November 01, 2024

Arduino balancing bot



I built an Arduino version of the balancing bot from old parts in my parts bin:
  • Arduino Mega2560
  • Motor Shield V1
  • 3v-to-5v level converter
  • MPU-9255
  • DC motors
  • 9V battery holder for Arduino
  • 4x AA battery holder for the motors

The Motor Shield V1 is really obsolete. The I2C pins are not passed through. That makes using it with the Arduino UNO impossible. So I switched to the Mega2560 that has the I2C pins duplicated at a different location. The 3.3v pin is still not passed through. That got fixed with a Dremel. The L293D chip on the motor shield is really inefficient and the voltage drop is significant.

There is a newer Motor Shield V2 without any of these problems. But I didn't want to spend $20. In addition, the new version uses I2C and I didn't feel like troubleshooting multiple devices on the I2C bus with a level converter.

The Arduino UNO R3 and to some extent the Mega2560 are obsolete too. The new Arduino UNO R4 has a far more efficient switching regulator, LED matrix display, and optional bluetooth and wifi support.

The MPU-9255 has been out of production for years.

The 3v-to-5v level converter is needed because the Arduino is a 5v device and the MPU-9255 is a 3v device. You really want to respect the voltages when it comes to I2C communications.

Connecting it all up is easy, right? Just add a few more power and ground pins on the motor shield and use wires with DuPont connectors:


Actually, no. 

DuPont connectors do not connect securely. Whenever the bot falls, some wires risk coming loose. Cheap pre-made wires with DuPont connectors also fail at an alarmingly high rate. 

Well, I found an alternative:


Wire wrapping to the rescue! Those tiny white wires are 30 AWG Kynar wire wrapping wires. You can wire wrap any rectangular post that is small enough to fit the wire wrapping tool. You can wire wrap DuPont pins! For female headers, wire wrap one side of a double male header and plug it in.

Wire wrapping is actually more secure than soldering. It is also easier to wrap or unwrap than to solder or de-solder. The Cray 1 was wire wrapped. That's good enough for my toy robot. It has gone out of fashion many decades ago though. Fortunately, you can still buy proper Kynar wire wrapping wires and a wire wrapping tool off your favorite online store. Get the tool that does modified wraps.

As for the code, I just ported the Javascript Microbit code to Arduino C.

The Motor Shield V1 can be controlled using the Adafruit Motor Shield library v1.0.1. That seems to work fine.

However, I couldn't find a MPU-9255 library that suited my needs. I ported my MPU-9255 code and even added accelerometer bias adjustments.

Tuning the PID parameters took a few hours. The PID scaling constants seem to depend on the mounting height of the sensor. The bot to stayed up for 2 hours before I shut it down.





Here's the code:

#include <Wire.h>
#include <AFMotor.h>

// Tuning Parameters
float TARGET_ANGLE = -3.1; // forward tilt in degrees
float SMOOTHING_FACTOR = 200;

float KE = 15;
float KD = KE/20;
float KI = KD/5;

const int MPU_ADDR = 0x68;
const int WHO_AM_I = 0x75;
const int REG_PWR_MGMT_1 = 0x6b;
const int REG_SIGNAL_PATH_RESET = 0x68;
const int REG_USER_CTRL = 0x6a;
const int REG_ACCEL_XOUT_H = 0x3b;
const int REG_ACCEL_YOUT_H = 0x3d;
const int REG_ACCEL_ZOUT_H = 0x3f;
const int REG_GYRO_XOUT_H = 0x43;
const int REG_GYRO_YOUT_H = 0x45;
const int REG_GYRO_ZOUT_H = 0x47;
const int REG_CONFIG = 0x1a;
const int REG_GYRO_CONFIG = 0x1b;
const int REG_ACCEL_CONFIG = 0x1c;
const int REG_ACCEL_CONFIG2 = 0x1d;
const int XG_OFFSET_H = 0x13;
const int YG_OFFSET_H = 0x15;
const int ZG_OFFSET_H = 0x17;
const int XA_OFFSET_H = 0x77;
const int YA_OFFSET_H = 0x7A;
const int ZA_OFFSET_H = 0x7D;

bool mpu_read(int reg, byte *data) {
Wire.beginTransmission(MPU_ADDR);
Wire.write(reg);
Wire.endTransmission(false);
int n = Wire.requestFrom(MPU_ADDR, 1);
if (n != 1) {
return false;
}
*data = Wire.read();
return true;
}

bool mpu_read_int16(int reg, short *data) {
Wire.beginTransmission(MPU_ADDR);
Wire.write(reg);
Wire.endTransmission(false);
int n = Wire.requestFrom(MPU_ADDR, 2);
if (n != 2) {
return false;
}
int h = Wire.read();
int l = Wire.read();
*data = (h << 8) | l;
return true;
}

void mpu_write(int reg, int data) {
Wire.beginTransmission(MPU_ADDR);
Wire.write(reg);
Wire.write(data & 0xff);
Wire.endTransmission();
}

void mpu_write_int16(int reg, int data) {
Wire.beginTransmission(MPU_ADDR);
Wire.write(reg);
Wire.write((data >> 8) & 0xff);
Wire.write(data & 0xff);
Wire.endTransmission();
}

/**
* Reset the MPU and configure the gyroscope to +- 2000 degrees/second and the accelerometer to +-16g.
* The low pass filter settings control how sensitive the sensors are to quick changes.
* In order of increasing sensitivity: 6, 5, 4, 3, 2, 1, 0, 7
* Info from MPU-9250 register map document.
* @param gyro_lpf Gyroscope low pass filter setting, eg: 0
* 7: 8kHz sampling rate, 3600Hz bandwidth, 0.17ms delay.
* 0: 8kHz sampling rate, 250Hz bandwidth, 0.97ms delay.
* 1: 1kHz sampling rate, 184Hz bandwidth, 2.9ms delay.
* 2: 1kHz sampling rate, 92Hz bandwidth, 3.9ms delay.
* 3: 1kHz sampling rate, 41Hz bandwidth, 5.9ms delay.
* 4: 1kHz sampling rate, 20Hz bandwidth, 9.9ms delay.
* 5: 1kHz sampling rate, 10Hz bandwidth, 17.85ms delay.
* 6: 1kHz sampling rate, 5Hz bandwidth, 33.48ms delay.
* @param accel_lpf Accelerometer low pass filter setting, eg: 0
* 7: 1kHz sampling rate, 420Hz 3dB bandwidth, 1.38ms delay.
* 0: 1kHz sampling rate, 218.1Hz 3dB bandwidth, 1.88ms delay.
* 1: 1kHz sampling rate, 218.1Hz 3dB bandwidth, 1.88ms delay.
* 2: 1kHz sampling rate, 99Hz 3dB bandwidth, 2.88ms delay.
* 3: 1kHz sampling rate, 44.8Hz 3dB bandwidth, 4.88ms delay.
* 4: 1kHz sampling rate, 21.2Hz 3dB bandwidth, 8.87ms delay.
* 5: 1kHz sampling rate, 10.2Hz 3dB bandwidth, 16.83ms delay.
* 6: 1kHz sampling rate, 5.05Hz 3dB bandwidth, 32.48ms delay.
*/

bool reset_mpu(int gyro_lpf = 0, int accel_lpf = 0) {
mpu_write(REG_PWR_MGMT_1, 0x80); // H_RESET, internal 20MHz clock
delay(200); // must delay after reset

mpu_write(REG_SIGNAL_PATH_RESET, 0x7); // GYRO_RST | ACCEL_RST | TEMP_RST
mpu_write(REG_USER_CTRL, 0x1); // SIG_COND_RST
mpu_write(REG_CONFIG, gyro_lpf);
mpu_write(REG_GYRO_CONFIG, 0x10); // GYRO_FS_SEL = 3, +-1000 dps, DLPF on
mpu_write(REG_ACCEL_CONFIG, 0x18); // ACCEL_FS_SEL = 3, +-16g, DLPF on
mpu_write(REG_ACCEL_CONFIG2, accel_lpf);
delay(200);
byte x = 255;
if (!mpu_read(REG_GYRO_CONFIG, &x)) {
return false;
}
if (x != 0x10) {
return false;
}
return true;
}

bool compute_biases() {
mpu_write_int16(XG_OFFSET_H, 0);
mpu_write_int16(YG_OFFSET_H, 0);
mpu_write_int16(ZG_OFFSET_H, 0);

const int N = 100;
const int MAX_VAR = 40;
float sum_x = 0, sum_y = 0, sum_z = 0;
float sum_ax = 0, sum_ay = 0, sum_az = 0;
float xs[N];
float ys[N];
float zs[N];
for (int i = 0; i < N; i++) {
short x;
short y;
short z;
if (!mpu_read_int16(REG_GYRO_XOUT_H, &x)) {
return false;
}
if (!mpu_read_int16(REG_GYRO_YOUT_H, &y)) {
return false;
}
if (!mpu_read_int16(REG_GYRO_ZOUT_H, &z)) {
return false;
}
sum_x += x;
sum_y += y;
sum_z += z;
xs[i] = x;
ys[i] = y;
zs[i] = z;
short ax;
short ay;
short az;
if (!mpu_read_int16(REG_ACCEL_XOUT_H, &ax)) {
return false;
}
if (!mpu_read_int16(REG_ACCEL_YOUT_H, &ay)) {
return false;
}
if (!mpu_read_int16(REG_ACCEL_ZOUT_H, &az)) {
return false;
}
sum_ax += ax;
sum_ay += ay;
sum_az += az;
delay(10);
}

float mean_x = sum_x / N;
float mean_y = sum_y / N;
float mean_z = sum_z / N;
float var_x = 0, var_y = 0, var_z = 0;
for (int i = 0; i < N; i++) {
float dx = xs[i] - mean_x;
var_x = var_x + dx * dx;
float dy = ys[i] - mean_y;
var_y = var_y + dy * dy;
float dz = zs[i] - mean_z;
var_z = var_z + dz * dz;
}
var_x = var_x / N;
var_y = var_y / N;
var_z = var_z / N;

float mean_ax = sum_ax / N;
float mean_ay = sum_ay / N;
float mean_az = sum_az / N;

Serial.print("Gyro: mean ");
Serial.print(mean_x);
Serial.print(", ");
Serial.print(mean_y);
Serial.print(", ");
Serial.print(mean_z);
Serial.print(" var ");
Serial.print(var_x);
Serial.print(", ");
Serial.print(var_y);
Serial.print(", ");
Serial.print(var_z);
Serial.print(" Accel: mean ");
Serial.print(mean_ax);
Serial.print(", ");
Serial.print(mean_ay);
Serial.print(", ");
Serial.println(mean_az);
set_gyro_bias(mean_x, mean_y, mean_z);
set_accel_bias(mean_ax, 0, mean_az);
return true;
}

void set_gyro_bias(int x_bias, int y_bias, int z_bias) {
mpu_write_int16(XG_OFFSET_H, -x_bias);
mpu_write_int16(YG_OFFSET_H, -y_bias);
mpu_write_int16(ZG_OFFSET_H, -z_bias);
}

bool set_accel_bias(short x_bias, short y_bias, short z_bias) {
short cur_x;
short cur_y;
short cur_z;
if (!mpu_read_int16(XA_OFFSET_H, &cur_x)) {
return false;
}
if (!mpu_read_int16(YA_OFFSET_H, &cur_y)) {
return false;
}
if (!mpu_read_int16(ZA_OFFSET_H, &cur_z)) {
return false;
}
cur_x -= x_bias;
cur_y -= y_bias;
cur_z -= z_bias;
cur_x &= ~1;
cur_y &= ~1;
cur_z &= ~1;
mpu_write_int16(XA_OFFSET_H, cur_x);
mpu_write_int16(YA_OFFSET_H, cur_y);
mpu_write_int16(ZA_OFFSET_H, cur_z);
return true;
}

//-----------------------------

AF_DCMotor *motor_left;
AF_DCMotor *motor_right;

void motor_move(float v /* -100 to 100 */) {
if (v > 0) {
motor_left->run(BACKWARD);
motor_right->run(FORWARD);
} else {
motor_left->run(FORWARD);
motor_right->run(BACKWARD);
v = -v;
}
if (v > 100) {
v = 100;
}
v = v * 0.7 + 185;
if (v < 195) {
v = 0;
}
motor_left->setSpeed(v);
motor_right->setSpeed(v);
}

void motor_coast() {
motor_left->run(RELEASE);
motor_right->run(RELEASE);
}

//-----------------------------

long last_time = 0;
float motor_out = 0;
int vertical_count = 0;
bool motor_on = false;
float est_angle = 0;
float last_err = 0;
float i_err = 0;


void setup() {
pinMode(LED_BUILTIN, OUTPUT);
for (int i = 0; i < 20; i++) {
digitalWrite(LED_BUILTIN, HIGH);
delay(100);
digitalWrite(LED_BUILTIN, LOW);
delay(100);
}

digitalWrite(SDA, HIGH);
digitalWrite(SCL, HIGH);

Wire.begin();
Wire.setClock(400000);
while (1) {
byte id;
if (mpu_read(WHO_AM_I, &id)) {
if (id == 0x73) {
if (reset_mpu(5, 5)) {
break;
}
}
}
delay(3000);
}
// add 32768/16g = 2048 to the accel axis pointing to ground
//compute_biases();

set_gyro_bias(27, -40, -43);
set_accel_bias(40, 58, 417);

motor_left = new AF_DCMotor(3);
motor_right = new AF_DCMotor(2);
motor_coast();

last_time = millis();
motor_out = 0;
vertical_count = 0;
motor_on = false;
est_angle = 0;
last_err = 0;
i_err = 0;
digitalWrite(LED_BUILTIN, HIGH);
delay(500);
}

bool read_accel_tilt_angle(float *angle) {
short accel_x;
short accel_z;

if (!mpu_read_int16(REG_ACCEL_XOUT_H, &accel_x)) {
return false;
}
if (!mpu_read_int16(REG_ACCEL_ZOUT_H, &accel_z)) {
return false;
}

*angle = atan2(accel_z, -accel_x) * RAD_TO_DEG;
return true;
}

void loop() {
long current_time = millis();
long delta_t = current_time - last_time;
if (delta_t < 5) {
return;
}
short gyro_y;
if (!mpu_read_int16(REG_GYRO_YOUT_H, &gyro_y)) {
return;
}
float accel_angle;
if (!read_accel_tilt_angle(&accel_angle)) {
return;
}
float gyro_angle_rate = float(gyro_y) * -1000.0 / 32768.0; // degrees/s
float gyro_angle_change = gyro_angle_rate * delta_t / 1000; // degrees
est_angle = ((SMOOTHING_FACTOR-1) * (est_angle + gyro_angle_change) + accel_angle) / SMOOTHING_FACTOR;
if (motor_on && (est_angle > 30 || est_angle < -30)) {
last_err = 0;
i_err = 0;
motor_coast();
motor_on = false;
}
float err = est_angle - TARGET_ANGLE;
if (motor_on) {
float d_err = (err - last_err) * 1000 / delta_t;
last_err = err;
i_err = i_err + err * delta_t;
float u = err * KE + d_err * KD + i_err * KI;
motor_out = u;
motor_move(motor_out);
} else if (err <= 5 && err >= -5) {
vertical_count = vertical_count + 1;
if (vertical_count > 100) {
vertical_count = 0;
last_err = 0;
i_err = 0;
motor_on = true;
}
} else if (err <= 5 && err >= -5) {
motor_on = true;
}
last_time = current_time;
}



October 31, 2024

Balancing bot 2024

Recently, I bought a new 3D printer. My 10+ year old printer was long gone. Getting it to print properly was hard, so hard that I stopped using it. Is the new printer any better?


Well, since my balancing bot from 2017 has fallen apart, let's rebuild it!



It has been interesting coming back to this toy after seven years. Surprisingly, all the electronics on the bot still worked. The soldered daughter board remains solid despite all the physical shocks from the bot falling down. An FS90R servo had a broken plastic gear, so that got replaced. The servos are now powered by 4x AA rechargeable batteries. The code is the same except for some tweaks to the PID parameters. The code did not age at all.

Redesigning all the parts took some time. I had certain changes in mind when redesigning the bot. I wanted the new frame to be bigger so that the parts are spread out and accessible. All parts, especially the batteries, must be securely attached.  

Printing was the easiest part. The printer just works out of the box. I could concentrate on designing instead of tinkering with the printer to get it to work. It is a reliable workhorse, just as it should be.

So, I have been making stuff, including yet another balancing bot:


November 01, 2020

Balancing Bot Update 2020

Since the last post three years ago, Micro:bit MakeCode has been updated.

The latest version is MakeCode v3 2020 Update. The balancing bot code was written using MakeCode v0. MakeCode v3 is not compatible with MakeCode v0.

The big incompatible change is that numbers in MakeCode v3 are now floating point while numbers in MakeCode v0 were 16 bit integers. MakeCode v3 also includes trigonometric functions in its library.

Here's the updated bot code that works with MakeCode v3. The Trig library should be removed from the custom.ts file. It is not needed anymore.

/**
 * Public domain. Use at your own risk!
 */
let TARGET_ANGLE = 155
let KE = 420
let KD = 8
let KI = 5
let motor_left_bias = -2;
let motor_right_bias = 2;
function control_loop() {
    motor_coast()
    let motor_out = 0;
    let vertical_count = 0;
    let motor_on = false
    let est_angle = read_accel_tilt_angle()
    let start_time = input.runningTime()
    let last_time = start_time
    let last_err = 0;
    let i_err = 0;
    while (true) {
        let current_time = input.runningTime()
        let delta_t = current_time - last_time
        last_time = current_time
        est_angle = updateAngle(est_angle, delta_t)
        if (motor_on && (est_angle > 3000 || est_angle < -3000)) {
            motor_coast()
            motor_on = false
        }
        let err = est_angle - TARGET_ANGLE
        if (motor_on) {
            let d_err = (err - last_err) * 1000 / delta_t
            last_err = err
            i_err = i_err + err * delta_t
            let u = err * KE + d_err * KD + i_err * KI
            motor_out = Math.clamp(-90, 90, u / 10000)
            motor_move(motor_out + motor_left_bias, motor_out + motor_right_bias)
        } else if (err <= 500 && err >= -500) {
            vertical_count = vertical_count + 1
            if (vertical_count > 100) {
                vertical_count = 0
                last_err = 0
                i_err = 0
                est_angle = read_accel_tilt_angle()
                motor_on = true
            }   
        } else {
            vertical_count = 0
        }        
        basic.pause(1)
    }
}

function read_gyro_angle_rate(): number {
    InvMPU.read_gyro()
    return -InvMPU.gyro_y
}

function read_accel_tilt_angle(): number {
    InvMPU.read_accel()
    return Math.round(Math.atan2(InvMPU.accel_z, -InvMPU.accel_x) * 18000 / Math.PI)
}

function updateAngle(old_angle: number, delta_t_ms: number): number {
    let accel_angle = read_accel_tilt_angle()
    let gyro_angle_rate = read_gyro_angle_rate() * 200000 / 32768
    let gyro_angle_change = gyro_angle_rate * delta_t_ms / 1000
    return (49 * (old_angle + gyro_angle_change) + accel_angle) / 50
}

function motor_coast() {
    pins.digitalWritePin(DigitalPin.P15, 0)
    pins.digitalWritePin(DigitalPin.P16, 0)
}

function motor_move(left: number, right: number) {
    pins.servoWritePin(AnalogPin.P15, 90 - right)
    pins.servoWritePin(AnalogPin.P16, 90 + left)
}

input.onButtonPressed(Button.A, function on_button_pressed_a() {
    TARGET_ANGLE = TARGET_ANGLE + 5
})

input.onButtonPressed(Button.B, function on_button_pressed_b() {
    TARGET_ANGLE = TARGET_ANGLE - 5
})

input.onButtonPressed(Button.AB, function on_button_pressed_ab() {
    basic.showNumber(TARGET_ANGLE)
})

if (InvMPU.find_mpu()) {
    basic.showIcon(IconNames.Happy)
    InvMPU.reset_mpu(5, 5)
    basic.pause(100)
    InvMPU.set_gyro_bias(5, 1, -13)
    control_loop()
} else {
    basic.showIcon(IconNames.No)
}

November 18, 2017

Self-balancing robot version 3 update!


It works! Now it balances on hard or soft floors for more than 30 minutes!



What changed?

Firstly, 2xAA rechargeable Eneloop batteries are insufficient to power those FS90R motors. The specification of the motor allows up to 6V. Two cells provide only around 2.7V total. I switch to 4xAA Eneloop batteries, providing around 5.4V. The motors were much much faster, more than twice as fast. The immediate consequence of this is that the PID parameters need to be re-tuned and scaled down to 10-20% of the values for 2xAA batteries.

Secondly, I turned up the builtin digital low pass filter in the MPU-9250 aggressively. Now it is set to 5 for both accelerometer and gyroscope. That translates to a sensor delay of 17ms and the 3dB bandwidth of about 10Hz. That is probably averaging around 17 samples at 1kHz sample rate. And that did the trick!

Here's a graph of motor power, gyroscope angular velocity and tilt angle.


The filtered angular velocity seldom exceeds 0.3 degrees per second. The filtered tilt angle seldom exceeds 1 degree. The motor power is mostly less than 10% of maximum power.

I've updated the InvenSense MPU-9255/MPU-9250/MPU-6500 module. You can now specify the low pass filter level for the accelerometer and gyroscope in the call to InvMPU.reset_mpu(). Copy this new version into your custom.ts.

The only changes from the version 1 code are the PID tuning parameters and the call InvMPU.reset_mpu(5, 5).

See the previous post on the parts for building version 3.



November 16, 2017

Self-balancing robot version 3


Version 1 was made out of Lego. It keeps breaking into pieces, the motors were not secured and it also contained the unnecessary Kitronic servo:lite board. So, I rebuilt it.

Parts:

The code for this version is identical to the code for version 1 except the tweek for a different orientation of the MPU-9255. With 2x AA batteries, identical PID parameters will work. With 4x AA batteries, the parameters have to be retuned.

But, alas, it still doesn't balance well on smooth hard floors!

It works fine on carpet or cushion even though it is only half the height of the version 1 robot. It just won't work on wood or marble floors!

After much tuning, I decided to record the motor response. I added two more wheels and turned the bot into a "car". Then I recorded the horizontal acceleration using the accelerometer in response to various motor control like a 1 second 66% power pulse. Here is a typical result with 2x AA batteries:


Why is the acceleration oscillating around zero? The amplitudes of the oscillations are much worse with 4x AA batteries.

Oh, the motor controller in the servo is a closed loop controller!

The closed-loop controller inside the FS90R is probably a variant of the standard PID controller. The oscillations are caused by the controller trying to match the output voltage to the pulse duration.

The accelerometer and gyroscope are picking up physical feedback from the controller's actions. On soft floor like carpet, the feedback is dampened physically. On hard floors, the sensors pick up random spikes that throws the PID algorithm off.

On top of that, the accelerometer only picks up the increase in motor speed after about 60ms!

In short, don't build a self-balancing robot using servo motors. Just use DC motors.

Update: I've fixed the problem and got it to work on hard floors too!