EP3849675B1

EP3849675B1 - Integrated method and system for the dynamic control of the speed of a treadmill

Info

Publication number: EP3849675B1
Application number: EP19778664.3A
Authority: EP
Inventors: Stefano MARCANDELLI; Alessandro CARMINATI; Ivan Belotti; Rudi PIRANI; Adriano PIZZOLANTE
Original assignee: Tecnobody SpA
Current assignee: Tecnobody SpA
Priority date: 2018-09-13
Filing date: 2019-09-05
Publication date: 2024-05-29
Anticipated expiration: 2039-09-05
Also published as: WO2020053711A1; EP3849675A1

Description

The present invention relates to an integrated method and an integrated system for the dynamic control of the speed of an exercise treadmill.
The first treadmill machine was produced over 50 years ago. Notwithstanding this, according to all the persons skilled in the art there still remains even today what amounts to its major limitation, namely, that of maintaining a fixed speed. This limitation has discouraged persons whose job is to analyse the walking and running capacities of subjects from using treadmills. One of the most interesting and revolutionary challenges of current research into treadmills is to render the walking and running thereon as natural as possible.
The present applicant currently markets a treadmill integrated with a 3D video camera and load cells, which enables evaluation of the movement of the user by providing space-time indicators of the subject's gait using the aforesaid two sensors.
In fact, for human beings, the most natural way of moving around is walking. Normal walking is seldom at a steady or constant speed but consists of continuous adjustments.
The improvements that can be obtained by exploiting a system for automatic control of walking speed are by now well known, and for this reason there exists, in the literature, a wide range of systems that endeavour to achieve the desired aim.
The majority of known control systems use infrared, ultrasound, or laser sensors for detecting the position of the user, and on the basis of this datum, accelerate or decelerate the belt, with the aim of maintaining a pre-set position, such as for example in the following papers: "An Interactive Treadmill Under a Novel Control Scheme for Simulating Overground Walking by Reducing Anomalous Force" by Jonghyun Kim, Hyung-Soon Park, and Diane L. Damiano, IEEE/ASME Transactions on Mechatronics, ; and "Making virtual walking real: Perceptual evaluation of a new treadmill control algorithm" by Jan L. Souman, Paolo Robuffo Giordano, Ilja Frissen, Alessandro De Luca, and Marc O. Ernst (in ACM Transactions on Applied Perception, Volume 7, Issue 2, February 2010).
Some studies exploit, instead, information coming from force sensors arranged underneath the belt in an endeavour to estimate the speed of the belt, such as for example in the patent No. US9526451 or in the paper "An intelligent treadmill system for running training: control of belt speed and biofeedback" by Akinori Nagano, Shoichi Kato, Kazutaka Iwao, and Zhi-wei Luo, 31st International Conference on Biomechanics in Sports (2013); as well as in the paper "An adaptive treadmill-style locomotion interface and its application in 3-D interactive virtual market system" by Haiwei Dong, Zhiwei Luo, Akinori Nagano, and Nikolaos Mavridis, Intelligent Service Robotics (July, 2012), whereas yet other researchers have used inertial sensors applied to the arms or legs of the subject in order to seek to bring back the measurement to the actual speed of the body, such as for example, in the paper "Ambulatory running speed estimation using an inertial sensor", Shuozhi Yang, Chris Mohr, and Qingguo Li, Gait & posture (July, 2011).
Other studies exploit, instead, information detected by a 3D video camera. For instance, it is possible to use a machine-learning algorithm to predict the speed at which a person wishes to move starting from his posture and from the position of his limbs, such as for example, in the document No. CN108114405 .
Unfortunately, all the methods cited above are subject to certain problems that render their wide-scale use problematical or even impossible, above all for reasons of safety.
Analysing the systems that use inertial sensors, it is immediately evident that deriving the speed of the user starting from the speed of a limb is a practice that is too approximate to be able to construct a reliable and safe system, this on account both of the subjectivity of the movement measured and of the absence of feedback, rendering the control system an open-loop system.
Systems that use force sensors set underneath the belt are perfectly valid for predicting the speed at which the user wishes to move; unfortunately, also these suffer from the absence of a feedback on which to close the control loop. Moreover, the estimation of the speed starting from the force suffers from the problem of drift, caused by the operations of integration that it is necessary to perform.
Systems that are based upon the use of sensors capable of detecting the distance of a body are, instead, very stable. They in fact make it possible to have a position feedback to be compared with a pre-set value (e.g., the centre of the belt), thus calculating an error that is to be minimised by varying the speed set for the belt. Also this method presents, however, marked limitations as regards achieving a natural walk: it is, in fact, not able to establish with the necessary promptness the intention of the user to accelerate. Having as sole feedback the position of the user means having to intervene on the speed only when the body of the subject has effectively displaced in space, it being necessary to face a compromise between the length necessary for the treadmill to allow the subject to safely accelerate and the acceleration that we want to set on the belt in order to follow the intentions of the subject. To cause the variation of speed of the user to be natural, the control system must seek to estimate as fast as possible the intention of the subject. The aim is not to intervene too sharply on the acceleration of the belt, which would otherwise cause a negative sensation for the
person, in addition to entailing safety problems. It would be possible to consider limiting the maximum acceleration of the belt, but this would cause the need to lengthen the treading surface of the treadmill beyond reasonable commercially acceptable values.
The aim of the present invention is to provide an integrated method for the dynamic control of the speed of a treadmill that will overcome the drawbacks of the prior art.
Another aim of the present invention is to provide a method that enables the user to replicate his normal walk on the treadmill.
According to the present invention, said aims and others still are achieved by an integrated method for the dynamic control of the speed of a treadmill according to the accompanying claims.
Further characteristics of the invention are described in the dependent claims.
The advantages of this solution as compared to the solutions of the prior art are numerous.
The control system according to the present invention is able to achieve excellent results both as regards user experience and as regards safety. It manages to estimate the speed of the subject using parameters coming from a 3D video camera that must be able to recognise the human body and estimate the position of each joint of the person at every instant, combined with a force sensor and, by using a purposely constructed fusion algorithm, to exploit the advantages of both, obtaining an estimation of the speed that is very fast thanks to the force data and very precise thanks to the compensation given by the position.
A treadmill according to the present invention, equipped with a control system, that is able to dynamically adapt the speed of the belt on the basis of the speed of the user, and is able to solve the problems described below.
In the treadmills provided with a system for evaluation of movement the only method for defining the speed that is most suited for the user is the empirical one. In fact, when a neurological/orthopaedic subject is required to walk on the treadmill in order to assess his/her condition, it is not possible to know beforehand the most suitable speed at which he/she can walk, but tests must be conducted before finding
the correct speed, with a consequent risk for the safety of the subject himself/herself. Moreover, during the rehabilitation stage, the speed of the subject is evolving continuously, and the control system enables adaptation to this variable speed.
Normally, it is not possible to use treadmills to conduct performance tests. The treadmill is incapable of adapting its speed in a natural way, but this can only be obtained by interaction between user and machine.
In the cases where the user of the treadmill is unable to withstand for a long time the effort due to walking, there arises the need for a continuous manual reset of the speed.
In treadmills provided with virtual reality, the experience of the user is not altogether immersive. The need to vary the speed by interacting with the treadmill constitutes a distraction for the user.
Moreover, all the systems operation of which is based upon the data coming from a single type of sensor, and hence a single physical quantity for control of the speed of the belt, present a lower level of precision and reliability as compared to a method that exploits the use of different sensors that detect two or more different physical quantities.
The characteristics and advantages of the present invention will emerge clearly from the ensuing detailed description of a practical embodiment thereof, illustrated by way of non-limiting example in the annexed drawings, wherein:

Figure 1 is a block diagram of an integrated system for the dynamic control of the speed of a treadmill, according to the present invention;
Figure 2 shows a first embodiment of a treadmill, according to the present invention;
Figure 3 shows a second embodiment of a treadmill, according to the present invention;
Figure 4 shows a third embodiment of a treadmill, according to the present invention;
Figure 5 shows a block diagram regarding calculation of the speeds V1, V2, and V3, according to the present invention;
Figure 6 shows a graph of the measurements made by the system regarding a user who, starting from a stationary condition on the treadmill, makes the first step, according to the present invention.

With reference to the attached figures, an integrated system for the dynamic control of the speed of a treadmill according to the present invention comprises: a treadmill 10 having a belt 11 that turns about two rollers 12; an encoder 12a for detecting the speed of said rollers; a 3D video camera 13 placed at the front of the treadmill 10, which shoots any object within a range 13a and in particular the user 14; a viewer 15; at least one sensor 16 for detecting horizontal forces applied on the belt 11, i.e., forces applied along the same longitudinal axis of the belt 11; a system 17 for acquisition of the measurements made by the sensor 16; a system 18 for acquisition of the data from the video camera 13, which is able to recognise the human body and estimate the position of the body joints in space and moreover determines the centre of mass COM of a user 14; and a data-processing unit 19, which receives the signals from the systems 17 and 18 and controls a motor 20 that moves the belt 11, for example by making one of the two rollers 12 rotate.
The 3D video camera 13 is preferably set at the front of the treadmill 10, but it may be located in other positions that make it, in any way, possible to shoot the body of the user 14 entirely.
The sensor 16 and the system 17 for acquisition of the horizontal force, are able to detect directly or indirectly the horizontal components of the forces (hence the components parallel to the treading surface of the belt 11) applied by the user 14. In order to function, said system requires one or more sensors 16, which can use the most disparate technologies.
It is possible to use: load cells (whether monoaxial, biaxial or triaxial); force transducers (of the strain-gauge type, piezoelectric type, optical type, or optical-fibre type); accelerometers (mechanical accelerometers, silicon accelerometers); inertial platforms (of a mechanical or electronic type); torque-meters or torque transducers (of the strain-gauge or piezoelectric type); pressure transducers (of the piezoelectric or mechanical type); and in any case all the technologies that enable direct and indirect measurement of a component of horizontal force applied on a treadmill.
The sensors 16 are connected to the structure (or to parts of the structure) of the treadmill.
The 3D video camera 13 is able to recognise the human body and to estimate the position of every joint thereof at any instant through body-tracking techniques adapted to the needs of the present application, i.e., to recognise a human body while it is moving on a treadmill. An example of body-tracking technique is SDK Kinect, which reconstructs the three-dimensional scene through an estimation of the depth map and recognises the human body within the area shot separating it from the background, finally estimating the position in space of the joints of the body detected.
The 3D video camera 13 consists of an RGB video camera and an infrared ray depth sensor, which is constituted by an infrared laser scanner and a video camera sensitive to the infrared of the laser. Thanks to this sensor, it is possible to obtain an RGB video image and a depth image. Some 3D video cameras that may be used in this application are, for example: Kinect One (Microsoft, Redmond, USA), Astra Pro (Orbbec, Troy, USA), RealSense (Intel, Santa Clara, USA), and LIPSedge (LIPS, Taipei, Taiwan).
In a first embodiment of the present invention, the treadmill 10 comprises a frame 30, two rollers 31 and 32, set at the ends of the frame 30, a sliding belt 33 looped around the two rollers 31 and 32, and a surface 34 for supporting the belt supported by triaxial force transducers 35, which are preferably set at the ends of the surface 34 and are able to detect the horizontal force components (along the axis L1) developed by the user 14.
The transducers 35 are set between the surface 34 for supporting the belt and the frame 30; in particular, the surface 34 rests upon the frame 30, via the transducers 35.
The treadmill further comprises supporting means 36, which support the frame 30 on the ground.
The triaxial force transducers will detect the horizontal components transmitted by the physical contact of the user 14 with the belt 33 and hence with the surface 34 for supporting the belt, which will transfer the forces to the sensitive elements.
This system is effective, but also the horizontal force component, that develops due to friction between the belt 33 and the surface 34 for supporting of the belt, is transmitted to the transducers 35, i.e., the force generated by the weight of the user 14 who is transported by the belt 33 over a surface 34 that not is altogether without friction. This force must be considered in the subsequent calculations carried out by the data-processing unit 19.
In a second embodiment of the present invention, the treadmill 10 comprises a frame 40, two rollers 41 and 42, set at the ends of the frame 40, of which the rear one 41 is mechanically connected to a torque-meter 43, which is able to detect the horizontal force components (along the axis L1) developed by the user 14, a sliding belt 44 looped around the two rollers 41 and 43, and a surface 45 for supporting the belt that rests on the frame 40.
The treadmill further comprises supporting means 46 that support the frame 40 on the ground.
The torque-meter 43 detects the torque applied preferably to the rear roller 41, and, knowing the radius of the roller, the data-processing unit 19 computes the horizontal components developed by the physical contact of the user 14 with the belt 44.
In this case, also the horizontal force component generated directly by the accelerations and decelerations of the motor itself is transmitted to the transducer 43 and must then be subtracted in the calculation made by the data-processing unit 19.
In a third embodiment of the present invention, the treadmill 10 is constituted by a frame 50, two rollers 51 and 52, set at the ends of the frame 50, a sliding belt 53 looped around the two rollers 51 and 52, and a surface 54 for supporting the belt coupled to the frame 50.
To obtain this measurement, the treadmill 10, through its frame 50, is supported by two skids 55 and 56 that enable the treadmill 10 to translate along the longitudinal axis L1.
Set between the frame 50 and the rear skid 55 is a spherical joint 57 connected to which is a connecting rod 58, which is connected to another spherical joint 59 set on a transducer 60 fixed to the ground.
The connecting rod 58 is hence constituted by a bar that connects the two spherical joints 57 and 59 set at its ends.
The transducer 60 detects the horizontal force components (along the axis L1) transmitted by the user to the treadmill 10 (hence not to the belt 53 or to the surface 54 for supporting the belt).
The connecting rod 58 is used for transmitting only the axial components acting thereon, hence, in this case, only the horizontal ones, given that the connecting rod 58 is oriented (with its longitudinal axis) parallel to the axis L1.
The video camera 13, by means of the system 18, recognises the body of the user 14 and estimates the positions of the body joints and in particular determines the centre of mass of a user 14, and hence determines the position of the user on the treadmill.
According to the present invention, the speed of the user is computed by means of the two measurement systems present in the treadmill, namely, a speed obtained from the transducer, denoted by V1, and a speed obtained from the 3D video camera, denoted by V2.
Then the two speeds are combined in a weighted way to determine a speed V3 that the motor, that causes rotation of the belt, must have.
To compute the speed V1, it is necessary for the force transducer 16, or rather 35 or 43 or 60, to detect the horizontal component of the anteroposterior propulsive force F_AP. The processing unit 19, thanks to the data coming from the encoder 12a, makes available the value of current speed of the belt and hence its acceleration (denoted by a_belt) and the weight of the subject (denoted by P). Thanks to these data it is possible to arrive at the acceleration a_COM of the centre of mass COM of the user. $a_{COM} = (F_{AP} + P * a_{belt}) / P$
Then, by integrating the acceleration a_COM, it is possible to compute the speed V1.
The process of calculation of the speed V2, via the 3D video camera, is carried out by evaluating the variation in time of the difference x_dif between the position of the centre of mass COM of the subject, denoted by x_COM, and a reference position on the treadmill, denoted by x_ref. Calculation of x_COM is carried out thanks to the 3D video camera, which is able to recognise the human body and to estimate the positions of the body joints. Using these body joints and the anthropometric tables, which give the structural dimensions and functional dimensions of a person, it is possible to estimate the centre of mass COM of the subject who is moving on the treadmill: $x_{COM} = \sum_{n = 1}^{14} [{jprox}_{n} + ({jdist}_{n} - {jprox}_{n}) * {ATcom}_{n}] * {ATmass}_{n}$
Where: n is to the n-th body segment of the fourteen body segments considered, i.e., the one taken into account; jprox_n is the position of the proximal joint of the n-th body segment; jdist_n is instead the position of the corresponding distal joint; ATcom_n is the anthropometric table that expresses the centre of mass of the n-th body segment; and finally ATmass_n is the anthropometric table that expresses the mass of the same. The fourteen body segments detected by the video camera are: right and left hands, right and left forearms, right and left arms, right and left feet, right and left legs, right and left thighs, torso and head.
The formula computes the centre of mass of each limb, assumed as a rigid body, and multiplies it by the percentage of body weight of that specific limb (given by the anthropometric table ATmass). To understand where the centre of mass of the limb is located, the anthropometric tables are used, which yield a value of between 0 and 1, where 0 corresponds to the COM being located exactly at the proximal point and 1 corresponds to the COM being located exactly at the distal point.
The sum of the contributions of all the limbs produces the position of the centre of mass of the subject.
The model that describes the kinematic between the treadmill and the subject is described in the following system, where V2 is the contribution of speed given by the video camera and v_COM is the speed of the user: ${\begin{matrix} x_{COM}' = v_{COM} - V 2 \\ y = x \end{matrix}$
The measurement that we want to control is y, which represents the measurable value of position of the COM of the subject, whereas the variation of the position of the COM is represented by x'_COM and is given by the difference between the speed of the belt and the speed of the subject (for example, if v_COM and V2 are identical, the variation of the COM is 0, and the subject remains in the same position).
To control this system and estimate the speed at which the subject is moving and hence the speed at which the belt is to be moved we can calculate $V 2 = k * (X_{COM} - X_{REF})'$
where k is the gain of the system and x_dif = (x_COM - x_REF)' is the variation in time of the difference between the position of the user and the reference position. It has been chosen to render this gain variable to be able to adjust the reactivity of the controller in a way depending upon the speed and acceleration at which the user is moving.
Specifically, during the braking step, we can intervene in a way that depends upon the speed (i.e., is directly proportional to the speed), and hence intervene with a higher k at a higher speed.
During the acceleration step, instead, k will be inversely proportional to the speed; i.e., for higher speeds, k will be lower, whereas, for lower speeds, k will be higher.
If the subject is accelerating, the gain assumes, for example, the value of 1.8 for low speeds and a value that decreases down to 1.6 for high speeds. Decrease in the gain during acceleration at high speed has the purpose of increasing the stability of the subject, rendering the system less sensitive and hence enabling a stabler running movement. In the case of deceleration, the value of the gain of the controller varies also in this case in a way that depends upon the speed at which the user is moving. Specifically, at low speeds, the variation must occur with smooth accelerations, with a k that, for example, varies between 1.8 and 2 for speeds of up to 4 km/h. In order to decelerate at higher speeds, instead, a greater reactivity of the control will be necessary and hence a k with higher values, for example with a value of 10 for a speed of 20 km/h. At this point, the values of V1 and V2 are then filtered by a sensor-fusion algorithm with the aim of computing the best value of speed to be applied to the belt.
The sensor-fusion algorithm is implemented through a complementary filter 70 where the noisier measurement V1 and the less noisy measurement V2 are filtered according to a dynamic parameter α.
A complementary filter is a filter having the general form z=a*x+(1-a)*y where x and y are the two measurements (V1 and V2), z is the output (V3), and a is the assigned weight.
The fact that the parameter of the filter is dynamic makes it possible to prioritise the value V1 at low speeds and the value V2 at high speeds, thus obtaining a suitable value of speed V3 during all phases of the movement.
The complementary filter 70 is able to understand at each instant (on the basis of the speed at which the subject is moving) the veracity of the measurements V1 and V2 and decide how to average the two to obtain a correct value V3, using the formula $V 3 (t) = α V 3 (t - 1) + (1 - α) V 2 (t) + α V 1 (t)$
The parameter α is the dynamic weight to be assigned to V2 and V1 and assumes, for example, a maximum value of 0.5 for a speed of 0.2 km/h and a minimum value of 0.02 for speeds higher than 1 km/h; i.e., it is inversely proportional to the speed.
This makes it possible to fully exploit the information coming from the sensors at low speeds and hence to have a very high predictive power, whereas, during walking and running, it makes it possible to use more the value deriving from the 3D video camera, which, as described previously, supplies a much stabler measurement (affording, however, a lower predictive power). The value coming from the sensors, for speeds higher than 1 km/h, hence concurs to a lesser extent as compared to that coming from the 3D video camera in the calculation of the total value of the measurement, but a value of 0.02 is sufficient for the filter to predict the intention of the subject to accelerate or decelerate. The complementary filter 70 hence enables estimation of the final speed to which the belt will be moved starting from the two speeds V1 and V2 estimated by the sensor and the 3D camera.
This solution does not, however, enable estimation of the error of V1 computed starting from the detection made by the sensor, on account of the operation of integration.
Calculation of the speed via numeric integration causes an effect of drift of the measurement of speed, which, even if accurately filtered, will affect the final value of V3.
To overcome this drawback and render the measurement of V3 as precise as possible, as an alternative to the complementary filter 70, a Kalman filter is used.
In this case, instead of having at input to the filter the speeds V1 and V2, directly sent at input to the Kalman filter is the anteroposterior force F_AP, as well as the variation in time of the difference between the position of the centre of mass of the subject x_COM and a reference position on the treadmill x_ref.
In particular, the Kalman filter is an algorithm that uses a series of measurements observed in time, containing noise, and produces the estimate of a quantity in a more accurate way as compared to algorithms based upon the use of a single starting measurement.
The Kalman filter in its generic formulation is given by ${\begin{matrix} {\dot{x}}_{t} = {Ax}_{t} + {Bu}_{t} + {rx}_{t} \\ z_{t} = {Cx}_{t} + {ry}_{t} \end{matrix}$
where:

x(t) is the state of the system;
A, B, and C are, respectively, the state-transition matrix, the input-control matrix, and the measurement-observation matrix;
u(t) is the control input vector and z(t) is the measurement input vector; and
rx(t) and ry(t) are, respectively, the measurement noise and the process noise.

Specifically, the algorithm that implements the Kalman filter takes the following form: ${\begin{matrix} v_{t} = F_{t} v_{t - 1} + B_{t} {fap}_{t} + w_{t} \\ x_{t} - x_{COMt} = H_{t} v_{t} + q_{t} \end{matrix}$
where:

vt is the speed at time t that is to be applied to the belt;
Ft is the transition matrix that represents, through a physico-mathematical model, the behaviour of a subject moving on a treadmill;
Bt is the control matrix that links the anteroposterior force fap_t, computed by the longitudinal force sensor when the user is running, to the speed to be set on the treadmill;
wt is the matrix that represents the statistical uncertainty of the measurement of anteroposterior force;
Ht is the observation matrix, which links the difference between the current position of the centre of mass of the subject at time t x_COMt, computed by the 3D video camera, and a reference position xref_t to the speed to be set on the treadmill; and
qt is the statistical uncertainty of the measurement of the position measured by the video camera.

All the sensors, the video camera and the motor are connected to the data-processing unit 19 for their management, and also all the processing operations are carried out by the data-processing unit 19.
A case of use is now proposed for providing a better description of operation of this system and enabling a clearer understand of the advantages thereof as compared to current speed-control methods.
Assuming that a user is stationary at the centre of the belt and is about to move and walk, when his centre of mass COM shifts forwards in order to start walking, the acceleration to which the COM is subjected is detected in the form of force by the sensor. The force datum is sent to the processing unit, which, via the sensor-fusion algorithm, i.e., the weighted combination between the difference x_dif = x_COM - x_ref and the anteroposterior force F_AP, or between their derivatives (V1, V2), computes an estimate of the speed of the user. The estimate is made by excluding the component of force due to acceleration of the belt, because this acceleration disturbs the measurement of the actual acceleration of the COM and hence of the real intention of the subject to accelerate.
The estimated value of speed is then sent to the motor taking into account the fact that an excessively sharp acceleration of the belt might lead to a gait of the subject that is far from natural, but if it were too low it might not conform with the intention of the user.
In the meantime, the 3D video camera has identified the displacement of the subject in space and can compute his real speed. The value of real speed is sent to the processing unit, which closes the control loop of the sensor-fusion algorithm by adjusting the value of speed set by the force sensor.
It should be emphasised what this system entails an effective benefit both as regards user experience and as regards stability. To obtain a good user experience, it is indispensable for the belt to reach, with the lowest acceleration possible, the speed at which the subject intends to walk, thus simulating in a realistic way the natural conditions of walking of the user on the ground. To do this, it is fundamental to manage to estimate as fast as possible the speed at which the user wishes to walk; this makes it possible to get the belt to start first and then to reach the suitable speed reducing the acceleration to a minimum. Figure 5 illustrates the comparison between the speed estimated starting from the data of the load cells V1 and the speed estimated starting from the position of the body joints detected by the 3D video camera V2. As may be seen, the speed V1 starts to have an appreciable value before the speed V2, proving how the information coming from the load cells has a predictive value. This behaviour is due both to a greater sensitivity of the sensor and because the position of the COM starts to move before the body makes a perceptible displacement.

Claims

An integrated method for the dynamic control of the speed of a treadmill (10)
having a belt (11) that turns about two rollers (12);

a motor (20) that sets said belt (11) in action; and comprises the following steps:
determining the position of the centre of mass (x_COM) of a user (14) who moves on said belt (11) by means of a 3D video camera (13) which consists of an RGB camera and an infrared ray depth sensor and is able to shoot said user entirely (14);

determining the difference (x_dif) between said position of the centre of mass (x_COM) measured and a pre-set reference position (x_ref);

determining the anteroposterior horizontal force (F_AP) of a user (14) who moves on said belt (11);

computing a weighted combination between said difference (x_dif) and said anteroposterior horizontal force (F_AP), using a data-processing unit (19), to obtain a third speed (V3);

applying said third speed (V3) to said belt (11) by means of said motor (20); wherein

the step of computing a weighted combination comprises the step of applying said difference (x_dif) and said anteroposterior horizontal force (F_AP) to a Kalman filter,

represented by the generic formula ${\begin{matrix} {\dot{x}}_{t} = {Ax}_{t} + {Bu}_{t} + {rx}_{t} \\ z_{t} = {Cx}_{t} + {ry}_{t} \end{matrix}$
where:
x(t) is the state of the system;

A, B, and C are, respectively, the state-transition matrix, the input-control matrix, and the measurement-observation matrix;

u(t) is the control input vector and z(t) is the measurement input vector; and

rx(t) and ry(t) are, respectively, the measurement noise and the process noise.
The method according to claim 1, characterised in that the step of computing a weighted combination comprises the steps of:
computing a first speed (V1) of said user (14) on the basis of said anteroposterior horizontal force (F_AP);

computing a second speed (V2) of said user (14) on the basis of said difference (x_COM);

processing said first speed (V1) and said second speed (V2) by means of a complementary filter (70) to obtain said third speed (V3).
The method according to claim 2, characterised in that said complementary filter (70) is represented by the formula: $V 3 (t) = αV 3 (t_{- 1}) + (1 - α) V 2 (t) + αV 1 (t)$
where:
α is the weight to be assigned;

V1 is said first speed;

V2 is said second speed.
An integrated system for the dynamic control of the speed of a treadmill (10) comprising:
a treadmill (10) having a belt (11) that turns about two rollers (12);

a motor (20) that sets said belt (11) in action;

at least one sensor (16), which is able to measure the anteroposterior horizontal force (F_AP) of a user (14) who moves on said belt (11);

a 3D video camera (13), which is able to shoot said user (14) entirely and determine the position of the centre of mass (x_COM) of said user (14) who moves on said belt (11);

a data-processing unit (19) for computing the difference (x_dif) between said position of the centre of mass (x_COM) measured and a pre-set reference position (x_ref), and for computing a weighted combination between said difference (x_dif) and said anteroposterior horizontal force (F_AP), to obtain a third speed (V3) to be applied to said motor (20);

said data-processing unit (19) applies a Kalman filter to said difference (x_dif) and to said anteroposterior horizontal force (F_AP); werein said Kalman filter is represented by the generic formula ${\begin{matrix} {\dot{x}}_{t} = {Ax}_{t} + {Bu}_{t} + {rx}_{t} \\ z_{t} = {Cx}_{t} + {ry}_{t} \end{matrix}$
where:
x(t) is the state of the system;

A, B, and C are, respectively, the state-transition matrix, the input-control matrix, and the measurement-observation matrix;

u(t) is the control input vector and z(t) is the measurement input vector; and

rx(t) and ry(t) are, respectively, the measurement noise and the process noise. [c3]
The system according to claim 4, characterised in that said data-processing unit (19) computes a first speed (V1) of said user (14) on the basis of said anteroposterior horizontal force (F_AP); computes a second speed (V2) of said user (14) on the basis of said difference (x_dif); and applies a complementary filter (70) to said first speed (V1) and to said second speed (V2) to obtain said third speed (V3).
The system according to claim 4, characterised in that said at least one sensor (16) comprises triaxial force transducers (35), set at the ends of the surface (34) for supporting said belt (11).
The system according to claim 4, characterised in that said at least one sensor (16) comprises a torque-meter (43) mechanically connected to a roller (41) of said belt (11).
The system according to claim 4, characterised in that said treadmill (10) comprises a frame (50), two rollers (51, 52), set at the ends of said frame (50), and a sliding belt (53) looped around the two rollers (51, 52); said frame (50) is supported by two skids (55, 56); set between said frame (50) and a skid (55) is a spherical joint (57) connected to which is a connecting rod (58) that is connected to another spherical joint (59) set on a transducer (60) fixed to the floor, in order to detect the horizontal force components transmitted by the user (14) to the treadmill (10).