Tau Theory Research Articles

Kinematic development of infants and their interaction with their mothers during specific tasks

Everyday social projects exhibit regular action patterns structured by their motor goals. Shared understanding is developed in infancy in participation in common motor projects by learning anticipations of their motor intention, such as during feeding, being picked up or put down, and in play. Co-operative, participatory games and rituals enacted every day by mothers and babies likely establish distinct, culturally specific motor styles. Generation of non-verbal embodied understanding is dependent on intent participation, and requires co-ordination and contingent timing of actions from both mother and baby. In this study, we examine the action patterns of mothers and their babies from Japan and Scotland during every day games and rituals. Goal-directed movements within these are analysed for their prospective control of action using General Tau Theory, a mathematicopyschophysical theory of prospective perceptual control of movement shown to be universally basic in animal motor control [3] and [4].

Bioinspired 4D Trajectory Generation for a UAS Rapid Point-to-Point Movement

A bioinspired trajectory generation approach for Unmanned Aerial System (UAS) rapid Point-to-Point (PTP) movement was presented. The approach was based on general tau theory developed by biologists from observing and studying the behavior of birds and some other animals. We applied the bioinspired approach to the rapid PTP movement problem of a rotary UAS and derived two different trajectory planning strategies, namely, the tau coupling strategy and the intrinsic tau gravity guidance strategy. Based on general tau theory, according to the dynamic model of UAS, we presented a new strategy named intrinsic tau jerk guidance which can fit the movement that the initial acceleration of the UAS is zero. With new strategies, flight trajectory generation examples with a UAS were presented. The kinematics and dynamics analyses of the UAS for rapid PTP movement were presented with simulation results which show that the generated trajectories were feasible.

Bio-inspired Trajectory Planning for Robot Catching Movements Based on Tau Theory

A bio-inspired trajectory planning method for robot reaching movement to catch an object is presented. The method is based on the Tau theory which has been established by cognitive science researchers from studying the natural motion patterns when animals(including humans) approaching and catching a target object. Based on the Tau theory, two fundamental motion strategies, namely, the Tau coupling strategy and the intrinsic Tau-g guidance strategy have been analyzed. In order to solve the problem that the initial acceleration value is nonzero in the intrinsic Tau-g guidance strategy, a new strategy, namely, the intrinsic constant jerk Tau guidance strategy is presented. The trajectory planning formulae based on the Tau theory are derived. Trajectory planning, kinetics analysis, dynamic analysis, computer simulation and experiments are performed on a 3-DOF planar manipulator. The results show that, by using the proposed method, the end-effector can achieve reaching the target position and attitude at the same definite time with good continuity of joint velocity and acceleration, and the trajectory in Cartesian space is a straight path with a smooth bell-shaped velocity profile.

Bio-Inspired Trajectory Generation for UAV Perching Movement Based on Tau Theory

This paper offers a bio-inspired trajectory generation method for UAV/MAV perching (i.e., the final approach to, and landing on, a target). The method is based on tau theory, which was established based on the study of the natural motion patterns of animals (including humans) when they approach a fixed or moving object for perching or capturing prey. In our research, tau theory is applied to the trajectory generation problem of an air vehicle for perching on a target object. Three bio-inspired strategies, namely the tau in the action gap strategy, the tau coupling strategy and the intrinsic tau gravity strategy are studied for perching tasks. A key parameter of the method inspired by biological systems is discussed. Two perching scenarios, one from a flight state (with non-zero initial velocity) and one from a hovering state (with zero initial velocity), are studied. Numerical simulations with a rotary vehicle are presented as examples to demonstrate the performance of the proposed approach. The simulation results show that the resulting flight trajectories meet all the desired requirements for the vehicle in perching on an object.

Four-dimensional guidance and control of movement using time-to-contact: Application to automated docking and landing of unmanned rotorcraft systems

This paper presents the development and experimental validation of a bio-inspired autopilot, called TauPilot, based on the ecological tau theory proposed by the psychologist David Lee. Tau theory postulates that animals and humans use a combination of simple guidance strategies and the tau variable (τ) (representing time-to-contact) to prospectively guide and control most of their purposeful movements. This research investigates the feasibility and effectiveness of applying tau theory principles to guidance and control of movement in four dimensions (three spatial dimensions plus time), with application to various crucial maneuvres of unmanned aircraft systems (UAS) such as braking, automated aerial docking and automatic landing. TauPilot includes a tau-guidance system, a tau-navigation system and a tau-controller, resulting in a four-dimensional (4D) guidance, navigation and control system that has the capability to accurately fit maneuvres or actions into 4D slots using only the universal temporal variable, tau. TauPilot has been integrated into two rotorcraft UAS and demonstrated in more than 1000 successful tau-controlled flights. TauPilot provided the UAS with the capability to perform the following maneuvres with high spatial and temporal accuracy: tau-braking, 4D straight- and curved-path tau-docking to a virtual target (a three-dimensional point in space), vertical and 4D coordinated tau-landing, and 4D tau-interception of a moving target point.

Tau Coupling Investigation Using Positive Wavelet Analysis

The investigation of motion guidance and its subsequent application using tau () theory relies on the accurate calculation of the coupling term between the (time to contact) of the motion and the appropriate guide. However, the traditional approach for this calculation can be numerically unstable, requires experience and skill to execute in a meaningful manner, is sensitive to the data selected, and has limited application when the motion information is incomplete or deviates from the ideal. To deal with these issues, a new approach, based on positive wavelet analysis, is proposed in this paper. The mother wavelet is constructed using the desired -guide shapes, with its scale considered to be defined by the maneuver period. The scale and time information of interest are found by searching for the best local correlation within the whitened original signal. An inverse dewhitening process is then used to reconstruct an approximation to the original motion signal. The adequacy of the positive wavelet method has been demonstrated using data obtained from piloted simulation test campaigns. The results show that the approach is not only feasible, but it has better numerical stability, reliability, enhanced performance, and wider applicability than those that have been used to date.

Temporal guidance of musicians’ performance movement is an acquired skill

The ancillary (non-sounding) body movements made by expert musicians during performance have been shown to indicate expressive, emotional, and structural features of the music to observers, even if the sound of the performance is absent. If such ancillary body movements are a component of skilled musical performance, then it should follow that acquiring the temporal control of such movements is a feature of musical skill acquisition. This proposition is tested using measures derived from a theory of temporal guidance of movement, "General Tau Theory" (Lee in Ecol Psychol 10:221-250, 1998; Lee et al. in Exp Brain Res 139:151-159, 2001), to compare movements made during performances of intermediate-level clarinetists before and after learning a new piece of music. Results indicate that the temporal control of ancillary body movements made by participants was stronger in performances after the music had been learned and was closer to the measures of temporal control found for an expert musician's movements. These findings provide evidence that the temporal control of musicians' ancillary body movements develops with musical learning. These results have implications for other skillful behaviors and nonverbal communication.

Asymmetric stochastic Tau Theory in car-following

In this paper, we examine the distribution of headways collected from Next Generation SIMulation (NGSIM) datasets. Statistics show that the observed headways follow a certain log-normal type distribution within each preselected velocity range. To explain this phenomenon, an asymmetric stochastic extension of the Tau Theory is proposed. This novel approach assumes that the observed headway distributions are due to drivers' continuous headway adjustment behaviours, and that the intensity of headway change is proportional to headway magnitude. The agreement between the model predictions and the empirical observations indicates that driving behaviours may be implicitly governed by the physiological Tau characteristics of drivers. Keywords: Close following, gap acceptance

Bio-inspired approach for a space manipulator to capture a tumbling object with minimal impact force

This paper presents a bio-inspired methodology aimed at achieving minimal impact force to the robot and the base satellite during a robotic capturing task for a satellite on-orbit servicing mission. First, from the assumed visual observation of the target satellite’s motion, an optimal time and target configuration for the capturing operation are obtained. The optimal time is a future time such that, when the robot touches the tumbling object, there will be zero or minimal attitude disturbance in the base satellite. Second, tau theory is employed to plan an end-effector motion trajectory which will be used to guide the robot to reach the target at the optimal time. Tau theory is utilised because it has been found to be the natural way that a human arm and some animals use to reach an object for capture, thus it has been optimised through the natural evolution and is worthy of study. Two simulation examples are given to show the performance of the presented methodology and comparisons with a traditional path planning method are discussed. A comparison of the method with a traditional path planning method is also discussed.

Prospective guidance in a free-swimming cell

A systems theory of movement control in animals is presented in this article and applied to explaining the controlled behaviour of the single-celled Paramecium caudatum in an electric field. The theory-General Tau Theory-is founded on three basic principles: (i) all purposive movement entails prospectively controlling the closure of action-gaps (e.g. a distance gap when reaching, or an angle gap when steering); (ii) the sole informational variable required for controlling gaps is the relative rate of change of the gap (the time derivative of the gap size divided by the size), which can be directly sensed; and (iii) a coordinated movement is achieved by keeping the relative rates of change of gaps in a constant ratio. The theory is supported by studies of controlled movement in mammals, birds and insects. We now show for the first time that it is also supported by single-celled paramecia steering to the cathode in a bi-polar electric field. General Tau Theory is deployed to explain this guided steering by the cell. This article presents the first computational model of prospective perceptual control in a non-neural, single-celled system.

Beyond “Error-Correction”

Beyond “Error-Correction”

Tau Guidance in Boundary-Avoidance Tracking - New Perspectives on Pilot-Induced Oscillations

DOI: 10.2514/1.54065 Tau theory, introduced to the flight control discipline as a model for natural guidance, is shown to provide an approach to predicting a class of adverse aircraft-pilot couplings described as boundary-avoidance tracking events and pilot-induced oscillations. These have previously been modeled a posterior as discrete events using timedependent feedback gains. Drawing on the prospective nature of the time-to-contact variable optical tau � , a new method is proposed for modeling such phenomenon and also for determining the critical incipience for this class of aircraft-pilotcoupling.Inthepresentstudy,theapproachhasbeenappliedtotauguidanceinarotorcrafttrajectory tracking maneuver, to predict the conditions under which aircraft-pilot couplings may occur. In addition, a strong correlation between motion and control activity and the derivatives of tau adds substance to the hypothesis that the pilot’sperceptualsystemworksdirectlywithinvariantsintheoptical flowduringvisualguidance.Resultsfrom flight simulation tests conducted at the University of Liverpool and complementary flight tests carried out with the National Research Council (Canada) advanced systems research aircraft in-flight simulator support the tau control hypothesis. The theory suggests ways that pilots could be alerted to the impending threat of such adverse aircraftpilot couplings.

Haptic distal spatial perception mediated by strings: Haptic “looming”.

Five experiments tested a haptic analog of optical looming, demonstrating string-mediated haptic distal spatial perception. Horizontally collinear hooks supported a weighted string held taut by a blindfolded participant's finger midway between the hooks. At the finger, the angle between string segments increased as the finger approached collinearity with the hooks, just as the optical angle subtended by an approaching object increases. The vertical force component at the finger is potentially informative for perception, approaching zero at finger-hook collinearity. In Experiment 1, participants judged hook height reasonably accurately. To retain force relationships but eliminate immediate skin contact, Experiment 2 employed a hand-held rod; results replicated those of Experiment 1. Experiment 3 replicated Experiment 2 using a ring instead of a rod. In all three experiments, estimated hook height closely paralleled actual height, r > .9. Experiments 4 and 5 showed that participants could project impending finger-hook collinearity when finger contact with the string was interrupted during its traverse. Perceivers' estimate errors were nearly perfectly predicted by height-force ratio relationships (Rs > .96). Outcomes are related to optical and acoustic looming, dynamic touch, tau theory, and Gibsonian perceptual theory.

Las bases psico-biológicas de la comunicación intersubjetiva en el arte

En estas páginas hacemos una breve revisión de las bases psico-biológicas sobre las que fundan las experiencias musicales, en particular las que posibilitan la comunicación entre el artista y el público. Nuestra mirada se centrará en las relaciones entre el sonido y el gesto como manifestaciones corporeizadas de las intención comunicativa del intérprete. Se revisan los conceptos de Formación Motívica Intrínseca y Pulso motor Intrínseco, y su relación con la idea de Cognición como sistema dinámico. Se tratan la teoría de los Osciladores Adaptativos Biológicos y la teoría Tau en tanto que con-tribuyen a entender el ensamble de coordinaciones sensorio-motrices en la ejecución. Posteriormente se desarrolla la incidencia de los mecanismos de simulación interna en la comunicación, para analizar finalmente el funcionamiento de estos procesos en la comunicación entre el intérprete cantante y el público.

Judging the ‘passability’ of dynamic gaps in a virtual rugby environment

Affordances have recently been proposed as a guiding principle in perception–action research in sport (Fajen, Riley, & Turvey, 2009). In the present study, perception of the ’passability’ affordance of a gap between two approaching defenders in rugby is explored. A simplified rugby gap closure scenario was created using immersive, interactive virtual reality technology where 14 novice participants (attacker) judged the passability of the gap between two virtual defenders via a perceptual judgment (button press) task. The scenario was modeled according to tau theory (Lee, 1976) and a psychophysical function was fitted to the response data. Results revealed that a tau-based informational quantity could account for 82% of the variance in the data. Findings suggest that the passability affordance in this case, is defined by this variable and participants were able to use it in order to inform prospective judgments as to passability. These findings contribute to our understanding of affordances and how they may be defined in this particular sporting scenario; however, some limitations regarding methodology, such as decoupling perception and action are also acknowledged.

The Dispersion of Water Proton Spin-Lattice Relaxation Rates in Aqueous Human Protein HC (α 1-Microglobulin) Solutions

The (1)H NMR Fast Field Cycling relaxometry was applied to study the molecular dynamics of the human protein HC (alpha (1)-microglobulin), its hydration and aggregation in solution state. The (1)H NMRD data have revealed the complex nature of the water/protein HC system resulting from the co-existence of monomer and dimer forms of the protein in solution as well as the presence of oligosaccharides linked to the polypeptide chain. A comparison of the average correlation time values <tau (c)> obtained from the model-free fits with the values predicted on the basis of hydrodynamic tau (r) theory, suggests that the dynamics in solution state is governed mainly by the dimer form of the protein HC (the dominant contribution to the water proton-spin lattice relaxation comes from exchanging protons from the surface of the dimer). The existence of small number of oligomeric forms of the protein HC in solutions is postulated because of the two-step shape of water proton spin-lattice relaxation rate dispersion profiles.

Detecting Deceptive Movement in 1 vs. 1 Based on Global Body Displacement of a Rugby Player

A key to success in many sports stems from the ability to anticipate what a player is going to do next. In sporting duels such as a 1 vs. 1 in rugby, the attacker can try and beat the defender by using deceptive movement. Those strategies involve an evolution of the centre of mass (COM) in the medio-lateral plane, from a minimal state to maximal displacement just before the final reorientation. The aim of this work is to consider this displacement as a motion-gap, as outlined in Tau theory, as a potential variable that may specify deceptive movement and as a means of comparing anticipatory performance between mid-level players and novices in rugby. Using a virtual reality set-up, 8 mid-level rugby players (ML) and 8 novices (NOV) observed deceptive (DM) and non-deceptive movements (NDM). The global framework used an occlusion time paradigm with four occlusion times. Participants had to judge the final direction of the attacker after the different cuts-off. For each movement and at each occlusion time, we coupled the ability to predict the good final direction with the value of the COM displacement in the medio-lateral (COM M/L) plane or with the Tau of this parameter (Tau COM). Firstly, results show that the Tau COM is a more predictive optical variable than the simple COM M/L. Secondly, this optical variable Tau COM is used by both groups, and finally, with a specific methodology we showed that mid-level players have significantly better anticipatory ability than the novice group.

TauG-guidance of transients in expressive musical performance

The sounds in expressive musical performance, and the movements that produce them, offer insight into temporal patterns in the brain that generate expression. To gain understanding of these brain patterns, we analyzed two types of transient sounds, and the movements that produced them, during a vocal duet and a bass solo. The transient sounds studied were inter-tone f (0)(t)-glides (the continuous change in fundamental frequency, f (0)(t), when gliding from one tone to the next), and attack intensity-glides (the continuous rise in sound intensity when attacking, or initiating, a tone). The temporal patterns of the inter-tone f (0)(t)-glides and attack intensity-glides, and of the movements producing them, all conformed to the mathematical function, tau (G)(t) (called tauG), predicted by General Tau Theory, and assumed to be generated in the brain. The values of the parameters of the tau (G)(t) function were modulated by the performers when they modulated musical expression. Thus the tau (G)(t) function appears to be a fundamental of brain activity entailed in the generation of expressive temporal patterns of movement and sound.

Investigation of the Flare Maneuver Using Optical Tau

Airline transport operations are carried out in a wide range of visual and instrument meteorological conditions. However, the pilot can choose to land the aircraft manually using the visual cues available for all but the most limiting of degraded visibilities. How this is achieved may seem rather obvious, but has challenged researchers for some time. Optical flow theory offers a solution: pilots detect motion from the surfaces over which they move. In a relatively recent incarnation, flow theory transforms motion into the temporal, time-to-contact parameter, tau. Research conducted at Liverpool has applied this theory to low-level helicopter flight. The present paper extends the application to the fixed-wing flare. Flight simulation results show that tau-guidance strategies exist for this maneuver. It is shown that, as expected from tau theory, the pilot-selected values of the rate of change of tau with time, tau-dot, and the tau-guide coupling constant, directly influence the acceptability of the touchdown rate achieved. Degraded visual environments are shown, under certain circumstances, to cause a breakdown in the tau relationships observed. Potential uses of these results are presented in terms of application to future pilot vision aids, which is the planned next stage of this work.

Progress in the development of guidance strategies for the landing flare manoeuvre using tau‐based parameters

PurposeTo provide a progress report into research conducted to establish guidelines for the development of guidance vision aids.Design/methodology/approachThe first stage of the research is to establish a coherent engineering basis for the methods of (visual) motion perception and control to inform the design of pilot aids that will support flight in degraded visual conditions, particularly when close to the ground. The next stage will then be to construct and evaluate synthetic displays that recover the visual cues necessary to allow flight in degraded visual conditions for a range of manoeuvres using the flight simulation facilities at the University of Liverpool (UoL). The research is guided by tau (time to contact) theory from the field of ecological psychology.FindingsThe closure of spatial gaps for a number of aircraft manoeuvres are presented in the tau domain. Analysis of the landing flare manoeuvre suggest that both a constant rate of change of tau strategy and an intrinsic tau‐guidance strategy will yield benefits in terms of touchdown descent rate if presented as display symbology.Research limitations/implicationsResults are presented from trials where only one professional pilot was used. Results from a wider population of pilots need to be analysed to ensure that the observed trends are generic.Practical implicationsThe reported results are being used in the next phase of the research project to inform the design of a guidance vision‐aid for the flare manoeuvre. These displays will be tested in flight simulation trials.Originality/valueThe research takes a theory of motion perception and applies it to aircraft guidance display technology.