NL2023506B1 - A method, a system and a computer program product for estimating positions of a subject's feet and centre of mass relative to each other - Google Patents

Abstract

The invention relates to a method for estimating positions of a subject’s feet and centre of mass relative to each other during gait. The method comprises a step of collecting measurement data from a first inertial measurement unit located at a first foot of the subject, from a second inertial measurement unit located at a second foot of the subject, and from a third inertial measurement unit located at a pelvis of the subject. Further, the method includes a step of evaluating relative positions of the first and second foot and the center of mass of the subject over time, using the measurement data of the first, second and third inertial measurement unit.

Description

P123281NL00 Title: A method, a system and a computer program product for estimating positions of a subject’s feet and centre of mass relative to each other The invention relates to a method for estimating positions of a subject’s feet and centre of mass relative to each other during gait.

Ambulatory estimation of gait measures is useful in understanding gait patterns in healthy subjects, and also recovery in people with gait impairment. One possible ambulatory method is to use Inertial Measurement Units, IMUs. IMUs include 3D accelerometers and 3D gyroscopes, and are small and wearable. They can be used to estimate full body kinematics, and also kinetics, if a full body suit of IMUs is used. A full body suit of IMUs provides information about the individual body segments, and applying biomechanical constraints as described e.g. in the article entitled “Xsens MVN : Full 6DOF Human Motion Tracking Xsens MVN ; Full 6DOF Human Motion Tracking Using Miniature Inertial Sensors”, Tech, Rep. 3, 2009 by Roetenberg et al. improves estimation of kinematics of individual segments. Drift caused by strap down inertial navigation is prevented by using biomechanical constraints regarding the measured segments. However, when reducing the number of sensors used, the number of possible biomechanical constraints is reduced and the influence of drift increases. Another approach to ambulatory estimation of gait is the use of ForceShoes™ (reference: Weenk 2015 and van Meulen 2016). This specially designed shoe consists of an IMU, and 3D force and moment sensor for each foot. An ultrasound sensor system can be added to the setup.

Traditionally, reliable drift reduced estimations of relative distances between each foot and the pelvis, where the center of mass is assumed to lie, are estimated by either using a full body suit, which has knowledge of all individual body segments, or using sensors that measure relative foot distance, such as infrared or ultrasound sensors as in the

ForceShoeTM. These estimations are used for measuring several spatio- temporal gait parameters, including the centre of mass, CoM, base of support, BoS, and Margin of Stability, MoS, while walking. These parameters are required for estimating gait and balance quality in people.

It is an object of the present invention to provide an improved method for estimating positions of a subject’s feet and center of mass relative to each other during gait. Thereto, according to the invention, a method is provided for estimating positions of a subject’s feet and center of mass relative to each other during gait, comprising the steps of: - collecting first measurement data from a first inertial measurement unit located at a first foot of the subject; - collecting second measurement data from a second inertial measurement unit located at a second foot of the subject; - collecting third measurement data of a center of mass from a third inertial measurement unit located at a pelvis of the subject, and - evaluating relative positions of the first and second foot and the center of mass of the subject over time, using the first, second and third measurement data.

By evaluating measurement data from IMUs at the feet and the pelvis of the subject, most preferably using only three IMUs, relative positions of the feet and the center of mass of the subject, as well as velocities thereof, can be estimated over time. This is usually performed using zero velocity update, ZVU, (reference: Skog 2010) for improving the estimations from a strapdown inertial navigation method. This provides change of positions and velocities of the feet over time during a step. There is eventual issue of drift between the feet and CoM, which can be reduced or eliminated using special biomechanical constraints. This is e.g. feasible by applying the theory of zero moment point, ZMP, which provides distance relations between said center of mass and the feet without the need for additional sensing. Generally, position and/or velocity estimations are in 3D.

Further, based on the estimations, spatio-temporal gait parameters, and also balance metrics such as the Base of Support, BoS, and/or the Margin of Stability, MoS, can be measured. The relative positions may be expressed in a global reference frame that changes with the direction of gait.

Further, based on only the third measurement data, i.e. data from the inertial measurement unit at the pelvis of the subject, force vector components exerted at the center of mass of the subject can be evaluated.

By using a special calibration method an initial estimate of orientation of the feet and pelvis can be improved. Optionally, an error extended Kalman filter, EEFK, estimates the orientation of the body during gait, which can be used for estimating the Ground Reaction Forces, GRF using just the third measurement data. The positions of the feet, CoM, and Ground Reaction Forces, GRF, can be estimated in a so-called current global frame, i.e. a fixed frame of reference for the body. Different methods of estimating current global frame are feasible including a first case of defining the frame based on the pelvis orientation and the average change in direction over a cycle. A second case could be based on defining the current global frame based on the change in translation of the foot over the ground before and after a step. In both cases, the vertical axis of the current global frame is determined using inclination of gravity. The information for this current global frame can either be obtained from only the third measurement for the first case, or the first and second measurement data for the second case. Based on the information described above, foot kinematics and kinetics can be estimated, e.g. using filtering techniques such as extended Kalman filters, for estimating foot and center of mass positions over time. The estimates can be improved based on inter segmental distances measured with application of the theory of zero moment point above other commonly used biomechanical constraints., including zero velocity update. Then, human spatial and temporal gait parameters, specifically, position and velocity of a subject’s feet and position and velocity of center of mass during gait, and balance metrics can be estimated, especially using only three inertial measurement units. Balance metrics stated here may include Base of Support, BoS, and Margin of Stability, MoS.

The invention also relates to a system, comprising a first, second and third inertial measurement unit for location at the feet and pelvis respectively, as well as a processing unit for receiving respective measurement data from the inertial measurement units and evaluating relative positions of the first and second foot and the center of mass of the subject over time.

Further, the invention relates to a computer program product. A computer program product may comprise a set of computer executable instructions stored on a data carrier, such as a CD or a DVD. The set of computer executable instructions, which allow a programmable computer to carry out the method as defined above, may also be available for downloading from a remote server, for example via the Internet, e.g. as an app.

Further advantageous embodiments according to the invention are described in the following claims.

It should be noted that the technical features described above or below may each on its own be embodied in a system or method, i.e. isolated from the context in which it is described, separate from other features, or in combination with only a number of the other features described in the context in which it is disclosed. Each of these features may further be combined with any other feature disclosed, in any combination.

The invention will now be further elucidated on the basis of a number of exemplary embodiments and an accompanying drawing. In the drawing: Fig. 1 shows a flow chart of a method according to the invention;

Fig. 2 shows a system according to the invention carried by person P to be monitored; Fig. 3 shows the person P shown in Fig. 2, and two right foot positions before and after a step, and the different sources for position 5 estimates; Fig. 4 shows trajectories of zero moment point and centre of pressure during a gait cycle; Fig. 5 shows trajectories of the feet and CoM in a top-down view; Fig. 6A shows a pelvis based current global frame; Fig. 6B shows a foot based current global frame; Fig. 7 shows transformation processes to transform different frames; Fig. 8 shows an EEKF filter used for a pelvis orientation; and, Fig. 9 shows the GRF estimated using the three IMUs.

It is noted that the figures show merely preferred embodiments according to the invention. In the figures, the same reference numbers refer to equal or corresponding parts.

In evaluating the theory of Zero moment point, ZMP, it is assumed that for a stable gait pattern, the moments around the center of mass, CoM, are zero. The ZMP follows the center of pressure, CoP. Solving the ZMP assumption, relations between ZMP, CoM, and distances between the feet can be derived. This could be translated to relative distances between each foot and the CoM. This could be potential information that can reduce drift in position estimations. Therefore, the assumptions of ZMP are possible as biomechanical constraints that could be useful as a measurement update for a proposed sensor fusion filter that tracks the velocities and positions of the feet and center of mass. The assumptions of ZMP may also be used to estimate relative segmental distances and reduce drift using methods other than sensor fusion. Note that the ZMP is considered similar to a Centroidal Moment Pivot, CMP, for this application (reference: Popovic 2005) Figure 1 shows a flow chart of a method according to the invention.

The method is used for estimating positions of a subject’s feet and CoM relative to each other during gait. The method 100 comprises a step of collecting 110 first measurement data from a first inertial measurement unit located at a first foot of the subject, a step of collecting 120 second measurement data from a second inertial measurement unit located at a second foot of the subject, a step of collecting 130 third measurement data from a third inertial measurement unit located at a pelvis of the subject, and a step of evaluating 140 relative positions of the first and second foot and the center of mass of the subject over time, using the first, second and third measurement data.

The step of evaluating relative positions can be performed using dedicated hardware structures, such as FPGA and/or ASIC components. Otherwise, the method can at least partially be performed using a computer program product comprising instructions for causing a processor of a computer system to perform the above described steps. The step can in principle be performed on a single processor. However it is noted that at least a sub-step can be performed on a separate processor, e.g. a sub-step of collecting measurement data.

Further, a step of building a sensor fusion filter for fusing information from strapdown inertial navigation including zero velocity update, ZVU, and relative foot positions, based on zero moment point, ZMP, to improve foot tracking as a function of time can be implemented in the computer program product. Also, the computer readable code may include code causing a processor to perform the further step of displaying the information in a frame of reference defined with respect to the pelvis or the direction of gait as described above as a current global frame.

Generally, in strapdown inertial navigation, the position, including velocity, of a body of interest is estimated from integrating the accelerations measured on the body, after orienting it appropriately to an outside reference frame using information from the body’s angular velocity.

The accelerations and angular velocities are measured using an accelerometer and (rate) gyroscope or angular velocity sensor, respectively, placed on the body.

Optionally, the method may also use magnetometer information.

The sensor that incorporates the accelerometer(s), and gyroscope(s) or angular velocity sensor(s), is called an inertial measurement unit or IMU.

A combined sensor unit including an IMU and a magnetometer is called an inertial and magnetic measurement unit.

Generally, when referring to an IMU, the IMU might be extended to incorporate information from a magnetometer that is separate or included in a combined sensor unit.

Figure 2 shows a system 1 according to the invention carried by person P to be monitored.

The system includes three IMU’s, e.g. a first IMU 2a mounted at a first, right foot, a second IMU 2b mounted at a second, left foot, and a third IMU 2c mounted at the pelvis of the person P.

CoM is denoted as a blue circle and its projection on the ground is GP.

XCoM is a virtual point on the ground which encodes the position of CoM including its velocity.

The centre of pressure, CoP, a yellow circle, is the point of contact of the body on the ground.

The ground reaction force, GRF, acts from CoP and is directed towards the CoM as is shown as F.

Tp is the trajectory of the CoM over time.

The system 1 further includes an on-body processing unit 3 that is arranged for receiving measurement data from the respective IMUs 2, and for evaluating relative positions of the first and second foot and the center of mass CoM of the subject over time, based on said data.

Optionally, the processing unit 3 can be arranged for generating on-body feedback signals for guiding / coaching the person P based on the measurements performed.

In the shown embodiment, the processing system 3 is carried by the person P.

Alternatively, the processing unit 3 is at least partly implemented as a separate stand-alone system, such as a stationary server, for performing at least a number of the above-mentioned steps, i.e. the step of evaluating the relative positions. Here, the system 1 includes merely three IMUs 2a-c.

When applying the above method, first, second and third measurement data are collected from the respective inertial measurement units IMUs, located at the feet and the pelvis of the subject to be evaluated. In an embodiment, the data is received wirelessly to the processing unit 3 located on or outside the body. All the three measurement data should be synchronized in time and stored on a storage system that may be implemented in the processing unit 3 for further processing. This processing may include relative positions of the first and second foot and the center of mass of the subject evaluated over time, using the first, second and third measurement data.

In principle, the method may further include a step of evaluating the velocity of the center of mass of the subject over time, preferably at any moment of time, from the third measurement data from the third inertial measurement unit and may also be based on a position estimation of the center of mass as a function of time. Alternatively or additionally, the velocity of the center of mass can be estimated at any moment in time from the velocity estimates of the feet which have been corrected with biomechanical constraints such as zero velocity update.

Also, force vector components exerted at the center of mass of the subject can be evaluated, using the first, second and third measurement data. Similarly, force vector components exerted at the center of mass of the subject can be evaluated, using only e.g. the third measurement data. Then, referring to Fig. 2, a single IMU setup could be applied, the person P then carrying a single IMU 2c at the pelvis, without IMUs at the feet. An orientation of the inertial measurement unit can be estimated, preferably, using an error extended Kalman filter.

Typically, position, velocity and/or force are evaluated in three- dimensional space, 3D.

Figure 3 shows the center of mass CoM of the person P shown in Fig. 2, and two right foot positions.

Specifically, a first position P1 of the right foot, before making a step, as well as a second position P2 of the right foot, after making the step, is shown.

A trajectory T that is made during the step is also depicted, connecting the first and second positions P1, P2. Tp is the trajectory of the CoM during this step.

The figure shows a vertical line L extending from the CoM vertically downwardly to a point GP at the ground.

GP is the projection of the CoM on the ground.

The second right foot position P2 is offset from the ground point GP with a distance OFF.

The distance OFF is also defined as the distance between the contact foot and CoM in the horizontal or ground plane.

Generally, a walking pattern repetitively includes a first phase wherein a first foot is resting on a support structure supporting the first foot, and a second foot is moving, followed by a second phase wherein the second foot is resting on a support structure supporting the second foot, and a first foot is moving.

When assessing the first phase, the method may include the step of determining a first estimation of the second foot position relative to the first foot, after a step of the second foot, applying the ZMP assumption that a moment around a center of mass of the subject vanishes.

Further, the method may then include a step of determining a second estimation of the second foot position relative to the first foot, after the step of the second foot, by applying strap-down navigation estimation of displacement of the second foot during the step of the second foot, combined with initial and final conditions that follow from zero velocity update, and an estimated position of the second foot relative to the first foot, before the step of the second foot.

This results in a trajectory similar to T as shown in Fig. 3 for the second foot.

Also, the method may include a step of improving an estimation of the second foot position relative to the first foot, after the step of the second foot, by combining the first and the second estimation of the second foot relative to the first foot, preferably taking into account uncertainties of the first and second estimation, preferably using a specifically designed sensor fusion filter.

Similarly, when assessing the second phase, the method may include the steps of performing a first estimation, a second estimation and an improved estimation of the first foot position relative to the second foot, after the step of the first foot, by performing the steps defined above wherein the first foot and the second foot have interchanged.

As indicated above, the method may also comprise of first estimate of determining the velocity of the center of mass of the subject, e.g. based on the third measurement data from the third inertial measurement unit located at a pelvis of the subject, preferably including a strap-down navigation estimation. A second estimate of the velocity of the center of mass may be derived as an average velocities of the feet while moving. A fusion of first and second estimate may advantageously be used to get an improved estimate of velocity of center of mass. Further, by fusing the velocities for obtaining an improved estimate may highly improve the estimates for positions later on.

Also, the position of the center of mass of the subject as a function of time relative to the first foot when the second foot is moving and relative to the second foot when the first foot is moving may be estimated by applying the ZMP assumption that a moment around a center of mass of the subject vanishes. This leads to the estimate OFF in Fig. 3. The estimation of the position of the center of mass may be improved by including the third measurement data from the third inertial measurement unit located at a pelvis of the subject, preferably including a strap-down navigation estimation.

The method may also comprise a step of estimating the position of the center of mass of the subject during double stance based on the third measurement data from the third inertial measurement unit located at a pelvis of the subject, preferably including a strap-down navigation estimation. This is shown as Tp in Fig. 3.

Advantageously, the position estimation of the center of mass can be improved by fusing all information about center of mass movements available over time, preferably using a specifically designed sensor fusion filter Preferably, a location, in particular the height of the center of mass of the subject, can be estimated based on measurement data from an inertial measurement unit located at the pelvis of the subject, preferably by applying strap-down inertial estimation and using biomechanical constraints regarding the height of the center of mass.

Foot kinematics and kinetics can be determined relative to a frame of reference that is stationary relative to the pelvis or stationary relative a direction of gait of the subject. The first case of defining a reference frame or current global frame relative to the pelvis is performed by utilizing an information about the average heading of the pelvis as the forward direction. The second case of defining a reference frame relative to direction of gait may include a step of estimating foot kinematics and kinetics over time, based on measurement data from a first inertial measurement unit located at a first foot, and measurement data from a second inertial measurement unit located at a second foot. The change in foot positions before and after a step can be used as the forward direction to estimate a new reference frame, or current global frame. All foot and center of mass kinematics and kinetics can be expressed in the current global frame that is continuously changing. In both first and second cases of defining this current global frame, the vertical provides one of the other axes of the current global frame.

In principle, balance metrics can then be estimated, based on the kinematics of the foot and the center of mass of the subject, e.g. by performing the steps of: - estimating a base of support defined by boundaries of the feet while in contact with the ground during walking; - estimating the base of support defined by projected boundaries of the feet if either one is not in contact with the ground during walking; - estimating an extrapolated center of mass, which includes the information of velocity and direction of walking, and - estimating a margin of stability, which is the distance between the extrapolated center of mass and the base of support.

The step of estimating foot kinematics and kinetics over time may include applying a filter method including an extended Kalman filter to measurement data.

Foot kinematics can be updated over time using the first distance between the position of the first foot and the center of mass of the subject, and/or the second distance between the position of the second foot and the center of mass of the subject, which are derived from the ZMP. The foot kinematics can also be updated over time using other biomechanical constraints.

Below, three exemplary implementations are described in more detail. The first exemplary implementation explains the theory of ZMP and validates it using high resolution optical tracking systems. The example also provides an idea of the sources of error regarding the assumptions of the theory of ZMP. The second exemplary implementation describes the feasibility of deriving GRF from the minimal sensor setup. The third exemplary implementation shows the structure of the sensor fusion filter that would enable estimating the positions of a subject’s feet and centre of mass by fusing information from different sources, including ZMP.

First exemplary implementation First, the assumptions of zero moment point are to be validated. As shown in Herr 2008 (Angular moment in human walking), the ZMP (similar to the Centroidal Moment Pivot, CMP, in Herr 2008), is a point where the ground reaction force would have to act to keep the horizontal component of the whole-body angular moment constant. When these moments around the CoM is zero, the ZMP coincides with the CoP. Therefore, first, the differences between ZMP and the CoP for walking in two conditions is studied: in a normal and a casted walking condition. Following this, a relation derived from the ZMP assumption that could provide relative distances between each foot and CoM is explored. Further, an IMU example 1s Illustrated to describe steps to implement the ZMP in IMU based sensor fusion approaches.

Seven healthy female subjects were asked to walk on the GRAIL (Motekforce Link, The Netherlands). The GRAIL consists of a split belt treadmill with force plates and ten VICON motion capture cameras to collect gait biomechanics. The setup measured the 3D ground reaction forces and also the 3D kinematics of the body positions. The subjects’ average age was 22.9+1.4 years, height was 1.78+0.06m, and weight was

73.4+5.4kg . The subjects were asked to walk for 5 minutes on the treadmill at 1.2 m/s. After this, a plaster technician casted the right foot of the subject and they were asked to walk again for 5 minutes at the same speed on the treadmill. Casting was done to induce asymmetry in gait.

It is known to use a complementary filter algorithm to estimate low and high frequency components of CoM from the 3D forces and moments measured from the ForceShoe™ . Here, we apply the algorithms to measurements from the GRAIL. The first stage estimates CoM from both foot kinetic and kinematic information by low pass filtering the CoP to estimate the position of CoM.

The total body CoP is estimated as follows from the force measurements on the GRAIL (Eq. 1). CoP, = Fra COP + Fz COP Fai tz, Feat Fz

All variables in (Eq. 1) are a function of time.

Equation (1) is depicted in the global frame with Z axis positive upwards along the vertical, and X positive along the walking direction.

Here, subscript r and ! stand for the right and left foot respectively, and subscript ax corresponds to either X or Y axes.

F: refers to the force in the Z axis.

The CoP. is then low pass filtered at 0.4 Hz to obtain the CoMa1r . The second algorithm estimates CoM from kinetic information alone by double integration of the net forces based on Newton's second law.

The acceleration of the body mass muy at the CoM is given as follows (Eq. 2). oF Crom = Mi pods +o Here, F is the net force vector acting on the body, and g is the gravitational acceleration.

The change in CoM position over time was derived from integrating the acon twice.

This results in Xco:in which was high pass filtered with a cut off at 0.4 Hz to obtain CoMax.nr . This is the same cut off as that of CoMax1.r’s low pass filter.

The CoMaxrr and CoMa1F are fused using a complementary filter to obtain the trajectory of CoM.

The theory of ZMP assumes that the moment around the CoM is zero for a stable walking trajectory.

Here, ZMP is a point on the ground, such that the cross product of a vector joining the CoM and ZMP and the ground reaction force vector (F) is zero.

This gives us the following equations (Eq. 3, 4, 5): rx F=0 (CoM — ZMP)__+F, = (CoM — ZMP),-F,

IMP _=(CoM_,—(r;- i Fz In (Eq. 4), ZMP; is zero as it lies on the floor, and r; can be estimated as height of pelvis from the GRAIL system.

Therefore, (Eq. 5) provides ZMP positions in X and Y axes.

This is then compared with the CoP estimated from the treadmill force plates using (Eq. 1). The difference between ZMP and CoM gives the value of OFF.

The relation between ZMP and CoM as shown in (Eq. 5) can be utilized as additional information about relative distance between the feet and CoM.

Therefore, they can be used as measurement updates for a sensor fusion filter, if the other variables are known.

For example, during swing phase of the left foot, the CoP of the body will lie under the right foot.

Although, in an IMU based approach it is not straight forward to measure CoP of each foot, the foot positions can be estimated using an IMU on each foot, and CoM can be tracked using a pelvis IMU.

We can provide an estimate for the right foot during left foot swing phase as (Eq. 6): POS gup CoMy 0 — (72 2 Here, posaxr is position of the right foot, and subscript si denotes instances of left foot swing phase.

We have assumed that the differences in ZMP and foot position is trivial.

Subsequently, we can derive an estimate for the left foot during the swing phase of the right foot (sr), Eq. 7. Fox PoSg, = COMars — (1; EE) We then compare posax» and p08ax1 with the true foot positions at the respective instances (s/ and sr). We compare the ZMP, measured in (Eqn. 5) with the CoP measured from the treadmill force plates in GRAIL.

Then, we compare the error as a percentage of subject's foot length (35) with Herr et al 2008. Following this, we compare posaxr and posax from (Eqn. 6) and (Eqn. 7) with foot positions measured by VICON in GRAIL. Following this, we plot the trajectories of the interesting parameters in an example with IMUs.

Fig. 4 shows the normalised trajectories of ZMP and CoP in the X and Y axes for both conditions: normal and casted. The graph shown is the normalised gait cycle averaged over all subjects. The shaded regions show the standard deviation of the trajectories. The first column denotes the normal condition and the second column denotes the casted condition. Each row corresponds to one axis in the global frame. The mean absolute RMS of the differences between the ZMP and CoP over the complete cycle is shown in table I for both conditions. In table II, we compare the mean RMS of the distance between the ZMP and CoP across the gait cycle normalised by foot length (53%) with that of Herr et al 2008. Further, in table III, the mean RMS of the differences between the D08a.r and posax1 and respective foot positions from GRAIL is shown for normal and casted walking conditions.

Figure 5 shows different trajectories in a top-down view. The dark green dotted line and blue dotted lines are the left and right foot trajectories respectively, estimated from the algorithm of Weenk et al 2015 from the foot IMUs. The red dotted line is the reference centre of mass (CoM) estimated by the ForceShoeTM. The solid yellow lines are possible estimates for left foot during right swing phase, and solid green lines are possible estimates for the right foot during left swing phase. These are estimated using the CoM and zero moment point assumptions. The triangles denote the starting position of the two feet.

In practice, (Eqn. 3) is not valid. The moments around the CoM oscillate around zero. Upper body angular rotations also cause moments around the CoM. This is a missing component in (Eqn. 3). However, here we look at how the ZMP and CoP agree, during straight walking, where the moments around the CoM may be really small.

Fig. 4 shows that there is close overlap between the trajectories of ZMP and CoP for the normalised gait cycle. The gait cycle begins with right heel strike and we can see the transition of the CoP from left to the right foot. The CoP falls completely under the right foot around 15% of the gait cycle. Following the left swing phase, we notice the left heel strike around 50% of the gait cycle, as the CoP starts to move towards the left foot. The trajectory continues to the next right heel strike which is the end of the gait cycle. Looking closer, we observe that the standard deviation of the trajectories (both ZMP and CoP) are smaller during the transition from one foot to the other. In both normal and casted conditions, the trajectory of ZMP is closer to the CoP in the Y axis during these transition (double stance) phases, when compared to the swing phases. This could suggest that the moments around the CoM are smaller during double stance phase, thereby showing lower differences in the ZMP and CoP trajectories during these instances.

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BORITSUNS ST RESPECTIVETSSTSNTEN Raan RAE IRE ES RIE ES ILE S| asin [Eea | TSE 04] URE TR] TEE] Table I shows these differences as mean RMS of the differences between ZMP and CoP over the whole gait cycle. It is seen that the casting increases the error margins of the differences. Casting could induce asymmetry, causing increased rotation of the upper body to compensate for the change in walking pattern, and therefore, we see the differences in Table I. Table IT shows the mean distance between ZMP and CoP across the gait cycle, normalised by foot length of the subjects.

Table III shows the differences between foot positions estimated from CoM using ZMP assumptions and true foot positions from GRAIL system. The larger errors can be explained by the fact that we are actually comparing ZMP estimates from CoM with foot positions. We assume ZMP to lie close to CoP for each foot, and further, assume differences between CoP and foot positions to be trivial. Therefore, the table III shows the error margins associated with these assumptions. Looking closer, the table shows that the error margins are around 9.5 cm in X axis, and about 1.6 cm in the Y axis, for the normal walking condition. They show larger deviations in case of casting. These margins give us an idea of the feasibility of using ZMP based assumptions for estimating foot positions from CoM.

The minimal sensing system could consist of three IMUs; one on each foot, and one at the pelvis as seen in Fig. 2. The foot IMUs could track the movement of the feet in 3D. Measurement updates such as zero velocity update will minimize the drift in the X and Z directions. The CoM can be tracked using a pelvis IMU. Fig. 5 shows the movement of the feet and CoM for an exemplary walking measurement where the subject walks forward for about 10 metres. The ZMP assumptions could be used during left swing to estimate relative position of CoM relative to right foot. Additionally, during right swing phase, we can estimate CoM relative to left foot. If we fuse all this information, we can estimate the relative positions between the two feet during subsequent stance phases. This removes the need for full body sensing, or an inter-foot distance sensor.

Eqn. 5 also requires knowledge of the height of the CoM and forces in 3D. CoM height can be measured by the pelvis IMU, with appropriate measurement updates. Estimating forces in 3D could be solved by the descriptions in the second exemplary implementation. If we assume that the body is only in contact with the ground, then the accelerations of the pelvis could be similar to the accelerations at the CoM. This is simply the specific ground reaction forces in 3D.

The current method assumes that the CoM position is used as a reference, and the estimates of the two feet could be corrected based on (Eqn. 6) and (Eqn. 7). An alternative method is to assume the right foot to be a reference point and then estimate the CoM, and subsequently, left foot position.

The errors in table III are majorly present as we compare ZMP with reference foot positions. Therefore, a possible solution could be to measure CoP during walking, as they show lower errors with ZMP, as can be seen in table I. In an ambulatory sensing setup, these errors could be solved by using a pressure insole to measure CoP providing more accurate relative distances between CoM and either foot.

This study shows possible applications of using ZMP assumptions to reduce the lateral drift during minimal sensing of gait using IMUs. The next step is indeed to build a sensor fusion algorithm that can implement these updates iteratively. It is advised that the assumptions are studied for different walking patterns.

Second exemplary implementation The ZMP assumption mentioned earlier requires the knowledge of whole body 3D GRE.

The main goal of the second exemplary implementation is thus to evaluate the feasibility of estimating whole body 3D GRF (GRF) from a single pelvis IMU, for different walking patterns seen in daily life.

The GRF can be estimated using Newton's law, given the mass of the body and accelerations measured at the centre of mass (CoM), assuming the body is only in contact with the ground.

A special calibration procedure, and an Error Extended Kalman Filter (EEKF) are used to estimate body orientation, in order to determine the 3D components of the GRE.

The other IMUs of the three IMU setup are placed on each foot.

Using these, a changing frame of reference, that depends on the direction of step being made, 1s employed to express the GRF.

This is opposed to a commonly used fixed global frame of reference.

A reference frame that is changing with the moving body is a better option than an arbitrary fixed global frame, to express kinetics of the moving body as it will always be relative to the direction of gait.

The GRF is then compared with that measured by the reference system, which is the ForceShoeTM, and also compared with results from existing literature.

GRF are usually expressed in a fixed global frame of reference.

This could be attributed to the fixed nature of force plates.

As shown in Fig.

GA and 6B, the global frame 3, has a predefined and fixed frame throughout the measurement.

However, ambulatory setups allow us to define frames that are associated with the moving or turning body.

For instance, pressure profiles, and centre of pressure patterns are expressed in foot frames.

Similarly, here we can define reference frames that are attached to the moving body.

There are two possible options.

One option is to have a frame of reference attached to the pelvis.

This would result in a frame defined along the anterio-posterior, and vertical axes of the body.

Alternatively, we could define reference frames based on the direction of steps being made.

The second method is easier to define for both the foot and pelvis segments, and is therefore preferred for this study.

Figure 6A shows a pelvis based current global frame, while Figure 6B shows a step based current global frame. Here, the first position P1 of the right foot before a step k is shown, as well as the second position P2 of the right foot, corresponding to the positions shown in Fig. 3. Similarly, the trajectory T that is made during the step k is depicted. Further, a trajectory Tp of the pelvis or CoM is shown.

Therefore, the changing reference frame or current global frame i, defined graphically in Fig. 6B depends on the direction of the step, and thus, changes for each step. We define the X axis of this frame as positive in the forward direction, defined by the line between the beginning and end of a step. The Z axis is positive upwards along the vertical. This provides the 4, for the current step, and is redefined for each step The sensors on the IMU, however, measure in their own frame of reference, 2, . This has to be transformed to the 2, per step. Figure 7 shows the transformation matrices required to transform different frames. First, each sensor was transformed to their respective segment (seg) frames 44 , using a simple calibration method. The segments of interest in this study are the pelvis (p), left foot (fI), and the right foot (fr). Then, the orientation of the segments have to be expressed in i, of a given step k. In order to estimate this, the change in foot position over the step k has to be known. In order to achieve this, first, the change in orientation of the segments are estimated in a reference frame 4-1) that was built in the previous step k-1. For simplicity, this reference frame is denoted as 3, . EEKF's are used to estimate this change in orientation during this step. Subsequently, the change in position of the moving foot can be estimated at the end of the step k. Once the initial and final positions are known, the rotation between the reference frames of the previous k — 1 and current k steps can be estimated as Ri, . This is used to transform to the 4). This can be redefined for each step, resulting in gep) for each step. In short, four frames of reference were used in this study: sensor frame (i) for each sensor, segment frames (pelvis %,, right foot y,, and left foot yi), reference frame defined by the previous step (,, ). and a current global frame defined by each step k (b4 ).The notations used in this study are tabulated in Table I.

The 3D accelerometer in the IMU provides the following signal in the sensor frame 3; Jans +64 {1} where a is the linear acceleration of the body, g is gravity, and eA is Gaussian white noise. The 3D rate gyroscope present in the IMU measures angular velocity in the sensor frame 36: yh =u Hh eg AB Where «is the angular velocity, b is a slowly varying offset, and #2 is the Gaussian noise.

In order to estimate the GRF, the accelerations at the CoM has to be known. Here, we assume that the pelvis moves with the CoM, and that all mass is concentrated at this point. Additionally, the feet are the only contact with the external world, and no additional load is carried by the body. Therefore, the pelvis IMU was used to estimate the accelerations at the CoM, and eventually the GRF. The foot IMUs were used to estimate the direction of the steps being made, to define the Fus.eter.

TABLE ©: Notations used, shown for an wiitrary vector & ein Bende Bk al th balan a’ ampeg Jans ts # dernative of 8 Ey shit a a 7 ane tE of & Bs Cassis cessat wils

Foot Contact and Step Detection: The method of Skog et al. 2010 was used to estimate the foot contact instances for the two feet. Step detection is important in estimating the current global frame. As the IMUs are synchronized in time, the double stance instances can be estimated. The time instance for a step was defined to start from the midpoint of a double stance event, and ends at the midpoint of the next double stance. Orientation in the different reference frames: The transformation between different frames are explained in the following sections. The static calibrations used to transform the sensor data to the respective segment frame are first described. Following this, the structure of the fusion filter, used to estimate changes in orientation of the segment in the previous global frame is described. This is finally followed by estimating and translating all information to the current global frame.

First, R*®**has to be estimated using the mounting frame calibration techniques described by Bonnet et al. 2009. The inclination estimate was estimated from (Eqn. 3a) during an initial standing still phase, during which the 3D accelerometer is expected to measure only gravity. The Y axis of the pelvis can be estimated by asking the subject to bend forward. Principal component analysis was applied to the gyroscope output to find the axis measuring largest angular rotation. The X axis of the pelvis can be estimated using right hand thumb rule, as seen in (Eqn. 3c). The orientation was then estimated using (Eqn. 3d). Ary i ize) Wy p= PAs) is) REY = SEY Hay ia) | Ros lary cer zeg] Gad) On the other hand, for the feet, the X axis was taken to lie along the direction of velocity vector for the first step being made. The Y axis was estimated using right hand thumb rule, and finally the rotation matrix was estimated using (Eqn. 3d). Following this, the change in orientation during movement has to be estimated.

For a given step k, the previous global frame #4 has been defined.

Note that the current global frame %, 4; can only be defined at the end of the current step.

Therefore, the change in orientation was first expressed in #4 using an EEKF.

The EEKF was used to track the R’**? i.e, the orientation of the segment 4, with respect to 4 for given instance i.

Here, 1 denotes the samples including the start and end of the current step k.

The EEKF filter used for the pelvis orientation is shown in Fig. 8 and was based on Weenk et al. 2015, and Kortier et al. 2014. Similar EEKFs were built for the other segments too.

The states included in the state vector (x) of the EEKF were orientation error &: and gyroscope bias

Band its covariance matrix was denoted as P.

The advantage of using an

EEKF for estimating orientation errors is that the inertial processes can be considered linear, if the errors are assumed to be small.

The state vector can be written as:

The initial orientation error Gons was assumed to be zero, and the initial gyroscope bias 5 was estimated from gyroscope output during the initial standing still phase, as the angular velocity should be zero.

An initial estimate of RP? has to be estimated.

For this, the direction of the first step being made was measured, by estimating the direction of the velocity vector of the foot that moved first.

This gave the direction of the X axis, and the Z axis was taken to be the vertical.

After estimating the Y axis using cross product, the RY>"® was estimated using (Eqn. 3d).

We started by making models for each of the states. First, the gyroscope bias error was modelled as a first-order Markov process (Eqn. 5): bi =h; 1+ ey; Here, e,‚; is white Gaussian noise associated with the process. Thus, the gyroscope bias was predicted as (Eqn. 6): b; =h;_; The gyroscope bias error h. can then be written as (Eqn. 7): bei = bi B; Equations 5, 6, and 7 gives us (Eqn. 8): Dei =Der1 — ey; Orientation can be estimated from orientation error as (Eqn. 9): RSS Rx RPT +6; ) Ù lg a, Here, [ij = | 82 0 =£, | Equation (9) is valid when orientation “ly Gy 0 errors are assumed to be small. Furthermore, we can derive orientation from angular velocity using (Eqn. 10) RFE®E = RFESE (gh, Thus, we have the derivative of orientation error as (Eqn. 11)

8. =&d,—h, After applying discretisation, we get (Eqn. 12) «FZ | à Te? Bei = I; + Tú + = tul J Beis + Tl — = wb, _y The Kalman filter prediction equation is given as x =FReq (13) TT. EN EN Tiss DE FE en en where Fas Ld 6 TE + 5 3 ì {143 EY UR ij 7 The covariance matrix is predicted using B, =FP;_ ‚F7 +Q (15) where, Q 15 the process noise covariance matrix.

The measurement updates were applied to the EEKF using the standard equations. The measurement used at any instance z to update the state vector is given in (Eqn. 16). ®* is the noise associated with this measurement. When H is known, the Kalman gain is estimated using (Eqn.

17). Then, the state matrix and the error covariance matrix were updated with (Eqn. 18) and (Eqn. 19) respectively. y; = Hx; + eg (15) K; = P HT (HP; HT +R) + (17) & = &; + K; (z,— Há;) (18) P, = (I -K;H)P; (19) It was assumed that on average, the accelerations at the pelvis measure inclination due to gravity. This can be true during forward walking or when making changes in walking direction. The orientation error was corrected based on the current prediction and expected inclination for the vertical axis. An estimate of the accelerometer output in the frame y,, can be estimated using the estimate of the orientation matrix as Hi Rp) (20) Then, (Eqn. 20) was applied to (Eqn. 3a) to estimate inclination at instance i. The difference between measured VAN and estimated $;* inclination, also referred to as Sy5%was then used to update the orientation error as shown below: yy” = a = R792 (1 +0; Jel — Rose Fi + ey = Res. 7 9, + ey The orientation estimate and gyroscope bias were updated using the resulting state vector.

RIE SRF (IG) bi” bi + be;

Using the estimates of the pelvis orientation RF*¥in each iteration, the accelerations were estimated from (Eqn. 20). The GRF can be estimated from the product of acceleration at the pelvis and body mass.

GRE? = Mass: RP (vi) The GRF estimated so far has been expressed in the previous global frame. This has to be transformed to «4; for the current step k. As the change in orientations have been estimated for the current step, the change in foot positions can be estimated. For this, a separate extended kalman filter (EKF) was developed. The EKF estimates the velocity and position of each foot. Zero velocity and zero height updates are used to improve these estimations. At the beginning of each step, the foot position and velocity are reinitialised as we are only interested in the change in position for a given step. The EKF then tracks the change in position and velocity for the current step. For example, in Fig. 6B, the right foot (shaded green) changes direction while making the step k. The change in position in the XY plane was measured between the start and end of this step. The forward direction, shown by the dotted line is the X axis, and the vertical is the Z axis. This gives us the new ,, for the step k. This was redefined for every new step being made, giving R°27s, and then we transform the GRE"? to the new 2.4 The GRF™ was found to have noisy peaks around foot contact. This was removed by identifying local maxima or minima around foot contact and using a polynomial function to smooth the peaks. Following this, the signal was low pass filtered using a zero-phase butterworth filter of order 4. However, it was observed that the cut off frequency of the filter influenced the resulting errors, and therefore the cut off frequency was adjusted to evaluate the optimum value.

A three IMU setup was used as seen in Fig. 2. One Xsens TM IMU was mounted at the pelvic region on the sacrum using a strap.

The IMU is placed such that it was at the midway point between the line connecting the left and right posterior superior iliac spine.

One IMU was placed on each foot at the midfoot region.

The MT Manager software was used to read the data from the IMU wirelessly, which was sampled at 100 Hz.

The ForceShoe™ was used as the reference system.

The data from ForceShoe™ were sent wirelessly to a PC, sampled at 100 Hz.

It was then low pass filtered twice at 10Hz using second order butterworth filter to ensure zero-phase lag.

The GRF measured by ForceShoe™ on each foot is summed to obtain the GRF, which is then transformed to the P,, aS defined above.

Seven healthy subjects were recruited for the study.

The inclusion criteria included subjects with no history of impaired gait or leg injury.

The subjects began by standing still for a few seconds, following which they were asked to bend the trunk forward thrice.

This was used to calibrate the sensor to segment orientation for the pelvis sensor.

The subjects were then asked to perform different walking tasks similar to daily life.

They were instructed to begin with their feet placed parallel.

Once the researcher gave the start sign, the subject walked along a given path.

The time taken between start and stop of the walking was measured using a stopwatch.

This activity was repeated six times.

The walking tasks are performed in the following different scenarios: 1) Normal Walk (NW): During this task, the subject was asked to walk at his preferred walking speed for 10 m. 2 L Walk (LW): During this task, the subject was asked to walk for 15 m and then turn right at a right angle and walk for another 10m.

3 Slow Walk (SW): During this task, the subject was asked to walk at a slower pace. They were guided by the use of a metronome beating at 50 beats per minute. Each beat corresponded to a heel strike. This frequency was used so that the subjects walked slower than 0.6 m/s.

4 Walk and Turn (WT): During this task, the subject was asked to walk for 10 m and then turn and walk back to start position.

sy Slalom Walk (SIW): During this task, the subject was asked to walk in a slalom pattern. Pylons were placed on the floor for this purpose.

Asymmetric Walk (AW): During this task, the subject was asked to walk in an asymmetric manner. The instruction given was to induce a stiff left knee and abduct the hip as much as possible on the right side.

First, an example of the estimations of GRF in 3D using the EEKF (GRFxr) and that of the ForceShoe™ (GRFrs) is shown in the changing reference frame ¢,,. Following this, the root mean square (RMS) of the differences between the instantaneous GRFxr and GRFrs were studied. Following this, their correlations (CORR), were analysed. The RMS and CORR were compared with that of the findings of Gurchiek et al. 2017. The difference in the angle between the estimated and reference GRF vectors {#4} in the plane perpendicular to the vertical was analysed.

Subsequently, the GRF estimated will be used to estimate relative distances between either foot and CoM as given by: In the above equation, subscript ax stands for the axis of interest and is either X or Y. Note that (Eqn. 25) is true only when the foot of interest is the only point of contact with the ground. Here, we see that the ratio of the forces in either X or Y axis with the Z axis is required to estimate the position of the foot of interest. Thus, the root mean square of the differences (rmsd) between the ratios calculated from GRFy; and GRFrs was estimated. The rmsd was then expressed as percentage of error as rRatxz and rRaty z, by normalising it with the range of the ratio measured from the reference GRFr:.

Some trials had to be excluded from the analysis due to issues with the sensor systems. However, it was made sure that each subject had at least three walking trials per task. Fig 9., wherein an example of the estimated GRF,;, and GRFrs in the changing reference frame ¥,, is seen.

GRFg 1s shown in blue, and the reference GRF;, is in red. Each row in the figure corresponds to an axis in Po, In this, the subject performs the LW task, where a turn to the right side is made at 35 seconds. This moment is shaded light red.

In Table IIT we compare the estimated post-processed instantaneous GRFg, and reference GRF;, for all walking tasks. The table shows the root mean square of differences (RMS), correlations (CORR), and also difference in 2D GRF vector angle in the XY plane 8, between the GRF;; and GRF;. Also shown are similar comparisons performed by Gurchiek et al. 2017 for their method. They measured the 3D GRF during two instances; Sprint Start (SS), and Change of Direction (CoD). These are short instances where the subject is about to start running (SS), or when they make a 45° change of direction (COD). Note that Gurchiek et al. 2017 uses a fixed global frame as opposed to a current global frame used in this study. The percentage error of the rmse (rRatxz , and rRaty z) calculated from GRFy;, and GRF;: is tabulated in Table IV.

The study aims to estimate GRF using a minimal IMU only setup. This has a lot of potential in ambulatory monitoring. Fig. 9 shows an example of the GRF, and GRFr: for the LW task. Here, the subject was asked to make a right turn, and the moment this occurs is denoted by a shaded rectangle.

We see that after the turn, the GRF look similar to their profiles in their respective axes Just before the turn.

However, if a fixed global frame, denoted as b, in Fig.

GB was used, then after the turn, the Fx would show a profile similar to that of Fv before the turn, and vice-versa.

Instead, as the frame used here is defined by the direction of steps being made, the profiles of Fx and Fy remain unchanged.

This representation of GRF represents the biomechanics of the body irrespective of the change in walking direction.

However, minor deviations can be noted at the moment of the turn, particularly in Fy, possibly due to a larger deviation in this axis when making the right turn.

In this study, an EEKF was tuned to be able to resolve the accelerations measured at the pelvis into 3D components of the GRF within a specific reference frame.

This is a tricky task as the contribution due to gravity is quite large as compared to the shear GRF.

This resulted in high frequency noise creeping in the X and Y axis.

TABLE III: Comparing the Estimated and Reference GRF values: Root Mean Square of the Differences (RMS), Correlations (CORR), and Difference in 2D GRF Vector Angle in the XY Plane (9d), and Findings of Gurchiek et al. 2017. NW BSS dma i Prk ESE EEE Lw HEELT BE EINE UAE DEE ASN EOE SEE BAER AH GET AOU | DTA ROE | 5) £84 WE | EERE Ides ay aah RUE | ERLE | NSL | ladda | SYNE ARTE FIET | AT INL | BOER A PEAT | Rag die | Sed ol - The tasks included are Normal Walk (NW), L Walk (LW), Slow Walk (SW), Walk and Turn (WT), Slalom Walk (SIW), and Asymmetrical Walk (AW). The tasks of Gurchiek et al. 2017 include Sprint Start (SS), and Change of Direction (COD).

TABLE IV: Root Mean Square of the Differences Between the Estimated and Reference GRF of the Ratio of GRF in either X or Y with the Z Axis, expressed as Percent Error of the Range of the Reference GRF Ten a] [5 [esas | ak ia | ow wim [572570] [Wr [aos ier [tao dam | sw [sss [neen]

Table ITI shows that the RMS between the GRF,;; and GRF;: is low across the different axes.

Additionally, CORR shows good agreement, especially in the X and Z axis.

The Y axis shows lower correlations, which seems to worsen for the AW task.

The AW task was meant to simulate gait impaired walking and is not a standardized test.

The subjects were given instructions about how to walk asymmetrically, but each of them chose a unique pattern.

Additionally, #4 shows quite some differences in the XY plane, which could be attributed to the low correlations in the Y axis.

A possible solution to improve the estimations in the Y axis, is to further analyse the biomechanics of the CoM for additional constraints or updates.

The RMS error margins could also be attributed to disagreements in transforming the measurement and reference system to the changing step frame Wig, Overall, for all tasks, the algorithm performs better than that of Gurchiek et al 2017. One of the reasons could be the use of an additional calibration method to estimate the sensor to segment orientation.

In this example, we show that GRF can be estimated with good confidence.

The ZMP equation further requires a ratio between two axes, and Table IV shows that on average there is a 13% error while measuring this ratio across walking tasks. This has to be acknowledged while solving (Eqn. 25). Looking closely, the AW task reflects the larger errors as seen earlier. Further, if we are able to measure the CoM kinematics, relative foot distance can be estimated.

Finally, it has to be noted that although foot IMUs were used to estimate the current global frames per step, they are not necessary for estimating the GRF during gait. It is possible to resolve the 3D components of GRF using only the pelvis IMU. As a measurement update, if an estimate of the forward CoM movement is known, it could be used to express the GRF in the pelvis based reference system, as also described above in Fig. GA.

If this setup is to be used in people with impaired gait, a separate validation study has to be performed on the population of interest. The AW task performed in this study may not hold true for gait patterns exhibited by gait impaired populations. The same argument holds for rapid walking or running scenarios.

These results show that it is feasible to monitor GRF in an ambulatory manner using simply an IMU on the pelvis. Foot IMUs are used to provide a reference frame that allows us to measure the GRF with respect to the moving and turning body. This study is the first step in developing a minimised and portable gait lab. Third exemplary implementation An extended Kalman filter EKF is built to track the velocity and position of the three segments in the current global frame 4.4 . For the pelvis IMU, we assume that the pelvis moves with the CoM, and that all mass is concentrated at this point. The EKF can therefore track the position and velocity of the CoM. Therefore, the pelvis segment will be hereto referred as the CoM. The state vector of the EKF is denoted as x and its covariance matrix as P. The states required for each segment are its 3D position p, and 3D velocity v. The state vector can be thus written as: Xoil Pea Py Vr Va VP {5 1) Initialisation: Before applying the EKF, the states for each segment and their covariance noises have to be initialized. The right foot is assumed to be the origin. The location of the CoM, and the left foot is input using the values from the reference system. They could also alternatively be measured using tape measure. All initial velocities Ys are set to zero. The initial noise values are set to be an arbitrary value.

2) Prediction: We start by making models for each of the elements in the state vector. The acceleration in the reference frame 4 for each segment is given as (Eqn. 6) £0PI PITY 2989 Ee a Recon (Ree | (Fay * Rian (R; : Var +1 The position and velocity can be estimated from acceleration using integration as follows (Eqn. 7 and 8) : #0 = 9 +78 ea ed EJ Te £4 5, Di +7 -¥ +d The Kalman filter prediction equation is given as Xy == Foy + Ween {0 FT, TY | wiers F L 8, 1) {HN Te og and u=| 2 °F {11d Trap and the covariance matrix is predicted using 95 Pi FP Pag {12}

where, Q is the process noise covariance matrix.

3) Measurement Update: The measurement updates are applied to the EEKF using the standard equations. The measurement used at any instance k to update the state vector is given in equation 13. €xis the noise associated with this measurement. When H is known, the Kalman gain is estimated using (Eqn. 14). Then, the state matrix is updated with (Eqn. 15), and the error covariance matrix is updated using (Eqn. 16).

= Bg + 85 Gm Ky = PIH (HP/H" + Ry in) Rom kD + Kgs, ~ HED {15 Poss KEP 1a} The measurement updates used are as follows.

e Zero Velocity Update: During foot contact instances, as estimated using Skog et al. 2010, the velocity of the feet are assumed to be zero. This can be implemented as a measurement update.

Heure Flop tE == ayy (7 with, Hep poo thie Ina Shad iN) we, Heist = Bhs hg Baga (1% e Zero Height Update: During the foot contact instances, we also have information regarding the height of the foot from the floor. Here, we assume that gait occurs over a flat ground.

Zas Boa XH Sun ann {0 WIR Flo py = (00 1 000 Bia) (33 aod, Hog e= 000001 has) ON e Minimum. Height Update: A minimum height check is also performed during the iteration of the EKF. The height of the feet are constantly assessed to see if it is above ground level. In case it drops below the ground, the height is reset to the initial height.

Zn = Hoan Et Emp = Painit With, Hyp rp = (0010000415) and, Hag: = (000001044, o CoM Velocity Update: The drift in the velocity of the CoM can be reduced using information about foot velocities. Here, we average the velocities of both feet, and apply a low pass filter to get the average instantaneous velocity of the CoM. This is also used as a measurement update.

Zoop = Hepp "X + Bp = Vang With, Heap = (03,15 aaa) e CoM Height Update: The CoM position may also drift as there are not many constraints available. However, we can assume that the height of the pelvis will not go beyond certain ranges given an upright gait. An ‘average’ height of the pelvis is estimated from the first two steps made. Then, a boundary of +0.25% 1s assumed. If the estimate of the pelvis exceeds this boundary, the pelvis height is reset to be the average height.

Zop = Happ X + Crop = Pang With, Her, = (Ogg 00 1 O9} where, [Darg *0.85 = Zap = Darg * 1.25] e Zero Moment Positions Update: The zero moment update is the main measurement update that restricts the two feet from drifting apart or towards each other. The 3D components of GRF are estimated using the methods shown in the second exemplary implementation. The relation between relative distances and GRF 1s given as Emp Hompo {32 with, Hoog gs (Dae Troe Bad 123

Similarly for left foot Kari Hop por Bj £35} with, Hop js (haa Isa Ús) ijs} Here ax denotes either X or Y axes.

The EKF mentioned above is to be applied in an iterative manner per step. Updates have been formulated on biomechanical constraints for each segment. This will allow the estimation of drift free positions of both feet and CoM over time using only three IMUs.

The invention is not restricted to the embodiments described above. It will be understood that many variants are possible.

These and other embodiments will be apparent for the person skilled in the art and are considered to fall within the scope of the invention as defined in the following claims. For the purpose of clarity and a concise description features are described herein as part of the same or separate embodiments. However, it will be appreciated that the scope of the invention may include embodiments having combinations of all or some of the features described.

Claims (27)

Conclusions Method for estimating positions of feet and center of mass of a person with respect to each other during walking, comprising the steps of: - collecting first measurement data from a first inertial measurement unit placed at a first foot of the person; - collecting second measurement data from a second intertial measurement unit placed at a second foot of the person; - collecting third measurement data from a third inertial measurement unit placed at a pelvis of the person, and - evaluating relative positions of the first and second foot and the center of mass of the person in time, using the first, second and third measurement data . The method of claim 1, further comprising a step of evaluating the velocity of the subject's center of mass over time. The method of claim 1 or 2, further comprising a step of evaluating force vector components applied to the center of mass of the person using the first, second and third measurement data. The method of claim 1 or 2, further comprising a step of evaluating force vector components applied to the subject's center of mass using only the third measurement data. A method according to any of the preceding claims, further comprising the steps of: assessing a first phase of walking in which a first foot rests on a support structure that supports the first foot and moves a second foot; - determining a first estimate of the second foot position relative to the first foot, after a step of the second foot, whereby the assumption is applied that a moment around a center of mass of the person is approaching zero. The method of claim 5, further comprising a step of determining a second estimate of the second foot position relative to the first foot, after the step of the second foot, by applying a strap-down navigation estimate of displacement of the second foot. foot during the step of the second foot, combined with initial and final conditions resulting from zero-speed update, and an estimated position of the second foot relative to the first foot, for the step of the second foot. The method of claim 6, further comprising a step of improving an estimate of the second foot position relative to the first foot, after the step of the second foot, by combining the first and the second estimate of the second foot. with respect to the first foot, preferably by considering uncertainties from the first and second estimates, preferably using a specifically designed sensor fusion filter. A method according to any one of the preceding claims, further comprising the steps of: - assessing a second phase of walking times with the first foot moving and the second resting on the support structure supporting the second foot; - performing a first estimate, a second estimate and an improved estimate of the first foot position with respect to the second foot, after the step of the first foot, by performing the steps defined in preceding claims 6-8 wherein the first foot and the second foot have been switched. A method according to any preceding claim, further comprising a step of estimating the position of the person's center of mass as a function of time relative to the first foot as the second foot moves and / or relative to the second. foot when the first foot moves, applying the assumption that a moment around a center of mass of the person approaches zero. A method according to claim 9, further comprising a step of improving the estimate of the center of mass position by including the third measurement data from the third inertial measurement unit located at a pelvis of the person, preferably with a strap-down navigation estimate. . A method according to any one of the preceding claims, further comprising a step of estimating the position of the center of mass of the person during double stance based on the third measurement data of the third inertial measurement unit placed at a pelvis of the person, preferably with a strap-down navigation estimate. A method according to any one of the preceding claims 9-11, wherein the center of mass position estimate is improved by fusing all information about center of mass movements available over time, preferably using a specifically designed sensor fusion filter. A method according to any one of the preceding claims 9-12, further comprising a step of estimating a velocity of the center of mass at each moment of time based on a position estimate of the center of mass as a function of time and optionally the third measurement data of the third inertial measurement unit. . The method of any preceding claim, further comprising a step of estimating a center of mass velocity from the feet velocity estimates. A method according to any one of the preceding claims, wherein a location, in particular the height of the center of mass of the person is estimated based on measurement data from an inertial measurement unit placed at the pelvis of the person, preferably by applying strap-down. inertial estimation and using biomechanical constraints with regard to the height of the center of mass. A method according to claim 15, wherein a ground reaction force applied to the center of mass of the person is estimated from acceleration data measured by the inertial measurement unit located at the pelvis of the person. Method according to claim 16, further comprising a step of estimating an orientation of the inertial measurement unit, preferably using an error-extended Kalman filter. A method according to any preceding claim, wherein foot kinematics and kinetics are determined with respect to a frame of reference that is stationary with respect to the pelvis or a direction of walking of the person. A method according to any preceding claim, further comprising a step of estimating foot kinematics and kinetics over time based on measurement data from a first inertial measurement unit placed at a first foot, measurement data from a second inertial measurement unit placed at a second foot, and measurement data of a third inertial measurement unit placed at the person's pelvis. The method of claim 19, further comprising a step of estimating equilibrium metrics, based on the kinematics of the foot and the center of mass of the person, by - estimating a basis of support defined by boundaries of the feet while in contact. being with the ground while walking; estimating the basis of support defined by projected boundaries of the feet when either one is not in contact with the ground while walking; - estimating an extrapolated center of mass, which includes the speed and direction information of walking, and - estimating a stability margin, which is the distance between the extrapolated center of mass and the base of support. The method of claim 19, wherein the step of estimating foot kinematics and kinetics over time comprises applying sensor fusion filters, such as an enhanced Kalman filter, to measurement data. A method according to claim 19 or 20, wherein the foot kinematics are updated in time using the first distance between the position of the first foot and the center of mass of the person, and / or the second distance between the position of the second foot and the person's center of mass. center of mass of the person. A method according to any preceding claim, wherein the foot kinematics are updated over time using biomechanical constraints. 24. System for estimating feet of a person relative to each other while walking, comprising a first inertial measurement unit for location at a first foot of a person, a second inertial measurement unit for location at a second foot of a person, and a third inertial measurement unit for location at a pelvis of the person, the system further comprising a processing unit adapted to: - receive first measurement data from the first inertial measurement unit; - receiving second measurement data from the second inertial measurement unit; - receiving third measurement data from the third inertial measurement unit, and - evaluating relative positions of the first and second foot and the center of mass of the person in time, using the first, second and third measurement data. 25. A computer program product for estimating a person's feet relative to each other while walking, the computer program product comprising computer readable code for causing a processor to perform the steps of: collecting first measurement data from a first inertial measurement unit located at a first foot of the person; - collecting second measurement data from a second inertial measurement unit placed at a second foot of the person; - collecting third measurement data from a third inertial measurement unit placed at a pelvis of the person, and - evaluating relative positions of the first and second foot and the center of mass of the person in time, using the first, second and third measurement data . A computer program product according to claim 25, comprising computer readable code for causing a processor to perform the further step of: constructing a sensor fusion filter to fuse information from strap-down inertial navigation and relative foot positions to track footings as a function of time to improve. A computer program product according to claim 26, comprising computer readable code for causing a processor to perform the further step of: - displaying the information in a frame of reference defined with respect to the pelvis or the direction of walking.