Tau Theory Research Articles

Developing a New Expected Goals Metric to Quantify Performance in a Virtual Reality Soccer Goalkeeping App called CleanSheet

As virtual reality (VR) sports training apps start to become more mainstream, it is important that human performance is measured from VR gameplay interaction data in a more meaningful way. CleanSheet is a VR training app that is played by over 100,000 users around the world. Many of those players are aspiring goalkeepers who want to use the app as a new way to train and improve their general goalkeeping performance. Whilst the leaderboards display how many shots players saved, these data do not take into account the difficulty of the shot faced. This study presents a regression model developed from a combination of existing expected goals (xG) models, goalkeeper performance metrics, and psychological research to produce a new shot difficulty metric called CSxG. Utilizing user save rate data as the target variable, a model was developed that incorporated three input variables relating to ball flight and in-goal positioning. Our analysis showed that the required rate of closure (RROC), adapted from Tau theory, was the most significant predictor of the proportion of goals conceded. A validation process evaluated the new xG model for CleanSheet by comparing its difficulty predictions against user performance data across players of varying skill levels. CSxG effectively predicted shot difficulty at the extremes but showed less accuracy for mid-range scores (0.4 to 0.8). Additional variables influencing shot difficulty, such as build-up play and goalpost size, were identified for future model enhancements. This research contributes to the advancement of predictive modeling in sports performance analysis, highlighting the potential for improved goalkeeper training and strategy development using VR technology.

Optimization-based planning of speech articulation using general Tau Theory

This paper presents a model of speech articulation planning and generation based on General Tau Theory and Optimal Control Theory. Because General Tau Theory assumes that articulatory targets are always reached, the model accounts for speech variation via context-dependent articulatory targets. Targets are chosen via the optimization of a composite objective function. This function models three different task requirements: maximal intelligibility, minimal articulatory effort and minimal utterance duration. The paper shows that systematic phonetic variability can be reproduced by adjusting the weights assigned to each task requirement. Weights can be adjusted globally to simulate different speech styles, and can be adjusted locally to simulate different levels of prosodic prominence. The solution of the optimization procedure contains Tau equation parameter values for each articulatory movement, namely position of the articulator at the movement offset, movement duration, and a parameter which relates to the shape of the movement’s velocity profile. The paper presents simulations which illustrate the ability of the model to predict or reproduce several well-known characteristics of speech. These phenomena include close-to-symmetric velocity profiles for articulatory movement, variation related to speech rate, centralization of unstressed vowels, lengthening of stressed vowels, lenition of unstressed lingual stop consonants, and coarticulation of stop consonants.

Tau Theory-Based Flare Control in Autonomous Helicopter Autorotation

A novel trajectory generation and control architecture for fully autonomous autorotative flare that combines rapid path generation with model-based control is proposed. The trajectory generation component uses optical Tau theory to compute flare trajectories for both longitudinal and vertical speed. These flare trajectories are tracked using a nonlinear dynamic inversion (NDI) control law. One convenient feature of NDI is that it inverts the plant model in its feedback linearization loop, which eliminates the need for gain scheduling. However, the plant model used for feedback linearization still needs to be scheduled with the flight condition. This key aspect is leveraged to derive a control law that is scheduled with linearized models of the rotorcraft flight dynamics obtained in steady-state autorotation, while relying on a single set of gains. Computer simulations are used to demonstrate that the NDI control law is able to successfully execute autorotative flare in the UH-60 aircraft. Autonomous flare trajectories are compared to piloted simulation data to assess similarities and discrepancies between piloted and automatic control approaches. Trade studies examine which combinations of downrange distances and altitudes at flare initiation result in successful autorotative landings.

Gene therapy: an alternative to treat Alzheimer's disease.

Alzheimer's disease (AD), a neuro-degenerative disease that primarily affects the elderly, is a worldwide phenomenon. Loss of memory, cognitive decline, behavioural changes, and many other signs are used to classify it. Various hypotheses that may contribute to Alzheimer's disease have been found during decades of survey, including tau theory, the amyloid theory, the cholinergic hypothesis, and the oxidative stress hypothesis. According to some theories, the two leading causes of AD are the accumulation of amyloid beta plaque and development of NFTs in the brain. The hippocampus and cerebral cortex are the primary sites where amyloid beta plaques gather in the body. NFT formation in the brain impairs the brain's neurons' potential of signalling. According to the age at which it manifests in a person, there are two subtypes of AD: 'LOAD (Late Onset Alzheimer's Disease)' and 'EOAD (Early Onset Alzheimer's Disease)'. Long-term research into AD treatment has resulted in the introduction of some medications that provided symptomatic relief to patients but did not alter the disease's pathophysiology, like cholinesterase inhibitors, inhibitors of tau aggregation, and monoclonal antibodies to Aβ aggregation. Even though the medications did not halt the progression of AD, researchers did not discontinue their work, which lead to the introduction of gene therapy - a recently created cutting-edge method of delivering genes to target sites where they can express the intended functionalities. Viral or non-viral vectors could be used to deliver the gene, each with advantages and limitations of their own. Gene therapy is proven to be a potential disease-modifying treatment for AD. This article discusses about gene therapy, its merits and demerits and the various ways of gene delivery. Additionally, it focuses on AD as the target for treatment through gene therapy, the pathophysiology of AD, and the multiple targets for gene therapy in the treatment of AD.

Modeling trajectories of human speech articulators using general Tau theory

This paper presents an application of general Tau theory to the modeling and analysis of articulatory trajectories in speech. We evaluated the model using electromagnetic articulometry data from 12 native speakers of English reading a common text, where trajectories of the following sensors were fitted: lower and upper lips, jaw, and three tongue sensors. Additionally, we analyzed trajectories of the lip aperture signal. Our experiments show that the general Tau theory model gives a better fit than existing (i) methods based on critically damped oscillators, and (ii) a method based on sequential target approximation. These findings support the hypothesis of Tau-guided movements of articulators during speech production. In the second part of the paper, our Tau theory analysis shows that articulatory movements follow similar velocity profile distributions across speakers. In particular, the value of the shape parameter κ of the Tau theory equation is identically distributed across speakers, following a unimodal distribution. The statistical mode of the distribution corresponds to the value of κ that generates a symmetric velocity profile. The analysis of the statistical distribution of κ values also reveals that its variance decreases when greater articulatory effort is required, such that produced articulatory effort remains close to that predicted by the theoretical minimal cost function based on forces acting on the moving articulator. This provides new evidence that articulatory effort is optimized during speech production.

General tau theory as a model to evaluate audiovisual interplay in interceptive actions

When interacting with the environment, sensory information is essential to guide movements. Picking up the appropriate sensory information (both visual and auditory) about the progression of an event is required to reach the right place at the right time. In this study, we aimed to see if general tau theory could explain the audiovisual guidance of movement in interceptive action (an interception task). The specific contributions of auditory and visual sensory information were tested by timing synchronous and asynchronous audiovisual interplays in successful interceptive trials. The performance was computed by using the tau-coupling model for information-movement guidance. Our findings revealed that while the auditory contribution to movement guidance did change across conditions, the visual contribution remained constant. In addition, when comparing the auditory and visual contributions, the results revealed a significant decrease in the auditory compared to the visual contribution in just one of the asynchronous conditions where the visual target was presented after the sound. This may be because more attention was drawn to the visual information, resulting in a decrease in the auditory guidance of movement. To summarize, our findings reveal how tau-coupling can be used to disentangle the relative contributions of the visual and auditory sensory modalities in movement planning.

Autonomous deck landing of a vertical take-off and landing unmanned aerial vehicle based on the tau theory

The research on autonomous landing of vertical take-off and landing (VTOL) unmanned aerial vehicles (UAVs) is well established. However, the research on autonomous deck landing using visual methods is relatively not so mature and many of them require the support of ground infrastructures. In order to reduce such dependencies, a ship landing guidance strategy based on on-board vision is studied. Considering the characteristics of the ship landing issue, we propose a three-phase landing scheme and a decision-making method to ensure landing safety is also studied. For improving the traditional two-dimensional (2D) optical-flow method, a three-dimensional (3D) velocity vector estimation method using image spherical optical flow is studied. Furthermore, a guidance law based on the tau theory is employed by only using the visual information of the line of sight to the target. In this phase, a trajectory-tracking controller is applied to generate the velocity commands of the UAV. Finally, the whole algorithm is validated by simulation in different wave conditions developed with Unity3D. Compared with traditional trajectory planning methods, our method does not require complex optimization iterations and can meet both the real-time and accuracy requirements of deck landing. The average tracking error of our method maintains in 0.2 m. Moreover, the whole algorithm runs efficiently at around 30 fps on a Raspberry-Pi 3B+ microcomputer which meets the real-time requirements.

Genetically modified mice for research on human diseases: A triumph for Biotechnology or a work in progress?

Abstract Genetically modified mice are engineered as models for human diseases. These mouse models include inbred strains, mutants, gene knockouts, gene knockins, and ‘humanized’ mice. Each mouse model is engineered to mimic a specific disease based on a theory of the genetic basis of that disease. For example, to test the amyloid theory of Alzheimer’s disease, mice with amyloid precursor protein genes are engineered, and to test the tau theory, mice with tau genes are engineered. This paper discusses the importance of mouse models in basic research, drug discovery, and translational research, and examines the question of how to define the “best” mouse model of a disease. The critiques of animal models and the caveats in translating the results from animal models to the treatment of human disease are discussed. Since many diseases are heritable, multigenic, age-related and experience-dependent, resulting from multiple gene-gene and gene-environment interactions, it will be essential to develop mouse models that reflect these genetic, epigenetic and environmental factors from a developmental perspective. Such models would provide further insight into disease emergence, progression and the ability to model two-hit and multi-hit theories of disease. The summary examines the biotechnology for creating genetically modified mice which reflect these factors and how they might be used to discover new treatments for complex human diseases such as cancers, neurodevelopmental and neurodegenerative diseases.

Spinal reflexive movement follows general tau theory

BackgroundTau theory explains how both intrinsically and perceptually guided movements are controlled by the brain. According to general tau theory, voluntary, self-paced human movements are controlled by coupling the tau of the movement (i.e., the rate of closure of the movement gap at its current closure rate) onto an intrinsically generated tau-guide (Lee in Ecol Psychol 10:221–250, 1998). To date there are no studies that have looked at involuntary movements, which are directly guided by innate patterns of neural energy generated at the level of the spinal cord or brain, and that can be explained by general tau theory. This study examines the guidance of an involuntary movement generated by the Patellar reflex in presence of a minimized gravitational field.ResultsThe results showed that the Patellar reflexive movement is strongly coupled to an intrinsic tau-guide particularly when the limb is not moving in the direction of gravity.ConclusionThese results suggest that the same principles of control underpin both voluntary and involuntary movements irrespective of whether they are generated in the brain or the spinal cord. Secondly, given that movements like the patellar reflex are visible from infancy, one might conclude that tau-guidance is an innate form of motor control, or neural blueprint, that has evolved over time.

A Bio-inspired trajectory planning method for robotic manipulators based on improved bacteria foraging optimization algorithm and tau theory.

In this paper, a novel bio-inspired trajectory planning method is proposed for robotic systems based on an improved bacteria foraging optimization algorithm (IBFOA) and an improved intrinsic Tau jerk (named Tau-J*) guidance strategy. Besides, the adaptive factor and elite-preservation strategy are employed to facilitate the IBFOA, and an improved Tau-J* with higher-order of intrinsic guidance movement is used to avoid the nonzero initial and final jerk, so as to overcome the computational burden and unsmooth trajectory problems existing in the optimization algorithm and traditional interpolation algorithm. The IBFOA is utilized to determine a small set of optimal control points, and Tau-J* is then invoked to generate smooth trajectories between the control points. Finally, the results of simulation tests demonstrate the eminent stability, optimality, and rapidity capability of the proposed bio-inspired trajectory planning method.

Bio-inspired guidance method for a soft landing on a Near-Earth Asteroid

Achieving a soft landing over the surface of small celestial bodies is an essential maneuver in space to advance the status of space exploration, sample collecting and in-situ resource utilization, among other on-orbit tasks. Landing on these bodies is challenging due to the reduced-gravity and airless environment. The correct planning of execution of the trajectory to land on the surface of the body is of cumbersome importance to prevent the vehicle from bouncing up and eventually reach escape velocity. In this paper, a bio-inspired trajectory planning method to land on the surface of a Near-Earth Asteroid (NEA) with zero relative velocity is proposed. The method is based on Tau theory, which has been demonstrated to explain the way that humans and some other animals’ approach to different target spots to perform tasks such as perching, landing, and grasping. We have selected the NEA Apophis asteroid as our case study due to its accessibility, and small rotational velocity and orbit condition code. Two landing scenarios are studied; one considers the case where the satellite is hovering at a low altitude; the other corresponds to a landing maneuver right after a deorbiting or breaking phase, which may cause residual initial velocity in the vehicle prior to the landing maneuver. Once the descending trajectory is obtained, a closed-loop controller is in charge of achieving trajectory tracking and calculating the continuous and on/off thrust control signals. The simulation results show that the introduced approach can achieve zero final relative velocity in both cases for different initial condition, which is a requirement for a soft landing. Besides, different kinematic behaviors can be obtained by modifying the single variable named the Tau constant. The particular advantages of the method with respect to a commonly used approach are devised and analyzed as well.

Plant Bioinspired Ecological Robotics.

Plants are movers, but the nature of their movement differs dramatically from that of creatures that move their whole body from point A to point B. Plants grow to where they are going. Bio-inspired robotics sometimes emulates plants' growth-based movement; but growing is part of a broader system of movement guidance and control. We argue that ecological psychology's conception of “information” and “control” can simultaneously make sense of what it means for a plant to navigate its environment and provide a control scheme for the design of ecological plant-inspired robotics. In this effort, we will outline several control laws and give special consideration to the class of control laws identified by tau theory, such as time to contact.

Principles of the Guidance of Exploration for Orientation and Specification of Action.

To control movement of any type, the neural system requires perceptual information to distinguish what actions are possible in any given environment. The behavior aimed at collecting this information, termed “exploration”, is vital for successful movement control. Currently, the main function of exploration is understood in the context of specifying the requirements of the task at hand. To accommodate for agency and action-selection, we propose that this understanding needs to be supplemented with a function of exploration that logically precedes the specification of action requirements with the purpose of discovery of possibilities for action—action orientation. This study aimed to provide evidence for the delineation of exploration for action orientation and exploration for action specification using the principles from “General Tau Theory.” Sixteen male participants volunteered and performed a laboratory-based exploration task. The visual scenes of different task-specific situations were projected on five monitors surrounding the participant. At a predetermined time, the participant received a simulated ball and was asked to respond by indicating where they would next play the ball. Head movements were recorded using inertial sensors as a measure of exploratory activity. It was shown that movement guidance characteristics varied between different head turns as participants moved from exploration for orientation to exploration for action specification. The first head turn in the trial, used for action-orientation, showed later peaks in the velocity profile and harder closure of the movement gap (gap between the start and end of the head-movement) in comparison to the later head turns. However, no differences were found between the first and the final head turn, which we hypothesized are used mainly for action orientation and specification respectively. These results are in support of differences in the function and control of head movement for discovery of opportunities for action (orientation) vs. head movement for specification of task requirements. Both are important for natural movement, yet in experimental settings,orientation is often neglected. Including both orientation and action specification in an experimental design should maximize generalizability of an experiment to natural behavior. Future studies are required to study the neural bases of movement guidance in order to better understand exploration in anticipation of movement.

Bio-Inspired Autonomous Visual Vertical and Horizontal Control of a Quadrotor Unmanned Aerial Vehicle

Near-ground manoeuvres, such as landing, are key elements in unmanned aerial vehicle navigation. Traditionally, these manoeuvres have been done using external reference frames to measure or estimate the velocity and the height of the vehicle. Complex near-ground manoeuvres are performed by flying animals with ease. These animals perform these complex manoeuvres by exclusively using the information from their vision and vestibular system. In this paper, we use the Tau theory, a visual strategy that, is believed, is used by many animals to approach objects, as a solution for relative ground distance control for unmanned vehicles. In this paper, it is shown how this approach can be used to perform near-ground manoeuvres in a vertical and horizontal manner on a moving target without the knowledge of height and velocity of either the vehicle or the target. The proposed system is tested with simulations. Here, it is shown that, using the proposed methods, the vehicle is able to perform landing on a moving target, and also they enable the user to choose the dynamic characteristics of the approach.

Bio-inspired Landing of Quadrotor using Improved State Estimation

This paper presents an improved state estimation technique - a fusion of Monocular SLAM (Simultaneous Localization and Mapping) and INS (Inertial Navigation System). It is utilized in landing a commercially available low cost quadrotor (Parrot AR Drone 2.0) in indoor environments along a trajectory generated by a bio-inspired guidance method. The method is based on Tau theory and facilitates safe and smooth landing of UAVs by closing motion gaps with zero relative velocity and acceleration. A depth camera (Microsoft Kinect) provides a helping hand in very accurate landing towards the end of the quadrotor’s trajectory. A dynamic inversion based controller is designed which works as a outer loop controller for the quadrotor.

TauG-guidance of dynamic balance control during gait initiation in patients with chronic fatigue syndrome and fibromyalgia

BackgroundImpaired postural control has been reported in static conditions in chronic fatigue syndrome and fibromyalgia, but postural control in dynamic tasks have not yet been investigated. Thus, we investigated measurements from a force plate to evaluate dynamic balance control during gait initiation in patients with chronic fatigue syndrome and fibromyalgia compared to matched healthy controls. MethodsThirty female participants (10 per group) performed five trials of gait initiation. Center of pressure (CoP) trajectory of the initial weight shift onto the supporting foot in the mediolateral direction (CoPX) was analyzed using General Tau Theory. We investigated the hypothesis that tau of the CoPX motion-gap (τCoPx) is coupled onto an intrinsic tauG-guide (τG) by keeping the relation τCoPx=KτG, where K is a scaling factor that determines the relevant kinematics of a movement. FindingsMean K values were 0.57, 0.55, and 0.50 in fibromyalgia, chronic fatigue syndrome, and healthy controls, respectively. Both patient groups showed K values significantly higher than 0.50 (P<0.05), indicating that patients showed poorer dynamic balance control, CoPX colliding with the boundaries of the base of support (K>0.5). InterpretationThe findings revealed a lower level of dynamic postural control in both fibromyalgia and chronic fatigue syndrome compared to controls.

Age- and Parkinson's disease-related evaluation of gait by General Tau Theory.

The degeneration of postural control in the elderly and patients with Parkinson's disease (PD) can be debilitating and may lead to increased fall risk. This study evaluated the changes in postural control during gait affected by PD and aging using a new method based on the General Tau Theory. Fifteen patients with PD, 11 healthy old adults (HOs), and 15healthy young adults (HYs) were recruited. Foot trajectories of each participant were monitored during walking by a three-camera Optotrak Certus(®) motion capture system. The anteroposterior direction of foot movement during stepping was analyzed by tau-G and tau-J guidance strategies. Two linear regression analyses suggested that the tau of the step-gap was strongly coupled onto the tau-J guidance during walking. The regression slope K could estimate the coupling ratio in the tau-coupling equation which reflects the performance of postural control during gait. The mean K value for the PD group, which was highest among the three groups, was approximately 0.5. Therefore, participants in the PD group walked with the poorest postural control and exhibited a relatively hard contact with the endpoint during stepping when compared with those in the HO and HY groups. The HY and HO groups obtained mean K values significantly lower than 0.5, which indicated that the gait was well controlled and ended at low speed with low deceleration. However, the HO group showed a decreased tendency for postural control, in which the mean K value was significantly higher than that of the HY group. The K value was moderately positively correlated with the double support time and negatively correlated with the stride length and walking speed. The tau-J coupling ratio can provide additional insight into gait disturbances and may serve as a reliable, objective, and quantitative tool to evaluate dynamic postural control during walking.

Development of Occupant-Preferred Landing Profiles for Personal Aerial Vehicles

With recent increased interest in autonomous vehicles and the associated technology, the prospect of realizing a personal aerial vehicle seems closer than ever. However, there is likely to be a continued requirement for any occupant of an air vehicle to be comfortable with both the automated portions of the flight and their ability to take manual control as and when required. This paper, using the approach to landing as an example maneuver, examines what a comfortable trajectory for personal aerial vehicle occupants might look like. Based upon simulated flight data, a “natural” flight trajectory is designed and then compared to constant deceleration and constant optic flow descent profiles. It is found that personal aerial vehicle occupants with limited flight training and no artificial guidance follow the same longitudinal trajectory as has been found for professionally trained helicopter pilots. Further, the final stages of the approach to hover can be well described using the Tau theory. For automatic flight, personal aerial vehicle occupants prefer a constant deceleration profile. For approaches flown manually, the newly designed natural profile is preferred.

Bio-inspired Collision-free 4D Trajectory Generation for UAVs Using Tau Strategy

Inspired by the general tau theory in animal motion planning, a collision-free four-dimensional (4D) trajectory generation method is presented for multiple Unmanned Aerial Vehicles (UAVs). This method can generate a group of optimal or near-optimal collision-free 4D trajectories, the position and velocity of which are synchronously planned in accordance with the arrival time. To enlarge the shape adjustment capability of trajectories with zero initial acceleration, a new strategy named intrinsic tau harmonic guidance strategy is proposed on the basis of general tau theory and harmonic motion. In the case of multiple UAVs, the 4D trajectories generated by the new strategy are optimized by the bionic Particle Swarm Optimization (PSO) algorithm. In order to ensure flight safety, the protected airspace zone is used for collision detection, and two collision resolution approaches are applied to resolve the remaining conflicts after global trajectory optimization. Numerous simulation results of the simultaneous arrival missions demonstrate that the proposed method can effectively provide more flyable and safer 4D trajectories than that of the existing methods.

Decentralized 4D Trajectory Generation for UAVs Based on Improved Intrinsic Tau Guidance Strategy

A decentralized four-dimensional (4D) trajectory generation method for unmanned aerial vehicles (UAVs), which uses the improved intrinsic tau gravity (tau-G) guidance strategy, is presented in this paper. Based on general tau theory, the current tau-G strategy can only generate the 4D trajectory with zero initial and final velocities, which is not appropriate for decentralized applications. By adding an initial velocity to the intrinsic movement of tau-G strategy, the improved tau-G strategy can synchronously guide the position and velocity to the desired values at the arrival time. In our decentralized 4D trajectory generation method, the improved tau-G strategy is used to plan the 4D trajectories for UAVs. To deal with environmental uncertainty and communication limitations, the receding horizon optimization driven by both sampling time and conflict events is utilized to renew trajectory parameters continually. The simulation results of challenging time-constrained tasks demonstrate that the proposed method can efficiently provide safer and lower-cost 4D trajectories.