Using Gimbal-Assisted Distance Sensors and an Inertial Measurement Unit

This study aims at creating low-cost, three-dimensional (3D), freehand ultrasound image reconstructions from commercial two-dimensional (2D) probes. The low-cost system that can be attached to a commercial 2D ultrasound probe consists of commercial ultrasonic distance sensors, a gimbal, and an inertial measurement unit (IMU). To calibrate irregular movements of the probe during scanning, relative position data were collected from the ultrasonic sensors that were attached to a gimbal. The directional information was provided from the IMU. All the data and 2D ultrasound images were combined using a personal computer to reconstruct 3D ultrasound image. The relative position error of the proposed system was less than 0.5%. The overall shape of the cystic mass in the breast phantom was similar to those from 2D and sections of 3D ultrasound images. Additionally, the pressure and deformations of lesions could be obtained and compensated by contacting the probe to the surface of the soft tissue using the acquired position data. The proposed method did not require any initial marks or receivers for the reconstruction of a 3D ultrasound image using a 2D ultrasound probe. Even though our system is less than $500, a valuable volumetric ultrasound image could be provided to the users.

Learning the Orientation of a Loosely-Fixed Wearable IMU Relative to the Body Improves the Recognition Rate of Human Postures and Activities

Features were developed which accounted for the changing orientation of the inertial measurement unit (IMU) relative to the body, and demonstrably improved the performance of models for human activity recognition (HAR). The method is proficient at separating periods of standing and sedentary activity (i.e., sitting and/or lying) using only one IMU, even if it is arbitrarily oriented or subsequently re-oriented relative to the body; since the body is upright during walking, learning the IMU orientation during walking provides a reference orientation against which sitting and/or lying can be inferred. Thus, the two activities can be identified (irrespective of the cohort) by analyzing the magnitude of the angle of shortest rotation which would be required to bring the upright direction into coincidence with the average orientation from the most recent 2.5 s of IMU data. Models for HAR were trained using data obtained from a cohort of 37 older adults (83.9 ± 3.4 years) or 20 younger adults (21.9 ± 1.7 years). Test data were generated from the training data by virtually re-orienting the IMU so that it is representative of carrying the phone in five different orientations (relative to the thigh). The overall performance of the model for HAR was consistent whether the model was trained with the data from the younger cohort, and tested with the data from the older cohort after it had been virtually re-oriented (Cohen's Kappa 95% confidence interval [0.782, 0.793]; total class sensitivity 95% confidence interval [84.9%, 85.6%]), or the reciprocal scenario in which the model was trained with the data from the older cohort, and tested with the data from the younger cohort after it had been virtually re-oriented (Cohen's Kappa 95% confidence interval [0.765, 0.784]; total class sensitivity 95% confidence interval [82.3%, 83.7%]).

Versatile Low-Cost Volumetric 3-D Ultrasound Platform for Existing Clinical 2-D Systems

Ultrasound imaging has indications across many areas of medicine, but the need for training and the variability in skill and acquired image quality among 2-D ultrasound users have limited its wider adoption and utilization. Low-cost volumetric ultrasound with a known frame of reference has the potential to lower these operator-dependent barriers and enhance the clinical utility of ultrasound imaging. In this paper, we improve upon our previous research-scanner-based prototype to implement a versatile volumetric imaging platform for existing clinical 2-D ultrasound systems. We present improved data acquisition and image reconstruction schemes to increase quality, streamline workflow, and provide real-time visual feedback. We present initial results using the platform on a Vimedix simulator, as well as on phantom and in vivo targets using a variety of clinical ultrasound systems and probes.

Almost periodic synchronization of quaternion-valued shunting inhibitory cellular neural networks with mixed delays via state-feedback control

This paper studies the drive-response synchronization for quaternion-valued shunting inhibitory cellular neural networks (QVSICNNs) with mixed delays. First, QVSICNN is decomposed into an equivalent real-valued system in order to avoid the non-commutativity of the multiplicity. Then, the existence of almost periodic solutions is obtained based on the Banach fixed point theorem. An novel state-feedback controller is designed to ensure the global exponential almost periodic synchronization. At the end of the paper, an example is given to illustrate the effectiveness of the obtained results.

Low-cost Volumetric Ultrasound by Augmentation of 2D Systems: Design and Prototype

Conventional two-dimensional (2D) ultrasound imaging is a powerful diagnostic tool in the hands of an experienced user, yet 2D ultrasound remains clinically underutilized and inherently incomplete, with output being very operator dependent. Volumetric ultrasound systems can more fully capture a three-dimensional (3D) region of interest, but current 3D systems require specialized transducers, are prohibitively expensive for many clinical departments, and do not register image orientation with respect to the patient; these systems are designed to provide improved workflow rather than operator independence. This work investigates whether it is possible to add volumetric 3D imaging capability to existing 2D ultrasound systems at minimal cost, providing a practical means of reducing operator dependence in ultrasound. In this paper, we present a low-cost method to make 2D ultrasound systems capable of quality volumetric image acquisition: we present the general system design and image acquisition method, including the use of a probe-mounted orientation sensor, a simple probe fixture prototype, and an offline volume reconstruction technique. We demonstrate initial results of the method, implemented using a Verasonics Vantage research scanner.

An Extended Kalman Filter-Based Attitude Tracking Algorithm for Star Sensors

Efficiency and reliability are key issues when a star sensor operates in tracking mode. In the case of high attitude dynamics, the performance of existing attitude tracking algorithms degenerates rapidly. In this paper an extended Kalman filtering-based attitude tracking algorithm is presented. The star sensor is modeled as a nonlinear stochastic system with the state estimate providing the three degree-of-freedom attitude quaternion and angular velocity. The star positions in the star image are predicted and measured to estimate the optimal attitude. Furthermore, all the cataloged stars observed in the sensor field-of-view according the predicted image motion are accessed using a catalog partition table to speed up the tracking, called star mapping. Software simulation and night-sky experiment are performed to validate the efficiency and reliability of the proposed method.

Motion of a nano-spheroid in a cylindrical vessel flow: Brownian and hydrodynamic interactions

We study the motion of a buoyant or a nearly neutrally buoyant nano-sized spheroid in a fluid filled tube without or with an imposed pressure gradient (weak Poiseuille flow). The fluctuating hydrodynamics approach and the deterministic method are both employed. We ensure that the fluctuation-dissipation relation and the principle of thermal equipartition of energy are both satisfied. The major focus is on the effect of the confining boundary. Results for the velocity and the angular velocity autocorrelations (VACF and AVACF), the diffusivities and the drag and the lift forces as functions of the shape, the aspect ratio, the inclination angle and the proximity to the wall are presented. For the parameters considered, the boundary modifies the VACF and AVACF such that three distinct regimes are discernible - an initial exponential decay followed by an algebraic decay culminating in a second exponential decay. The first is due to the thermal noise, the algebraic regime is due both to the thermal noise and the hydrodynamic correlations, while the second exponential decay shows the effect of momentum reflection from the confining wall. Our predictions display excellent comparison with published results for the algebraic regime (the only regime for which earlier results exist). We also discuss the role of the off-diagonal elements of the mobility and the diffusivity tensors that enable the quantifications of the degree of lift and margination of the nanocarrier. Our study covers a range of parameters that are of wide applicability in nanotechnology, microrheology and in targeted drug delivery.

Real-Time Motion Tracking for Mobile Augmented/Virtual Reality Using Adaptive Visual-Inertial Fusion

In mobile augmented/virtual reality (AR/VR), real-time 6-Degree of Freedom (DoF) motion tracking is essential for the registration between virtual scenes and the real world. However, due to the limited computational capacity of mobile terminals today, the latency between consecutive arriving poses would damage the user experience in mobile AR/VR. Thus, a visual-inertial based real-time motion tracking for mobile AR/VR is proposed in this paper. By means of high frequency and passive outputs from the inertial sensor, the real-time performance of arriving poses for mobile AR/VR is achieved. In addition, to alleviate the jitter phenomenon during the visual-inertial fusion, an adaptive filter framework is established to cope with different motion situations automatically, enabling the real-time 6-DoF motion tracking by balancing the jitter and latency. Besides, the robustness of the traditional visual-only based motion tracking is enhanced, giving rise to a better mobile AR/VR performance when motion blur is encountered. Finally, experiments are carried out to demonstrate the proposed method, and the results show that this work is capable of providing a smooth and robust 6-DoF motion tracking for mobile AR/VR in real-time.

An Acceleration-Based Gait Assessment Method for Children with Cerebral Palsy

With the aim of providing an objective tool for motion disability assessment in clinical diagnosis and rehabilitation therapy of cerebral palsy (CP) patients, an acceleration-based gait assessment method was proposed in this paper. To capture gait information, three inertial measurement units (IMUs) were placed on the lower trunk and thigh, respectively. By comparing differences in the gait acceleration modes between children with CP and healthy subjects, an assessment method based on grey relational analysis and five gait parameters, including Pearson coefficient, variance ratio, the number of extreme points, harmonic ratio and symmetry was established. Twenty-two children with cerebral palsy (7.49 ± 2.86 years old), fourteen healthy adults (24.2 ± 1.55 years old) and ten healthy children (7.03 ± 1.49 years old) participated in the gait data acquisition experiment. The results demonstrated that, compared to healthy subjects, the symptoms and severity of motor dysfunction of CP children could result in abnormality of the gait acceleration modes, and the proposed assessment method was able to effectively evaluate the degree gait abnormality in CP children.

Model-based extended quaternion Kalman filter to inertial orientation tracking of arbitrary kinematic chains

Inertial orientation tracking is still an area of active research, especially in the context of out-door, real-time, human motion capture. Existing systems either propose loosely coupled tracking approaches where each segment is considered independently, taking the resulting drawbacks into account, or tightly coupled solutions that are limited to a fixed chain with few segments. Such solutions have no flexibility to change the skeleton structure, are dedicated to a specific set of joints, and have high computational complexity. This paper describes the proposal of a new model-based extended quaternion Kalman filter that allows for estimation of orientation based on outputs from the inertial measurements unit sensors. The filter considers interdependencies resulting from the construction of the kinematic chain so that the orientation estimation is more accurate. The proposed solution is a universal filter that does not predetermine the degree of freedom at the connections between segments of the model. To validation the motion of 3-segments single link pendulum captured by optical motion capture system is used. The next step in the research will be to use this method for inertial motion capture with a human skeleton model.

Simultaneous Motion and Structure Estimation by Fusion of Inertial and Vision Data

For mobile robotics, head gear in augmented reality (AR) applications or computer vision, it is essential to continuously estimate the egomotion and the structure of the environment. This paper presents the system developed in the SmartTracking project, which simultaneously integrates visual and inertial sensors in a combined estimation scheme. The sparse structure estimation is based on the detection of corner features in the environment. From a single known starting position, the system can move into an unknown environment. The vision and inertial data are fused, and the performance of both Unscented Kalman filter and Extended Kalman filter are compared for this task. The filters are designed to handle asynchronous input from visual and inertial sensors, which typically operate at different and possibly varying rates. Additionally, a bank of Extended Kalman filters, one per corner feature, is used to estimate the position and the quality of structure points and to include them into the structure estimation process. The system is demonstrated on a mobile robot executing known motions, such that the estimation of the egomotion in an unknown environment can be compared to ground truth.

Fast Ego-motion Estimation with Multi-rate Fusion of Inertial and Vision

This paper presents a tracking system for ego-motion estimation which fuses vision and inertial measurements using EKF and UKF (Extended and Unscented Kalman Filters), where a comparison of their performance has been done. It also considers the multi-rate nature of the sensors: inertial sensing is sampled at a fast sampling frequency while the sampling frequency of vision is lower. the proposed approach uses a constant linear acceleration model and constant angular velocity model based on quaternions, which yields a non-linear model for states and a linear model in measurement equations. Results show that a significant improvement is obtained on the estimation when fusing both measurements with respect to just vision or just inertial measurements. It is also shown that the proposed system can estimate fast-motions even when vision system fails. Moreover, a study of the influence of the noise covariance is also performed, which aims to select their appropriate values at the tuning process. The setup is an end-effector mounted camera, which allow us to pre-define basic rotational and translational motions for validating results.

Nonholonomic motion planning for minimizing base disturbances of space manipulators based on multi-swarm PSO

Because space manipulators must satisfy the law of conservation of momentum, any motion of a manipulator within a space-manipulator system disturbs the position and attitude of its free-floating base. In this study, the authors have designed a multi-swarm particle swarm optimization (PSO) algorithm to address the motion planning problem and so minimize base disturbances for 6-DOF space manipulators. First, the equation of kinematics for space manipulators in the form of a generalized Jacobian matrix (GJM) is introduced. Second, sinusoidal and polynomial functions are used to parameterize joint motion, and a quaternion representation is used to represent the attitude of the base. Moreover, by transforming the planning problem into an optimization problem, the objective function is analyzed and the proposed algorithm explained in detail. Finally, numerical simulation results are used to verify the validity of the proposed algorithm.

Heading Estimation for Indoor Pedestrian Navigation Using a Smartphone in the Pocket

Heading estimation is a central problem for indoor pedestrian navigation using the pervasively available smartphone. For smartphones placed in a pocket, one of the most popular device positions, the essential challenges in heading estimation are the changing device coordinate system and the severe indoor magnetic perturbations. To address these challenges, we propose a novel heading estimation approach based on a rotation matrix and principal component analysis (PCA). Firstly, through a related rotation matrix, we project the acceleration signals into a reference coordinate system (RCS), where a more accurate estimation of the horizontal plane of the acceleration signal is obtained. Then, we utilize PCA over the horizontal plane of acceleration signals for local walking direction extraction. Finally, in order to translate the local walking direction into the global one, we develop a calibration process without requiring noisy compass readings. Besides, a turn detection algorithm is proposed to improve the heading estimation accuracy. Experimental results show that our approach outperforms the traditional uDirect and PCA-based approaches in terms of accuracy and feasibility.

Orthopaedic Rehabilitation Device Actuated with Pneumatic Muscles

Year after year recovery clinics worldwide report significant numbers of lower limb bearing joint disabilities. An effective method for the speedy rehabilitation of patients with such afflictions is Continuous Passive Motion (CPM), drawing upon a range of specific equipment.

This paper presents an innovative constructive solution for such orthopaedic rehabilitation equipment, designed to ensure a swift reintegration of patients at as low a cost as possible. The absolute novelty consists in the utilization of the linear pneumatic muscle as actuator of the orthopaedic rehabilitation equipment, thus achieving a light and highly compliant construction that satisfies safety requirements related to man-machine interaction. Pneumatic muscles are bio-inspired actuation systems characterized by a passive variable compliant behaviour. This property, deployed in rehabilitation systems, enables the development of human friendly devices, which are comfortable for the patients, and capable of safe interaction.

This paper presents the constructive schematic of the orthopaedic rehabilitation equipment, the structure of the actuation and positioning system, and several of its functional characteristics.

Propagation of soft tissue artifacts to the center of rotation: a model for the correction of functional calibration techniques

This paper presents a mathematical model for the propagation of errors in body segment kinematics to the location of the center of rotation. Three functional calibration techniques, usually employed for the gleno-humeral joint, are studied: the methods based on the pivot of the instantaneous helical axis (PIHA) or the finite helical axis (PFHA), and the "symmetrical center of rotation estimation" (SCoRE). A procedure for correcting the effect of soft tissue artifacts is also proposed, based on the equations of those techniques and a model of the artifact, like the one that can be obtained by double calibration. An experiment with a mechanical analog was performed to validate the procedure and compare the performance of each technique. The raw error (between 57 and 68mm) was reduced by a proportion of between 1:6 and less than 1:15, depending on the artifact model and the mathematical method. The best corrections were obtained by the SCoRE method. Some recommendations about the experimental setup for functional calibration techniques and the choice of a mathematical method are derived from theoretical considerations about the formulas and the results of the experiment.

Enhancing indoor inertial pedestrian navigation using a shoe-worn marker

We propose a novel hybrid inertial sensors-based indoor pedestrian dead reckoning system, aided by computer vision-derived position measurements. In contrast to prior vision-based or vision-aided solutions, where environmental markers were used-either deployed in known positions or extracted directly from it-we use a shoe-fixed marker, which serves as positional reference to an opposite shoe-mounted camera during foot swing, making our system self-contained. Position measurements can be therefore more reliably fed to a complementary unscented Kalman filter, enhancing the accuracy of the estimated travelled path for 78%, compared to using solely zero velocities as pseudo-measurements.

Hierarchical information fusion for global displacement estimation in microsensor motion capture

This paper presents a novel hierarchical information fusion algorithm to obtain human global displacement for different gait patterns, including walking, running, and hopping based on seven body-worn inertial and magnetic measurement units. In the first-level sensor fusion, the orientation for each segment is achieved by a complementary Kalman filter (CKF) which compensates for the orientation error of the inertial navigation system solution through its error state vector. For each foot segment, the displacement is also estimated by the CKF, and zero velocity update is included for the drift reduction in foot displacement estimation. Based on the segment orientations and left/right foot locations, two global displacement estimates can be acquired from left/right lower limb separately using a linked biomechanical model. In the second-level geometric fusion, another Kalman filter is deployed to compensate for the difference between the two estimates from the sensor fusion and get more accurate overall global displacement estimation. The updated global displacement will be transmitted to left/right foot based on the human lower biomechanical model to restrict the drifts in both feet displacements. The experimental results have shown that our proposed method can accurately estimate human locomotion for the three different gait patterns with regard to the optical motion tracker.

A Multiple Model Approach to Track Head Orientation With Delta Quaternions

Virtual reality and augmented reality environments using helmet-mounted displays create a sense of immersion by closely coupling user head motion to display content. Delays in the presentation of visual information can destroy the sense of presence in the simulation environment when it causes a lag in the display response to user head motion. The effect of display lag can be minimized by predicting head orientation, allowing the system to have sufficient time to counteract the delay. In this paper, anew head orientation prediction technique is proposed that uses a multiple delta quaternion (DQ) extended Kalman filter to track angular head velocity and angular head acceleration. This method is independent of the device used for orientation measurement, relying on quaternion orientation as the only measurement data. A new orientation prediction algorithm is proposed that estimates future head orientation as a function of the current orientation measurement and a predicted change in orientation, using the velocity and acceleration estimates. Extensive experimentation shows that the new method improves head orientation prediction when compared to single filter DQ prediction.

An adaptive-gain complementary filter for real-time human motion tracking with MARG sensors in free-living environments

High-resolution, real-time data obtained by human motion tracking systems can be used for gait analysis, which helps better understanding the cause of many diseases for more effective treatments, such as rehabilitation for outpatients or recovery from lost motor functions after a stroke. In order to achieve real-time ambulatory human motion tracking with low-cost MARG (magnetic, angular rate, and gravity) sensors, a computationally efficient and robust algorithm for orientation estimation is critical. This paper presents an analytically derived method for an adaptive-gain complementary filter based on the convergence rate from the Gauss-Newton optimization algorithm (GNA) and the divergence rate from the gyroscope, which is referred as adaptive-gain orientation filter (AGOF) in this paper. The AGOF has the advantages of one iteration calculation to reduce the computing load and accurate estimation of gyroscope measurement error. Moreover, for handling magnetic distortions especially in indoor environments and movements with excessive acceleration, adaptive measurement vectors and a reference vector for earth's magnetic field selection schemes are introduced to help the GNA find more accurate direction of gyroscope error. The features of this approach include the accurate estimation of the gyroscope bias to correct the instantaneous gyroscope measurements and robust estimation in conditions of fast motions and magnetic distortions. Experimental results are presented to verify the performance of the proposed method, which shows better accuracy of orientation estimation than several well-known methods.

Variable-State-Dimension Kalman-based Filter for orientation determination using inertial and magnetic sensors

In this paper a quaternion-based Variable-State-Dimension Extended Kalman Filter (VSD-EKF) is developed for estimating the three-dimensional orientation of a rigid body using the measurements from an Inertial Measurement Unit (IMU) integrated with a triaxial magnetic sensor. Gyro bias and magnetic disturbances are modeled and compensated by including them in the filter state vector. The VSD-EKF switches between a quiescent EKF, where the magnetic disturbance is modeled as a first-order Gauss-Markov stochastic process (GM-1), and a higher-order EKF where extra state components are introduced to model the time-rate of change of the magnetic field as a GM-1 stochastic process, namely the magnetic disturbance is modeled as a second-order Gauss-Markov stochastic process (GM-2). Experimental validation tests show the effectiveness of the VSD-EKF, as compared to either the quiescent EKF or the higher-order EKF when they run separately.

A Comparative Study of Three Inverse Kinematic Methods of Serial Industrial Robot Manipulators in the Screw Theory Framework

In this paper, we compare three inverse kinematic formulation methods for the serial industrial robot manipulators. All formulation methods are based on screw theory. Screw theory is an effective way to establish a global description of rigid body and avoids singularities due to the use of the local coordinates. In these three formulation methods, the first one is based on quaternion algebra, the second one is based on dual-quaternions, and the last one that is called exponential mapping method is based on matrix algebra. Compared with the matrix algebra, quaternion algebra based solutions are more computationally efficient and they need less storage area. The method which is based on dual-quaternion gives the most compact and computationally efficient solution. Paden-Kahan sub-problems are used to derive inverse kinematic solutions. 6-DOF industrial robot manipulator's forward and inverse kinematic equations are derived using these formulation methods. Simulation and experimental results are given.

Quaternion-valued nonlinear adaptive filtering

A class of nonlinear quaternion-valued adaptive filtering algorithms is proposed based on locally analytic nonlinear activation functions. To circumvent the stringent standard analyticity conditions which are prohibitive to the development of nonlinear adaptive quaternion-valued estimation models, we use the fact that stochastic gradient learning algorithms require only local analyticity at the operating point in the estimation space. It is shown that the quaternion-valued exponential function is locally analytic, and, since local analyticity extends to polynomials, products, and ratios, we show that a class of transcendental nonlinear functions can serve as activation functions in nonlinear and neural adaptive models. This provides a unifying framework for the derivation of gradient-based learning algorithms in the quaternion domain, and the derived algorithms are shown to have the same generic form as their real- and complex-valued counterparts. To make such models second-order optimal for the generality of quaternion signals (both circular and noncircular), we use recent developments in augmented quaternion statistics to introduce widely linear versions of the proposed nonlinear adaptive quaternion valued filters. This allows full exploitation of second-order information in the data, contained both in the covariance and pseudocovariances to cater rigorously for second-order noncircularity (improperness), and the corresponding power mismatch in the signal components. Simulations over a range of circular and noncircular synthetic processes and a real world 3-D noncircular wind signal support the approach.

Estimating three-dimensional orientation of human body parts by inertial/magnetic sensing

User-worn sensing units composed of inertial and magnetic sensors are becoming increasingly popular in various domains, including biomedical engineering, robotics, virtual reality, where they can also be applied for real-time tracking of the orientation of human body parts in the three-dimensional (3D) space. Although they are a promising choice as wearable sensors under many respects, the inertial and magnetic sensors currently in use offer measuring performance that are critical in order to achieve and maintain accurate 3D-orientation estimates, anytime and anywhere. This paper reviews the main sensor fusion and filtering techniques proposed for accurate inertial/magnetic orientation tracking of human body parts; it also gives useful recipes for their actual implementation.

Visual-Inertial Sensor Fusion: Localization, Mapping and Sensor-to-Sensor Self-calibration

Visual and inertial sensors, in combination, are able to provide accurate motion estimates and are well suited for use in many robot navigation tasks. However, correct data fusion, and hence overall performance, depends on careful calibration of the rigid body transform between the sensors. Obtaining this calibration information is typically difficult and time-consuming, and normally requires additional equipment. In this paper we describe an algorithm, based on the unscented Kalman filter, for self-calibration of the transform between a camera and an inertial measurement unit (IMU). Our formulation rests on a differential geometric analysis of the observability of the camera—IMU system; this analysis shows that the sensor-to-sensor transform, the IMU gyroscope and accelerometer biases, the local gravity vector, and the metric scene structure can be recovered from camera and IMU measurements alone. While calibrating the transform we simultaneously localize the IMU and build a map of the surroundings, all without additional hardware or prior knowledge about the environment in which a robot is operating. We present results from simulation studies and from experiments with a monocular camera and a low-cost IMU, which demonstrate accurate estimation of both the calibration parameters and the local scene structure.

A comparison between HMLP and HRBF for attitude control

In this paper the problem of controlling the attitude of a rigid body, such as a Spacecraft, in three-dimensional space is approached by introducing two new control strategies developed in hypercomplex algebra. The proposed approaches are based on two parallel controllers, both derived in quaternion algebra. The first is a feedback controller of the proportional derivative (PD) type, while the second is a feedforward controller, which is implemented either by means of a hypercomplex multilayer perceptron (HMLP) neural network or by means of a hypercomplex radial basis function (HRBF) neural network. Several simulations show the performance of the two approaches. The results are also compared with a classical PD controller and with an adaptive controller, showing the improvements obtained by using neural networks, especially when an external disturbance acts on the rigid body. In particular the HMLP network gave better results when considering trajectories not presented during the learning phase.

A fast quaternion-based orientation optimizer via virtual rotation for human motion tracking

For real-time ambulatory human motion tracking with low-cost inertial/magnetic sensors, a computationally efficient and robust algorithm for estimating orientation is critical. This paper presents a quaternion-based orientation optimizer for tracking human body motion, using triaxis rate gyro, accelerometer, and magnetometer signals. The proposed optimizer uses a Gauss-Newton (G-N) method for finding the best-fit quaternion. In order to decrease the computing time, the optimizer is formulated using a virtual rotation concept that allows very fast quaternion updates compared to the conventional G-N method. In addition, to guard against the effects of fast body motions and temporary ferromagnetic disturbances, a situational measurement vector selection procedure is adopted in conjunction with the G-N optimizer. The accuracy of orientation estimates is validated experimentally, using arm motion trials.

Head orientation prediction: delta quaternions versus quaternions

Display lag in simulation environments with helmet-mounted displays causes a loss of immersion that degrades the value of virtual/augmented reality training simulators. Simulators use predictive tracking to compensate for display lag, preparing display updates based on the anticipated head motion. This paper proposes a new method for predicting head orientation using a delta quaternion (DQ)-based extended Kalman filter (EKF) and compares the performance to a quaternion EKF. The proposed framework operates on the change in quaternion between consecutive data frames (the DQ), which avoids the heavy computational burden of the quaternion motion equation. Head velocity is estimated from the DQ by an EKF and then used to predict future head orientation. We have tested the new framework with captured head motion data and compared it with the computationally expensive quaternion filter. Experimental results indicate that the proposed DQ method provides the accuracy of the quaternion method without the heavy computational burden.

The Cartesian Path Planning of Free-Floating Space Robot using Particle Swarm Optimization

The Cartesian path planning of free-floating space robot is much more complex than that of fixed-based manipulators, since the end-effector pose (position and orientation) is path dependent, and the position-level kinematic equations can not be used to determine the joint angles. In this paper, a method based on particle swarm optimization (PSO) is proposed to solve this problem. Firstly, we parameterize the joint trajectory using polynomial functions, and then normalize the parameterized trajectory. Secondly, the Cartesian path planning is transformed to an optimization problem by integrating the differential kinematic equations. The object function is defined according to the accuracy requirement, and it is the function of the parameters to be defined. Finally, we use the Particle Swarm Optimization (PSO) algorithm to search the unknown parameters. The approach has the following traits: 1) The limits on joint angles, rates and accelerations are included in the planning algorithm; 2) There exist not any kinematic and dynamic singularities, since only the direct kinematic equations are used; 3) The attitude singularities do not exist, for the orientation is represented by quaternion; 4) The optimization algorithm is not affected by the initial parameters. Simulation results verify the proposed method.

Influence of the 3D inverse dynamic method on the joint forces and moments during gait

The joint forces and moments are commonly used in gait analysis. They can be computed by four different 3D inverse dynamic methods proposed in the literature, either based on vectors and Euler angles, wrenches and quaternions, homogeneous matrices, or generalized coordinates and forces. In order to analyze the influence of the inverse dynamic method, the joint forces and moments were computed during gait on nine healthy subjects. A ratio was computed between the relative dispersions (due to the method) and the absolute amplitudes of the gait curves. The influence of the inverse dynamic method was negligible at the ankle (2%) but major at the knee and the hip joints (40%). This influence seems to be due to the dynamic computation rather than the kinematic computation. Compared to the influence of the joint center location, the body segment inertial parameter estimation, and more, the influence of the inverse dynamic method is at least of equivalent importance. This point should be confirmed with other subjects, possibly pathologic, and other movements.