Geometric Trajectory Research Articles

Optimal curvature-smooth transition and efficient feedrate optimization method with axis kinematic limitations for linear toolpath

In industrial areas, the machining performance with linear G01 code is a crucial indicator to evaluate the computer numerical control (CNC) systems and many researchers have presented various methods to deal with the corner tracking issue. However, the axis jerk limitations are not satisfied well and the different axis kinematic limitations are not considered in most researches, which will reduce the machining efficiency and machining quality simultaneously. In this paper, a novel method including trajectory planning, feedrate scheduling, and interpolating is proposed to obtain better machining quality and higher machining efficiency. In trajectory planning, a B-spline curve is utilized to smooth the linear toolpath and obtain a curvature-smooth trajectory, which is third-order geometry continuous. Thereby, a time-optimal method for the geometric continuous trajectory is proposed based on linear programming algorithm in the feedrate scheduling and the bounded multi-constraints, including axis velocity, axis acceleration, axis jerk, and feedrate. Moreover, it can be seen that the proposed method is near Bang-bang control. To reduce the computation time of the optimal numerical method, an efficient method with a look-ahead window around the transition B-spline curve is applied. In the interpolation stage, a novel interpolation method about arc-length is proposed to improve computation efficiency. Finally, simulation and experiment are conducted to show superiorities of the proposed method to the already existing approaches. The results show that the cycling time of the proposed method is reduced by more than 7% than G2 method and 20% than G3 method with better contour performance.

PROTOTYPE OF LINE FOLLOWER ROBOT APLIED TO INDUSTRIAL CUTTING OF TWO AXIS

Currently, the geometric trajectory control of the most updated industrial machinery usually uses computer numerical control to perform complex cuts in two axis, demanding qualified operators in G and M programming language, which is characteristic of CNC equipment. The above features demand a hard economic investment and training. On the other hand, the semi-manual equipment is highly dependent on the operator and specialized tooling, restricting portability and field complex activities. This paper shows part of methodology applied to the design of a prototype robot, which is based on infrared tracking of lines; a technique that has not been exploited in two dimensional production process. However, which counteracts issues such as low portability, limited intuition operating, high operation time and hard economic investment.

Composite pulses in N-level systems with SU(2) symmetry and their geometrical representation on the Majorana sphere.

High fidelity and robustness in population inversion is very desirable for many quantum control applications. We expand composite pulse schemes developed for two-level dynamics and present an analytic solution for the coherent evolution of an N-level quantum system with SU(2) symmetry, for achieving high fidelity and robust population inversion. Our approach offers a platform for accurate steering of the population transfer in physical multi-level systems, which is crucial for fidelity in quantum computation and achieving fundamental excitations in nuclear magnetic resonances and atomic physics. We also introduce and discuss the geometrical trajectories of these dynamics on the Majorana sphere as an interpretation, allowing us to gain physical insight on the dynamics of many-body or high-dimensional quantum systems.

Quasi-Polar-Based FFBP Algorithm for Miniature UAV SAR Imaging Without Navigational Data

Because of flexible geometric configuration and trajectory designation, time-domain algorithms become popular for unmanned aerial vehicle (UAV) synthetic aperture radar (SAR) applications. In this paper, a new quasi-polar-coordinate-based fast factorized back-projection (FFBP) algorithm combined with data-driven motion compensation is proposed for miniature UAV-SAR imaging. By utilizing wavenumber decomposition, the analytical spectrum of a quasi-polar grid image is obtained, where the phase errors arising from the trajectory deviations can be conveniently investigated and the phase autofocusing can be compatibly incorporated. Different from the conventional FFBP based on a polar coordinate system, the proposed algorithm operates in a quasi-polar coordinate system, where the phase errors become spacial invariant and can be accurately estimated and easily compensated. Moreover, the relationship between phase errors and nonsystematic range cell migration (NsRCM) is revealed according to the analytical image spectrum, based on which the NsRCM correction is developed to further improve the image focusing quality for high-resolution SAR applications. Promising experimental results from the raw data experiments of miniature UAV-SAR test bed are presented and analyzed to validate the advantages of the proposed algorithm.

Geometric analysis-based trajectory planning and control for underactuated capsule systems with viscoelastic property

This paper proposes a novel geometric analysis-based trajectory planning approach for underactuated capsule systems with viscoelastic property. The idea is to reduce complexity and to characterize coupling by imposing a harmonic drive and then to compute the dynamics projection onto a hyper-manifold, such that the issue of trajectory planning is converted into geometric analysis and trajectory optimization. The objective is to obtain optimal locomotion performance in terms of tracking error, average capsule speed and energy efficacy. Firstly, an analytical two-stage velocity trajectory is given based on control indexes and dynamic constraints. A locomotion-performance index is then proposed and evaluated to identify the optimal viscoelastic parameters. The trajectory is optimally parameterized through rigorous analysis. A nonlinear tracking controller is designed using collocated partial feedback linearization. For the sake of efficiency in progression and energy, the proposed method provides a novel approach in characterizing and planning motion trajectory for underactuated capsule systems such that the optimal locomotion can be achieved. Simulation results demonstrate the effectiveness and feasibility of the proposed method.

Virtual and Remote Laboratory with the Ball and Plate System

This paper presents a virtual and remote laboratory of the ball and plate system with augmented reality. The ball and plate is a non-linear, multi-variable and open-loop unstable system. Due to its inherent complexity, presents challenging problems, such as: 1) point stabilization control, to carry the ball to a specific position and hold it there, and 2) trajectory tracking control, in which the goal is to make the ball follows a predefined geometric trajectory (square and circle) minimizing the tracking error. The laboratory is composed by two parts: 1) a virtual laboratory developed in Easy Java Simulations (EJS), which is a 3D interactive simulation of the system; 2) a remote laboratory (developed with EJS and LabVIEW) to connect via Internet to a pilot plant of the system, situated in the laboratory. This laboratory is used in the Systems and Control Engineering Master Program offered by Universidad Nacional de Educacion a Distancia and Universidad Complutense de Madrid.

An Efficient Approach of Time-Optimal Trajectory Generation for the Fully Autonomous Navigation of the Quadrotor

In this work, a time-optimal trajectory generation approach is developed for the multiple way-point navigation of the quadrotor based on the nonuniform rational B-spline (NURBS) curve and linear programming. To facilitate this development, the dynamic model of the quadrotor is formulated first. Then, the geometric trajectory regarding multiple way-point navigation is constructed based on the NURBS curve. With the constructed geometric trajectory, a time-optimal interpolation problem is imposed considering the velocity, acceleration, and jerk constraints. This optimization problem is solved in two steps. In the first step, a preliminary result is obtained by solving a linear programming problem without jerk constraints. Then by introducing properly relaxed jerk constraints, a second linear programming problem is formulated based on the preliminarily obtained result, and the time-optimal problem can be fully solved in this way. Subsequently, a nonlinear trajectory tracking controller is developed to track the generated trajectory. The feasibilities of the proposed trajectory generation approach as well as the tracking controller are verified through both simulations and real-time experiments. With enhanced computational efficiency, the proposed approach can generate trajectory for an indoor environment with the smooth acceleration profile and moderate velocity V≈1 m/s in real-time, while guaranteeing velocity, acceleration, and jerk constraints: Vmax=1 m/s, Amax=2 m/s2, and Jmax=5 m/s3. In such a case, the trajectory tracking controller can closely track the reference trajectory with cross-tracking error less than 0.05 m.

Spontaneous symmetry breaking for geometrical trajectories of actin-based motility in three dimensions.

Actin-based motility is important for many cellular processes. In this article we extend our previous studies of an actin-propelled circular disk in two dimensions to an actin-propelled spherical bead in three dimensions. We find that for an achiral load the couplings between the motion of the load and the actin network induce a series of bifurcations, starting with a transition from rest to moving state, followed by a transition from straight to planar curves, and finally a further transition from motion in a plane to one with torsion. To address the intriguing, experimentally observed chiral motility of the bacterium Listeria monocytogenes, we also study the motility of a spherical load with a built-in chirality. For such a chiral load, stable circular trajectories are no longer found in numerical simulations. Instead, helical trajectories with handedness that depends on the chirality of the load are found. Our results reveal the relation between the symmetry of actin network and the trajectories of actin-propelled loads.

Geometrical Vertical Trajectory Optimization – Comparative Performance Evaluation of Phase versus Phase and Altitude-Dependent Preferred Gradient Selection

This paper presents a comparative analysis of the results of two vertical flight trajectory optimization strategies, obtained using a new geometrical trajectory optimization algorithm developed at the Laboratory of Applied Research in Active Controls, Avionics and AeroServoElasticity LARCASE. The first strategy geometrically constructs the vertical flight trajectory as function of the along-the-track distance and altitude constraints associated with each way point in the flight plan, and a preferred gradient value described as a function of the flight phase and altitude. The second strategy employs a preferred gradient value dependent only on the flight phase. The optimization criterion is represented by the minimization of the total number of climb, horizontal, and descent trajectory segments. The comparison of the optimized trajectories generated using the two strategies are performed relative to the number of trajectory segments and their gradient values. The novelty and the advantage of the presented algorithm is the fact that it allows the construction of an optimal vertical flight trajectory without performing time and resources-intensive computations employing an aircraft performance model.

Automatic Parallel Parkinkg Maneuver with Geometric Continuous-Curvature and Trajectory Regenation

This paper presents a trajectory generation method for the automatic parallel parking. In the first place, a continuouscurvature path satisfying geometric constraints is generated. During the automated tracking of the trajectory, following errors might appear. Then, if necessary, a new trajectory is generated to correct these errors. The regeneration method presents the same advantages as for the initial path generation (continuous curvature) and allows correcting the deviation of the vehicle. Moreover, the complete functional architecture including the path generation is presented in this article to illustrate the execution of the parking maneuver.

Symbolic Trajectories

Due to the proliferation of GPS-enabled devices in vehicles or with people, large amounts of position data are recorded every day and the management of such mobility data, also called trajectories, is a very active research field. A lot of effort has gone into discovering “semantics” from the raw geometric trajectories by relating them to the spatial environment or finding patterns, for example, by data mining techniques. A question is how the resulting “meaningful” trajectories can be represented or further queried. In this article, we propose a systematic study of annotated trajectory databases . We define a very simple generic model called symbolic trajectory to capture a wide range of meanings derived from a geometric trajectory. Essentially, a symbolic trajectory is just a time-dependent label; variants have sets of labels, places, or sets of places. They are modeled as abstract data types and integrated into a well-established framework of data types and operations for moving objects. Symbolic trajectories can represent, for example, the names of roads traversed obtained by map matching, transportation modes, speed profile, cells of a cellular network, behaviors of animals, cinemas within 2km distance, and so forth. Symbolic trajectories can be combined with geometric trajectories to obtain annotated trajectories. Besides the model, the main technical contribution of the article is a language for pattern matching and rewriting of symbolic trajectories. A symbolic trajectory can be represented as a sequence of pairs (called units) consisting of a time interval and a label. A pattern consists of unit patterns (specifications for time interval and/or label) and wildcards, matching units and sequences of units, respectively, and regular expressions over such elements. It may further contain variables that can be used in conditions and in rewriting. Conditions and expressions in rewriting may use arbitrary operations available for querying in the host DBMS environment, which makes the language extensible and quite powerful. We formally define the data model and syntax and semantics of the pattern language. Query operations are offered to integrate pattern matching, rewriting, and classification of symbolic trajectories into a DBMS querying environment. Implementation of the model using finite state machines is described in detail. An experimental evaluation demonstrates the efficiency of the implementation. In particular, it shows dramatic improvements in storage space and response time in a comparison of symbolic and geometric trajectories for some simple queries that can be executed on both symbolic and raw trajectories.

Divergence of craniofacial developmental trajectories among avian embryos.

Morphological divergence among related species involves changes to developmental processes. When such variation arises in development has garnered considerable theoretical interest relating to the broader issue of how development may constrain evolutionary change. The hourglass model holds that while early developmental events may be highly evolvable, there is a phylotypic stage when key developmental events are conserved. Thus, evolutionary divergence among related species should tend to arise after such a stage of reduced evolvability and, consequently, reduced variation among species. We test this prediction by comparing developmental trajectories among three avian species of varying relatedness (chick, quail, and duck) to locate their putative point of divergence. Three-dimensional geometric morphometrics and trajectory analyses were used to measure the significance of the facial shape variation observed among these species. Duck embryos, being more distantly related, differed from the more closely-related chick and quail embryos in the enlargement of their frontonasal prominences. Phenotypic trajectory analyses demonstrated divergence of the three species, most notably, duck. The results demonstrate that the two more closely related species share similar facial morphologies for a longer time during development, while ducks diverge. This suggests a surprising lability of craniofacial development during early face formation. Developmental Dynamics 244:1158-1167, 2015. © 2015 Wiley Periodicals, Inc.

SU-F-BRB-16: A Spreadsheet Based Automatic Trajectory GEnerator (SAGE): An Open Source Tool for Automatic Creation of TrueBeam Developer Mode Robotic Trajectories

Purpose: To automate creation and delivery of robotic linac trajectories with TrueBeam Developer Mode, an open source spreadsheet-based trajectory generation tool has been developed, tested and made freely available. The computing power inherent in a spreadsheet environment plus additional functions programmed into the tool insulate users from the underlying schema tedium and allow easy calculation, parameterization, graphical visualization, validation and finally automatic generation of Developer Mode XML scripts which are directly loadable on a TrueBeam linac. Methods: The robotic control system platform that allows total coordination of potentially all linac moving axes with beam (continuous, step-and-shoot, or combination thereof) becomes available in TrueBeam Developer Mode. Many complex trajectories are either geometric or can be described in analytical form, making the computational power, graphing and programmability available in a spreadsheet environment an easy and ideal vehicle for automatic trajectory generation. The spreadsheet environment allows also for parameterization of trajectories thus enabling the creation of entire families of trajectories using only a few variables. Standard spreadsheet functionality has been extended for powerful movie-like dynamic graphic visualization of the gantry, table, MLC, room, lasers, 3D observer placement and beam centerline all as a function of MU or time, for analysis of the motions before requiring actual linac time. Results: We used the tool to generate and deliver extended SAD “virtual isocenter” trajectories of various shapes such as parameterized circles and ellipses. We also demonstrated use of the tool in generating linac couch motions that simulate respiratory motion using analytical parameterized functions. Conclusion: The SAGE tool is a valuable resource to experiment with families of complex geometric trajectories for a TrueBeam Linac. It makes Developer Mode more accessible as a vehicle to quickly translate research ideas into machine readable scripts without programming knowledge. As an open source initiative, it also enables researcher collaboration on future developments. I am a full time employee at Varian Medical Systems, Palo Alto, California

A KPCA spatio-temporal differential geometric trajectory cloud classifier for recognizing human actions in a CBVR system

We describe a new algorithm for distinguishing human actions in videos, called the differential geometric trajectory cloud (DGTC) method that captures both fine and large scale structure of the covariant transformed spatio-temporal optical flow field. We show the utility of our algorithm in the context of a content based video retrieval (CBVR) system, where specific frames from a full length video (or separate video shots in a database) are identified containing a queried human action. In the DGTC method, the local geometry of the spatio-temporal covariant eigenspace curves, unique to each human action, are characterized by the Frenet–Serret basis equations, thereby specifying the local time averaged curvature and torsion, as well as providing a means for defining a mean osculating hyperplane for the entire trajectory. To classify a human action from a query, our system uses an adaptive distance metric between the covariant transformed query trajectory and each of the trajectories from all of the actions in the training set. Based upon the separation of between the query and each class, the distance uses either large or small scale information about the trajectory: for large separations, the distance is the separation between trajectory cloud centroids, while for small and intermediate separations the distance is based upon the mean hyperplane orientation obtained from the time averaged curvature and torsion of the trajectory. Our system can function in real-time and has an accuracy greater than 93% for multiple action recognition within video repositories. We also demonstrate the use of our CBVR system locating specific frame positions of trained actions in two full featured films.

Evaluation of phase bunching in the central region of a cyclotron by a radial probe with a plastic scintillator

A new technique for evaluating the phase bunching performance in the central region of a cyclotron was developed. A newly-developed radial probe with a 6-mm-wide, 5-mm-height plastic scintillator was applied to analysis of the correlation between the internal beam phase distribution and the initial beam phase, defined by adjusting the relative RF phase of the beam buncher. The phase distribution measurement system, comprising the radial probe equipped with a plastic scintillator and the signal-processing modules, had a sufficiently good time resolution of 45ps full-width at half-maximum for the phase bunching evaluation. The correlations between the buncher phase and the measured phase distribution for the acceleration harmonic number h=1 and 2 were consistent with the calculation result of the geometric trajectory analysis. For h=1 case of a 107MeV 4He2+ beam, the internal beam phase region spread over 71 RF degrees full-width at quarter-maximum (FWQM) for the acceptable buncher phase region of 48 RF degrees, and no evidence of the phase bunching effect was observed. For h=2 case of a 260MeV 20Ne7+ beam, the internal beam phase region for the acceptable buncher phase region of 59 RF degrees was compressed into 21 RF degrees FWQM. The phase bunching effect was sharply evident for h=2, and contributed to increase of the acceptable beam phase region and the beam intensity per phase width.

Optimal Motion Planning for Robotic Manipulators

This paper presents a time-optimal path planning scheme for a robot manipulator to track a specified geometric Cartesian trajectory. It considers actuator constraints, the full robot dynamics. In order to make full use of the motors capacity, the bound torques are determined by considering the bound of the generated heat. The velocity limit and the bound acceleration (deceleration) are determined by combining with dynamics. We utilize the phase plane analysis technique to generate the minimum time trajectory.

PS14 モンテカルロ解析によるSOFC燃料極製造時の焼結挙動に初期粉末構造が及ぼす影響評価

Composite sintering is a critical fabrication process strongly correlated with an initial performance of solid oxide fuel cells. However, the controlling a composite sintering is still matter of debate because of its inherent complexities of the microstructural evolution during sintering. In this study, we numerically predict the sintering behavior of NiO-YSZ composites using a three-dimensional POTTS Monte Carlo simulation. We show that the green density, grain size distribution, composite volume fraction of the initial composite powder have a great impact on the densification rate and the geometric trajectories during sintering.

Optimal Sensor Trajectories for Mobile Underwater Target Positioning with Noisy Range Measurements

There is considerable interest in reducing the number of sensors/beacons involved in underwater positioning/navigation systems since this has the potential to drastically reduce the costs and the time spent in deploying, calibrating, and recovering acoustic equipment at sea. Motivated by these considerations, we address the problem of single underwater target positioning based on acoustic range measurements between the target and a moving sensor at the sea surface. In particular, the goal of the present work is to compute optimal geometric trajectories for the surface sensor that will, in a well defined sense, maximize the range-related information available for underwater target positioning and tracking. To this effect, the Fisher Information Matrix and the maximization of its determinant are used to determine the sensor trajectory that yields the most accurate positioning of the target, while the latter describes a preplanned trajectory. It is shown that the optimal trajectory depends on the velocity of the sensor, the velocity and trajectory of the target, the sampling time between measurements, the measurement error model, and the number of measurements used to compute the FIM. Simulation examples illustrate the key results derived.

Convex time-optimal robot path following with Cartesian acceleration and inertial force and torque constraints

In time-optimal robot path following, a predetermined geometric trajectory is followed exactly in a time-optimal way considering system constraints, for example, actuator constraints. For a simplified robotic manipulator, this optimization problem can be reformulated into a convex optimization problem when only considering some system constraints. In this article, the convex approach is extended to account for Cartesian acceleration constraints and in turn account for inertial forces and torques acting on a load held by the robot. The focus of this article is on the reformulation of these Cartesian acceleration and inertial forces and torques to preserve the convexity of the optimization problem. We present a series of applications that result in solving a convex optimization problem, illustrating the practicality of the proposed reformulations.

Geometric analysis of phase bunching in the central region of cyclotron

An optimum condition for realizing phase bunching in the central region of a cyclotron was quantitatively clarified by a simplified geometric trajectory analysis of charged particles from the first to the second acceleration gap. The phase bunching performance was evaluated for a general case of a cyclotron. The phase difference of incident particles at the second acceleration gap depends on the combination of four parameters: the acceleration harmonic number h, the span angle θD of the dee electrode, the span angle θF from the first to the second acceleration gap, the ratio RV of the peak acceleration voltage between the cyclotron and ion source. Optimum values of θF for phase bunching were limited by the relationship between h and θD, which is 90°/h+θD/2≤θF≤180°/h+θD/2, and sinθF>0. The phase difference with respect to the reference particle at the second acceleration gap is minimized for voltage-ratios between two and four for an initial phase difference within 40 RF degrees. Although the slope of the first acceleration gap contributes to the RF phase at which the particles reach the second acceleration gap, phase bunching was not affected. An orbit simulation of the AVF cyclotron at the Japan Atomic Energy Agency verifies the evaluation based on geometric analysis.