With the spectacular victories of Guga, Brazil was able to stop being the country of football to become the land of tennis, and beginners in learning to handle the racket can already count on help from Science. Together with specialists from various countries, led by the German psychologist Dagmar Sternad (of Pennsylvania State University in the United States), the Brazilian physicist Marcos Duarte, a professor at the School of Physical Education and Sport of the University of São Paulo (USP), have discovered an infallible recipe for controlling the tennis ball, so easy that even a robot is capable of managing it.
“The conventional idea is that the player spends all of his time watching the ball and the racket, and unconsciously makes the necessary adjustments to correct the movement. However, this demands lots of attention and contrasts with the easiness of the act. Consequently, we propose an alternative model, based on chaos theory” explains the researcher.
Their research was published in January in the Physical Review Edition, of the American Physical Society, and had an account given on the website of the magazineNature . Another article from the group will be circulated in October in the Journal of Experimental Psychology. However, the investigation of the movement of hitting the ball is, so to speak, but a side road on the itinerary of this young physicist, post doctorate from Pennsylvania University. His main objectives for the study are the control mechanisms of posture and of human equilibrium. In either area, Duarte has made useful and incisive discoveries.
In order to describe the movement of the ball, he used a model created, in the study of cosmic rays, by the Italian physicist Enrico Fermi (1901-1954). “We are dealing with a model of dynamic systems, whose non-linear equations bring within them the idea of chaos”, says Duarte. “From that point onwards, we concluded that, instead of controlling at each instant the position and velocity of the ball and the racket, all that a person has to do is to brake the racket before hitting the ball.” If this one and only factor – the slowing of the racket, or that is to say, its negative acceleration (deceleration) – were respected , the result would be a dynamically stable system in which any alteration in the movement of the ball would be diminished or corrected by consecutive interactions with the racket.
Vision and impact
The exact opposite would occur if the acceleration of the racket were to be positive. In this case, an eventual alteration would be accentuated, until it turned the movement of the ball uncontrollable. The third possibility, a nil acceleration (equal to zero) – that is, the movement of the racket with constant velocity –, would produce an indifferent state, in which the alterations could progress or regress, depending on other factors.
The model is to not just reconstruct the study done by Fermi at the end of the decade of the 40s, the novelty comes in its application to tennis. “Initially, we did a simulation of the model on a computer. Afterwards we confirmed the forecast results in experiments with human beings”, tells Duarte. “These individuals had no previous experience with tennis, but, after learning the task, they arrived, in theory, very close to the ideal acceleration: a negative value but not excessive. It was enough to control this single variable in order to obtain adroitness.”
To isolate the phenomenon and to avoid the effects produced by other factors – such as, for example, the lateral inclination of the racket –, in one of the experiments the researchers coupled to it a device like a seesaw. The tests moved the “seesaw” and this communicated the movement of the racket. In this manner, the trajectory of the racket remained rigorously registered in a vertical plane.
“We also attempted to eliminate various peripheral pieces of information, such as those provided by vision and by the sensation of movement as a result of the impact of the ball on the racket”, informs the physicist. To comply with the first condition, it was enough to blindfold the people. The second demanded a more complicated contrivance: to connect a robotic arm between the subject and the racket. “To our surprise, we verified that the performance of the individuals is more harmed by the elimination of movement information than by the suppression of vision.”
Training a robot
With everything that they had learned in the experiments, they arrived at the most entertaining step: to teach a robot to hit the ball. They didn’t do this in the classical manner, with TV cameras accompanying the movements of the racket and of the ball and computers calculating, moment by moment, their trajectories. It was enough to program the robot to give to the racket a negative acceleration of the appropriate intensity.
“This robot is not being developed to play tennis with Guga. It has the ability of a child of two years, and this is the maximum that we can aim at for at the moment”, says Duarte. “When we consider that, in a game essentially mental such as chess, the Deep Blue robot was capable of beating the Russian world champion Garry Kasparov, it gives us an idea of how complex is the movement of the human body.”
The physicist knows well what he is speaking about, because his research line, focused on the control of posture and of equilibrium, makes clear all of the complexity involved in an activity as simple as standing on one’s feet. In these studies, which have already brought him eight published papers in international specialized magazines, the Brazilian had as his supervisor during his post doctorate studies the Russian mathematician Vladimir Zatsiorsky. We are speaking of the ex-director of the legendary Central Institute of Physical Culture of the former Soviet Union, the champion factory responsible for the gold medals of the Olympic teams. Zatsiorsky, who today lives in the United States and has re-directed his attention from the area of gymnastic sports to health, continues his collaboration with Duarte.
“We want to discover how the human being controls his posture, so that we can understand how he loses that control”, underlines the researcher. This question is especially significant for the elderly. One in three people over 65 years of age falls at least once a year. Also, these falls, which generally end up in fractures of the hip or femur, are, through their complications, the second highest factor of deaths by accident. In the United States, the burden of these accidents on the health services is of the order of billions of dollars per year.
For this reason, governments and private institutions of various countries are investing large sums of money in the study of the natural mechanics of posture control and equilibrium. As part of his project, Duarte has just complete the mounting, in the School of Physical Education of USP, a laboratory which has the most advanced investigation equipment on this theme.
A force plate
On a small platform on the floor of his laboratory, the researcher points to a piece of equipment which he considers to be the most important: a force plate which measures whatever force is placed upon it. Its working is analogous to a scale, but, while this only determines one’s weight – a vertical force, from top to bottom –, the plate is capable of detecting forces that take place in all directions, as well as their points of application. “We ask a person to stand on top of it for half an hour, and through software that we have developed, we are capable of identifying, classifying and quantifying, all of the changes of posture that occur during this period of time”, he explains.
One of the objectives is to study the so called natural erect posture, the one people assume for example when they are on their feet, waiting for a bus.”We never stay totally immobile”, assures Duarte. “While on our feet, our body carries out all of the time small oscillations that help us to relieve fatigue. On average, we carry out a change of posture every thirty seconds.”These changes can be reduced to three basic types. The first is the shift that happens when the subject changes his mean position, for example, transferring the weight from one foot to the other. The second, the fidget , is a rapid movement of returning to the previous position. The third, called drift , is the tendency that people have to divert, or that is to move slowly from one side to another.
The shift and the fidget had been known for a long time. They are natural mechanisms that allow the effort to transfer from a determined group of muscles to others, stimulate the blood circulation and relieve the pressure on the support points previously solicited, in a way which prevents edemas. The contribution of the researcher was to rigorously quantify these movements, only previously registered in a subjective manner.
Variation is fractal
However, the drift is a new discovery, a very slow movement that can only be observed thanks to the ability of the apparatus. Its cause is much more difficult to determine. Why do people drift? Why do we tilt sluggishly to one side and then return with equal slowness to the same position? “We discovered that the reading on the force plate, that gives the information about how the individual controls his posture and equilibrium, is a fractal”, answers. Fractals are patterns that keep repeating on different scales of space or of time simultaneously.
To say that the reading on the plate is a fractal is the same as saying that the shift, fidget and the drift are variations, in different scales of the same movement. “If we adopt the shift as a reference, we can say that the fidget is composed of two very rapid shifts , of opposite senses, while the drift is a shift of long term duration”, he explains.
For him, this association perhaps clarifies the mystery of the drift, which appears to be a body strategy that allows for obtaining the same effects produced by the shift with less consumption of energy per unit of time. In another way, it is an intelligent form of changing the support points, of redistributing the weight and of promoting the circulation of the blood.
The current phase of the studies already allows us to have the first idea of how a healthy adult controls his posture. Beginning from there, it is possible to begin to understand the progressive loss of control that accompanies aging, principally in those who do not practice an adequate and regular physical activity. To control the movement anterior-posterior, that is – the oscillations back and forth, the human being uses basically the ankles and the thighs. With aging, there tends to occur a loss of the so called peripheralsensibility. The more distant a part of the body is from the brain, the less sensibility the person has in that region. As a result, the maneuvering through the ankles begins to be overlooked in relation to the maneuvering through the thighs.
The problem is that the two maneuverings are not equivalent from the physical point of view. To demonstrate this principle, the researcher asked the reporter himself to stand on his feet and oscillate backwards and forwards. There really is a noticeable difference. If the oscillation is done from the ankles, we push down onto the floor clearly vertical forces. If we transfer the oscillation to the thighs, these forces become practically horizontal. The consequences are predictable:
“When he experiences a sharp loss of equilibrium, the elderly person resorts to his thighs to re-establish equilibrium. With this, he applies to the floor forces that are almost horizontal. If he is walking on a carpet with little adherence to the floor or on a slippery surface, he has a high probability of falling”, concludes Duarte. One of his objectives is to construct an experimental prototype that allows for measuring the two maneuvers and to help people develop those in which they feel the greater difficulty. For the elderly who lose control over their ankles, training would offer the prospect of recovery, at least partially, of this ability.
A Study of Postural Equilibrium and of the Walking of the Elderly on the Ground and in Aquatic Surroundings (nº 00/03624-5); Modality Young Researcher Program; Coordinator Marcos Duarte – Physical Education Faculty of USP; Investment R$ 223,795.04 and US$ 100,596.04