Real-time Trajectory Research Articles

Unsupervised learning for real-time and continuous gait phase detection.

Individuals with lower limb impairment after a stroke or spinal cord injury require rehabilitation, but traditional methods can be challenging for both patients and therapists. Robotic systems have been developed to help; however, they currently cannot detect the continuous gait phase in real time, hindering their effectiveness. To address this limitation, researchers have attempted to develop gait phase detection in general using fuzzy logic algorithms and neural networks. However, there is a paucity of research on real-time and continuous gait phase detection. In light of this gap, we propose an unsupervised learning method for real-time and continuous gait phase detection. This method employs windows of real-time trajectories and a pre-trained model, utilizing trajectories from treadmill walking data, to detect the real-time and continuous gait phase of human on overground locomotion. The neural network model that we have developed exhibits an average time error of less than 11.51 ms across all walking conditions, indicating its suitability for real-time applications. Specifically, the average time error during overground walking at different speeds is 11.20 ms, which is comparatively lower than the average time error observed during treadmill walking, where it is 12.42 ms. By utilizing this method, we can predict the real-time phase using a pre-trained model from treadmill walking data collected with a full motion capture system, which can be performed in a laboratory setting, thereby eliminating the need for overground walking data, which can be more challenging to obtain due to the complexity of the setting.

Hitchhiker: A Quadrotor Aggressively Perching on a Moving Inclined Surface Using Compliant Suction Cup Gripper

Perching on the surface of moving objects, like vehicles, could extend the flight time and range of quadrotors. Suction cups are usually adopted for surface attachment due to their durability and large adhesive force. To seal on a surfaces, suction cups must be aligned with the surface and possess proper relative tangential velocity. However, quadrotors’ attitude and relative velocity errors would become significant when the object surface is moving and inclined. To address this problem, we proposed a real-time trajectory planning algorithm. The time-optimal aggressive trajectory is efficiently generated through multimodal search in a dynamic time-domain. The velocity errors relative to the moving surface are alleviated. To further adapt to the residual errors, we design a compliant gripper using self-sealing cups. Multiple cups in different directions are integrated into a wheel-like mechanism to increase the tolerance to attitude errors. The wheel mechanism also eliminates the requirement of matching the attitude and tangential velocity. Extensive tests are conducted to perch on static and moving surfaces at various inclinations. Results demonstrate that our proposed system enables a quadrotor to reliably perch on moving inclined surfaces (up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.07m/s$</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">$90^\circ$</tex-math> </inline-formula> ) with a success rate of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$70\%$</tex-math> </inline-formula> or higher. The efficacy of the trajectory planner is also validated. Our gripper has larger adaptability to attitude errors and tangential velocities than conventional suction cup grippers. The success rate increases by 45% in dynamic perches. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper was motivated by the problem of perching on moving inclined surfaces using quadrotors. It can be used for perching on the various angled surfaces of an automobile to save energy and enlarge flight distance. It can also be exploited in air-ground cooperative tasks. In recent years, various grippers and trajectory planning methods have been devised to enable quadrotors to perch on static inclined surfaces. These strategies can not be used for perching on moving inclined surfaces. The task poses high requirements for the efficiency of trajectory planning and the grippers’ adaptability to pose errors. This paper proposes a real-time planning method to generate trajectories. The trajectories respect kinematic and motor lift constraints. They allow large attitude maneuvering of quadrotors. A multimodal search in a dynamic time-domain is developed to seek the minimum feasible time for the trajectory planner. Considering large pose errors in dynamic perching, a compliant gripper based on multiple independent suction cups is designed. The wheel and multidirectional layout of cups increase the adaptability to attitude and velocity errors. Results suggest that the proposed system is effective and reliable. In practice, our multiple cups would add weight penalty and increase the drag. The suction cups should be placed close to a quadrotor’s central axis to reduce the drag and disturbance in flow. The proposed system relies on an external motion capture system. In future research, we will focus on onboard sensing and control methods to achieve perching on moving inclined surfaces outdoors.

STEAM: Spatial Trajectory Enhanced Attention Mechanism for Abnormal UAV Trajectory Detection

Accurate unmanned aerial vehicle (UAV) trajectory tracking is crucial for the successful execution of UAV missions. Traditional global positioning system (GPS) methods face limitations in complex environments, and visual observation becomes challenging with distance and in low-light conditions. To address this challenge, we propose a comprehensive framework for UAV trajectory verification, integrating a range-based ultra-wideband (UWB) positioning system and advanced image processing technologies. Our key contribution is the development of the Spatial Trajectory Enhanced Attention Mechanism (STEAM), a novel attention module specifically designed for analyzing and classifying UAV trajectory patterns. This system enables real-time UAV trajectory tracking and classification, facilitating swift and accurate assessment of adherence to predefined optimal trajectories. Another major contribution of our work is the integration of a UWB system for precise UAV location tracking, complemented by our advanced image processing approach that includes a deep neural network (DNN) for interpolating missing data from images, thereby significantly enhancing the model’s ability to detect abnormal maneuvers. Our experimental results demonstrate the effectiveness of the proposed framework in UAV trajectory tracking, showcasing its robust performance irrespective of raw data quality. Furthermore, we validate the framework’s performance using a lightweight learning model, emphasizing both its computational efficiency and exceptional classification accuracy.

Real-time continuous handwritten trajectories recognition based on a regression-based temporal pyramid network

Real-time continuous handwritten trajectories recognition based on a regression-based temporal pyramid network

Construction of a Real-Time Ship Trajectory Prediction Model Based on Ship Automatic Identification System Data

The extraction of ship behavior patterns from Automatic Identification System (AIS) data and the subsequent prediction of travel routes play crucial roles in mitigating the risk of ship accidents. This study focuses on the Wuhan section of the dendritic river system in the middle reaches of the Yangtze River and the partial reticulated river system in the northern part of the Zhejiang Province as its primary investigation areas. Considering the structure and attributes of AIS data, we introduce a novel algorithm known as the Combination of DBSCAN and DTW (CDDTW) to identify regional navigation characteristics of ships. Subsequently, we develop a real-time ship trajectory prediction model (RSTPM) to facilitate real-time ship trajectory predictions. Experimental tests on two distinct types of river sections are conducted to assess the model’s reliability. The results indicate that the RSTPM exhibits superior prediction accuracy when compared to conventional trajectory prediction models, achieving an approximate 20 m prediction accuracy for ship trajectories on inland waterways. This showcases the advancements made by this model.

Stretchable triboelectric sensor array for real-time tactile sensing based on coaxial printing

With the rapid development of flexible and wearable electronics, tactile sensor array has shown great potential to detect diverse external stimuli in human–machine interactions and robotic intelligence. In this study, we developed triboelectric sensor array (TSA) with cross-laminated electrode via low-cost coaxial printing technique with the advantages of high precision, high efficiency and excellent uniformity. The results show that the proposed cross-laminated electrode based TSA possesses the characteristics of easy-fabrication process, high-sensitivity, long-term mechanical endurance and real-time trajectory sensing capacity. It can generate the maximum output voltage of 15.98 V at a frequency 4 Hz and vertical force 5 N in single electrode mode, and the maximum power is about 3.9 μW. Besides, TSA shows excellent stability under harsh mechanical bending, twisting and stretching deformation and even waterproof capability. This work offers a previously unexplored strategy for shortening individual design and fabrication cycle of flexible electronics, and promoting the potential application for stretchable sensor array in electronic skin, tactile detection and human–machine interactions.

A hierarchical control approach for virtual coupling in metro trains

AbstractAs an emerging technology, virtual coupling improves the efficiency and flexibility of metro services by forming multiple trains (units) as a virtually coupled train set (VCTS) without mechanical couplers. However, to realize the desired VCTS operation in practical metro services, a significant gap to be filled is that the implicit and nonlinear safety constraints are hard to be addressed in real‐time control. Thus, this paper proposes a hierarchical control approach with a two‐layer framework. In the upper layer, a trajectory planning method is designed, which addresses the safety constraints and prescribes a reference trajectory for each unit. In the lower layer, a model predictive control approach is constructed, by which each unit accurately tracks its reference trajectory in real time. Afterward, the proposed hierarchical control approach is employed to realize VCTS inter‐station operation in field tests. The average tracking error of speed is around 8 cm/s and the stopping error is less than 12 cm. The following distance between two units in VCTS is reduced to less than 105 m at the speed of 80 km/h, which is a breakthrough in the development of VCTS.

Stealthy attack detection based on controlled invariant subspace for autonomous vehicles

Autonomous driving offers a convenient and comfortable means of transportation, while the addition of external communication interfaces renders the vehicle communication more vulnerable to cyber attacks. In contrast to conventional attacks, well-designed stealthy attacks are more adept at evading conventional detectors. To address this problem, this paper proposes a robust detector based on controlled invariant subspace to identify stealthy attacks. This paper stands out not only by relying on the vehicle dynamics model for system state estimation, but rather by employing a real-time trajectory space generation method. Our detector develops a rapidly expanding random tree method based on offline incremental learning to generate trajectory subspace, and any trajectories that diverge from this subspace are identified as anomalies. Additionally, this paper designs distance measurement method that combines the linear quadratic regulation algorithm with a radial basis function neural network while also taking into account the vehicle's dynamic performance constraints. To assess the theoretical performance of the proposed detector, this paper presents rigorous proofs that demonstrate the asymptotical optimality of the generated trajectory and the robustness of the stealthy attack detection method based on controlled invariant subspace. Finally, simulation results demonstrate that the proposed robust detector can effectively identify stealthy attacks and outperforms advanced techniques in terms of accuracy and false-positive rate.

On the Interplay Between Sensing and Communications for UAV Trajectory Design

The unmanned aerial vehicles (UAVs) are envisioned as promising aerial facilities for providing advanced communication services as well as sensing functionalities in the next-generation wireless system. This paper considers a UAV-enabled integrated sensing and communications (ISAC) system, where a moving ground user (GU) is simultaneously tracked by multiple UAVs and receives the downlink communication information transmitted from the UAV. In particular, to jointly enhance the sensing and communication (S&C) performance, optimizing the UAV moving trajectory is demanded. To achieve this goal, we first harness the extended Kalman filtering (EKF) method for predicting and tracking the motion parameters of GU at each time slot, which relies on the range measurements extracted from the sensing echoes at the base station (BS). Afterward, we formulate a weighted optimization problem that addresses the design of UAV trajectories and GU-UAV association simultaneously, incorporating the consideration of real-time downlink communication rates and the Cramér-Rao bound (CRB) for GU tracking. The problem further is constrained by the maximum consumed power, maximum traveling distance, and minimum collision avoidance distance. As a step forward, to address the resultant non-convex problem, we develop an efficient iterative algorithm to obtain a near-optimal solution by utilizing the successive convex approximate (SCA) technique. Specifically, we alternately solve the GU-UAV association and the real-time trajectory design problem at each time slot. Finally, our numerical simulations illustrate that our proposed algorithm can track the GU accurately while meeting the sensing-centric and/or communication-centric requirements.

When UAVs Meet ISAC: Real-Time Trajectory Design for Secure Communications

When UAVs Meet ISAC: Real-Time Trajectory Design for Secure Communications

Hardware–Software Embedded System for Real-Time Trajectory Planning of Multi-Axis Machine Using B-Spline Curve Interpolation Algorithm

This paper proposes a B-spline trajectory algorithm to realize multi-axis trajectory interpolation and analyzes the operating accuracy in an embedded system. However, the existing trajectory generation method needs to use computer-aided manufacturing (CAM) software to convert the interpolating trajectory into G code and download the code into the computer numerical control (CNC) system for processing. In this paper, the method of third-degree B-spline interpolation is proposed to generate a curved surface trajectory, and the trajectory generated by this algorithm can be run directly into a CNC system. The precision analysis of the ISO parameter segmentation interpolation algorithm and the theory of constant velocity motion is also presented. The significance of this project is that it designs a complete set of embedded systems, including hardware circuit design and software logic design, and uses low-cost STM32 architecture to realize a B-spline constant-speed interpolation algorithm, which is verified on CNC polishing equipment. A simulation conducted with the MATLAB software and the B-spline curve interpolation experiments performed on a multi-axis polishing machine tool demonstrate the effectiveness and accuracy of the optimized third-degree B-spline algorithm.

A Hierarchical Control Strategy for a Rigid-Flexible Coupled Hexapod Bio-Robot.

The motion process of legged robots contains not only rigid-body motion but also flexible motion with elastic deformation of the legs, especially for heavy loads. Hence, the characteristics of the flexible components and their interactions with the rigid components need to be considered. In this paper, a hierarchical control strategy for robots with rigid-flexible coupling characteristics is proposed. This strategy involves (1) leg force prediction based on real-time motion trajectories and feedforward compensation for the error caused by flexible components; (2) building upon the centroid dynamics model of the rigid-body chassis, the centroid trajectories (centroid angular momentum (CAM) and centroid linear momentum (CLM)) and the body trajectory are taken into account to derive the optimal drive torque for maintaining body stability; (3) finally, the precise force control of the hydraulic drive units is achieved through the sliding mode control algorithm, integrating the dynamic model of the flexible legs. The proposed methods are validated on a giant hexapod robot weighing 3.5 tons, demonstrating that the introduced approach can reduce the robot's vibrations.

Trajectory generation and tracking control for aggressive tail-sitter flights

We address the theoretical and practical problems related to the trajectory generation and tracking control of tail-sitter UAVs. Theoretically, we focus on the differential flatness property with full exploitation of actual UAV aerodynamic models, which lays a foundation for generating dynamically feasible trajectory and achieving high-performance tracking control. We have found that a tail-sitter is differentially flat with accurate (not simplified) aerodynamic models within the entire flight envelope, by specifying coordinate flight condition and choosing the vehicle position as the flat output. This fundamental property allows us to fully exploit the high-fidelity aerodynamic models in the trajectory planning and tracking control to achieve accurate tail-sitter flights. Particularly, an optimization-based trajectory planner for tail-sitters is proposed to design high-quality, smooth trajectories with consideration of kinodynamic constraints, singularity-free constraints, and actuator saturation. The planned trajectory of flat output is transformed into state trajectory in real time with optional consideration of wind in environments. To track the state trajectory, a global, singularity-free, and minimally parameterized on-manifold MPC is developed, which fully leverages the accurate aerodynamic model to achieve high-accuracy trajectory tracking within the whole flight envelope. The proposed algorithms are implemented on our quadrotor tail-sitter prototype, “Hong Hu,” and their effectiveness are demonstrated through extensive real-world experiments in both indoor and outdoor field tests, including agile SE(3) flight through consecutive narrow windows requiring specific attitude and with speed up to 10 m/s, typical tail-sitter maneuvers (transition, level flight, and loiter) with speed up to 20 m/s, and extremely aggressive aerobatic maneuvers (Wingover, Loop, Vertical Eight, and Cuban Eight) with acceleration up to 2.5 g. The video demonstration is available at https://youtu.be/2x_bLbVuyrk.

Optimal virtual tube planning and control for swarm robotics

This paper presents a novel method for efficiently solving a trajectory planning problem for swarm robotics in cluttered environments. Recent research has demonstrated high success rates in real-time local trajectory planning for swarm robotics in cluttered environments, but optimizing trajectories for each robot is still computationally expensive, with a computational complexity from O ( k ( n t , ε ) n t 2 ) to O ( k ( n t , ε ) n t 3 ) where n t is the number of parameters in the parameterized trajectory, ε is precision, and k ( n t , ε ) is the number of iterations with respect to n t and ε . Furthermore, the swarm is difficult to move as a group. To address this issue, we define and then construct the optimal virtual tube, which includes infinite optimal trajectories. Under certain conditions, any optimal trajectory in the optimal virtual tube can be expressed as a convex combination of a finite number of optimal trajectories, with a computational complexity of O ( n t ) . Afterward, a hierarchical approach including a planning method of the optimal virtual tube with minimizing energy and distributed model predictive control is proposed. In simulations and experiments, the proposed approach is validated and its effectiveness over other methods is demonstrated through comparison.

Automatic Video Traffic Surveillance System with Number Plate Character Recognition Using Hybrid Optimization-Based YOLOv3 and Improved CNN

Recently, the increased count of surveillance cameras has manipulated the demand criteria for a higher effective video coding process. Moreover, the ultra-modern video coding standards have appreciably enhanced the efficiency of video coding, which has been developed for gathering common videos over surveillance videos. Various vehicle recognition techniques have provided a challenging and promising role in computer vision applications and intelligent transport systems. In this case, most of the conventional techniques have recognized the vehicles along with bounding box depiction and thus failed to provide the proper locations of the vehicles. Moreover, the position details have been vigorous in terms of various real-time applications trajectory of vehicle’s motion on the road as well as movement estimation. Numerous advancements have been offered throughout the years in the traffic surveillance area through the random propagation of intelligent traffic video surveillance techniques. The ultimate goal of this model is to design and enhance intelligent traffic video surveillance techniques by utilizing the developed deep learning techniques. This model has the ability to handle video traffic surveillance by measuring the speed of vehicles and recognizing their number plates. The initial process is considered the data collection, in which the traffic video data is gathered. Furthermore, the vehicle detection is performed by the Optimized YOLOv3 deep learning classifier, in which the parameter optimization is performed by using the newly recommended Modified Coyote Spider Monkey Optimization (MCSMO), which is the combination of Coyote Optimization Algorithm (COA) and Spider Monkey Optimization (SMO). Furthermore, the speed of the vehicles has been measured from each frame. For high-speed vehicles, the same Optimized YOLOv3 is used for detecting the number plates. Once the number plates are detected, plate character recognition is performed by the Improved Convolutional Neural Network (ICNN). Thus, the information about the vehicles, which are violating the traffic rules, can be conveyed to the vehicle owners and Regional Transport Office (RTO) to take further action to avoid accidents. From the experimental validation, the accuracy and precision rate of the designed method achieves 97.53% and 96.83%. Experimental results show that the proposed method achieves enhanced performance when compared to conventional models, thus ensuring the security of the transport system.

Real-time taxi spatial anomaly detection based on vehicle trajectory prediction

Taxi services have long faced difficulties with unethical taxi drivers taking detours, especially when passengers are unfamiliar with their surroundings. Therefore, it is important to monitor taxis’ operation to enhance the quality of taxi services. In this paper, we mainly study the anomaly detection of taxi trajectories in the spatial dimension with a novel taxi anomaly detection framework based on real-time vehicle trajectory prediction. The framework is termed as TAPS and consists of two stages: the offline training stage and the online anomaly detection stage. In the first stage, a vehicle prediction model is established by training recommended routes provided by a navigation platform to predict a taxi’s next locations. The second step is to detect the taxi’s anomalous trajectories by measuring the consistency between its current and predicted positions as well as the relationship between these two positions and the origin. The effectiveness and timeliness of TAPS are evaluated in a real-world case study. The experiment results show that compared with two baselines, TAPS achieves greater Accuracy, Precision and F1 score to detect anomalous trajectories. This proposed framework can serve as a fundamental tool to detect anomalous trajectories for taxi passengers and companies.

Point feature correction based rolling shutter modeling for EKF-based visual-inertial odometry

The application of consumer-grade rolling-shutter (RS) cameras in visual inertial odometry (VIO) systems deserves attention. In previous works, VIO systems with RS cameras usually adopt different dimensions of RS modeling to represent the camera motion. Although the complex camera motion expression improves accuracy, adding more variables greatly increases the computation load. Therefore, considering the limitations of camera motion modeling, this paper introduces a point feature correction strategy to improve the performance of the system in terms of both speed and accuracy. The optimized camera poses and high-frequency inertial measurement unit (IMU) are employed to correct the point features in the RS image to new pixel coordinates in the global shutter view (in the middle of the RS image readout time) by epipolar transfer. At the same time, we handle the zero velocity and abnormal cases of RS modeling to improve the robustness of the system. Furthermore, the readout time of the RS camera is self-calibrated online during the state augmentation stage and can quickly converge and stabilize to near the true value. The readout time of the RS camera is locally observable, except for two degenerate motions. Experimental results demonstrate that the proposed method outperforms the state-of-the-art methods on a public dataset in terms of accuracy and computational cost. We port our algorithm to an Android-based mobile phone and our system outputs real-time trajectories on the mobile phone. Then, we use the motion capture system to obtain the ground truth phone pose to test the performance of our algorithm.

Toward safer highway work zones: An empirical analysis of crash risks using improved safety potential field and machine learning techniques

Due to complex traffic conditions, transition areas in highway work zones are associated with a higher crash risk than other highway areas. Understanding risk-contributing features in transition areas is essential for ensuring traffic safety on highways. However, conventional surrogate safety measures (SSMs) are quite limited in identifying the crash risk in transition areas due to the complex traffic environment. To this end, this study proposes an improved safety potential field, named the Work-Zone Crash Risk Field (WCRF). The WCRF force can be used to measure the crash risk of individual vehicles that enter a work zone considering the influence of multiple features, upon which the overall crash risk of the road segment in a specific time window can be estimated. With the overall crash risk used as a label, the time-window-based traffic data are used to train and validate an eXtreme Gradient Boosting (XGBoost) classifier, and the Shapley Additive Explanations (SHAP) method is integrated with the XGBoost classifier to identify the key risk-contributing traffic features. To assess the proposed approach, a case study is conducted using real-time vehicle trajectory data collected in two work zones along a highway in China. The results demonstrate that the WCRF-based SSM outperforms conventional SSMs in identifying crash risks in work zone transition areas on highways. In addition, we perform lane-based analysis regarding the impact of setting up work zones on highway safety and investigate the heterogeneity in risk-contributing features across different work zones. Several interesting findings from the analysis are reported in this paper. Compared to existing SSMs, the WCRF-based SSM offers a more practical and comprehensive way to describe the crash risk in work zones. The approach using the developed WCRF technique offers improved capabilities in identifying key risk-contributing features, which is expected to facilitate the development of safety management strategies for work zones.

Probabilistic Dual-Space Fusion for Real-Time Human-Robot Interaction.

For robots in human environments, learning complex and demanding interaction skills from humans and responding quickly to human motions are highly desirable. A common challenge for interaction tasks is that the robot has to satisfy both the task space and the joint space constraints on its motion trajectories in real time. Few studies have addressed the issue of hyperspace constraints in human-robot interaction, whereas researchers have investigated it in robot imitation learning. In this work, we propose a method of dual-space feature fusion to enhance the accuracy of the inferred trajectories in both task space and joint space; then, we introduce a linear mapping operator (LMO) to map the inferred task space trajectory to a joint space trajectory. Finally, we combine the dual-space fusion, LMO, and phase estimation into a unified probabilistic framework. We evaluate our dual-space feature fusion capability and real-time performance in the task of a robot following a human-handheld object and a ball-hitting experiment. Our inference accuracy in both task space and joint space is superior to standard Interaction Primitives (IP) which only use single-space inference (by more than 33%); the inference accuracy of the second order LMO is comparable to the kinematic-based mapping method, and the computation time of our unified inference framework is reduced by 54.87% relative to the comparison method.

Design of an optimized gait planning generator for a quadruped robot using the decision tree and random forest workspace model

AbstractReal-time gait trajectory planning is challenging for legged robots walking on unknown terrain. In this paper, to realize a more efficient and faster motion control of a quadrupedal robot, we propose an optimized gait planning generator (GPG) based on the decision tree (DT) and random forest (RF) model of the robot leg workspace. First, the framework of this embedded GPG and some of the modules associated with it are illustrated. Aiming at the leg workspace model described by DT and RF used in GPG, this paper introduces in detail how to collect the original data needed for training the model and puts forward an Interpolation Labeling with Dilation and Erosion (ILDE) data processing algorithm. After the DT and RF models are trained, we preliminarily evaluate their performance. We then present how these models can be used to predict the location relation between a spatial point and the leg workspace based on its distributional features. The DT model takes only 0.00011 s to process a sample, while the RF model can give the prediction probability. As a complement, the PID inverse kinematic model used in GPG is also mentioned. Finally, the optimized GPG is tested during a real-time single-leg trajectory planning experiment and an unknown terrain recognition simulation of a virtual quadrupedal robot. According to the test results, the GPG shows a remarkable rapidity for processing large-scale data in the gait trajectory planning tasks, and the results can prove it has an application value for quadruped robot control.