Topics

1. Accelerometer
2. Gyroscope
3. Global Angles
4. Help with scripts

The following topics walk you through how to process and analyze the data collected from the accelerometers. They are followed by a short discussion.

Review

In this exercise, the IMU was affixed to the upper back (or chest) of the participant. For the first two seconds of data collection, the participant was instructed to stand still. The participant was then asked to perform a squat at a smooth (or relaxed) pace, pause for two seconds, and then perform another squat at a faster pace.

Discussion

Why use resultant acceleration?

For the squat,  the instructions set up Real-Time Insight to visualize the acceleration in a single axis (ie, the x-axis). This mimicked the instructions within the Visualize section of the Accelerometer module in the Education mode; that is, we suggested the squat is analyzed as a linear movement inline with one of the accelerometer's axes. When the participant is in their initial position (ie, standing), this makes sense, as the direction of the x-axis is well-aligned with the vertical axis, which is how the center of mass would typically move during the squat (Figure 1). However, as the participant squats, the sensor x-axis starts to diverge from this vertical axis while the z-axis becomes more aligned with the vertical axis (Figure 2). As such, examining the squat with just one axis may no longer be practical. Is there a better approach, using the data captured from Real-Time Insight?

                   

Let's first consider what data is exported in Real-Time Insight. In addition to the individual axes, Real-Time Insight enables you to visualize and export the resultant acceleration, which is the overall magnitude of acceleration. As the participant was unlikely to have too much forward/backward and side-to-side movement during the squat, using the resultant acceleration is an approach that is likely to yield better insights than looking at just one individual sensor axis. In an ideal scenario, knowing the orientation of the sensor at each moment in the squat would yield the most precise results. This would enable us to calculate the components of each sensor axis that was in the direction of the vertical axis. This can be an important consideration if you're conducting a similar study on your own.

Analyzing the graph

Within the Accelerometer Practice module, the Analyze page helped to interpret the shape of the curve calculated during the A-B-A movement. We can use a similar strategy here when analyzing the squat. The following analysis assumes that the sensor was oriented 'logo-up'. Here is a sample graph of the movement with some key events marked and explained below:

Key stages in a squat

A: Rest – Participant is standing still

B: Initial (downward) acceleration – Participant begins to descend in their squat

C: Max (downward) acceleration – Participant is still descending in their squat

D: Peak (downward) velocity – When the acceleration crosses zero, it signifies a peak in velocity. When the acceleration transitions from negative to positive, this indicates a peak negative velocity. Participant is still descending in their squat, but the rate at which they are descending has decreased (ie, less negative)

E: Maximum squat depth – Participant transitions from going down in their squat to standing back up.

A trend to note is that a peak in acceleration (C) always precedes a peak in velocity (D), when acceleration crosses from negative to positive, which is then followed by the peak in position (E), when velocity crosses from negative to positive (not shown). 

Things to think about...

When analyzing the data, you may want to think about these additional points. We will include discussions of each of these questions (and others) in a future update.

1. Using the knowledge about the first half of the squat (down), can you identify the events in the second half (up)?
2. In the Acceleration module within Education, we discussed the trade-off between using the low-g and high-g accelerometers. How would the analysis be different if the high-g accelerometer data was analyzed instead?
3. Can we integrate the data to get velocity? What considerations may be required? (Hint: Look at the Practice_Gyroscope sheet for an idea on how you can integrate the data within the worksheet itself).

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The following topics walk you through how to analyze the data collected from the gyroscope. They are followed by a short discussion.

Review

In this exercise, the IMU was affixed to the (left) wrist of the participant. For the first two seconds of data collection, the participant was instructed to stand still. The participant was then asked to perform a bicep hammer curl at a smooth (or relaxed) pace, pause for two seconds, and then perform another bicep hammer curl at a faster pace.

Discussion

Why the z-axis?

Before we begin interpreting, is it clear why the z-axis was chosen for analysis? To help explain, let's first identify three stages of the movement: 0 degrees, 45 degrees, and 90 degrees.

      

Next, let's look at the sensor in isolation  (ie, independently of the movement). What is the orientation of just the sensor? It should look something like this:

Of all the exercises within the Gyroscope Education module, which rotation did this match most? Hopefully, you also chose the rotation about the z-axis.

 

What makes this difficult to interpret is the fact that the sensor's point of rotation is not the middle of the sensor, but rather the elbow. As such, there is not only rotation of the sensor, but displacement too. However, when we are looking at the gyroscope data, we really only need to look at how its orientation changes to help us determine its direction of rotation and angular velocity.

Analyzing the graph

Within the Gyroscope Education module, the Analyze page helped to identify the difference between a positive and negative angular rotation and interpret the shape of the curve as the sensor was rotated 90 degrees in both directions. We can use a similar strategy here when analyzing the bicep hammer curl. The following analysis assumes that the sensor was placed as advised in the module (ie, top of logo on the thumb side). Here is a sample graph of the movement with some key stages identified:

Key stages in a bicep hammer curl

A: Rest – Participant is standing still with their (left) arm by their side.

B: Initial (negative) angular velocity – Participant begins to flex their elbow; sensor is rotating clockwise (ie, negative).

C: Max (negative) angular velocity – Participant is still flexing their elbow, but the rate of angular velocity change begins to decrease.

D: Angular velocity approaches zero – As the angular velocity transitions from negative to positive, this signifies when the elbow has reached maximum flexion.

Integration

Within the Practice_Gyroscope example, the angular velocity data was integrated to provide an 'angle'. Angle is in quotation marks because it can be unclear what this angle represents: we can see that the angle is changing, but what does it actually tell us about the orientation of the arm at that time? What we need is some information about the sensor's original orientation. This is the exact reason why we instructed the participant to stand with their arm at their side so that the initial condition would be known. Even so, we don't know if the elbow was straight or bent to 15 degrees,, but at least we have some initial frame of reference.

As mentioned, one thing that is difficult about integrating the angular velocity is the noise and drift within a gyroscope. We can see its effects particularly in the third and fourth flexion-extension cycle. Its unlikely that the participant hyper-extended the elbow more with each cycle. Instead, this shows how those sources of error accumulate over time and effect the angle estimation. This is a very important consideration when trying to use gyroscopes alone to measure orientation directly.

Things to think about...

When analyzing the data, you may want to think about these additional points. We will include discussions of each of these questions (and others) in a future update

1. Using the events from the first half of the movement, can you identify the events in the second half?
2. How could we reduce the effects of the noise and drift in the gyroscope using simple calculations in the sheet?

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The following topics walk you through one way that you can analyze the global angle data. They are followed by a short discussion.

Review

In this exercise, the IMU was strapped to the (left) wrist of the participant.  For the first two seconds of data collection, the participant was instructed to start with their arm by their side and thumb pointing forwards. The participant was then asked to perform three separate movements, with two seconds between each, beginning from this initial position: an elbow flexion-extension (ie, hammer curl), shoulder abduction, and forearm pronation. As data was collected in Real-Time Insight, you should have been able to view the angle outputs as the movements were performed.

What is a global angle?

If you recall, a global angle is the orientation of the sensor's Local Coordinate System (LCS) relative to a Global Coordinate System (GCS). Global angles are a commonly used measurement (eg, foot contact angle or pelvic tilt), though they may not often be referred to as such. To take either measurement, some determination was used to establish the orientation of the GCS. In a traditional motion capture environment, a calibration wand is used to establish the GCS, while in clinical settings, the physician is likely to use the ground or a table to establish their reference system. With an IMU, this is inherently more difficult because the IMU itself establishes the GCS and it cannot simply be seen by the naked eye.

Local angles

What makes IMUs somewhat difficult to interpret is that their individual sensors (accelerometer, gyroscope, and magnetometer) all output their data relative to their own LCS while global angles outputs its data relative to the GCS. So is there a way that we can convert the global angles back into the same coordinate system as the individual sensors?

The following topics walk you through how to convert your global angles into local angles using sample scripts.

Interpreting and understanding processed data

Now that we have processed the data, is it clear how the data was re-aligned and what its purpose is? Let's first look at the graph for the global angles (ie, Original Orientation). If you recall, the participant was asked to remain still with the arm to the side for the first two seconds. You should be able to see this flat line at the beginning. To examine the first movement (elbow flexion-extension), we recommended looking at the z-axis.  Looking at the data post-collection, we can see that the angles in the other axes (x and y) changed with the movement as well. What is going on? Remember, this is a global angle, so it is the orientation of the IMU relative to the GCS. Unless the LCS of the sensor was aligned perfectly with the GCS, we would expect the cross-talk observed here. The exact amount of cross-talk will vary as it ultimately depends on how the IMU was oriented relative to the GCS during the trial. We should see this cross talk in the other two movements as well, which makes it difficult to tell whether the angle in an axis is changing because of the movement or due to the cross-talk. So what we really want to do is to isolate the outputs to the specific axis in which we expected the movement to occur. In other words, we want to convert the global angles to an angle relative to its LCS – a local angle!

Let's take a closer look at how this was done in the sample script.

Going back to the initial step in the set of instructions, the participant was told to stand still with their arm at their side for the first 2 seconds. The purpose of this step was to calibrate a new, known reference system using the global angle of this static pose and use it to re-calibrate all future global angles during the set of movements. In other words, all angles are relative to this static position and not the GCS after this calibration step. However, this is not a simple 'zeroing' process; that is, we cannot simply subtract the global angle during the static pose from the entire data set. Instead we need to convert the global angles into a rotation matrix (also known as a direct cosine matrix) or a quaternion. In this script, we decided to use rotation matrices. As such, the global angles of each frame (currently expressed in helical angles) are converted to a rotation matrix and compared to the rotation matrix of the static pose to obtain a relative rotation matrix. This relative rotation matrix represents the change in orientation of the IMU relative to that initial static pose. We can then convert this back into a helical angle so that we can interpret it visually (ie, Re-aligned Orientation).

Looking at the Re-aligned Orientation graph, the angles now seem to be more isolated to the axis that we might have initially expected. The predominant angle change during elbow flexion-extension is in the z-axis, the shoulder ab/adduction is in the x-axis and the ulnar/radial rotation is about the y-axis. However, there still seems to be some cross-talk. What is going on here? First, we likely didn't take the re-aligning far enough – we would actually want to align it to the coordinate system of the joint. This is difficult without additional information and in this particular set of exercises, two joints were moving. This is a first glimpse into some of the challenges of calculating a joint angle from IMUs. Second, human movements are not always 'pure' in that they don't always occur in one axis even though they may appear to do so to the naked eye. As you were performing the elbow flexion-extension, regardless of how hard you tried to isolate the movement in the local z-axis of the IMU, there would always be some angular change in the x and y axes.  

Things to think about...

When analyzing the data, you may want to think about these additional points. We will include discussions of each of these questions (and others) in a future update

1. In the gyroscope practice example, we noted the effects of noise and drift on the angle. Can you compare the integrated gyroscope data with the re-aligned global angles? How do they compare?
2. Using what you have learned from converting global angles into local angles, can you devise a strategy that would enable you to find the relative angle between IMUs? That is, can you calculate what the orientation of one IMU is relative to another? As a hint, what is the first thing calculated when the data has been extracted from the sensor?

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