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Electronics Help with a rotomotion IMU clone

Discussion in 'Modding' started by I'm_Not_A_Monster, 9 Feb 2006.

  1. I'm_Not_A_Monster

    I'm_Not_A_Monster Hey, eat this...

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    i'm working on cloning a Rotomotion 4DOF Inertial Measurement Unit, and i can't find any Tokin CG-16D's out there (there is already a thread of mine deatiling this, but feel free to link a store with them in stock here). Unless someone posts a link to one here, i guess i'll have to go with an Analog Devices ADXRS150, which updates @ 150o/second, the CG-16D updates @ 90o/second.

    so now i am faced with two problems. i'm afraid the code i got with the schematics won't work with a different gyro (not to mention one that updates @ different speeds); and the connections are different.

    since there are some frickin' smart people here, can someone help me interface an ADXRS150 where a Tokin CG-16D was supposed to go? since BGA chips are hard for me to solder, i'm going to buy two from sparkfun already mounted on a breakout board. the pinout from that board is:
    1) ST1
    2) ST2
    3) TEMP
    4) +2.5V
    5) RATE
    6) GND
    7) +5V

    the CG-16D has four leads, as follows:
    1) GND
    2) Out
    3) Vcc
    4) Ref

    i'll post the code right below this post. there are two different versions i got, Tilt.C and Tilt.H, i'll post both.
     
  2. I'm_Not_A_Monster

    I'm_Not_A_Monster Hey, eat this...

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    Tilt.C

    /* -*- indent-tabs-mode:T; c-basic-offset:8; tab-width:8; -*- vi: set ts=8:
    * $Id: tilt.c,v 1.1 2003/07/09 18:23:29 john Exp $
    *
    * 1 dimensional tilt sensor using a dual axis accelerometer
    * and single axis angular rate gyro. The two sensors are fused
    * via a two state Kalman filter, with one state being the angle
    * and the other state being the gyro bias.
    *
    * Gyro bias is automatically tracked by the filter. This seems
    * like magic.
    *
    * Please note that there are lots of comments in the functions and
    * in blocks before the functions. Kalman filtering is an already complex
    * subject, made even more so by extensive hand optimizations to the C code
    * that implements the filter. I've tried to make an effort of explaining
    * the optimizations, but feel free to send mail to the mailing list,
    * autopilot-devel@lists.sf.net, with questions about this code.
    *
    *
    * (c) 2003 Trammell Hudson <hudson@rotomotion.com>
    *
    *************
    *
    * This file is part of the autopilot onboard code package.
    *
    * Autopilot is free software; you can redistribute it and/or modify
    * it under the terms of the GNU General Public License as published by
    * the Free Software Foundation; either version 2 of the License, or
    * (at your option) any later version.
    *
    * Autopilot is distributed in the hope that it will be useful,
    * but WITHOUT ANY WARRANTY; without even the implied warranty of
    * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
    * GNU General Public License for more details.
    *
    * You should have received a copy of the GNU General Public License
    * along with Autopilot; if not, write to the Free Software
    * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
    *
    */
    #include <math.h>


    /*
    * Our update rate. This is how often our state is updated with
    * gyro rate measurements. For now, we do it every time an
    * 8 bit counter running at CLK/1024 expires. You will have to
    * change this value if you update at a different rate.
    */
    static const float dt = ( 1024.0 * 256.0 ) / 8000000.0;


    /*
    * Our covariance matrix. This is updated at every time step to
    * determine how well the sensors are tracking the actual state.
    */
    static float P[2][2] = {
    { 1, 0 },
    { 0, 1 },
    };


    /*
    * Our two states, the angle and the gyro bias. As a byproduct of computing
    * the angle, we also have an unbiased angular rate available. These are
    * read-only to the user of the module.
    */
    float angle;
    float q_bias;
    float rate;


    /*
    * R represents the measurement covariance noise. In this case,
    * it is a 1x1 matrix that says that we expect 0.3 rad jitter
    * from the accelerometer.
    */
    static const float R_angle = 0.3;


    /*
    * Q is a 2x2 matrix that represents the process covariance noise.
    * In this case, it indicates how much we trust the acceleromter
    * relative to the gyros.
    */
    static const float Q_angle = 0.001;
    static const float Q_gyro = 0.003;


    /*
    * state_update is called every dt with a biased gyro measurement
    * by the user of the module. It updates the current angle and
    * rate estimate.
    *
    * The pitch gyro measurement should be scaled into real units, but
    * does not need any bias removal. The filter will track the bias.
    *
    * Our state vector is:
    *
    * X = [ angle, gyro_bias ]
    *
    * It runs the state estimation forward via the state functions:
    *
    * Xdot = [ angle_dot, gyro_bias_dot ]
    *
    * angle_dot = gyro - gyro_bias
    * gyro_bias_dot = 0
    *
    * And updates the covariance matrix via the function:
    *
    * Pdot = A*P + P*A' + Q
    *
    * A is the Jacobian of Xdot with respect to the states:
    *
    * A = [ d(angle_dot)/d(angle) d(angle_dot)/d(gyro_bias) ]
    * [ d(gyro_bias_dot)/d(angle) d(gyro_bias_dot)/d(gyro_bias) ]
    *
    * = [ 0 -1 ]
    * [ 0 0 ]
    *
    * Due to the small CPU available on the microcontroller, we've
    * hand optimized the C code to only compute the terms that are
    * explicitly non-zero, as well as expanded out the matrix math
    * to be done in as few steps as possible. This does make it harder
    * to read, debug and extend, but also allows us to do this with
    * very little CPU time.
    */
    void
    state_update(
    const float q_m /* Pitch gyro measurement */
    )
    {
    /* Unbias our gyro */
    const float q = q_m - q_bias;

    /*
    * Compute the derivative of the covariance matrix
    *
    * Pdot = A*P + P*A' + Q
    *
    * We've hand computed the expansion of A = [ 0 -1, 0 0 ] multiplied
    * by P and P multiplied by A' = [ 0 0, -1, 0 ]. This is then added
    * to the diagonal elements of Q, which are Q_angle and Q_gyro.
    */
    const float Pdot[2 * 2] = {
    Q_angle - P[0][1] - P[1][0], /* 0,0 */
    - P[1][1], /* 0,1 */
    - P[1][1], /* 1,0 */
    Q_gyro /* 1,1 */
    };

    /* Store our unbias gyro estimate */
    rate = q;

    /*
    * Update our angle estimate
    * angle += angle_dot * dt
    * += (gyro - gyro_bias) * dt
    * += q * dt
    */
    angle += q * dt;

    /* Update the covariance matrix */
    P[0][0] += Pdot[0] * dt;
    P[0][1] += Pdot[1] * dt;
    P[1][0] += Pdot[2] * dt;
    P[1][1] += Pdot[3] * dt;
    }


    /*
    * kalman_update is called by a user of the module when a new
    * accelerometer measurement is available. ax_m and az_m do not
    * need to be scaled into actual units, but must be zeroed and have
    * the same scale.
    *
    * This does not need to be called every time step, but can be if
    * the accelerometer data are available at the same rate as the
    * rate gyro measurement.
    *
    * For a two-axis accelerometer mounted perpendicular to the rotation
    * axis, we can compute the angle for the full 360 degree rotation
    * with no linearization errors by using the arctangent of the two
    * readings.
    *
    * As commented in state_update, the math here is simplified to
    * make it possible to execute on a small microcontroller with no
    * floating point unit. It will be hard to read the actual code and
    * see what is happening, which is why there is this extensive
    * comment block.
    *
    * The C matrix is a 1x2 (measurements x states) matrix that
    * is the Jacobian matrix of the measurement value with respect
    * to the states. In this case, C is:
    *
    * C = [ d(angle_m)/d(angle) d(angle_m)/d(gyro_bias) ]
    * = [ 1 0 ]
    *
    * because the angle measurement directly corresponds to the angle
    * estimate and the angle measurement has no relation to the gyro
    * bias.
    */
    void
    kalman_update(
    const float ax_m, /* X acceleration */
    const float az_m /* Z acceleration */
    )
    {
    /* Compute our measured angle and the error in our estimate */
    const float angle_m = atan2( -az_m, ax_m );
    const float angle_err = angle_m - angle;

    /*
    * C_0 shows how the state measurement directly relates to
    * the state estimate.
    *
    * The C_1 shows that the state measurement does not relate
    * to the gyro bias estimate. We don't actually use this, so
    * we comment it out.
    */
    const float C_0 = 1;
    /* const float C_1 = 0; */

    /*
    * PCt<2,1> = P<2,2> * C'<2,1>, which we use twice. This makes
    * it worthwhile to precompute and store the two values.
    * Note that C[0,1] = C_1 is zero, so we do not compute that
    * term.
    */
    const float PCt_0 = C_0 * P[0][0]; /* + C_1 * P[0][1] = 0 */
    const float PCt_1 = C_0 * P[1][0]; /* + C_1 * P[1][1] = 0 */

    /*
    * Compute the error estimate. From the Kalman filter paper:
    *
    * E = C P C' + R
    *
    * Dimensionally,
    *
    * E<1,1> = C<1,2> P<2,2> C'<2,1> + R<1,1>
    *
    * Again, note that C_1 is zero, so we do not compute the term.
    */
    const float E =
    R_angle
    + C_0 * PCt_0
    /* + C_1 * PCt_1 = 0 */
    ;

    /*
    * Compute the Kalman filter gains. From the Kalman paper:
    *
    * K = P C' inv(E)
    *
    * Dimensionally:
    *
    * K<2,1> = P<2,2> C'<2,1> inv(E)<1,1>
    *
    * Luckilly, E is <1,1>, so the inverse of E is just 1/E.
    */
    const float K_0 = PCt_0 / E;
    const float K_1 = PCt_1 / E;

    /*
    * Update covariance matrix. Again, from the Kalman filter paper:
    *
    * P = P - K C P
    *
    * Dimensionally:
    *
    * P<2,2> -= K<2,1> C<1,2> P<2,2>
    *
    * We first compute t<1,2> = C P. Note that:
    *
    * t[0,0] = C[0,0] * P[0,0] + C[0,1] * P[1,0]
    *
    * But, since C_1 is zero, we have:
    *
    * t[0,0] = C[0,0] * P[0,0] = PCt[0,0]
    *
    * This saves us a floating point multiply.
    */
    const float t_0 = PCt_0; /* C_0 * P[0][0] + C_1 * P[1][0] */
    const float t_1 = C_0 * P[0][1]; /* + C_1 * P[1][1] = 0 */

    P[0][0] -= K_0 * t_0;
    P[0][1] -= K_0 * t_1;
    P[1][0] -= K_1 * t_0;
    P[1][1] -= K_1 * t_1;

    /*
    * Update our state estimate. Again, from the Kalman paper:
    *
    * X += K * err
    *
    * And, dimensionally,
    *
    * X<2> = X<2> + K<2,1> * err<1,1>
    *
    * err is a measurement of the difference in the measured state
    * and the estimate state. In our case, it is just the difference
    * between the two accelerometer measured angle and our estimated
    * angle.
    */
    angle += K_0 * angle_err;
    q_bias += K_1 * angle_err;
    }
     
  3. I'm_Not_A_Monster

    I'm_Not_A_Monster Hey, eat this...

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    Tilt.H

    /* -*- indent-tabs-mode:T; c-basic-offset:8; tab-width:8; -*- vi: set ts=8:
    * $Id: tilt.h,v 1.1 2003/07/09 18:23:29 john Exp $
    *
    * 1 dimensional tilt sensor using a dual axis accelerometer
    * and single axis angular rate gyro. The two sensors are fused
    * via a two state Kalman filter, with one state being the angle
    * and the other state being the gyro bias.
    *
    * Gyro bias is automatically tracked by the filter. This seems
    * like magic.
    *
    * Please see the file tilt.c for more details on the implementation.
    * This header only has comments for the use of the module, not the
    * inner workings.
    *
    * (c) 2003 Trammell Hudson <hudson@rotomotion.com>
    *
    *************
    *
    * This file is part of the autopilot onboard code package.
    *
    * Autopilot is free software; you can redistribute it and/or modify
    * it under the terms of the GNU General Public License as published by
    * the Free Software Foundation; either version 2 of the License, or
    * (at your option) any later version.
    *
    * Autopilot is distributed in the hope that it will be useful,
    * but WITHOUT ANY WARRANTY; without even the implied warranty of
    * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
    * GNU General Public License for more details.
    *
    * You should have received a copy of the GNU General Public License
    * along with Autopilot; if not, write to the Free Software
    * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
    *
    */
    #ifndef _tilt_h_
    #define _tilt_h_

    /*
    * Our two states, the angle and the gyro bias. As a byproduct of computing
    * the angle, we also have an unbiased angular rate available. These are
    * read-only to the user of the module.
    */
    extern float angle;
    extern float q_bias;
    extern float rate;


    /*
    * state_update is called every dt with a biased gyro measurement
    * by the user of the module. It updates the current angle and
    * rate estimate.
    *
    * The pitch gyro measurement should be scaled into real units, but
    * does not need any bias removal. The filter will track the bias.
    */
    extern void
    state_update(
    const float q_m /* Pitch gyro measurement */
    );


    /*
    * kalman_update is called by a user of the module when a new
    * accelerometer measurement is available. ax_m and az_m do not
    * need to be scaled into actual units, but must be zeroed and have
    * the same scale.
    *
    * This does not need to be called every time step, but can be if
    * the accelerometer data are available at the same rate as the
    * rate gyro measurement.
    */
    extern void
    kalman_update(
    const float ax_m, /* X acceleration */
    const float az_m /* Z acceleration */
    );

    #endif
     
  4. davew

    davew What's a Dremel?

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    The degrees per second value refers to the maximum measured "rate of turning" not how often it is updated I think.

    For example the CG-16D would output +5V when spinning at 90 degrees per second and the other +5V at 150 degrees per second.

    If that code is supposed to output an angle rather than a rate of change of angle then I guess some values will need changing to use the 150 degree per second range. Alternatively maybe you could scale the result to fit the same range as the other gyro before it gets to that code.


    As for the pinout ST1 and ST2 are just test pins that output +0.66V or -0.66V on the rate pin when taken high. So to give functionality of the CG-16D could just be taken low and left. TEMP appears to be a temperature output which you could just not use if you want. Rate is equivalent to Out. The 2.5V is a voltage reference so should be equivalent to ref. I couldn't find data sheets for the CG-16D so I don't know if supply voltage etc is the same?
     
  5. I'm_Not_A_Monster

    I'm_Not_A_Monster Hey, eat this...

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    i think i'm going to pay someone here to fix this code and write some code to interpret that signal and convert it to PWM so the motor controllers can drive the wheels at the right speed.

    anybody interested?

    .:EDIT:.
    heres the original code for Trevor Blackwells Segway it is uses the 2DOF version of the IMU i'm making for balance, and it uses a RoboteQ dual channel motor controller. Im going to use a OSMC on each motor (but with only two IRF1405 MOSFETS on each leg of the H-Bridge) [i bolded where it was bolded on his site]
    Code:
    [B]Inputs[/B] 
    angle, angle_rate: [B]the tilt angle of the scooter in radians and its derivative in radians/sec [/B] 
    steer_knob: [B]the reading from the steering knob, between -1 and +1.[/B] 
    [B]Balance[/B] 
    balance_torque = 5.0 * (angle - rest_angle) + 0.4 * angle_rate 
    [B]Limit top speed by tilting back[/B] 
    overspeed = max(0, cur_speed - 0.5) 
    if (overspeed > 0) { 
      overspeed_integral = min(0.4, overspeed_integral + min(0.2, overspeed+0.05) * dt) 
    } 
    else { 
      overspeed_integral = max(0, overspeed_integral - 0.04*dt) 
    } 
    rest_angle = 0.4*overspeed + 0.7*overspeed_integral 
    [B]Steer. Decrease steering rate at high speed[/B] 
    steer_cmd = 0.07/(0.3+abs(cur_speed)) * steer_knob 
    [B]Track current speed[/B] 
    cur_speed += 1.2 * balance_torque * dt 
    [B]Differential steering[/B] 
    left_motor_pwm = balance_torque + cur_speed + steer_cmd 
    right_motor_pwm = balance_torque + cur_speed - steer_cmd 
    [B]Outputs[/B] 
    left_motor_pwm [B]and[/B] right_motor_pwm [B]directly set the duty cycle of the pulse width modulator for the wheel controller, and range from -1 to +1 (+1 is 100% forward, -1 is 100% reverse.)[/B] 
     
    Last edited: 10 Feb 2006

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