AU2018100564A4 - The invention of using integrated circuit board with embedded IMU algorithms to for Cricket equipment (ball) traction. Usage of gyroscope, accelerometer and magnetometer (compass) injected into the cricket ball acquires readings during ball motions. Embedded processor performs calculations of ball’s orientation and earth referenced acceleration. Data is transmitted wirelessly to the client's equipment about the flight: velocity, flight time, revolution rate, flight distance. - Google Patents

Abstract

Abstract The invention of using microcontroller integrated circuit board with embedded IMU algorithms for sport equipment (ball) traction. Usage of inexpensive components as gyroscope, accelerometer and magnetometer injected into the ball acquires readings during ball motions. Embedded processor performs calculations of ball's orientation and earth referenced acceleration. Wireless data transmission reduces the need of physical connection between microcontroller and requestor's equipment. In this context the equipment is any device which supports wireless data transmission like smartphone, personal computer and smart-watch. Each round or ball feed takes recording and processes the data for a short period of time (no more than 30 seconds). During this period the human which interacts with the invention performs relevant action by feeding the ball. Each round is transmitted back to the client to represent relevant information about the flight: velocity, flight time, revolution rate, flight distance. 8$ TuhDown at 4274 j M/Sec Time cycle: 0 le pmt at324 22 Meters 20$ Time cy cle: 0 - __4ca6 .. 3 M /Sec

Description

Konstantin Rebrov April 30, 2018

This document describes the principle of providing inexpensive real time spot analytical system with the reference to the Cricket game. The solution has been developed to track flight trajectory, revolution rate, and velocity with a set of sensors embedded in the ball. The model is not tied to the Cricket in particular therefore the same approach can be used in the similar areas like baseball, tennis or golf.

The overall solution diagram provided in the Figure 1 (see drawing document)

The prototype has been developed with the following key components Figure 2 (see drawing document) 1) ESP8266 - wifi module and L106 32-bit RISC microprocessor 2) MPU9250 sensor with accelerometer, gyroscope and magnetometer

Mathematical model Position and rotation matrix

According to Euler's rotation theorem [1][3] the rotation of a rigid body (or three-dimensional coordinate system with the fixed origin) is described by a single rotation about some axis. Such a rotation may be uniquely described by a minimum of three real parameters. Flowever, for various reasons, there are several ways to represent it. Many of these representations use more than the necessary minimum of three parameters, although each of them still has only three degrees of freedom. An example where rotation representation is used is in computer vision, where an automated observer needs to track a target. Let's consider a rigid body, with three orthogonal unit vectors fixed to its body (representing the three axes of the object's local coordinate system). The basic problem is to specify the orientation of these three unit vectors, and hence the rigid body, with respect to the observer's coordinate system, regarded as a reference placement in space. The ultimate goal is to describe the 3D trajectory and ball's telemetry in the 6 degrees of freedom (6Dof) as per Figure 3 (see drawings document)

In order to do that the best way is to use quaternion. Quaternions, that form a four-dimensional vector space, have proven very useful in representing rotations due to several advantages above the classical Euler representations mentioned above [2]. Given that Euler vector [3] usage might lead to the Gimbal lock. A quaternion representation of rotation is written as a vector (normalized quaternion)

Equation 1

The above-mentioned triad of unit vectors is also called a basis. Specifying the coordinates (components) of vectors of this basis in its current (rotated) position, in terms of the reference (non-rotated) coordinate axes, will completely describe the rotation. The three unit vectors that form the rotated basis each consist of 3 coordinates, yielding a total of 9 parameters. The orthogonal matrix (post-multiplying a column vector) corresponding to a clockwise/left-handed (looking along positive axis to origin) rotation by the unit quaternion q = qi} {- iqi + jq2 f kq3

Equation 2 where qO, is equivalent to qi, ql is qj, q2, etc. The solution is using Sebastian Madgwick [5][8] algorithm to derive the quaternion which is applicable to inertial measurement units (IMUs) consisting of tri-axis gyroscopes and accelerometers, and magnetic angular rate and gravity (MARG) sensor arrays that also include tri-axis magnetometers. The MARG implementation incorporates magnetic distortion compensation. The algorithm uses a quaternion representation, allowing accelerometer and magnetometer data to be used in an analytically derived and optimized gradient descent algorithm to compute the direction of the gyroscope measurement error as a quaternion derivative. Performance has been evaluated empirically using a commercially available orientation sensor and reference measurements of orientation obtained using an optical measurement system. Performance was also benchmarked against the propriety Kalman-based [6][7] algorithm of orientation sensor. In the algorithm the quaternion needs to be converted back to Euler angles to be presented in the client device. Euler angles ψ, Θ and φ in the so called aerospace sequence describe an orientation of frame achieved by the sequential rotations ψ = Atan2 (2^2¾ — 2qiqi*2ql + 2¾ ~ l) Θ = —sin-1 (2q2q\ + 2qiq.i) φ = Atan2 (2¾^ — 2qiq2,2q^ + — l)

Equation 3

Given by the inhomogeneous expression the rotation matrix can be described as follows "l — 2{q* + gjj) 2(qiq2 - φιφι) 2(<7o92 + ¢1¾) R = 2(qiq2 + qQq3) 1 - 2{q\ + q$) 2(¾¾ -qoqi) m2(qiqs - <7o<?2) 2(g0<?l +ί2φ) 1 ~ 2(<?1 +¾).

Equation 4

Where R is the rotation matrix.

Earth referenced acceleration

Using the equation 4 it's possible to subtract gravity acceleration and get Earth referenced acceleration. The accelerometer comprised a tri-axial accelerometer with a dynamic range of g. (g = 9.81 m*sA2). The static condition no movement, vector magnitude^ 1 g should indicate the Z axis as 9.81 m*s-2 and the remaining axis's are 0. Rotating accelerometer upside-down will show Z acceleration becomes negative as -9.81 m*sA2. Rotating accelerometer with a slight tilt on one side will spread the gravity across X, Y and Z axis. In order to get pure side acceleration it's required to apply rotation matrix on top of raw reading from the sensor. Given the quaternion is derived the earth referenced acceleration can be calculated as per below

Xearth = (l - 2(ql + £?!)) x

Xraw + (2(¾¾ -¾¾)) X braw + (2(90¾ + 91¾)) X ^raw bearth (2(9i92 + q09s)) X %raw + (l - 2(9i + 932)) x ^raw + (2(9293 - 9o9i)) X Zraw dearth ~ ^(2(9l93 — 9o92)) X %raw ~b (2(9o9l "b 929s)) X braw ~b (b — 2(9i "b 92)) X ^raw^j ~ 9.81

Equation 5

Where Xraw, Yraw and Zraw are values from accelerometer sensor. Xearth, Yearth and Zearth are calculated earth referenced acceleration excluding tilts from all three axes.

Virtual gyroscope

The gyroscope is the critical component in the Madgwick's [8] orientation algorithm. Gyroscopes are very sensitive and accurate. However there is a limitation in commercially popular sensors at around 6 revolutions per second (rps). 2000 dps (degree per second on each axis) [4]. Meanwhile even an amateur player can throw the ball at much higher revolution rate. It is also important mentioning the limitation usually manifested only at one axis. Roughly the diagram below is showing phases of the ball motion with the mapping to the diagram of a typical profile of gyroscope sensors output. Figure 4 (see drawings document)

At each given measurement the limit of gyroscope is on one axis. In order to get the most accurate orientation during the flight period the virtual gyro is used when sensor hits the limit of 2000 deps. For other two axes the real gyro data is used. The method below describes how to get approximate values of angels for each side.

The sensor accelerometer, Gp, and magnetometer, Bp, readings measured after the three rotations Rz(iJj) then Ry(0) and finally Rx(<t>) are described by the equations:

Equation 6

The tilt-compensated virtual algorithm first calculates the roll and pitch angles φ and Θ from the accelerometer reading by pre-multiplying Equation 6 by the inverse roll and pitch rotation matrices. Where the vector contains the three components of gravity measured by the accelerometer. cos Θ 0 sin θ 10 0 px 0 10 0 cos φ -sin φ Gpy = 0

v -sin Θ 0 cos Θ 0 sin0 )\GpJ cos Θ sin Osin φ sin 8cos φ ^px f ^ ^ 0 —Ξΐηφ (Jpy = 0 v -sin Θ cos Osin φ cos 0cos φ ) J \g'

Equation 7 The expansion of equation 6 The y component of Equation 7 defines the roll angle φ as:

Gpv cos φ - Gpzsin φ — 0 => ιαη( φ ) = I -^1

Equation 8 Roll angle

The x component of Equation 7 gives the pitch angle Θ as

Equation 9 Pitch angle

With the angles φ and Θ known from the accelerometer, the magnetometer reading can be de-rotated to correct for the sensor orientation

Equation 10 Yaw angle ψ where ψ is computed relative to magnetic north. The yaw angle φ is therefore the required tilt-compensated sensor heading.

The method above is used to derive approximate rotation rate of the axis which is experiencing high revolution rate during the ball flight.

Client software

On the client side the data is received as an array of 1) Earth Referenced acceleration for each of three-axis 2) Converted Euler angles from the quaternion 3) Milliseconds passed from the moment microcontroller started

Integrating of each side the java-script software is plotting the ball 3D trajectory till the moment ball touches the ground. The touch down point is derived as a spike in the acceleration. Figure 5 (see drawings document)

Reference list 1) https://en.wikipedia.org/wiki/Conversion between quaternions and Euler angles 2) https://en.wikipedia.org/wiki/Rotation formalisms in three dimensions#Conversion formulae be tween formalisms 3) https://en.wikipedia.org/wiki/Euler angles 4) https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3634007/ 5) http://x-io.co.uk/res/doc/madgwick internal report.pdf 6) LEFFERTS, E.J., MARKLEY, F. L, AND SHUSTER, M. D. Kalman filtering for spacecraft attitude estimation. Journal of Guidance, Control, and Dynamics 5, 5 (1982), 417-429. 7) LIANG, W. Y., Ml AO, W. T., HONG, L. J., LEI, X. C., AND CHEN, Z. Attitude estimation for small helicopter using extended kalman filter. In Robotics, Automation and Mechatronics, 2008 IEEE Conference on (2008), IEEE, pp. 577-581. 8) MADGWICK, S. An efficient orientation filter for inertial and inertial/magnetic sensor arrays. Report x-io and University of Bristol (UK) (2010).

Claims (1)

1. Claims Konstantin Rebrov 30 April 2018 (a) In General The invention of using microcontroller integrated circuit board with embedded IMU algorithms to for sport equipment (ball) traction. Usage of inexpensive components as gyroscope, accelerometer and magnetometer injected into the ball acquires readings during ball motions. Embedded processor performs calculations of ball's orientation and earth referenced acceleration. Wireless data transmission reduces the need of physical connection between microcontroller and requestor's equipment. In this context the equipment is any device which supports wireless data transmission like smartphone, personal computer and smart-watch. Each round or ball feed takes recording and processes the data for a short period of time (no more than 30 seconds). During this period the human which interacts with the invention performs relevant action by feeding the ball. Each round is transmitted back to the client to represent relevant information about the flight: velocity, flight time, revolution rate, flight distance (b) Conclusion.— The designed solution provides telemetry data of sport's equipment (ball in this context) in motion. In this context the Cricket game is used as a primary area of the claim.