Endpoint Trajectory Research Articles

Design of PI regulators for dynamic systems with constrained control and fixed endpoints of trajectories

The problem of optimal control for time-varying linear systems with fixed endpoints of trajectories is considered. A corresponding quadratic objective functional depends on the control, the state of the object and on its integral. New technique of designing the PI controller for the automatic control systems with box constraints on values of control is proposed. The problem is solved by using Lagrange multipliers of a special type.

Dual Sticky Hierarchical Dirichlet Process Hidden Markov Model and Its Application to Natural Language Description of Motions.

In this paper, a new nonparametric Bayesian model called the dual sticky hierarchical Dirichlet process hidden Markov model (HDP-HMM) is proposed for mining activities from a collection of time series data such as trajectories. All the time series data are clustered. Each cluster of time series data, corresponding to a motion pattern, is modeled by an HMM. Our model postulates a set of HMMs that share a common set of states (topics in an analogy with topic models for document processing), but have unique transition distributions. The number of HMMs and the number of topics are both automatically determined. The sticky prior avoids redundant states and makes our HDP-HMM more effective to model multimodal observations. For the application to motion trajectory modeling, topics correspond to motion activities. The learnt topics are clustered into atomic activities which are assigned predicates. We propose a Bayesian inference method to decompose a given trajectory into a sequence of atomic activities. The sources and sinks in the scene are learnt by clustering endpoints (origins and destinations) of trajectories. The semantic motion regions are learnt using the points in trajectories. On combining the learnt sources and sinks, the learnt semantic motion regions, and the learnt sequence of atomic activities, the action represented by a trajectory can be described in natural language in as automatic a way as possible. The effectiveness of our dual sticky HDP-HMM is validated on several trajectory datasets. The effectiveness of the natural language descriptions for motions is demonstrated on the vehicle trajectories extracted from a traffic scene.

Virtual Sensor for Kinematic Estimation of Flexible Links in Parallel Robots.

The control of flexible link parallel manipulators is still an open area of research, endpoint trajectory tracking being one of the main challenges in this type of robot. The flexibility and deformations of the limbs make the estimation of the Tool Centre Point (TCP) position a challenging one. Authors have proposed different approaches to estimate this deformation and deduce the location of the TCP. However, most of these approaches require expensive measurement systems or the use of high computational cost integration methods. This work presents a novel approach based on a virtual sensor which can not only precisely estimate the deformation of the flexible links in control applications (less than 2% error), but also its derivatives (less than 6% error in velocity and 13% error in acceleration) according to simulation results. The validity of the proposed Virtual Sensor is tested in a Delta Robot, where the position of the TCP is estimated based on the Virtual Sensor measurements with less than a 0.03% of error in comparison with the flexible approach developed in ADAMS Multibody Software.

The innovative concept of three-dimensional hybrid receptor modeling

The aim of this study was to improve the current understanding of air pollution transport processes at regional and long-range scale. For this purpose, three-dimensional (3D) potential source contribution function and concentration weighted trajectory models, as well as new hybrid receptor model, concentration weighted boundary layer (CWBL), which uses a two-dimensional grid and a planetary boundary layer height as a frame of reference, are presented. The refined approach to hybrid receptor modeling has two advantages. At first, it considers whether each trajectory endpoint meets the inclusion criteria based on planetary boundary layer height, which is expected to provide a more realistic representation of the spatial distribution of emission sources and pollutant transport pathways. Secondly, it includes pollutant time series preprocessing to make hybrid receptor models more applicable for suburban and urban locations. The 3D hybrid receptor models presented herein are designed to identify altitude distribution of potential sources, whereas CWBL can be used for analyzing the vertical distribution of pollutant concentrations along the transport pathway.

Does the Finger-to-Nose Test measure upper limb coordination in chronic stroke?

BackgroundWe aimed to kinematically validate that the time to perform the Finger-to-Nose Test (FNT) assesses coordination by determining its construct, convergent and discriminant validity.MethodsExperimental, criterion standard study. Both clinical and experimental evaluations were done at a research facility in a rehabilitation hospital. Forty individuals (20 individuals with chronic stroke and 20 healthy, age- and gender-matched individuals) participated.. Both groups performed two blocks of 10 to-and-fro pointing movements (non-dominant/affected arm) between a sagittal target and the nose (ReachIn, ReachOut) at a self-paced speed. Time to perform the test was the main outcome. Kinematics (Optotrak, 100Hz) and clinical impairment/activity levels were evaluated. Spatiotemporal coordination was assessed with slope (IJC) and cross-correlation (LAG) between elbow and shoulder movements.ResultsCompared to controls, individuals with stroke (Fugl-Meyer Assessment, FMA-UE: 51.9 ± 13.2; Box & Blocks, BBT: 72.1 ± 26.9%) made more curved endpoint trajectories using less shoulder horizontal-abduction. For construct validity, shoulder range (β = 0.127), LAG (β = 0.855) and IJC (β = −0.191) explained 82% of FNT-time variance for ReachIn and LAG (β = 0.971) explained 94% for ReachOut in patients with stroke. In contrast, only LAG explained 62% (β = 0.790) and 79% (β = 0.889) of variance for ReachIn and ReachOut respectively in controls. For convergent validity, FNT-time correlated with FMA-UE (r = −0.67, p < 0.01), FMA-Arm (r = −0.60, p = 0.005), biceps spasticity (r = 0.39, p < 0.05) and BBT (r = −0.56, p < 0.01). A cut-off time of 10.6 s discriminated between mild and moderate-to-severe impairment (discriminant validity). Each additional second represented 42% odds increase of greater impairment.ConclusionsFor this version of the FNT, the time to perform the test showed construct, convergent and discriminant validity to measure UL coordination in stroke.

Trajectories of Stress, Depressive Symptoms, and Immunity in Cancer Survivors: Diagnosis to 5 Years.

Five-year disease endpoint trajectories are available for every cancer site. In contrast, there are few longitudinal, biobehavioral studies of survivors extending beyond the first or second year following diagnosis. This gap is addressed with stress, depressive symptom, and immunity data from breast cancer patients followed continuously for 5 years. Women (N = 113) diagnosed and surgically treated for breast cancer and awaiting adjuvant therapy completed self-report measures of stress and depressive symptoms and provided blood for immune assays [natural killer cell cytotoxicity (NKCC) and T-cell blastogenesis]. Assessments (N = 12) were repeated every 4 to 6 months for 5 years. Multiphase linear mixed models show phases of change and identified specific time points of change. Cancer stress shows two distinct phases of decline, with the change point being 12 months. In contrast, a steep decline in depressive symptoms occurs by 7 months, with stable, low levels thereafter. NKCC shows a steady upward trajectory through 18 months and upper limit stability thereafter, whereas there was no reliable trajectory for T-cell blastogenesis. For the first time, trajectories and specific time points of change in biobehavioral data for breast cancer survivors are provided, traced through 5 years. Following diagnosis, the breast survivor experience is one of a co-occurrence of change (recovery) in psychologic and innate immunity markers from diagnosis to18 months, and a pattern of stability (depression, NKCC) or continued improvement (stress) through year 5. These data provide new directions for survivorship care and detail of the biobehavioral trajectory. Clin Cancer Res; 23(1); 52-61. ©2016 AACR.

Objects Versus Shadows as Influences on Perceived Object Motion.

The motion trajectory of an object’s cast shadow has been shown to alter the perceived trajectory of a casting object, an effect that holds even if the cast shadow appears unrealistic. This raises the question of whether a cast shadow per se is necessary for this influence, a question that has been studied only with stationary targets. We examined the relative influence of a shadow and a spherical object on the perceived motion trajectory of an identical spherical object, using a paradigm similar to Kersten, Mamassian, and Knill's ball-in-box animation. We recorded both depth and height estimates of the perceived end-point of the target trajectory as a function of various target and context trajectories. Both shadows and objects significantly influenced the perceived trajectory of the target, though the influence of the shadow was overall stronger. We conjecture that the influence of the object reveals the assumption that similar objects moving at the same speed and in similar directions are perceived to move within the same plane, a plane subject to a fronto-parallel bias.

Instrumental indices for upper limb function assessment in stroke patients: a validation study.

BackgroundRobotic exoskeletons are increasingly being used in objective and quantitative assessment of upper limb (UL) movements. A set of instrumental indices computed during robot-assisted reaching tasks with the Armeo®Spring has been proven to assess UL functionality. The aim of this study was to test the construct validity of this indices-based UL assessment when used with patients who have had a stroke.MethodsForty-four 45- to 79-year-old stroke patients with a Wolf Motor Function Test ability score (WMFT-FAS) ranging from 10 to 75 and a Motricity Index (MI) ranging from 14 to 33 at shoulder and elbow were enrolled, thus covering a wide range of impairments. Residual UL function was assessed by both the WMFT-FAS and the WMFT-TIME, as well as by a set of 9 numerical indices assessing movement accuracy, velocity and smoothness computed from a 3D endpoint trajectory obtained during the “Vertical Capture” task of the Armeo®Spring device. To explore which variables better represented motor control deficits, the Mann-Whitney U Test was used to compare patients’ indices to those obtained from 25 healthy individuals. To explore the inner relationships between indices and construct validity in assessing accuracy, velocity and smoothness, a factor analysis was carried out. To verify the indices concurrent validity, they were compared to both WMFT-FAS and WMFT-TIME by the Spearman’s correlation coefficient.ResultsSeven indices of stroke subjects were significantly different from those of healthy controls, with effect sizes in the range 0.35–0.74. Factor analysis confirmed that specific subsets of indices belonged to the domains of accuracy, velocity and smoothness (discriminant validity). One accuracy index, both velocity indices and two smoothness indices were significantly correlated with WMFT-FAS and WMFT-TIME (|rho| = 0.31–0.50) (concurrent validity). One index for each of the assessed movement domains was proven to have construct validity (discriminant and concurrent) and was selected. Moreover, the indices were able to detect differences in accuracy, velocity and/or smoothness in patients with the same WMFT level.ConclusionsThe proposed index-based UL assessment can be used to integrate and support clinical evaluation of UL function in stroke patients.

Effects of shoe heel height on the end-point and joint kinematics of the locomotor system when crossing obstacles of different heights

High-heeled shoes increase the risk of falling during walking, especially in the presence of obstacles. The study aimed to compare the end-point (foot/shoe) trajectories and joint angles of the lower extremities in 12 healthy females crossing obstacles of different heights while barefoot and when wearing narrow-heeled shoes (heel heights: 3.9, 6.3 and 7.3 cm). During obstacle-crossing, young females in narrow-heeled shoes maintained the same leading toe-clearance as when barefoot, irrespective of the heel height, primarily through increased plantarflexion of the leading swing ankle. However, the shoe heel-clearance was significantly reduced when compared with barefoot, presumably related to the difficulty in precisely sensing the position of the shoe-heel tip. With an increasing obstacle height, the toe-clearance, heel-clearance and shoe heel-clearance were reduced linearly, indicating an increasing risk of tripping over the obstacle. The results will be helpful for the design and development of strategies to reduce the risk of falling when wearing narrow-heeled shoes.Practitioner Summary: Knowledge of the influence of narrow-heeled shoes and obstacles on lower limb joint and end-point kinematics helps in shoe design to address fall risks. Compared to barefoot, narrow-heeled shoes reduced shoe heel-clearances, which were further reduced linearly with increasing obstacle height, indicating an increasing risk of tripping over the obstacle.

Drawing ellipses in water: evidence for dynamic constraints in the relation between velocity and path curvature.

Several types of continuous human movements comply with the so-called Two-Thirds Power Law (2/3-PL) stating that velocity (V) is a power function of the radius of curvature (R) of the endpoint trajectory. The origin of the 2/3-PL has been the object of much debate. An experiment investigated further this issue by comparing two-dimensional drawing movements performed in air and water. In both conditions, participants traced continuously quasi-elliptic trajectories (period T=1.5s). Other experimental factors were the movement plane (horizontal/vertical), and whether the movement was performed free-hand, or by following the edge of a template. In all cases a power function provided a good approximation to the V-R relation. The main result was that the exponent of the power function in water was significantly smaller than in air. This appears incompatible with the idea that the power relationship depends only on kinematic constraints and suggests a significant contribution of dynamic factors. We argue that a satisfactory explanation of the observed behavior must take into account the interplay between the properties of the central motor commands and the visco-elastic nature of the mechanical plant that implements the commands.

High Precision Neural Decoding of Complex Movement Trajectories using Recursive Bayesian Estimation with Dynamic Movement Primitives.

Brain-machine interfaces (BMIs) are a rapidly progressing technology with the potential to restore function to victims of severe paralysis via neural control of robotic systems. Great strides have been made in directly mapping a user's cortical activity to control of the individual degrees of freedom of robotic end-effectors. While BMIs have yet to achieve the level of reliability desired for widespread clinical use, environmental sensors (e.g. RGB-D cameras for object detection) and prior knowledge of common movement trajectories hold great potential for improving system performance. Here we present a novel sensor fusion paradigm for BMIs that capitalizes on information able to be extracted from the environment to greatly improve the performance of control. This was accomplished by using dynamic movement primitives to model the 3D endpoint trajectories of manipulating various objects. We then used a switching unscented Kalman filter to continuously arbitrate between the 3D endpoint kinematics predicted by the dynamic movement primitives and control derived from neural signals. We experimentally validated our system by decoding 3D endpoint trajectories executed by a non-human primate manipulating four different objects at various locations. Performance using our system showed a dramatic improvement over using neural signals alone, with median distance between actual and decoded trajectories decreasing from 31.1 cm to 9.9 cm, and mean correlation increasing from 0.80 to 0.98. Our results indicate that our sensor fusion framework can dramatically increase the fidelity of neural prosthetic trajectory decoding.

Factors Controlling Low-Cloud Evolution over the Eastern Subtropical Oceans: A Lagrangian Perspective Using the A-Train Satellites

Abstract A Lagrangian technique is developed to sample satellite data to quantify and understand factors controlling temporal changes in low-cloud properties (cloud cover, areal-mean liquid water path, and droplet concentration). Over 62 000 low-cloud scenes over the eastern subtropical/tropical oceans are sampled using the A-Train satellites. Horizontal wind fields at 925 hPa from the ERA-Interim are used to compute 24-h, two-dimensional, forward, boundary layer trajectories with trajectory locations starting on the CloudSat/CALIPSO track. Cloud properties from MODIS and AMSR-E are sampled at the trajectory start and end points, allowing for direct measurement of the temporal cloud evolution. The importance of various controls (here, boundary layer depth, lower-tropospheric stability, and precipitation) on cloud evolution is evaluated by comparing cloud evolution for different initial values of these controls. Viewing angle biases are removed and cloud anomalies (diurnal and seasonal cycles removed) are used throughout to quantify cloud evolution relative to the climatological-mean evolution. Cloud property anomalies show temporal changes similar to those expected for a stochastic red noise process, with linear relationships between initial anomalies and their mean 24-h changes. This creates a potential bias when comparing the evolutions of sets of trajectories with different initial anomalies; three methods are introduced and evaluated to account for this. Results provide statistically robust observational support for theoretical/modeling studies by showing that low clouds in deep boundary layers and under weak inversions are prone to break up. Precipitation shows a more complex and less statistically significant relationship with cloud breakup. Cloud cover in shallow precipitating boundary layers is more persistent than in deep precipitating boundary layers. Liquid water path and cloud droplet concentration decrease more rapidly for precipitating clouds and in deep boundary layers.

Topological trajectory classification with filtrations of simplicial complexes and persistent homology

In this work, we present a sampling-based approach to trajectory classification which enables automated high-level reasoning about topological classes of trajectories. Our approach is applicable to general configuration spaces and relies only on the availability of collision free samples. Unlike previous sampling-based approaches in robotics which use graphs to capture information about the path-connectedness of a configuration space, we construct a multiscale approximation of neighborhoods of the collision free configurations based on filtrations of simplicial complexes. Our approach thereby extracts additional homological information which is essential for a topological trajectory classification. We propose a multiscale classification algorithm for trajectories in configuration spaces of arbitrary dimension and for sets of trajectories starting and ending in two fixed points. Using a cone construction, we then generalize this approach to classify sets of trajectories even when trajectory start and end points are allowed to vary in path-connected subsets. We furthermore show how an augmented filtration of simplicial complexes based on an arbitrary function on the configuration space, such as a costmap, can be defined to incorporate additional constraints. We present an evaluation of our approach in 2-, 3-, 4- and 6-dimensional configuration spaces in simulation and in real-world experiments using a Baxter robot and motion capture data.

Proximal arm kinematics affect grip force-load force coordination.

During object manipulation, grip force is coordinated with load force, which is primarily determined by object kinematics. Proximal arm kinematics may affect grip force control, as proximal segment motion could affect control of distal hand muscles via biomechanical and/or neural pathways. The aim of this study was to investigate the impact of proximal kinematics on grip force modulation during object manipulation. Fifteen subjects performed three vertical lifting tasks that involved distinct proximal kinematics (elbow/shoulder), but resulted in similar end-point (hand) trajectories. While temporal coordination of grip and load forces remained similar across the tasks, proximal kinematics significantly affected the grip force-to-load force ratio (P = 0.042), intrinsic finger muscle activation (P = 0.045), and flexor-extensor ratio (P < 0.001). Biomechanical coupling between extrinsic hand muscles and the elbow joint cannot fully explain the observed changes, as task-related changes in intrinsic hand muscle activation were greater than in extrinsic hand muscles. Rather, between-task variation in grip force (highest during task 3) appears to contrast to that in shoulder joint velocity/acceleration (lowest during task 3). These results suggest that complex neural coupling between the distal and proximal upper extremity musculature may affect grip force control during movements, also indicated by task-related changes in intermuscular coherence of muscle pairs, including intrinsic finger muscles. Furthermore, examination of the fingertip force showed that the human motor system may attempt to reduce variability in task-relevant motor output (grip force-to-load force ratio), while allowing larger fluctuations in output less relevant to task goal (shear force-to-grip force ratio).

Mass–count plots for crystal size control

We present measurements from batch crystallization as a trajectory in the phase space mapped out by the crystal mass and the total chord count. This new perspective yields a framework for monitoring and controlling crystallization that has two beneficial attributes: first, crystallization is seen as movement—we find that this fosters an intuitive understanding of crystallization kinetics; and, second, the problem of controlling the average crystal size is cast as a trajectory-endpoint control problem—we find that this promotes the development of spatially-oriented control schemes.The utility of the proposed framework is demonstrated by application. In particular, we apply the framework to: 1) elucidate the effects of simple temperature manipulations on the crystallization kinetics; 2) interpret the actions applied by supersaturation control (SSC) and direct nucleation control (DNC) to produce large crystals; and 3) develop a control scheme—termed spatially-guided action trajectory endpoint control (sGATEC)—that can be applied to produce crystals of pre-selected average size.

Survival and ice nucleation activity of bacteria as aerosols in a cloud simulation chamber

Abstract. The residence time of bacterial cells in the atmosphere is predictable by numerical models. However, estimations of their aerial dispersion as living entities are limited by a lack of information concerning survival rates and behavior in relation to atmospheric water. Here we investigate the viability and ice nucleation (IN) activity of typical atmospheric ice nucleation active bacteria (Pseudomonas syringae and P. fluorescens) when airborne in a cloud simulation chamber (AIDA, Karlsruhe, Germany). Cell suspensions were sprayed into the chamber and aerosol samples were collected by impingement at designated times over a total duration of up to 18 h, and at some occasions after dissipation of a cloud formed by depressurization. Aerosol concentration was monitored simultaneously by online instruments. The cultivability of airborne cells decreased exponentially over time with a half-life time of 250 ± 30 min (about 3.5 to 4.5 h). In contrast, IN activity remained unchanged for several hours after aerosolization, demonstrating that IN activity was maintained after cell death. Interestingly, the relative abundance of IN active cells still airborne in the chamber was strongly decreased after cloud formation and dissipation. This illustrates the preferential precipitation of IN active cells by wet processes. Our results indicate that from 106 cells aerosolized from a surface, one would survive the average duration of its atmospheric journey estimated at 3.4 days. Statistically, this corresponds to the emission of 1 cell that achieves dissemination every ~ 33 min m−2 of cultivated crops fields, a strong source of airborne bacteria. Based on the observed survival rates, depending on wind speed, the trajectory endpoint could be situated several hundreds to thousands of kilometers from the emission source. These results should improve the representation of the aerial dissemination of bacteria in numeric models.

Effects of concurrent physical and cognitive demands on arm movement kinematics in a repetitive upper-extremity precision task

The effect of concurrent physical and cognitive demands on arm motor control is poorly understood. This exploratory study compared movement kinematics in a repetitive high-precision pipetting task with and without additional concurrent cognitive demands in the form of instructions necessary to locate the correct target tube. Thirty-five healthy female subjects performed a standardized pipetting task, transferring liquid repeatedly from one pick-up tube to different target tubes. In the reference condition, lights indicated the target tube in each movement cycle, while the target tube had to be deciphered from a row and column number on a computer screen in the condition with additional cognitive demands. Kinematics of the dominant arm was assessed using the central tendency and variability of the pipette-tip end-point trajectory and joint kinematics properties of the shoulder and elbow. Movements slowed down (lower velocities and higher area under the movement curves) and trajectory variability increased in the condition with additional cognitive demands, but there were no changes in the kinematics properties such as joint range of motion, times of acceleration and deceleration (as indicated by the time to peak velocity), average angles, or phase relationships between angle and angular velocity of shoulder or elbow movements between the two conditions. Further, there were also no differences in the size or structure of variability of the shoulder and elbow joint angles, suggesting that subjects could maintain the motor repertoire unaltered in the presence of these specific additional cognitive demands. Further studies should address motor control at other levels of concurrent cognitive demands, and with motor tasks that are less automated than the pipetting task used in the present study, so as to gain an increased understanding of the effect of concurrent cognitive demands for other activities of relevance to daily life.

Finding ways to reach the right endpoint

Theoretical Biology Most complex systems have an element of randomness: Even if we can describe them exactly at one point in time, we don't know for certain where they will be next. Scientists use stochastic equations to compute the many possible trajectories these systems can take. If we constrain both end points of such trajectories, the usual approach of calculating all trajectories and rejecting those that do not end at the desired final point can be very inefficient. Zhao et al. introduced an approach in which they modified the probabilities for moving from one state to the next, so that the system was guaranteed to reach the set final state. The authors used examples from population genetics to illustrate the power of the method. J. Theor. Biol. 363 , 419 (2014).

Control of a Group of Mobile Robots Based on Formation Abstraction and Decentralized Locational Optimization

In this paper, we propose a new method of controlling a group of mobile robots based on formation abstraction. The shape of a formation is represented by a deformable polygon, which is constructed by bending a rectangle, to go through narrow spaces without colliding with obstacles. If the trajectory of the front end point, as well as the width and the length of the formation, are given, the formation automatically reshapes itself to fit the area through which the front part of the group has already safely passed. Furthermore, the robots continuously try to optimize their positions to decrease the risk of collisions by integrating a decentralized locational optimization algorithm into the formation control. We show that the objective function, taking into account the distance between robots, does not decrease for fixed and nonconvex polygonal formation shapes if the zero-order hold control is applied for a sufficiently short sampling period. We also analyze the influence of the decentralized locational optimization algorithm on the objective function in the case of variable formations. The effectiveness of the proposed method is demonstrated in both simulations and real robot experiments.

Multi-level trajectory learning for traffic behavior detection and analysis

Motion patterns can be learnt automatically based on object trajectories data extracted by means of video tracking, which is an effective approach for modeling and analyzing traffic behavior. In this paper, a multi-level motion pattern learning approach for traffic behavior analysis is presented, which takes into account the spatial characteristics, direction characteristics, and type characteristics of trajectories. At the spatial level, improved Hausdorff distance measurement is applied to construct a spatial similarity matrix of the trajectories collected, and spectral clustering is used to achieve spatial pattern learning. At the directional level, the start and end points of trajectories are fitted using a Gaussian mixed model to extract the distribution of entry and exit zones. Then, the direction pattern is obtained from the regional centers of the pairwise distribution zones. At the type level, the type pattern is acquired through a K-means clustering algorithm that considers multiple classification features of trajectories. Based on the learned multi-level motion patterns, abnormal behavior detection algorithms are further developed by means of pattern matching. Finally, our approach is tested with several video sequences from real-world traffic scenarios. Some typical traffic behaviors in the test scenarios are successfully recognized and analyzed and examples of abnormal traffic behaviors are also reliably detected.