Absolute Positional Accuracy Research Articles

Is it possible to generate accurate 3D point clouds with UAS-LIDAR and UAS-RGB photogrammetry without GCPs? A case study on a beach and rocky cliff

ContextRecently, Unoccupied Aerial Systems (UAS) with photographic or Light Detection and Ranging (LIDAR) sensors have incorporated on-board survey-grade Global Navigation Satellite Systems that allow the direct georeferencing of the resulting datasets without Ground Control Points either in Real-Time (RTK) or Post-Processing Kinematic (PPK) modes. These approaches can be useful in hard-to-reach or hazardous areas. However, the resulting 3D models have not been widely tested, as previous studies tend to evaluate only a few points and conclude that systematic errors can be found.ObjectivesWe test the absolute positional accuracy of point clouds produced using UAS with direct-georeferencing systems.MethodsWe test the accuracy and characteristics of point clouds produced using a UAS-LIDAR (with PPK) and a UAS-RGB (Structure-from-Motion or SfM photogrammetry with RTK and PPK) in a challenging environment: a coastline with a composite beach and cliff. The resulting models of each processing were tested using as a benchmark a point cloud surveyed simultaneously by a Terrestrial Laser Scanner.ResultsThe UAS-LIDAR produced the most accurate point cloud, with homogeneous cover and no noise. The systematic bias previously observed in the UAS-RGB RTK approaches are minimized using oblique images. The accuracy observed across the different surveyed landforms varied significantly.ConclusionsThe UAS-LIDAR and UAS-RGB with PPK produced unbiased point clouds, being the latter the most cost-effective method. For the other direct georeferencing systems/approaches, the acquisition of GCP or the co-registration of the resulting point cloud is still necessary.

Trajectory error compensation method for grinding robots based on kinematic calibration and joint variable prediction

Trajectory accuracy, a crucial metric in assessing the dynamic performance of grinding robots, is influenced by the uncertain movement of the tool center point, directly impacting the surface quality of processed workpieces. This article introduces an innovative method for compensating trajectory errors. Initially, a strategy for error compensation is derived using differential kinematics theory. Subsequently, a robot kinematic calibration method utilizing ring particle swarm optimization (RPSO) is proposed to address static errors in the grinding robot. Simultaneously, a method for predicting robot joint variables based on a dual-channel feedforward neural network (DCFNN) is designed to mitigate dynamic errors. Finally, a simulation platform is developed to validate the proposed method. Simulation analysis using extensive data demonstrates an 89.3% improvement in absolute position accuracy and a 74.2% reduction in error fluctuation range, outperforming sparrow search algorithm (SSA), improved mayfly algorithm (IMA), multi-representation integrated predictive neural network (MRIPNN), etc. Algorithmic comparison reveals that kinematic calibration significantly reduces the average trajectory error, while joint variable prediction notably minimizes error fluctuation. Validation through trajectory straightness testing and a 3D printing propeller grinding experiment achieves a trajectory straightness of 0.2425 mm. Implementing this method enables achieving 86.1% surface machining allowance within tolerance, making it an optimal solution for grinding robots.

Bio-inspired machine-learning aided geo-magnetic field based AUV navigation system

The navigational accuracy of sea animals and trans-ocean birds provides inspiration in using geo-magnetic field (GMF) for realizing strategic truly autonomous underwater vehicles (AUV) capable of determining their absolute position on earth, without the aid of ship-referenced acoustic baseline systems. Supervised Machine Learning algorithms are applied on the GMF intensity data obtained from NOAA World Magnetic Model for a 900 km2 within the Indian mineral exploratory area in the Central Indian Ocean, with a resolution of 50 m, considering the sensitivity of commercially available magnetometers. It is identified that, for AUVs equipped with magnetometers with a detection sensitivity of 0.1 nT, the supervisory random forest regression and decision tree algorithm trained with priori GMF data, could provide trajectory guidance to AUVs with an absolute mean position accuracy in 2D plane, with reference to the last known position from Integrated Navigation system aided initially with GPS and with acoustic positioning in underwater. Circular Error Probable (CEP 50) of 53 m and 56 m, respectively. The scalar GMF anomaly navigation demonstrated to be a viable GPS-alternative navigation system could be extended to larger areas with inclination and declination vectors, as unique identifiers.

Accuracy Compensation Based on Optimized Neural Network for a Robotic Patient Positioning System with 6 Degrees of Freedom Used in Proton Therapy System

Proton therapy for tumor treatment is a typical application of nuclear technology. For proton therapy systems, robotic patient positioning systems (PPSs) are increasingly used because of their high flexibility and efficiency. Most robotic PPSs are developed based on industrial robots, which have good repeatability but low absolute position accuracy (1 to 3 mm) and do not satisfy the requirement of highly precise treatment. In this study, an optimized algorithm, named the Back Propagation Neural Network (BPNN) algorithm based on particle swarm optimization, is proposed to improve the performance of absolute positioning accuracy. A comparison of the training for the traditional BPNN and the optimized algorithm is presented. A series of experiments with different payload weights and tools is implemented to validate the performance of the proposed method. The training results show that the proposed method can improve the average predicted positioning error from 0.55 to 0.38 mm. The results of the experiment with a calibration tool show that the average position error is reduced from 4.10 to 0.32 mm. The results of the experiment with a carbon fiber couch top show that the average and maximal positioning errors are 0.35 and 0.77 mm, respectively. All the results verify the feasibility of the proposed method in this study in improving the position accuracy of the robotic PPS.

Building 3D CityGML models of mining industrial structures using integrated UAV and TLS point clouds

Mining industrial areas with anthropogenic engineering structures are one of the most distinctive features of the real world. 3D models of the real world have been increasingly popular with numerous applications, such as digital twins and smart factory management. In this study, 3D models of mining engineering structures were built based on the CityGML standard. For collecting spatial data, the two most popular geospatial technologies, namely UAV-SfM and TLS were employed. The accuracy of the UAV survey was at the centimeter level, and it satisfied the absolute positional accuracy requirement of creating all levels of detail (LoD) according to the CityGML standard. Therefore, the UAV-SfM point cloud dataset was used to build LoD 2 models. In addition, the comparison between the UAV-SfM and TLS sub-clouds of facades and roofs indicates that the UAV-SfM and TLS point clouds of these objects are highly consistent, therefore, point clouds with a higher level of detail and accuracy provided by the integration of UAV-SfM and TLS were used to build LoD 3 models. The resulting 3D CityGML models include 39 buildings at LoD 2, and two mine shafts with hoistrooms, headframes, and sheave wheels at LoD 3.

A Multimodal Robust Simultaneous Localization and Mapping Approach Driven by Geodesic Coordinates for Coal Mine Mobile Robots

Mobile robots in complex underground coal mine environments are still unable to achieve accurate pose estimation and the real-time reconstruction of scenes with absolute geographic information. Integrated terrestrial-underground localization and mapping technologies have still not been effectively developed. This paper proposes a multimodal robust SLAM method based on wireless beacon-assisted geographic information transmission and lidar-IMU-UWB elastic fusion mechanism (LIU-SLAM). In order to obtain the pose estimation and scene models consistent with the geographic information, the construction of two kinds of absolute geographic information constraints based on UWB beacons is proposed. An elastic multimodal fusion state estimation mechanism is designed based on incremental factor graph optimization. A tightly coupled lidar-inertial odometry is firstly designed to construct the lidar-inertial local transformation constraints, which are further integrated with the absolute geographic constraints by UWB anchors through a loosely coupled approach. Extensive field tests based on coal mine robots have been conducted in scenarios such as underground garages and underground coal mine laneways. The results show that the proposed geodesic-coordinate driven multimode robust SLAM method can obtain absolute localization accuracy within 25 cm with practical robustness and real-time performance in different underground application scenarios. The wireless beacon-assisted geodesic-coordinate transmission strategy can provide a plug-and-play customized solution for precise positioning and scene modeling in complex scenarios of various coal mine robot application.

Robot 10 parameter compensation method based on Newton–Raphson method

AbstractIn this study, a novel kinematic calibration method is proposed to improve the absolute positioning accuracy of 6R robot. This method can achieve indirect compensation of the 25 parameters of modified Denavit–Hartenberg (MDH). The procedures of the method are threefold. Firstly, the 25-parameter errors model of MDH is initially established. However, only the errors of 10 parameters can be directly compensated in the 25-parameter errors model, since the inverse kinematics algorithm has to meet Pieper criterion. Subsequently, a calibration method is proposed to improve accuracy of the absolute position, which uses the Newton–Raphson method to transform the 25-parameter errors into 10-parameter errors (namely T-10 parameter model). Finally, the errors corresponding to 10 parameters in the T-10 parameters model are identified through the least square method. The calibration performances of T-10 parameters model are comprehensively validated by experimentation on two ER6B-C60 robots and one RS010N robot. After kinematic calibration, the average absolute positioning accuracy of the three robots can be improved by about 90%. The results indicate that the proposed calibration method can achieve more precise absolute positioning accuracy and has a wider range of universality.

Smoothened Absolute Kinematic Position Estimation Of Leo Satellite Using Gps Observables

In this paper, our objective is to use the navigation signals (pseudorange and carrier phase measurements) from GPS to kinematically estimate the absolute position of a low Earth orbit satellite and its receiver clock biases. GPS observables can estimate the precise position of a satellite in near real time. The GPS satellite navigation file is downloaded from Scripps Orbit and Permanent Array Centre (SOPAC) website for starting epoch of 01-01-2016 00:00 UT. The observables are then generated for a Low-Earth-Orbit (LEO) satellite at an altitude of 901.4 km. The absolute position is estimated using pseudorange measurements. The accuracies obtained are (5.68 8.04 6.17) m in ECEF frame. This estimated absolute position is then smoothened with the time-differenced carrier phase measurements. The Kalman filter gains are computed in near real time. The smoothened accuracies obtained are (2.24 2.60 2.6982) m in ECEF frame, thus showing improved estimated absolute position accuracy.

A Wafer Pre-Alignment Algorithm Based on Weighted Fourier Series Fitting of Circles and Least Squares Fitting of Circles.

The wafer pre-aligner is a crucial component in the lithography process to correct the wafer center and notch orientation. To improve the precision and the efficiency of pre-alignment, a new method to calibrate the center and the orientation of a wafer based on the weighted Fourier series fitting of circles (WFC) method and the least squares fitting of circles (LSC) method, respectively, is proposed. The WFC method effectively suppressed the influence of the outliers and had high stability compared with the LSC method when fitted to the center of the circle. While the weight matrix degenerated to the identity matrix, the WFC method degenerated into the Fourier series fitting of circles (FC) method. The fitting efficiency of the FC method is 28% higher than that of the LSC method, and the fitting accuracy of the center of the FC method is the same as that of the LSC method. In addition, the WFC method and the FC method perform better than the LSC method in radius fitting. The pre-alignment simulation results showed that the absolute position accuracy of the wafer was ±2 µm, the absolute direction accuracy was 0.01°, and the total calculation time was less than 3.3 s in our platform.

Continuous Decimeter-Level Positioning in Urban Environments Using Multi-Frequency GPS/BDS/Galileo PPP/INS Tightly Coupled Integration

Time- and precision-critical applications, such as autonomous driving, have extremely rigorous standards for continuous high-precision positioning. The importance of precise point positioning (PPP) technology for self-navigation equipment is self-evident by delivering decimeter-/centimeter-level absolute position accuracy in a global coordinate framework. Nevertheless, the prolonged initialization period renders PPP almost too difficult to be widely used for time-critical applications in real transportation scenarios, for example, in city canyons and overpasses. We proposed a method to accomplish continuous decimeter-level positioning by leveraging triple-frequency GNSS observations with an Inertial Navigation System (INS) aiding in urban environments. In the proposed method, the inertial measurements and the original tri-frequency pseudorange and carrier phase measurements are tightly fused in an extended Kalman filter to obtain the optimal state estimate. Afterwards, with precise extra-wide-lane (EWL) and wide-lane (WL) Uncalibrated Phase Delay (UPD) products, the EWL and WL ambiguities can be resolved sequentially to implement instantaneous decimeter-level positioning. Exploiting the short-term high-precision characteristic of the INS, the continuity of the PPP solution can be ameliorated noticeably, and the ability of decimeter-level positioning can be maintained effortlessly throughout the navigation process. With land vehicle data collected, several experiments are undertaken to comprehensively assess the capability of the proposed system in urban scenarios, taking the solution obtained by a commercial post-processing software as the reference. The single-epoch decimeter-level position estimation can be captured instantaneously for WL ambiguity-fixed PPP solutions. Furthermore, for WL ambiguity-fixed PPP/INS-integrated solutions, the position estimation is better than 0.2 m for horizontal components and improved by 40–90% compared with that of the WL ambiguity-fixed PPP solutions. More importantly, the availability rate of positioning accuracy is better than 0.3 m in the horizontal direction and 0.5 m in the up direction reaching 93.91%, whereas it is only 53.78% for WL ambiguity-fixed PPP solutions. Overall, the WL ambiguity-fixed PPP/INS-integrated solutions have the favorable performance to maintain continuous decimeter-level positioning for self-navigation equipment, even if full GNSS outages are encountered.

Precise Robot Calibration Method-Based 3-D Positioning and Posture Sensor

This article presents a distance accuracy technique for zero-offset industrial robot calibration based on 3-D positioning and posture (3DPP) sensor along with modified Denavit–Hartenberg (MDH) for robot kinematics identification. Industrial robots’ distance and positioning accuracy tend to diminish rapidly due to repetitive tasks and heavy loads. Many aspects can be involved in reducing the distance and positioning accuracy of the industrial robot; therefore, using the proper sensors and identification methods is essential to increase or restore the accuracy back to the original state. Normally, maintenance requires apparatus made specifically for robot kinematic calibration which are costly, time-consuming, and must be done by trained operators, while traditional calibration techniques suffer from cumulative error between the calibration device coordinates and robot coordinates. In this article, a 3DPP measurement device and MDH robot kinematic identification method is proposed for a six-degree-of-freedom (6DOF) industrial manipulator calibration, and a distance error calibration model is applied. The results indicate that the proposed 3DPP sensor and calibration model based on MDH improved the absolute position accuracy and distance accuracy greatly, the positioning maximum and average error were reduced by 94% and 96% respectively, and the distance maximum and average error were reduced by 95% and 96% respectively. The experimental results confirm the efficiency of the sensor and proposed method.

Robust Accurate LiDAR-GNSS/IMU Self-Calibration Based on Iterative Refinement

Light detection and ranging (LiDAR) and global navigation satellite system (GNSS)/inertial measurement unit (IMU) have been widely used in autonomous driving systems. LiDAR-GNSS/IMU calibration directly affects the performance of vehicle localization and perception. Current calibration methods require specific vehicle movements or scenarios with artificial calibration markers to keep the problem well-constrained, which are empirical, time-consuming, and poorly automated. To solve this problem, this article proposes a novel self-calibration method based on both relative and absolute motion constraints. Initial calibration parameters are calculated with relative motion constraints derived from LiDAR odometry. To eliminate the impact of odometry drift and enhance the observability of translation parameters, calibration parameters are iteratively refined by tightly coupling both relative and absolute motion constraints derived from scan-global map matching. Tests on simulation and ground datasets show that the proposed method is robust and accurate with RMSEs of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10^{-{3^{\circ} }}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10^{-3}$ </tex-math></inline-formula> m for rotation and translation, respectively. Further mapping and localization experiments with calculated calibration parameters present a state-of-the-art absolute localization accuracy of about 3 cm.

Performance Analysis of Hybrid Kinematic Mechanism for Fusion Reactor Maintenance

The hybrid kinematic mechanism (HKM) as an alternative remote handling subsystem of the Demonstration Fusion Power Plant (DEMO) breeding blanket (BB) is undergoing extensive theoretical analysis and feasibility verification. In this paper, the forward and inverse kinematic models of the HKM are derived by combining the Newtonian iterative method and the analytical method. Cartesian space trajectory planning is designed based on the trajectories of the HKM lifting of inboard and outboard BBs. The continuous smooth inverse kinematic solutions in the HKM joint space are obtained based on the polynomial interpolation method. For the characteristics of the HKM piston thread driving, the end-effector position error caused by the degradation of the spherical joint into a universal joint is analyzed and calculated. During the lifting of the left inboard BB, there is a maximum absolute error ∆P = 3.1 mm, and as the error continues to expand to the bottom of the BB it causes a risk of collision. Combining the overall effects of driving control, rigid–flexible coupling, etc., on position accuracy, an open-loop variable parameter error compensation plan based on the Levenberg–Marquardt (LM) nonlinear damping least-squares algorithm is proposed and validated in this paper. The simulation results show that the maximum absolute error after compensation is less than 1 mm as the mesh density increases, and the absolute position accuracy can be further improved by local mesh encryption. This study verifies the feasibility of the HKM as a BB remote handling subsystem and provides an option for high-precision control of the HKM.

Constructal Evaluation of Polynomial Meta-Models for Dynamic Thermal Absorptivity Forecasting for Mixed-Mode nZEB Heritage Building Applications

The intelligent and appropriate regulation of indoor temperatures within heritage buildings is crucial for achieving nearly Zero-Energy Building (nZEB) standards, since the technical improvement of the envelope and the overall shape of heritage buildings should be very limited in order to preserve the buildings’ authenticity. Thermal comfort is a very important factor that influences the energy performance of a building and the wellbeing of its end users. The present paper focuses on the development of a dynamic thermal human stress model that aimed to accurately predict the necessary garment insulation within a typical high-inertia heritage building. Two different statistical approaches (a Hoke D6 design and a composite factorial design) were employed for the development of this meta-model adapted to a typical mixed-mode heritage building seeking to obtain nZEB classification. Thermal human stress was modeled through the prediction of the thermal absorptivity (b) in accordance with the updated ASHRAE 55 model. Physically measured indoor climate parameters, outdoor meteorological data, and building operational information were coupled to the subjective sensorial dimensions of the problem with the aim of identifying the necessary garment insulation levels within heritage buildings composed of high-thermal-mass materials (for example, stone, concrete, and ceramic tiles). Our investigation focused on the parameter directly linked to the cold/warm sensations experienced due to clothing insulation: thermal absorptivity (b). In brief, the present paper proposes a third-order regression polynomial model that facilitates the calculation of thermal absorptivity, relying on adaptive thermal comfort concepts. The meta-model was then evaluated using Adrian Bejan’s constructal law after conducting entropy analysis. The constructal evaluation of the meta-model revealed the characteristic size of the domain regarding variable thermal absorptivity (b) and identified the necessary evolution of the model in order to increase its forecasting capacity. Thus, the model provided accurate forecasting for thermal absorptivity values greater than 50 Ws−1/2 m−2K and will be developed further to improve its absolute location accuracy for scenarios wherein the thermal absorptivity value is lower than 50 Ws−1/2 m−2K.

Use of unmanned aerial vehicle (UAV) for mapping, and accuracy assessment of the orthophoto with and without using GCPs: A case study in Nepal

The conventional methods of aerial photogrammetry using helicopters or airplanes are costly and challenging for small areas. For a developing country like Nepal, where Geospatial data is in high demand, a new competitive approach is essential for rapid spatial data acquisition at a low cost and time. This article demonstrates how this can be achieved using one of the evolving remote sensing technology, Unmanned Aerial Vehicles (UAVs). The application of UAVs is rapidly increasing in Nepal due to its capability of acquiring images remotely and the potential to provide data with a very high spatial and temporal resolution even in inaccessible terrain at a relatively low cost. Here, the performance of UAVs for topographical surveying and mapping has been investigated, along with the comparison between orthophoto obtained using GCPs, and without using GCPs. For this study, a DJI Phantom 3 Advanced quadcopter collected about 700 images at a flying height of 50 m above the settlement area. An orthophoto of 3.78 cm GSD covering 40.83 hectares of area was produced. With appropriate ground control points, an absolute positional accuracy of 0.035 m RMSE was achieved, whereas the output obtained without using GCPs was satisfactory. This study also highlights the use of a High-Performance Computing (HPC) system and open-source platform for rapid image processing.

Control of a Wheelchair-Mounted 6DOF Assistive Robot With Chin and Finger Joysticks.

Throughout the last decade, many assistive robots for people with disabilities have been developed; however, researchers have not fully utilized these robotic technologies to entirely create independent living conditions for people with disabilities, particularly in relation to activities of daily living (ADLs). An assistive system can help satisfy the demands of regular ADLs for people with disabilities. With an increasing shortage of caregivers and a growing number of individuals with impairments and the elderly, assistive robots can help meet future healthcare demands. One of the critical aspects of designing these assistive devices is to improve functional independence while providing an excellent human–machine interface. People with limited upper limb function due to stroke, spinal cord injury, cerebral palsy, amyotrophic lateral sclerosis, and other conditions find the controls of assistive devices such as power wheelchairs difficult to use. Thus, the objective of this research was to design a multimodal control method for robotic self-assistance that could assist individuals with disabilities in performing self-care tasks on a daily basis. In this research, a control framework for two interchangeable operating modes with a finger joystick and a chin joystick is developed where joysticks seamlessly control a wheelchair and a wheelchair-mounted robotic arm. Custom circuitry was developed to complete the control architecture. A user study was conducted to test the robotic system. Ten healthy individuals agreed to perform three tasks using both (chin and finger) joysticks for a total of six tasks with 10 repetitions each. The control method has been tested rigorously, maneuvering the robot at different velocities and under varying payload (1–3.5 lb) conditions. The absolute position accuracy was experimentally found to be approximately 5 mm. The round-trip delay we observed between the commands while controlling the xArm was 4 ms. Tests performed showed that the proposed control system allowed individuals to perform some ADLs such as picking up and placing items with a completion time of less than 1 min for each task and 100% success.

파라미터 중복성을 제거한 로봇 매니퓰레이터의 위치 기반 기구학 캘리브레이션

Industrial robot manipulators require high absolute position accuracy of the end effector to perform precise and complex tasks. However, manufacturing errors cause differences between nominal and actual parameters, and errors between the expected and actual positions of the end effector, resulting in undesired lower absolute position accuracy. Accordingly, to increase the absolute position accuracy of the end effector, kinematic calibration is required to correct the nominal parameters close to the actual parameters. However, in this study, redundancy of parameters may occur from the overlapping degrees of freedom of parameters in adjacent frames, which causes the problem of unnecessarily correcting many parameters in the optimization process. Thus, to solve this problem and use only the necessary parameters, this paper focuses on the linear relationship of redundant parameters and proposes a method of automatically discriminating and removing it through the Pearson Correlation Analysis. Additionally, through simulations on the two manipulator models, we verify the accuracy of redundancy of parameters determined by the proposed method, and demonstrate consistency and efficiency by comparing the results before and after redundancy removal.

Positional Accuracy Improvement of an Industrial Robot Using Feedforward Compensation and Feedback Control

Abstract Industrial robots play an important role in the transformation and upgrading of aviation manufacturing technology by their advantages of high flexibility, high efficiency, and low costs compared to the conventional computerised numerical control machine. However, due to the serial structure design of the main body, the industrial robot has low absolute positional accuracy, which limits its popularization and application in the field of high-precision manufacturing. The purpose of this paper is to develop a robot accuracy improvement method using feedforward compensation and joint closed-loop feedback correction considering the influence of joint backlash. The experimental results show that the positional error of the compensated robot by the proposed method is reduced from 0.76 mm to 0.18 mm under no-load conditions, and the hole's positional accuracy is to 0.25 mm in the robotic drilling experiment.

Dynamic behavior and path accuracy of an industrial robot with a CNC controller

The application of industrial robots in the field of machining is gradually increasing, but their low absolute position accuracy and low stiffness affect the improvement of machining accuracy. Computer numerical control (CNC) has good performance to control the motion accuracy in the machine tool. Therefore, it is proposed to improve the motion accuracy of robots. This article utilizes a stereo high-speed camera to track robot motion. Circular paths running under the CNC system are planned to evaluate its performance, which includes path accuracy, motion velocity, and acceleration. The performance of identical paths running in a conventional robot controller is evaluated for comparison. Based on the experimental analysis, the CNC system, which has more functionalities for acceleration regulation, can get better path accuracy and stability. It indicates that acceleration control has a significant effect on path accuracy and motion velocity. The acceleration profile in a conventional robot controller resembles a triangle. By default, the maximum acceleration value is adopted for the motion planning. Therefore, its accelerating and decelerating phase is much shorter than that of the CNC system, which could lead to instability. Both Step-shaped and trapezoidal acceleration profiles in the CNC system improve the dynamic behavior of the robot. Considering the trade-off between path accuracy and motion velocity, the Step-shaped acceleration profile can be applied to the optimization of the traditional robot motion control.

Lie Group Modelling for an EKF-Based Monocular SLAM Algorithm

This paper addresses the problem of monocular Simultaneous Localization And Mapping on Lie groups using fiducial patterns. For that purpose, we propose a reformulation of the classical camera model as a model on matrix Lie groups. Thus, we define an original-state vector containing the camera pose and the set of transformations from the world frame to each pattern, which constitutes the map’s state. Each element of the map’s state, as well as the camera pose, are intrinsically constrained to evolve on the matrix Lie group SE(3). Filtering is then performed by an extended Kalman filter dedicated to matrix Lie groups to solve the visual SLAM process (LG-EKF-VSLAM). This algorithm has been evaluated in different scenarios based on simulated data as well as real data. The results show that the LG-EKF-VSLAM can improve the absolute position and orientation accuracy, compared to a classical EKF visual SLAM (EKF-VSLAM).