Estimation Of Foot Kinematics Computer Science Essay

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Estimating human foot kinematics relative to earth as reference frame, plays an exclusively role in development of Inertial Navigation Systems. A novel filtering algorithm that estimates foot kinematics, such as position, velocity, and orientation is proposed. Inertial Measurement Unit (IMU), which comprises of 3 axis accelerometers, magnetometers, and angular rate sensors, provides the input data for this algorithm. Novel methods incorporated in this filtering algorithm are for orientation estimation and position estimation.

Accurate foot orientation estimates are obtained during both static and dynamic motion using an adaptive-gain complementary filter. Accurate position estimates are obtained by integrating acceleration data, which has been corrected for drift errors using zero velocity updates. Zero velocity detectors are used to estimate instances of foot stance and swing and to establish the appropriate times for velocity error correction technique to the algorithm.

IMU data for a set of foot gestures was conceived and the software program for decoding the user's foot motions was developed using MATLAB. Assessments based on the accuracy of the position and orientation estimate indicates that during leveled ground forward gait, the gyroscope signals hold the most reliable information for zero velocity detection.

I. INTRODUCTION

A. Trend in Navigation technology

Global Positioning System (GPS) may be considered one of the most notable inventions of the 20th century. GPS has also found many civilian applications, including a vast amount of consumer products that range from navigation for automobiles, boats, and aircraft, to the location of an individual with a GPS-equipped cellular telephone.

While the applications of GPS in both military and civilian domains are vast, the system does have some drawbacks. One limitation of GPS concerns the availability of the transmitted signals. Since it is necessary to have signal reception from at least four GPS satellites to calculate position fixes, some locations may not receive adequate satellite coverage. It has been widely established that places such as dense urban environments, valleys and canyons, and heavily forested regions suffer from occlusion problems. The GPS signal also is attenuated as it propagates through the exterior walls of building structures to the point that indoor navigation becomes difficult.

A second limitation of GPS is that the update rate for some applications may not be sufficient. For example, a vehicle traveling at high speed, such as a tactical or strategic aircraft, or one capable of accelerated maneuvering, will traverse a substantial distance in a short amount of time. It is necessary that some means of exacting position in between the GPS updates be implemented.

In general, navigation systems can be classified into one of two types. The first may be thought of as an absolute navigation system. In this type, the navigation system makes position estimates that are referenced to an installed infrastructure. Each new position update, therefore, is derived wholly from a new set of measurements. Attractive feature of this type of system is that errors that occurred in past position estimates do not propagate into future estimates. A disadvantage, however, is that this type of navigation system requires good "line-of-sight" to the infrastructure. Examples of these types of systems include GPS, Loran-C, and celestial navigation.

Alternatively, a relative (or incremental) navigation system is one where new position estimates are computed with respect to previous ones. Often, this is called dead reckoning navigation. The INS is an example of this type of position tracking system, wherein acceleration measurements are doubly integrated at the end of each sample interval to derive position.

A well-known limitation of this type of system is that position errors tend to grow, and the system must be periodically reinitialized. An advantage, on the other hand, is that the relative navigation system does not require the use of an infrastructure; therefore, it can be used in those places where the infrastructure of the absolute navigation system is unavailable.

II. Objective for Personal Navigation

The primary objective of my work is to develop a personal navigation system (PNS) that uses novel algorithm to estimate foot kinematics based on Inertial Measurement Unit [IMU] data. Data from foot mounted IMU, will provide acceleration and gyro information which will then be processed to derive an updated position of the user. The strap down navigation algorithm will be adapted to utilize an adaptive-gain quaternion-based complementary. Furthermore, the strap-down algorithm will incorporate the concept of zero-velocity updates to determine the instances of the foot swing and stance periods.

A study of the performance of four zero-velocity detectors, namely the acceleration moving variance detector [MV] [5] [6], the acceleration magnitude detector [MAG] [7], the angular rate energy detector [ARE] [8], and Stance Hypothesis Optimal detector [SHOE] [9] will be done. Assessment will be done based on the accuracy of the position solution provided by the navigation system employing the detector to perform the zero-velocity update.

III PRIMARY CONTRIBUTION

My work describes a self-contained method for estimating the kinematics of the human foot during normal walking motion. The method is based on the use of IMU's attached to the foot.

The primary contributions of the work are the following.

An adaptive-gain quaternion based complementary filter design to accurately estimate foot orientation during static stance and dynamic swing phases,

Comparative study on 4 -ZVU methods,

Accurate position estimation by integrating ZVU corrected acceleration data,

Simulation results for position & attitude based on real world IMU data.

IV ZERO VELOCITY DETECTION

A. DRIFT ERROR

One of the first tests that Moore conducted was to simply move the MARG sensor through a straight line. Here, the sensor was placed on a table top and slid through a linear distance of one meter. Figure 4.1 shows the drift error. Acceleration is seen in the top-most plot. In this test, the sensor was stationary for approximately six seconds prior to its translation across the table. After its trajectory was completed, the sensor was kept stationary for another seven seconds, approximately.

These errors arise because the accelerometer's output exhibits two behaviors that must be taken into consideration-bias and drift. Bias is the nonzero output measured when the accelerometer undergoes no acceleration. Drift is the randomly varying portion of the sensor output often referred to as noise.

Figure 4.1 Result of one meter translation of IMU.

Integrating the resulting velocity data gives the final distance of 12.44 meters, a considerable error when compared to the actual distance of one meter. Upon closer inspection of the velocity plot, one observes that prior to the sensor's motion, as well as immediately after its motion, the velocity is nonzero. Integration of this nonzero data in the velocity is responsible for the gross error in the computed distance.

B. DRIFT ERROR MITIGATION

These errors may be mitigated through a two-step process:

First, since the sensor undergoes no acceleration outside of the time period between six and eight seconds, the acceleration during those times may be equated to zero. Subsequent numerical integration of the data will eliminate this component of error.

Secondly, the measured acceleration between six and eight seconds will also be influenced by the sensor bias and drift. To minimize this effect, the zero velocity update was employed.

Figure 4.2 Result of IMU translation - after ZUPT.

These errors arise because the accelerometer's output exhibits two behaviors that must be taken into consideration-bias and drift. Bias is the nonzero output measured when the accelerometer undergoes no acceleration. Drift is the randomly varying portion of the sensor output often referred to as noise.

V ZVD - COMPARATIVE STUDY

Zero velocity detectors were evaluated based on data from an instep mounted IMU (MicroStrain 3DX-GX2) with a dynamic range of +-18g and 1200 deg/s, and a sample rate of 250 Hz. The inertial measurement unit (IMU) was mounted in the right shoe sole of the user, and the user was made to walk in a closed loop trajectory at gait speed of 5 km/h and 7 km/h.

Parameters used in ZVU detectors:

Standard deviation of the accelerometer noise (sigma_a) = 0.01 [m/s^2]

Standard deviation of the gyroscope noise (sigma_g) = 0.1*pi/180 [rad/s].

Window size of the zero-velocity detector (N) = 3 [samples]

Threshold used in the zero-velocity detector (gamma) = 0.3e5

Figure 4.3 IMU sensor data

A. ACCELERATION-MOVING VARIANCE DETECTOR (MV)

The moving variance detector is solely based upon the accelerometer data and is mathematically defined as follows:

……………… (4.1)

Acceleration-moving variance detector within the GLRT framework considers the fact that the orientation of the accelerometer assembly is constant when the IMU is stationary, but neglects the fact that the magnitude of the specific force vector is equal to g.

MATLAB result:

Figure 4.4 Test statistics from MV detector

B. ACCELERATION-MAGNITUDE DETECTOR (MAG)

The acceleration-magnitude detector is another detector proposed in the literature [2], and is often used as a supplement to the moving variance detector. The acceleration magnitude detector checks if the measured specific force vector is close to g, and if that is the case, concludes that the IMU is stationary. It is mathematically defined as follows:

……………… (4.2)

Acceleration Magnitude detector within the GLRT framework is based on the fact that the magnitude of the specific force vector is g when the IMU is stationary, but neglecting the fact that the direction of the vector should be constant.

Simulation result from MATLAB:

Figure 4.5 Test statistics from MAG detector

C. ANGULAR RATE ENERGY DETECTOR (ARE)

The Angular Rate Energy Detector is another detector proposed in the literature [2], were only the energy in the gyroscope signal is used to detect when the IMU is stationary.

……………… (4.3)

Simulation result from MATLAB:

Figure 4.6 Test statistics from ARE detector

D. STANCE HYPOTHESIS OPTIMAL DETECTOR (SHOE)

The Stance Hypothesis Optimal detector is another detector proposed in the literature [2]. If the mean square error of fitting a vector of magnitude g with the direction of the average specific force vector to the accelerometer data in combination with the energy in the gyroscope signal, each weighted by the quality of the measurements, falls below the threshold γ, the GLRT chooses the hypothesis that the IMU is stationary. It is mathematically defined as follows:

……………… (4.4)

Simulation result from MATLAB:

Figure 4.7 Test statistics from SHOE detector

E. PERFORMANCE EVALUATION

The problem of detecting the time epochs when zero-velocity updates are required in a foot-mounted pedestrian navigation system was investigated with detectors in the literature, namely,

The Acceleration-Moving Variance (MV) detector,

The Acceleration-Magnitude (MAG) detector,

The Angular Rate Energy (ARE) detector and

The Stance Hypothesis Optimal (SHOE) detector

From figures [4.4] - [4.7], we infer that the test statistics of the acceleration-moving variance detector and the acceleration-magnitude detector are an order of magnitude smaller than those of the angular rate energy detector and the SHOE detector. Two possible reasons for this:

The signal-to-noise ratios in the signals from gyroscopes are higher than the signal-to-noise ratios in the signals from the accelerometers and

There is more knowledge about the signals from the gyroscopes than about the signals from the accelerometers under the hypothesis that the IMU is stationary.

From figures [4.6] - [4.7], we infer that the Angular Rate Energy detector and the SHOE detector have the highest performance, and behave basically in the same manner indicating that

The gyroscope signal holds the most reliable information for stationary detection.

The accelerometer measurements only bring marginal additional information.

VI Position estimation

The nonlinear and unstable nature of a foot-mounted INS filtering makes a general performance analysis difficult. The performance is dependent on the true trajectory in a nontrivial way.

Figure 5.1 Tested Trajectory for INS evaluation

The main obstacle is that the position errors are strongly coupled with the heading errors via the true (relative) position. A heading error of 0.5 degrees gives a relative position error of 1% of the traveled end-to-end point distance. However, if the user then walks back the same distance, the position errors cancel out. Scale errors are canceled out likewise. Trajectory chosen for study: a closed-loop symmetric trajectory (figure 5.1) in which the heading and other trajectory induced errors largely cancel themselves out.

By studying the errors in such trajectories, we can get a rough separation of the position errors induced by the heading errors and the other error sources. Generally, the gyroscopes were calibrated prior to recording the trajectories but not between individual trajectory measurements.

Figure 5.2 Performance of ZUPT

For a closed-loop trajectory, the initial heading alignment errors cancel out, but for a straight-line trajectory they will not. Performance varies with the zero velocity detectors [table 5.1]

Table 5.1 ZUPT performance report

5.2 SENSOR BIAS & OFFSET

The output of a given sensor is composed of two parts. One component represents the true value of the physical phenomenon to be quantified-acceleration, angular rate, or the magnetic flux density. The second component in the sensor output is an error, which degrades the overall accuracy of the desired measurement.

These errors can be represented as: Bias error and scale-factor error. The purpose of the calibration is to mitigate these errors.

Figure 5.3 IMU scale factor

5.3 COVARIANCE ESTIMATED

Behavior and performance of the system with & without sensor bias & offset:

Figure 5.4 Performance of FMFA - no bias/offset

Figure 5.5 Performance of FMFA - with bias/offset

5.4 OBSERVATION

Examination of the main features of human walking motion was necessary to understand two fundamental states-the swing phase and the stance phase. Two essential components of the PNS were also introduced here. The first being the zero-velocity updates, which provided a means of reducing the error in the computed velocity and subsequently in the computed position. A second component of the PNS was the algorithm for estimating human foot position during normal walking based on estimates of foot orientation, velocity, acceleration, and gait phase from inertial/magnetic sensor measurements. Orientation estimation was accomplished by a quaternion-based complementary filter that uses a variable scalar gain factor to blend the high frequency information provided by angular rate sensors and the low-frequency information provided by accelerometers and magnetometers.

Foot acceleration is directly measured by the accelerometers of the IMMU. However, the measurements are represented in the sensor or body coordinate frame. For many applications, it is desirable to have foot acceleration in the earth coordinate frame. With foot orientation readily available as a result of the quaternion-based complementary filter, foot acceleration in the body coordinate frame is conveniently converted into the earth coordinate frame using the foot orientation quaternion. Foot velocity is obtained by numerically integrating corrected foot acceleration measurements obtained during the swing phase. Due to sensor noise, accelerometer measurements tend to drift. The drift is corrected using the ZVU technique, which is based on the fact that foot velocity is known to be zero during stance phases. The corrected foot velocity is integrated to obtain foot position.

Simulations and experiments were conducted to evaluate the algorithm. The experimental results suggest that the achievable position accuracy of the algorithm is about 1% of the total walked distance. The simulation study suggests that sensor biases are the main source of the position error.

CONCLUSION

Orientation estimation was accomplished by a quaternion-based complementary filter that uses a variable scalar gain factor to blend the high frequency information provided by angular rate sensors and the low-frequency information provided by accelerometers and magnetometers.

With foot orientation readily available as a result of the quaternion-based complementary filter, foot acceleration in the body coordinate frame is conveniently converted into the earth coordinate frame using the foot orientation quaternion. Foot velocity is obtained by numerically integrating corrected foot acceleration measurements obtained during the swing phase. Due to sensor noise, accelerometer measurements tend to drift. The drift is corrected using the ZVU technique, which is based on the fact that foot velocity is known to be zero during stance phases. The corrected foot velocity is integrated to obtain foot position.

6.1 FUTURE WORK

A focus of future work will be to implement the filtering algorithm in microcontroller & interface with IMU sensor. Such techniques might include some preliminary measurements with the sensor installed in its intended field of use, thereby providing a sort of in situ calibration. The calibration method for three-axis accelerometers and magnetometers will be considered because it only involves arbitrary rotations of sensor modules without the need of special calibration equipment.

Further study is required here to assess the limits of precision of MEMS-based sensor technology and evaluation of other sensor architectures when they are available. The filter gains of the complementary filter and the tuning parameters within the gait phase detection algorithm should be examined in terms of their influence on the overall performance when the larger user group is considered.

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