Line Trajectory Research Articles

Adaptive Trajectory Tracking Control for Underactuated Unmanned Surface Vehicle Subject to Unknown Dynamics and Time-Varing Disturbances

This paper proposes an adaptive trajectory tracking control strategy for underactuated unmanned surface vehicles subject to unknown dynamics and time-varing external disturbances. In short, the goal of this paper is to provide a control strategy that allows an underactuated unmanned surface vehicle to track a time dependent trajectory. First, a first-order sliding surface is introduced into the design of surge control law to converge to surge tracking error, and then a second-order sliding surface is hired to design yaw control law to deal with sway motion tracking error. Meanwhile, neural network minimum learning parameter method, which has a smaller amount of computation than a multilayer neural network, is employed to preserve the control law robustness against unknown dynamics and time-varing disturbances induced by wind, waves and ocean currents. Furthermore, much effort is made to obtain uniform ultimate bounded stability for the closed-loop control system. Finally, the numerical simulation experiments of straight line and circle trajectory tracking have been given to prove the correctness and feasibility of the proposed control strategy.

The Effect of Coils Area's Ratio and their Separated Distance on the Optical Performance of the Condenser-Objective Magnetic Lens

The work handles the design of an asymmetric double polepiece magnetic lens for the condenser-objective mode having optimum properties through the change of coils area's ratio and their separated distance, which leads to a highest flux density peak of the magnetic field with a lowest spherical aberration coefficient, at the relativistic corrected voltage (Vr=200 kV) and excitation of (NI=10.5 kA-t). The calculation has been made for the magnetic flux lines trajectories and optical properties to limit the defects in the lens and consequently improve the optical performance of the condenser-objective magnetic lens

Iterative reconstruction with boundary detection for carbon ion computed tomography

In heavy ion radiation therapy, improving the accuracy in range prediction of the ions inside the patient’s body has become essential. Accurate localization of the Bragg peak provides greater conformity of the tumor while sparing healthy tissues. We investigated the use of carbon ions directly for computed tomography (carbon CT) to create the relative stopping power map of a patient’s body. The Geant4 toolkit was used to perform a Monte Carlo simulation of the carbon ion trajectories, to study their lateral and angular deflections and the most likely paths, using a water phantom. Geant4 was used to create carbonCT projections of a contrast and spatial resolution phantom, with a cone beam of 430 MeV/u carbon ions. The contrast phantom consisted of cranial bone, lung material, and PMMA inserts while the spatial resolution phantom contained bone and lung material inserts with line pair (lp) densities ranging from 1.67 lp cm−1 through 5 lp cm−1. First, the positions of each carbon ion on the rear and front trackers were used for an approximate reconstruction of the phantom. The phantom boundary was extracted from this approximate reconstruction, by using the position as well as angle information from the four tracking detectors, resulting in the entry and exit locations of the individual ions on the phantom surface. Subsequent reconstruction was performed by the iterative algebraic reconstruction technique coupled with total variation minimization (ART-TV) assuming straight line trajectories for the ions inside the phantom. The influence of number of projections was studied with reconstruction from five different sets of projections: 15, 30, 45, 60 and 90. Additionally, the effect of number of ions on the image quality was investigated by reducing the number of ions/projection while keeping the total number of projections at 60. An estimation of carbon ion range using the carbonCT image resulted in improved range prediction compared to the range calculated using a calibration curve.

Tool profile design for the mold for machining the bush of cone screw seawater hydraulic pump

Design method of the tool profile for machining the mold was found to facilitate the casting or extrusion of the bush of cone screw seawater hydraulic pump within this paper. Mathematical expression of the theoretical tool profile was established, as well as equation of the contact line between mold and tool surface, based on meshing theory and coordinate transformation theory. As solving contact condition involves implicit functions and trigonometric functions, only with methods of numerical discretization analysis by using the fzero function to solve single-variable nonlinear equations, can the contact line trajectory and theoretical curve of tool profile be obtained quickly and accurately. The tool profile design for manufacturing the mold lays a foundation for the processing of pump bush.

Whole body motion generation of 18-DOF biped robot on flat surface during SSP & DSP

The present work explains the dynamically balanced gait generation of an 18-DOF biped robot on a flat surface during both double support phase (DSP) and single support phase (SSP). To generate the said gaits, cubic polynomial trajectories are assumed to be followed by the swing foot and wrist end of the hand. Further, the hip joint is assumed to follow a straight line and cubic polynomial trajectories in the sagittal and frontal planes, respectively. A closed form solution methodology based on inverse kinematics is used for determining the joint angles made by various links of the biped robot. Once the gait related to upper and lower limbs of the two legged robot is generated, the balance of the generated gait is decided by finding the position of zero moment point (ZMP). Moreover, Lagrange–Euler formulation is used for calculating the dynamics of the biped robot. Further, the effectiveness of the developed algorithm in terms of generating dynamically balanced gaits on flat surface has been verified in computer simulations. Further, the generated gait has been tested on a real biped robot.

Application of computer processing of experimental data from analysis of chip formation zone on photoelastic models

In the experiments carried out using photomechanical method, only the isochrome pattern is directly recorded on photoelastic models and the isoclines (lines of equal angles of inclination of the principal stresses) must be traced manually for each of the fixed values of the polarization planes. Further processing is also performed manually, isostatic lines (trajectories of principal stresses) are constructed from the isocline pattern, and the field of the slip lines, or maximum tangential stresses, is constructed from the obtained isostatic field. Such multi-step path (isoclines-isostatic lines-slip lines) containing manual processing at each stage leads to accumulation of errors. The research presented in the article largely removes these problems. In order to actualize a load similar to the one acting on the wedge front surface, a large-scale photoelastic model and a special experimental stand were developed. The scale of the model (10:1) was chosen as great as practicable from the condition of its placement in the optical field of the PPU-7 (plane polarization unit). The scheme of chip formation, the shape of the photoelastic model and its loading is given. The scheme of the stand for loading the chip formation zone of the model under study is described. The task of reducing labor intensity of the experimental part and increasing the accuracy of the obtained results was solved by using a digital camera and a specially developed technology for computer processing of photograms. Pressure diagram describes the nature of loading models in experiments. The results of the experiments were presented in the form of a series of digital photographs subjected to further computer processing, the purpose of which was to obtain isocline mesh, construct isostatic lines field, and then fields of slip lines. Analysis of the application of digital recording and computer processing of photograms significantly reduce time of performing the experimental part by abandoning the traditional method of drawing isoclines on tracing paper. In addition, the accuracy of the fields of the isostatic and slip lines increases because in the initial for their construction isocline field errors that are unavoidable with manual fixation are eliminated.

Preoperative Exposure of Sigmoid Sinus Trajectory in Posterolateral Cranial Base Approaches Using a New Landmark Through a Neurosurgical Perspective.

The location of burr holes in posterolateral cranial base approaches should be appropriate to provide an adequate operative field, and surgical freedom is crucial for bone window opening. The aim of this study was to search for more convenient and easily detectable landmarks in comparison with current landmarks in posterolateral cranial base surgery. Twenty 3-dimensional reconstructed head and neck computed tomography angiography images (group 1) and 20 cadaver heads (group 2) were evaluated. An imaginary line connecting the angle of the mandible and the mastoid tip was extended upward. A second line passing through the lateral edge of the zygomatic arch was also extended posteriorly. The authors examined if the first line met with the sigmoid sinus throughout its course and determined the location of the intersection point of these 2 lines relative to the sigmoid-transverse sinus junction. The intersection point did not correspond to the sinus region in 3 images from group 1 and 4 specimens from group 2. The matching of the mandibula-mastoid line trajectory with the sigmoid sinus course was unacceptable in 4 images and 5 cadavers. For venous anatomy preservation and anatomic skull base fossa orientation during posterolateral cranial base approaches, upward extension of the mandibula-mastoid line can be a proper landmark for surgical planning in this region. The authors' proposed superficial anatomical line and intersection point over the skull could be used as a reliable indicator for the external projection of the sigmoid sinus and an appropriate initial burr-hole location.

The dynamics and Lorentz transformation of magnetic nulls

Having previously treated the problem of the Lorentz transformation properties of static field lines around magnetic neutral points, it is time to explore the properties of dynamic nulls. We discuss the relativistic motion of magnetic nulls accounting for both the linear and the second order structure of the magnetic field. It is found that the dynamics of a magnetic null is given by a world line trajectory of the null point and the changing fieldline structure. The dynamics of magnetic null structure is also explored, showing the significance of both the null structure and the flow pattern. We describe relativistic transformation properties of the appearance and annihilation of magnetic nulls, where the previously proposed null region is used as an invariant identification of topological transition and bifurcation processes.

Theoretically exact backprojection filtration algorithm for multi-segment linear trajectory

A theoretically exact backprojection filtration algorithm is proved and implemented for image reconstruction from a multi-segment linear trajectory assuming fan-beam geometry. The reconstruction formula is based on a concept of linear PI-line (L-PI) proposed in our previous work. The proof is completed in two consecutive steps. In the first step, it is proved that theoretically exact image reconstruction can be obtained on an arbitrary L-PI line from an infinite straight-line trajectory. In the second step, it is shown that accurate image reconstruction can be achieved from a multi-segment line trajectory by introducing a weight function to deal with the data redundancy. Numerical implementation and simulation results validate the correctness of our theoretical results.

Robotic excavator trajectory control using an improved GA based PID controller

Abstract In order to achieve excellent trajectory tracking performances, an improved genetic algorithm (IGA) is presented to search for the optimal proportional-integral-derivative (PID) controller parameters for the robotic excavator. Firstly, the mathematical model of kinematic and electro-hydraulic proportional control system of the excavator are analyzed based on the mechanism modeling method. On this basis, the actual model of the electro-hydraulic proportional system are established by the identification experiment. Furthermore, the population, the fitness function, the crossover probability and mutation probability of the SGA are improved: the initial PID parameters are calculated by the Ziegler-Nichols (Z-N) tuning method and the initial population is generated near it; the fitness function is transformed to maintain the diversity of the population; the probability of crossover and mutation are adjusted automatically to avoid premature convergence. Moreover, a simulation study is carried out to evaluate the time response performance of the proposed controller, i.e., IGA based PID against the SGA and Z-N based PID controllers with a step signal. It was shown from the simulation study that the proposed controller provides the least rise time and settling time of 1.23 s and 1.81 s, respectively against the other tested controllers. Finally, two types of trajectories are designed to validate the performances of the control algorithms, and experiments are performed on the excavator trajectory control experimental platform. It was demonstrated from the experimental work that the proposed IGA based PID controller improves the trajectory accuracy of the horizontal line and slope line trajectories by 23.98% and 23.64%, respectively in comparison to the SGA tuned PID controller. The results further indicate that the proposed IGA tuning based PID controller is effective for improving the tracking accuracy, which may be employed in the trajectory control of an actual excavator.

Humanoid Robot Cooperative System by Machine Vision

This article presents a supervised control position system, based on image processing and oriented to the cooperative work between two humanoid robots that work autonomously. The first robot picks up an object, carry it to the second robot and after that the same second robot places it in an endpoint, this is achieved through doing movements in straight line trajectories and turns of 180 degrees. Using for this the Microsoft Kinect , finding for each robot and the reference object its exact spatial position, through the color space conversion and filtering, derived from the information of the RGB camera that counts and obtains this result using the information transmitted from the depth sensor, obtaining the final location of each. Through programming in C #, and the developed algorithms that allow to command each robot in order to work together for transport the reference object, from an initial point, delivering this object from one robot to the other and depositing it in an endpoint. This experiment was tested performed the same trajectory, under uniform light conditions, achieving each time the successful delivering of the object

On the Magnetic Squashing Factor and the Lie Transport of Tangents

Abstract The squashing factor (or squashing degree) of a vector field is a quantitative measure of the deformation of the field line mapping between two surfaces. In the context of solar magnetic fields, it is often used to identify gradients in the mapping of elementary magnetic flux tubes between various flux domains. Regions where these gradients in the mapping are large are referred to as quasi-separatrix layers (QSLs), and are a continuous extension of separators and separatrix surfaces. These QSLs are observed to be potential sites for the formation of strong electric currents, and are therefore important for the study of magnetic reconnection in three dimensions. Since the squashing factor, Q, is defined in terms of the Jacobian of the field line mapping, it is most often calculated by first determining the mapping between two surfaces (or some approximation of it) and then numerically differentiating. Tassev & Savcheva have introduced an alternative method, in which they parameterize the change in separation between adjacent field lines, and then integrate along individual field lines to get an estimate of the Jacobian without the need to numerically differentiate the mapping itself. But while their method offers certain computational advantages, it is formulated on a perturbative description of the field line trajectory, and the accuracy of this method is not entirely clear. Here we show, through an alternative derivation, that this integral formulation is, in principle, exact. We then demonstrate the result in the case of a linear, 3D magnetic null, which allows for an exact analytical description and direct comparison to numerical estimates.

To Pass or Not to Pass: Modeling the Movement and Affordance Dynamics of a Pick and Place Task.

Humans commonly engage in tasks that require or are made more efficient by coordinating with other humans. In this paper we introduce a task dynamics approach for modeling multi-agent interaction and decision making in a pick and place task where an agent must move an object from one location to another and decide whether to act alone or with a partner. Our aims were to identify and model (1) the affordance related dynamics that define an actor's choice to move an object alone or to pass it to their co-actor and (2) the trajectory dynamics of an actor's hand movements when moving to grasp, relocate, or pass the object. Using a virtual reality pick and place task, we demonstrate that both the decision to pass or not pass an object and the movement trajectories of the participants can be characterized in terms of a behavioral dynamics model. Simulations suggest that the proposed behavioral dynamics model exhibits features observed in human participants including hysteresis in decision making, non-straight line trajectories, and non-constant velocity profiles. The proposed model highlights how the same low-dimensional behavioral dynamics can operate to constrain multiple (and often nested) levels of human activity and suggests that knowledge of what, when, where and how to move or act during pick and place behavior may be defined by these low dimensional task dynamics and, thus, can emerge spontaneously and in real-time with little a priori planning.

Defect-free optimal synthesis of crank-rocker linkage using nature-inspired optimization algorithms

This paper proposes the synthesis of a human knee exoskeleton using the reduced number of necessary and sufficient constraints. The proposed human knee exoskeleton consists of a defect-free crank-rocker mechanism capable of accurately moving its coupler point along the prescribed trajectory. For synthesizing the crank-rocker mechanism based on proposed reduced number of constraints, an optimization problem is formulated to synthesize the mechanism. An algorithm based on teaching-learning-based-optimization (TLBO) is presented to solve this highly nonlinear optimization problem. The optimization minimizes the error between generated and prescribed trajectory and simultaneously avoids any defect in the synthesized mechanism. The penalty method is used to manage all the constraints. Besides a realistic nontrivial example of human knee flexion/extension, a straight line trajectory is also considered to demonstrate the effectiveness of the refinement scheme in the optimal syntheses of planar crank-rocker linkage free from all defects. The optimization problem is solved using well-established nature-inspired algorithms such as genetic algorithm (GA), particle swarm algorithm (PSO), and teaching-learning-based-optimization (TLBO) algorithm. It is found that TLBO is computationally more efficient than other algorithms used here. Additionally, the proposed human knee exoskeleton model is experimentally validated for one gait cycle.

An adaptive velocity planning method for multi-DOF robot manipulators

Multi-degrees of freedom robot manipulators are widely used in the manufacturing areas. Trajectory planning of the end effector is the most important while the hardest task for the use of the manipulators. An adaptive velocity planning method for multi-degrees of freedom robots with a predefined path is proposed in this article, which is based on interpolation technology. A resolved motion acceleration control strategy based on a fixed-distance movement is proposed, along with an adaptive time interpolation correction algorithm to achieve the speed planning for multi-degrees of freedom manipulators. Besides the accuracy and efficiency, more attentions were paid on the velocity control at turning points along the path, so that a transient vibration and a transient overshoot can be avoided, leading to a stable movement of the robot. A fold line trajectory and a circular-line connected trajectory were implemented on a 6-degrees of freedom robot manipulator. Simulations and experimental results show that the proposed method is efficient and effective.

Analytical model for determination of the unipolar ionic saturation current during positive corona discharge for geometries comprising cylindrical emitter electrodes

This paper presents an analytical model for the assessment of the unipolar corona saturation current limit for positive corona discharge in air, based on the determination of the field line lengths and trajectories. The model is applicable to emitter electrodes with a cylindrical surface facing a plane or an identical cylindrical collector electrode, if their spatial characteristics, the ion mobility of the surrounding medium and the applied voltage are known. Experimental investigation is performed to compare the results of the unipolar corona saturation current limit from the proposed model to the actual corona current flow in an experimental setup that comprises cylindrical emitters of various radii, facing a plane electrode. Both the total current amplitude and the current density distribution over the collecting electrode's surface have been examined.

Simultaneous automatic segmentation of multiple needles using 3D ultrasound for high-dose-rate prostate brachytherapy.

Sagittally reconstructed 3D (SR3D) ultrasound imaging shows promise for improved needle localization for high-dose-rate prostate brachytherapy (HDR-BT); however, needles must be manually segmented intraoperatively while the patient is anesthetized to create a treatment plan. The purpose of this article was to describe and validate an automatic needle segmentation algorithm designed for HDR-BT, specifically capable of simultaneously segmenting all needles in an HDR-BT implant using a single SR3D image with ~5 mm interneedle spacing. The segmentation algorithm involves regularized feature point classification and line trajectory identification based on the randomized 3D Hough transform modified to handle multiple straight needles in a single image simultaneously. Needle tips are identified based on peaks in the derivative of the signal intensity profile along the needle trajectory. For algorithm validation, 12 prostate cancer patients underwent HDR-BT during which SR3D images were acquired with all needles in place. Needles present in each of the 12 images were segmented manually, providing a gold standard for comparison, and using the algorithm. Tip errors were assessed in terms of the 3D Euclidean distance between needle tips, and trajectory error was assessed in terms of 2D distance in the axial plane and angular deviation between trajectories. In total, 190 needles were investigated. Mean execution time of the algorithm was 11.0 s per patient, or 0.7 s per needle. The algorithm identified 82% and 85% of needle tips with 3D errors ≤3 mm and ≤5 mm, respectively, 91% of needle trajectories with 2D errors in the axial plane ≤3 mm, and 83% of needle trajectories with angular errors ≤3°. The largest tip error component was in the needle insertion direction. Previous work has indicated HDR-BT needles may be manually segmented using SR3D images with insertion depth errors ≤3 mm and ≤5 mm for 83% and 92% of needles, respectively. The algorithm shows promise for reducing the time required for the segmentation of straight HDR-BT needles, and future work involves improving needle tip localization performance through improved image quality and modeling curvilinear trajectories.

Behavior of self-propelled acetone droplets in a Leidenfrost state on liquid substrates

It is demonstrated that non-coalescent droplets of acetone can be formed on liquid substrates. The fluid flows around and in an acetone droplet hovering on water are recorded to shed light on the mechanisms which might lead to non-coalescence. For sufficiently low impact velocities, droplets undergo a damped oscillation on the surface of the liquid substrate but at higher velocities clean bounce-off occurs. Comparisons of experimentally observed static configurations of floating droplets to predictions from a theoretical model for a small non-wetting rigid sphere resting on a liquid substrate are made and a tentative strategy for determining the thickness of the vapor layer under a small droplet on a liquid is proposed. This strategy is based on the notion of effective surface tension. The droplets show self-propulsion in straight line trajectories in a manner which can be ascribed to a Marangoni effect. Surprisingly, self-propelled droplets can become immersed beneath the undisturbed water surface. This phenomenon is reasoned to be drag-inducing and might provide a basis for refining observations in previous work.

Design and Implementation of PID Control-based FSM Algorithm on Line Following Robot

Finite State Machine (FSM) is a control system methodology that describes system’s behavior using three things, namely: state, event, and action. On a program, the system would be in one active state. The system can switch or move to another state if it gets a certain input or event. In this paper, FSM based on Proportional-Integral-Derivative (PID) controller algorithm will be implemented on line follower robot. PID controller is one of system control methods that many used recently. FSM based on PID controller is implemented to keep robot tracking the line trajectory as well. The test result shows that designed algorithm can work well and can be used as a based algorithm of this robot.Keywords: algorithm, Finite State Machine (FSM), Proportional-Integral-Derivative (PID), robot, line follower

Self-steering partially coherent beams

We introduce a class of shape-invariant partially coherent beams with a moving guiding center which we term self-steering partially coherent beams. The guiding center of each such beam evolves along a straight line trajectory which can be engineered to make any angle with the x-axis. We show that the straight line trajectory of the guiding center is the only option in free space due to the linear momentum conservation. We experimentally generate a particular subclass of new beams, self-steering Gaussian Schell beams and argue that they can find applications for mobile target tracing and trapped micro- and/or nanoparticle transport.