Here's another fantastic piece of technology - the gismo I will describe is a combination of 3-axis Gyroscope, 3-axis Accelerometer - and ... more!
This is it, mounted on the GY-521 breakout board, available from Amazon:
The whole board is about 20 mm by about 15 mm, and it cost £3.10 including delivery!! It comes with an 8-pin header which needs to be soldered on.
The black chip in the centre is the InvenSense MPU-6050 which contains a MEMS (Microelectromechanical System) gyroscope and MEMS accelerometer, all in one chip, called an Inertial Measurement Unit (IMU). Because each has 3 DOF [3 degrees of freedom (X, Y and Z outputs)], the IMU is said to have 6 degrees of freedom. The IMU also contains a microprocessor [embedded Digital Motion Processor (DMP)] which carries out some basic calculations involving quaternions. (That's where the maths become difficult). It even monitors its own chip temperature (and this can be read out) for real-time data correction.
However, apart from its very impressive performance, which is simple to understand, getting it to work is not easy, and understanding the extensive mathematics and the lengthy code is far from easy.
Gyroscope
Let me first explain what a gyroscope (or gyro) is: The early types of gyroscope included a spinning wheel of some kind. Because of the angular momentum involved, the device tries to maintain its position in space, and will resist forces which try to turn it away from its present position. One kind of electronic gyroscope uses a piezoelectric vibrating crystal which will also resist external forces. The device will generate an electrical signal when it detects such a Coriolis force and this signal can be processed to give information about the angular velocity, or rate of rotation about each of its axes. However, gyro readings 'creep' over time and so on its own, a gyro would not be useful for controlling orientation.Accelerometer
An accelerometer is a bit different. This device, also with micro-mechanical components, if falling freely, will generate no signal. On the other hand, an accelerometer at rest on the surface of the Earth will experience the acceleration due to gravity. If the device rotates on an axis other than the vertical, its resulting acceleration in the vertical direction will be an angular component of gravity. It could be moving fast, but if it's free falling or rotating freely, its output will say 'no acceleration'. So the accelerometer on its own would also not be enough to maintain orientation.Quaternions
The outputs from both the gyro and the accelerometer can be combined using a complementary filter or more accurately, using a Kalman filter. Geek Mom Debra at http://www.geekmomprojects.com/gyroscopes-and-accelerometers-on-a-chip/ gives a great explanation of how the complementary filter can combine the gyro and accelerometer data. Using quaternions, allowing angles of greater than 180 degrees to be calculated, provides an alternative to the Euler angle co-ordinate system which overcomes a problem known as gymbal lock. Gymbal lock occurs when two of the rotational axes come into alignment, thus reducing the number of degrees of freedom.Quaternions were conceived by Irish mathematician William Rowan Hamilton in 1843 as he crossed the Broom Bridge over Dublin's Royal Canal. Today they are fundamental to space ship, robotic and many other control systems as they give a means of avoiding a fourth gymbal in a gyroscope which would be necessary to overcome gymbal lock.
The in-built microprocessor (DMP) calculates the quaternions, and the Arduino sketch can output a stream of numbers representing rotations in all directions.
However, the Arduino Integrated Development Environment (IDE) doesn't have a graphical capability, so if a graphical representation is required, it's necessary to use a further coding IDE called the "Processing" IDE. The code, like Java, is quite similar to the Arduino sketch code.
Arduino code
Here's the Arduino code:
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| // I2C device class (I2Cdev) demonstration Arduino sketch for MPU6050 class using DMP (MotionApps v2.0) | |
| // 6/21/2012 by Jeff Rowberg <jeff@rowberg.net> | |
| // Updates should (hopefully) always be available at https://github.com/jrowberg/i2cdevlib | |
| // | |
| // Changelog: | |
| // 2013-05-08 - added seamless Fastwire support | |
| // - added note about gyro calibration | |
| // 2012-06-21 - added note about Arduino 1.0.1 + Leonardo compatibility error | |
| // 2012-06-20 - improved FIFO overflow handling and simplified read process | |
| // 2012-06-19 - completely rearranged DMP initialization code and simplification | |
| // 2012-06-13 - pull gyro and accel data from FIFO packet instead of reading directly | |
| // 2012-06-09 - fix broken FIFO read sequence and change interrupt detection to RISING | |
| // 2012-06-05 - add gravity-compensated initial reference frame acceleration output | |
| // - add 3D math helper file to DMP6 example sketch | |
| // - add Euler output and Yaw/Pitch/Roll output formats | |
| // 2012-06-04 - remove accel offset clearing for better results (thanks Sungon Lee) | |
| // 2012-06-01 - fixed gyro sensitivity to be 2000 deg/sec instead of 250 | |
| // 2012-05-30 - basic DMP initialization working | |
| /* ============================================ | |
| I2Cdev device library code is placed under the MIT license | |
| Copyright (c) 2012 Jeff Rowberg | |
| Permission is hereby granted, free of charge, to any person obtaining a copy | |
| of this software and associated documentation files (the "Software"), to deal | |
| in the Software without restriction, including without limitation the rights | |
| to use, copy, modify, merge, publish, distribute, sublicense, and/or sell | |
| copies of the Software, and to permit persons to whom the Software is | |
| furnished to do so, subject to the following conditions: | |
| The above copyright notice and this permission notice shall be included in | |
| all copies or substantial portions of the Software. | |
| THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR | |
| IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, | |
| FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE | |
| AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER | |
| LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, | |
| OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN | |
| THE SOFTWARE. | |
| =============================================== | |
| */ | |
| // I2Cdev and MPU6050 must be installed as libraries, or else the .cpp/.h files | |
| // for both classes must be in the include path of your project | |
| #include "I2Cdev.h" | |
| #include "MPU6050_6Axis_MotionApps20.h" | |
| //#include "MPU6050.h" // not necessary if using MotionApps include file | |
| // Arduino Wire library is required if I2Cdev I2CDEV_ARDUINO_WIRE implementation | |
| // is used in I2Cdev.h | |
| #if I2CDEV_IMPLEMENTATION == I2CDEV_ARDUINO_WIRE | |
| #include "Wire.h" | |
| #endif | |
| // class default I2C address is 0x68 | |
| // specific I2C addresses may be passed as a parameter here | |
| // AD0 low = 0x68 (default for SparkFun breakout and InvenSense evaluation board) | |
| // AD0 high = 0x69 | |
| MPU6050 mpu; | |
| //MPU6050 mpu(0x69); // <-- use for AD0 high | |
| /* ========================================================================= | |
| NOTE: In addition to connection 3.3v, GND, SDA, and SCL, this sketch | |
| depends on the MPU-6050's INT pin being connected to the Arduino's | |
| external interrupt #0 pin. On the Arduino Uno and Mega 2560, this is | |
| digital I/O pin 2. | |
| * ========================================================================= */ | |
| /* ========================================================================= | |
| NOTE: Arduino v1.0.1 with the Leonardo board generates a compile error | |
| when using Serial.write(buf, len). The Teapot output uses this method. | |
| The solution requires a modification to the Arduino USBAPI.h file, which | |
| is fortunately simple, but annoying. This will be fixed in the next IDE | |
| release. For more info, see these links: | |
| http://arduino.cc/forum/index.php/topic,109987.0.html | |
| http://code.google.com/p/arduino/issues/detail?id=958 | |
| * ========================================================================= */ | |
| // uncomment "OUTPUT_READABLE_QUATERNION" if you want to see the actual | |
| // quaternion components in a [w, x, y, z] format (not best for parsing | |
| // on a remote host such as Processing or something though) | |
| #define OUTPUT_READABLE_QUATERNION | |
| // uncomment "OUTPUT_READABLE_EULER" if you want to see Euler angles | |
| // (in degrees) calculated from the quaternions coming from the FIFO. | |
| // Note that Euler angles suffer from gimbal lock (for more info, see | |
| // http://en.wikipedia.org/wiki/Gimbal_lock) | |
| //#define OUTPUT_READABLE_EULER | |
| // uncomment "OUTPUT_READABLE_YAWPITCHROLL" if you want to see the yaw/ | |
| // pitch/roll angles (in degrees) calculated from the quaternions coming | |
| // from the FIFO. Note this also requires gravity vector calculations. | |
| // Also note that yaw/pitch/roll angles suffer from gimbal lock (for | |
| // more info, see: http://en.wikipedia.org/wiki/Gimbal_lock) | |
| //#define OUTPUT_READABLE_YAWPITCHROLL | |
| // uncomment "OUTPUT_READABLE_REALACCEL" if you want to see acceleration | |
| // components with gravity removed. This acceleration reference frame is | |
| // not compensated for orientation, so +X is always +X according to the | |
| // sensor, just without the effects of gravity. If you want acceleration | |
| // compensated for orientation, us OUTPUT_READABLE_WORLDACCEL instead. | |
| //#define OUTPUT_READABLE_REALACCEL | |
| // uncomment "OUTPUT_READABLE_WORLDACCEL" if you want to see acceleration | |
| // components with gravity removed and adjusted for the world frame of | |
| // reference (yaw is relative to initial orientation, since no magnetometer | |
| // is present in this case). Could be quite handy in some cases. | |
| //#define OUTPUT_READABLE_WORLDACCEL | |
| // uncomment "OUTPUT_TEAPOT" if you want output that matches the | |
| // format used for the InvenSense teapot demo | |
| #define OUTPUT_TEAPOT | |
| #define LED_PIN 13 // (Arduino is 13, Teensy is 11, Teensy++ is 6) | |
| bool blinkState = false; | |
| // MPU control/status vars | |
| bool dmpReady = false; // set true if DMP init was successful | |
| uint8_t mpuIntStatus; // holds actual interrupt status byte from MPU | |
| uint8_t devStatus; // return status after each device operation (0 = success, !0 = error) | |
| uint16_t packetSize; // expected DMP packet size (default is 42 bytes) | |
| uint16_t fifoCount; // count of all bytes currently in FIFO | |
| uint8_t fifoBuffer[64]; // FIFO storage buffer | |
| // orientation/motion vars | |
| Quaternion q; // [w, x, y, z] quaternion container | |
| VectorInt16 aa; // [x, y, z] accel sensor measurements | |
| VectorInt16 aaReal; // [x, y, z] gravity-free accel sensor measurements | |
| VectorInt16 aaWorld; // [x, y, z] world-frame accel sensor measurements | |
| VectorFloat gravity; // [x, y, z] gravity vector | |
| float euler[3]; // [psi, theta, phi] Euler angle container | |
| float ypr[3]; // [yaw, pitch, roll] yaw/pitch/roll container and gravity vector | |
| // packet structure for InvenSense teapot demo | |
| uint8_t teapotPacket[14] = { '$', 0x02, 0,0, 0,0, 0,0, 0,0, 0x00, 0x00, '\r', '\n' }; | |
| // ================================================================ | |
| // === INTERRUPT DETECTION ROUTINE === | |
| // ================================================================ | |
| volatile bool mpuInterrupt = false; // indicates whether MPU interrupt pin has gone high | |
| void dmpDataReady() { | |
| mpuInterrupt = true; | |
| } | |
| // ================================================================ | |
| // === INITIAL SETUP === | |
| // ================================================================ | |
| void setup() { | |
| // join I2C bus (I2Cdev library doesn't do this automatically) | |
| #if I2CDEV_IMPLEMENTATION == I2CDEV_ARDUINO_WIRE | |
| Wire.begin(); | |
| TWBR = 24; // 400kHz I2C clock (200kHz if CPU is 8MHz) | |
| #elif I2CDEV_IMPLEMENTATION == I2CDEV_BUILTIN_FASTWIRE | |
| Fastwire::setup(400, true); | |
| #endif | |
| // initialize serial communication | |
| // (115200 chosen because it is required for Teapot Demo output, but it's | |
| // really up to you depending on your project) | |
| //Serial.begin(115200); | |
| Serial.begin(57600); //seems to work best for me (KC), with Quaternion option | |
| //Serial.begin(38400); | |
| while (!Serial); // wait for Leonardo enumeration, others continue immediately | |
| // NOTE: 8MHz or slower host processors, like the Teensy @ 3.3v or Ardunio | |
| // Pro Mini running at 3.3v, cannot handle this baud rate reliably due to | |
| // the baud timing being too misaligned with processor ticks. You must use | |
| // 38400 or slower in these cases, or use some kind of external separate | |
| // crystal solution for the UART timer. | |
| // initialize device | |
| Serial.println(F("Initializing I2C devices...")); | |
| mpu.initialize(); | |
| // verify connection | |
| Serial.println(F("Testing device connections...")); | |
| Serial.println(mpu.testConnection() ? F("MPU6050 connection successful") : F("MPU6050 connection failed")); | |
| // wait for ready | |
| Serial.println(F("\nSend any character to begin DMP programming and demo: ")); | |
| while (Serial.available() && Serial.read()); // empty buffer | |
| while (!Serial.available()); // wait for data | |
| while (Serial.available() && Serial.read()); // empty buffer again | |
| // load and configure the DMP | |
| Serial.println(F("Initializing DMP...")); | |
| devStatus = mpu.dmpInitialize(); | |
| // supply your own gyro offsets here, scaled for min sensitivity | |
| mpu.setXGyroOffset(220); | |
| mpu.setYGyroOffset(76); | |
| mpu.setZGyroOffset(-85); | |
| mpu.setZAccelOffset(1788); // 1688 factory default for my test chip | |
| // make sure it worked (returns 0 if so) | |
| if (devStatus == 0) { | |
| // turn on the DMP, now that it's ready | |
| Serial.println(F("Enabling DMP...")); | |
| mpu.setDMPEnabled(true); | |
| // enable Arduino interrupt detection | |
| Serial.println(F("Enabling interrupt detection (Arduino external interrupt 0)...")); | |
| attachInterrupt(0, dmpDataReady, RISING); | |
| mpuIntStatus = mpu.getIntStatus(); | |
| // set our DMP Ready flag so the main loop() function knows it's okay to use it | |
| Serial.println(F("DMP ready! Waiting for first interrupt...")); | |
| dmpReady = true; | |
| // get expected DMP packet size for later comparison | |
| packetSize = mpu.dmpGetFIFOPacketSize(); | |
| } else { | |
| // ERROR! | |
| // 1 = initial memory load failed | |
| // 2 = DMP configuration updates failed | |
| // (if it's going to break, usually the code will be 1) | |
| Serial.print(F("DMP Initialization failed (code ")); | |
| Serial.print(devStatus); | |
| Serial.println(F(")")); | |
| } | |
| // configure LED for output | |
| pinMode(LED_PIN, OUTPUT); | |
| } | |
| // ================================================================ | |
| // === MAIN PROGRAM LOOP === | |
| // ================================================================ | |
| void loop() { | |
| // if programming failed, don't try to do anything | |
| if (!dmpReady) return; | |
| // wait for MPU interrupt or extra packet(s) available | |
| while (!mpuInterrupt && fifoCount < packetSize) { | |
| // other program behavior stuff here | |
| // . | |
| // . | |
| // . | |
| // if you are really paranoid you can frequently test in between other | |
| // stuff to see if mpuInterrupt is true, and if so, "break;" from the | |
| // while() loop to immediately process the MPU data | |
| // . | |
| // . | |
| // . | |
| } | |
| // reset interrupt flag and get INT_STATUS byte | |
| mpuInterrupt = false; | |
| mpuIntStatus = mpu.getIntStatus(); | |
| // get current FIFO count | |
| fifoCount = mpu.getFIFOCount(); | |
| // check for overflow (this should never happen unless our code is too inefficient) | |
| if ((mpuIntStatus & 0x10) || fifoCount == 1024) { | |
| // reset so we can continue cleanly | |
| mpu.resetFIFO(); | |
| Serial.println(F("FIFO overflow!")); | |
| // otherwise, check for DMP data ready interrupt (this should happen frequently) | |
| } else if (mpuIntStatus & 0x02) { | |
| // wait for correct available data length, should be a VERY short wait | |
| while (fifoCount < packetSize) fifoCount = mpu.getFIFOCount(); | |
| // read a packet from FIFO | |
| mpu.getFIFOBytes(fifoBuffer, packetSize); | |
| // track FIFO count here in case there is > 1 packet available | |
| // (this lets us immediately read more without waiting for an interrupt) | |
| fifoCount -= packetSize; | |
| #ifdef OUTPUT_READABLE_QUATERNION | |
| // display quaternion values in easy matrix form: w x y z | |
| mpu.dmpGetQuaternion(&q, fifoBuffer); | |
| Serial.print("quat\t"); | |
| Serial.print(q.w); | |
| Serial.print("\t"); | |
| Serial.print(q.x); | |
| Serial.print("\t"); | |
| Serial.print(q.y); | |
| Serial.print("\t"); | |
| Serial.println(q.z); | |
| #endif | |
| #ifdef OUTPUT_READABLE_EULER | |
| // display Euler angles in degrees | |
| mpu.dmpGetQuaternion(&q, fifoBuffer); | |
| mpu.dmpGetEuler(euler, &q); | |
| Serial.print("euler\t"); | |
| Serial.print(euler[0] * 180/M_PI); | |
| Serial.print("\t"); | |
| Serial.print(euler[1] * 180/M_PI); | |
| Serial.print("\t"); | |
| Serial.println(euler[2] * 180/M_PI); | |
| #endif | |
| #ifdef OUTPUT_READABLE_YAWPITCHROLL | |
| // display Euler angles in degrees | |
| mpu.dmpGetQuaternion(&q, fifoBuffer); | |
| mpu.dmpGetGravity(&gravity, &q); | |
| mpu.dmpGetYawPitchRoll(ypr, &q, &gravity); | |
| Serial.print("ypr\t"); | |
| Serial.print(ypr[0] * 180/M_PI); | |
| Serial.print("\t"); | |
| Serial.print(ypr[1] * 180/M_PI); | |
| Serial.print("\t"); | |
| Serial.println(ypr[2] * 180/M_PI); | |
| #endif | |
| #ifdef OUTPUT_READABLE_REALACCEL | |
| // display real acceleration, adjusted to remove gravity | |
| mpu.dmpGetQuaternion(&q, fifoBuffer); | |
| mpu.dmpGetAccel(&aa, fifoBuffer); | |
| mpu.dmpGetGravity(&gravity, &q); | |
| mpu.dmpGetLinearAccel(&aaReal, &aa, &gravity); | |
| Serial.print("areal\t"); | |
| Serial.print(aaReal.x); | |
| Serial.print("\t"); | |
| Serial.print(aaReal.y); | |
| Serial.print("\t"); | |
| Serial.println(aaReal.z); | |
| #endif | |
| #ifdef OUTPUT_READABLE_WORLDACCEL | |
| // display initial world-frame acceleration, adjusted to remove gravity | |
| // and rotated based on known orientation from quaternion | |
| mpu.dmpGetQuaternion(&q, fifoBuffer); | |
| mpu.dmpGetAccel(&aa, fifoBuffer); | |
| mpu.dmpGetGravity(&gravity, &q); | |
| mpu.dmpGetLinearAccel(&aaReal, &aa, &gravity); | |
| mpu.dmpGetLinearAccelInWorld(&aaWorld, &aaReal, &q); | |
| Serial.print("aworld\t"); | |
| Serial.print(aaWorld.x); | |
| Serial.print("\t"); | |
| Serial.print(aaWorld.y); | |
| Serial.print("\t"); | |
| Serial.println(aaWorld.z); | |
| #endif | |
| #ifdef OUTPUT_TEAPOT | |
| // display quaternion values in InvenSense Teapot demo format: | |
| teapotPacket[2] = fifoBuffer[0]; | |
| teapotPacket[3] = fifoBuffer[1]; | |
| teapotPacket[4] = fifoBuffer[4]; | |
| teapotPacket[5] = fifoBuffer[5]; | |
| teapotPacket[6] = fifoBuffer[8]; | |
| teapotPacket[7] = fifoBuffer[9]; | |
| teapotPacket[8] = fifoBuffer[12]; | |
| teapotPacket[9] = fifoBuffer[13]; | |
| Serial.write(teapotPacket, 14); | |
| teapotPacket[11]++; // packetCount, loops at 0xFF on purpose | |
| #endif | |
| // blink LED to indicate activity | |
| blinkState = !blinkState; | |
| digitalWrite(LED_PIN, blinkState); | |
| } | |
| } |
Processing code
and here's the Processing code which reads the Arduino data and performs some neat 3D drawing:
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| // I2C device class (I2Cdev) demonstration Processing sketch for MPU6050 DMP output | |
| // 6/20/2012 by Jeff Rowberg <jeff@rowberg.net> | |
| // Updates should (hopefully) always be available at https://github.com/jrowberg/i2cdevlib | |
| // | |
| // Changelog: | |
| // 2012-06-20 - initial release | |
| /* ============================================ | |
| I2Cdev device library code is placed under the MIT license | |
| Copyright (c) 2012 Jeff Rowberg | |
| Permission is hereby granted, free of charge, to any person obtaining a copy | |
| of this software and associated documentation files (the "Software"), to deal | |
| in the Software without restriction, including without limitation the rights | |
| to use, copy, modify, merge, publish, distribute, sublicense, and/or sell | |
| copies of the Software, and to permit persons to whom the Software is | |
| furnished to do so, subject to the following conditions: | |
| The above copyright notice and this permission notice shall be included in | |
| all copies or substantial portions of the Software. | |
| THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR | |
| IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, | |
| FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE | |
| AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER | |
| LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, | |
| OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN | |
| THE SOFTWARE. | |
| =============================================== | |
| */ | |
| import processing.serial.*; | |
| import processing.opengl.*; | |
| import toxi.geom.*; | |
| import toxi.processing.*; | |
| // NOTE: requires ToxicLibs to be installed in order to run properly. | |
| // 1. Download from http://toxiclibs.org/downloads | |
| // 2. Extract into [userdir]/Processing/libraries | |
| // (location may be different on Mac/Linux) | |
| // 3. Run and bask in awesomeness | |
| ToxiclibsSupport gfx; | |
| Serial port; // The serial port | |
| char[] teapotPacket = new char[14]; // InvenSense Teapot packet | |
| int serialCount = 0; // current packet byte position | |
| int aligned = 0; | |
| int interval = 0; | |
| //DA - added the variable below to fix byte alignment over the Serial port | |
| boolean gotFirstDataByte = false; | |
| float[] q = new float[4]; | |
| Quaternion quat = new Quaternion(1, 0, 0, 0); | |
| float[] gravity = new float[3]; | |
| float[] euler = new float[3]; | |
| float[] ypr = new float[3]; | |
| void setup() { | |
| // 300px square viewport using OpenGL rendering | |
| size(300, 300, OPENGL); | |
| gfx = new ToxiclibsSupport(this); | |
| // setup lights and antialiasing | |
| lights(); | |
| smooth(); | |
| // display serial port list for debugging/clarity | |
| println(Serial.list()); | |
| // get the first available port (use EITHER this OR the specific port code below) | |
| // DA - changed the port to second one in the list (for my laptop) | |
| String portName = Serial.list()[5]; | |
| // get a specific serial port (use EITHER this OR the first-available code above) | |
| //String portName = "COM7"; | |
| // open the serial port | |
| //DA - changed the serial data rate to 38400 | |
| //port = new Serial(this, portName, 38400); | |
| port = new Serial(this, portName, 57600); //Seems to work best for me (KC), with Quaternion option | |
| // send single character to trigger DMP init/start | |
| // (expected by MPU6050_DMP6 example Arduino sketch) | |
| port.write('r'); | |
| //DA - I added two more of these because the program seems to hang otherwise | |
| port.write('r'); | |
| port.write('r'); | |
| port.write('r'); | |
| port.write('r'); | |
| port.write('r'); | |
| } | |
| void draw() { | |
| if (millis() - interval > 1000) { | |
| // resend single character to trigger DMP init/start | |
| // in case the MPU is halted/reset while applet is running | |
| port.write('r'); | |
| interval = millis(); | |
| } | |
| // black background | |
| background(0); | |
| // translate everything to the middle of the viewport | |
| pushMatrix(); | |
| translate(width / 2, height / 2); | |
| // 3-step rotation from yaw/pitch/roll angles (gimbal lock!) | |
| // ...and other weirdness I haven't figured out yet | |
| //rotateY(-ypr[0]); | |
| //rotateZ(-ypr[1]); | |
| //rotateX(-ypr[2]); | |
| // toxiclibs direct angle/axis rotation from quaternion (NO gimbal lock!) | |
| // (axis order [1, 3, 2] and inversion [-1, +1, +1] is a consequence of | |
| // different coordinate system orientation assumptions between Processing | |
| // and InvenSense DMP) | |
| float[] axis = quat.toAxisAngle(); | |
| rotate(axis[0], -axis[1], axis[3], axis[2]); | |
| // draw main body in red | |
| fill(255, 0, 0, 200); | |
| box(10, 10, 200); | |
| // draw front-facing tip in blue | |
| fill(0, 0, 255, 200); | |
| pushMatrix(); | |
| translate(0, 0, -120); | |
| rotateX(PI/2); | |
| drawCylinder(0, 20, 20, 8); | |
| popMatrix(); | |
| // draw wings and tail fin in green | |
| fill(0, 255, 0, 200); | |
| beginShape(TRIANGLES); | |
| vertex(-100, 2, 30); vertex(0, 2, -80); vertex(100, 2, 30); // wing top layer | |
| vertex(-100, -2, 30); vertex(0, -2, -80); vertex(100, -2, 30); // wing bottom layer | |
| vertex(-2, 0, 98); vertex(-2, -30, 98); vertex(-2, 0, 70); // tail left layer | |
| vertex( 2, 0, 98); vertex( 2, -30, 98); vertex( 2, 0, 70); // tail right layer | |
| endShape(); | |
| beginShape(QUADS); | |
| vertex(-100, 2, 30); vertex(-100, -2, 30); vertex( 0, -2, -80); vertex( 0, 2, -80); | |
| vertex( 100, 2, 30); vertex( 100, -2, 30); vertex( 0, -2, -80); vertex( 0, 2, -80); | |
| vertex(-100, 2, 30); vertex(-100, -2, 30); vertex(100, -2, 30); vertex(100, 2, 30); | |
| vertex(-2, 0, 98); vertex(2, 0, 98); vertex(2, -30, 98); vertex(-2, -30, 98); | |
| vertex(-2, 0, 98); vertex(2, 0, 98); vertex(2, 0, 70); vertex(-2, 0, 70); | |
| vertex(-2, -30, 98); vertex(2, -30, 98); vertex(2, 0, 70); vertex(-2, 0, 70); | |
| endShape(); | |
| popMatrix(); | |
| } | |
| void serialEvent(Serial port) { | |
| interval = millis(); | |
| while (port.available() > 0) { | |
| int ch = port.read(); | |
| // DA - Added this next if statement because we seem to be getting | |
| // off byte boundary with initialization warnings | |
| if(!gotFirstDataByte) { | |
| if (ch == '$') { | |
| gotFirstDataByte = true; | |
| } else { | |
| return; | |
| } | |
| } | |
| //println("Char: " + (char)ch); | |
| //println((char)ch + " " + aligned + " " + serialCount); | |
| if (aligned < 4) { | |
| // make sure we are properly aligned on a 14-byte packet | |
| if (serialCount == 0) { | |
| if (ch == '$') aligned++; else aligned = 0; | |
| } else if (serialCount == 1) { | |
| if (ch == 2) aligned++; else aligned = 0; | |
| } else if (serialCount == 12) { | |
| if (ch == '\r') aligned++; else aligned = 0; | |
| } else if (serialCount == 13) { | |
| if (ch == '\n') aligned++; else aligned = 0; | |
| } | |
| //println((char)ch + " " + aligned + " " + serialCount); | |
| serialCount++; | |
| if (serialCount == 14) serialCount = 0; | |
| } else { | |
| if (serialCount > 0 || ch == '$') { | |
| teapotPacket[serialCount++] = (char)ch; | |
| if (serialCount == 14) { | |
| serialCount = 0; // restart packet byte position | |
| // get quaternion from data packet | |
| q[0] = ((teapotPacket[2] << 8) | teapotPacket[3]) / 16384.0f; | |
| q[1] = ((teapotPacket[4] << 8) | teapotPacket[5]) / 16384.0f; | |
| q[2] = ((teapotPacket[6] << 8) | teapotPacket[7]) / 16384.0f; | |
| q[3] = ((teapotPacket[8] << 8) | teapotPacket[9]) / 16384.0f; | |
| for (int i = 0; i < 4; i++) if (q[i] >= 2) q[i] = -4 + q[i]; | |
| // set our toxilibs quaternion to new data | |
| quat.set(q[0], q[1], q[2], q[3]); | |
| /* | |
| // below calculations unnecessary for orientation only using toxilibs | |
| // calculate gravity vector | |
| gravity[0] = 2 * (q[1]*q[3] - q[0]*q[2]); | |
| gravity[1] = 2 * (q[0]*q[1] + q[2]*q[3]); | |
| gravity[2] = q[0]*q[0] - q[1]*q[1] - q[2]*q[2] + q[3]*q[3]; | |
| // calculate Euler angles | |
| euler[0] = atan2(2*q[1]*q[2] - 2*q[0]*q[3], 2*q[0]*q[0] + 2*q[1]*q[1] - 1); | |
| euler[1] = -asin(2*q[1]*q[3] + 2*q[0]*q[2]); | |
| euler[2] = atan2(2*q[2]*q[3] - 2*q[0]*q[1], 2*q[0]*q[0] + 2*q[3]*q[3] - 1); | |
| // calculate yaw/pitch/roll angles | |
| ypr[0] = atan2(2*q[1]*q[2] - 2*q[0]*q[3], 2*q[0]*q[0] + 2*q[1]*q[1] - 1); | |
| ypr[1] = atan(gravity[0] / sqrt(gravity[1]*gravity[1] + gravity[2]*gravity[2])); | |
| ypr[2] = atan(gravity[1] / sqrt(gravity[0]*gravity[0] + gravity[2]*gravity[2])); | |
| // output various components for debugging | |
| //println("q:\t" + round(q[0]*100.0f)/100.0f + "\t" + round(q[1]*100.0f)/100.0f + "\t" + round(q[2]*100.0f)/100.0f + "\t" + round(q[3]*100.0f)/100.0f); | |
| //println("euler:\t" + euler[0]*180.0f/PI + "\t" + euler[1]*180.0f/PI + "\t" + euler[2]*180.0f/PI); | |
| //println("ypr:\t" + ypr[0]*180.0f/PI + "\t" + ypr[1]*180.0f/PI + "\t" + ypr[2]*180.0f/PI); | |
| */ | |
| } | |
| } | |
| } | |
| } | |
| } | |
| void drawCylinder(float topRadius, float bottomRadius, float tall, int sides) { | |
| float angle = 0; | |
| float angleIncrement = TWO_PI / sides; | |
| beginShape(QUAD_STRIP); | |
| for (int i = 0; i < sides + 1; ++i) { | |
| vertex(topRadius*cos(angle), 0, topRadius*sin(angle)); | |
| vertex(bottomRadius*cos(angle), tall, bottomRadius*sin(angle)); | |
| angle += angleIncrement; | |
| } | |
| endShape(); | |
| // If it is not a cone, draw the circular top cap | |
| if (topRadius != 0) { | |
| angle = 0; | |
| beginShape(TRIANGLE_FAN); | |
| // Center point | |
| vertex(0, 0, 0); | |
| for (int i = 0; i < sides + 1; i++) { | |
| vertex(topRadius * cos(angle), 0, topRadius * sin(angle)); | |
| angle += angleIncrement; | |
| } | |
| endShape(); | |
| } | |
| // If it is not a cone, draw the circular bottom cap | |
| if (bottomRadius != 0) { | |
| angle = 0; | |
| beginShape(TRIANGLE_FAN); | |
| // Center point | |
| vertex(0, tall, 0); | |
| for (int i = 0; i < sides + 1; i++) { | |
| vertex(bottomRadius * cos(angle), tall, bottomRadius * sin(angle)); | |
| angle += angleIncrement; | |
| } | |
| endShape(); | |
| } | |
| } |
Here's the setup for power and the I 2C connections:
GY 521 VCC to Arduino 3.3V
GY 521 GND to Arduino GND
GY 521 SCL to Arduino Analog pin 5, A5
GY 521 SDA to Arduino Analog pin 4, A4
GY 521 INT (interrupt) to Arduino Digital pin 2
Here's the video: The window on the right shows the Processing IDE.
Here's the demo up close:
Until about 20 seconds into the 2nd video (10 s into the first video), the chip seems to go through a calibration routine, so that it 'gets its bearings' and it appears to monitor the degree of gyro creep, after which presumably a correction is applied to remove that creep. The vagueness in the above statement is because the manufacturers have not divulged the exact details about how this calibration is achieved.
After this stage in the video, the movement in 3 dimensions is caused by me rotating the mini breadboard containing the GY-521 and then moving it about so that it rotates about its X, Y and Z axes.
I must acknowledge Geek Mom Debra once more. Her excellent blog at http://www.geekmomprojects.com/mpu-6050-dmp-data-from-i2cdevlib/ is where I got her tweaked code, and I'm looking forward to seeing her "side-by-side comparison" between the embedded Digital Motion Processor and complementary filter data when it appears.
Note that the option I have chosen in the Arduino sketch is (lines 84 to 87):
// uncomment "OUTPUT_READABLE_QUATERNION" if you want to see the actual// quaternion components in a [w, x, y, z] format (not best for parsing// on a remote host such as Processing or something though)#define OUTPUT_READABLE_QUATERNION
The quaternion option is immune from gymbal lock. I found that the baud rate of 57600, which must be set the same on both Arduino and Processing code, worked best for me.
The aeroplane no longer, if turned through certain large angles, makes sudden 'flips' or simply freezes or even goes into what can only be described as 'the jitters'. The reference HERE tells the story about the Apollo 11 Moon mission on 20-Jul-69 when the IMU (Inertial Measurement Unit) froze due to gymbal lock.
Mmmmmmmm..... I wonder what this little device could be used for....
What's all this stuff about a teapot?? Well apparently the original demonstration used a 3-dimensional teapot which rotated. Now it's just a primitive plane, but it's still called a teapot!!
