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firmware.ino
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#include <Wire.h>
#include <Adafruit_PWMServoDriver.h>
#include <math.h>
// Create the PCA9685 driver instance
Adafruit_PWMServoDriver pwm = Adafruit_PWMServoDriver();
// ----- Servo Parameters -----
// The PCA9685 uses a 12-bit resolution (0–4095). When running at 60 Hz,
// one period is ~16.67ms. With pulse widths between 500us and 2500us,
// the corresponding counts are approximately:
const uint16_t SERVOMIN = 123; // ~500us pulse
const uint16_t SERVOMAX = 614; // ~2500us pulse
// Helper function to set a servo (by channel) to an angle in degrees (0-180)
void setServo(uint8_t channel, float angle) {
// Map the angle to a pulse width (in PCA9685 counts)
uint16_t pulse = SERVOMIN + (uint16_t)((angle / 180.0) * (SERVOMAX - SERVOMIN));
pwm.setPWM(channel, 0, pulse);
}
// ----- Global Variables and Constants for IK -----
unsigned long interval = 1;
unsigned long previousMillis = 0;
float Pi = 3.141592653589793;
float G_C = 50.00; // ground clearance
float Y_Offset;
float D;
float d;
float R;
float Coxa = 36.00;
float Femur = 50.00;
float Tibia = 85.00;
float Alpha_1;
float Alpha_2;
float Theta_1;
float Theta_2;
float Theta_3;
float X_1, Y_1, Z_1;
float X_2, Y_2, Z_2;
float X_3, Y_3, Z_3;
float X_4, Y_4, Z_4;
// ----- Inverse Kinematics Functions -----
void Rumus_IK_1() {
if (Z_1 > 0.00) {
D = sqrt(pow(X_1, 2) + pow(Z_1, 2));
Theta_1 = (atan(X_1 / Z_1)) * (180.00 / Pi);
d = D - Coxa;
Y_Offset = G_C - Y_1;
R = sqrt(pow(d, 2) + pow(Y_Offset, 2));
Alpha_1 = (acos(Y_Offset / R)) * (180.00 / Pi);
Alpha_2 = (acos((pow(Femur, 2) + pow(R, 2) - pow(Tibia, 2)) / (2 * Femur * R))) * (180.00 / Pi);
Theta_2 = Alpha_1 + Alpha_2;
Theta_3 = (acos((pow(Femur, 2) + pow(Tibia, 2) - pow(R, 2)) / (2 * Femur * Tibia))) * (180.00 / Pi);
}
else if (Z_1 == 0.00) {
D = sqrt(pow(X_1, 2) + pow(Z_1, 2));
Theta_1 = 90.00;
d = D - Coxa;
Y_Offset = G_C - Y_1;
R = sqrt(pow(d, 2) + pow(Y_Offset, 2));
Alpha_1 = (acos(Y_Offset / R)) * (180.00 / Pi);
Alpha_2 = (acos((pow(Femur, 2) + pow(R, 2) - pow(Tibia, 2)) / (2 * Femur * R))) * (180.00 / Pi);
Theta_2 = Alpha_1 + Alpha_2;
Theta_3 = (acos((pow(Femur, 2) + pow(Tibia, 2) - pow(R, 2)) / (2 * Femur * Tibia))) * (180.00 / Pi);
}
else if (Z_1 < 0.00) {
D = sqrt(pow(X_1, 2) + pow(Z_1, 2));
Theta_1 = 90.00 + (90.00 - fabs((atan(X_1 / Z_1)) * (180.00 / Pi)));
d = D - Coxa;
Y_Offset = G_C - Y_1;
R = sqrt(pow(d, 2) + pow(Y_Offset, 2));
Alpha_1 = (acos(Y_Offset / R)) * (180.00 / Pi);
Alpha_2 = (acos((pow(Femur, 2) + pow(R, 2) - pow(Tibia, 2)) / (2 * Femur * R))) * (180.00 / Pi);
Theta_2 = Alpha_1 + Alpha_2;
Theta_3 = (acos((pow(Femur, 2) + pow(Tibia, 2) - pow(R, 2)) / (2 * Femur * Tibia))) * (180.00 / Pi);
}
}
void Rumus_IK_2() {
if (Z_2 > 0.00) {
D = sqrt(pow(X_2, 2) + pow(Z_2, 2));
Theta_1 = (atan(X_2 / Z_2)) * (180.00 / Pi);
d = D - Coxa;
Y_Offset = G_C - Y_2;
R = sqrt(pow(d, 2) + pow(Y_Offset, 2));
Alpha_1 = (acos(Y_Offset / R)) * (180.00 / Pi);
Alpha_2 = (acos((pow(Femur, 2) + pow(R, 2) - pow(Tibia, 2)) / (2 * Femur * R))) * (180.00 / Pi);
Theta_2 = Alpha_1 + Alpha_2;
Theta_3 = (acos((pow(Femur, 2) + pow(Tibia, 2) - pow(R, 2)) / (2 * Femur * Tibia))) * (180.00 / Pi);
}
else if (Z_2 == 0.00) {
D = sqrt(pow(X_2, 2) + pow(Z_2, 2));
Theta_1 = 90.00;
d = D - Coxa;
Y_Offset = G_C - Y_2;
R = sqrt(pow(d, 2) + pow(Y_Offset, 2));
Alpha_1 = (acos(Y_Offset / R)) * (180.00 / Pi);
Alpha_2 = (acos((pow(Femur, 2) + pow(R, 2) - pow(Tibia, 2)) / (2 * Femur * R))) * (180.00 / Pi);
Theta_2 = Alpha_1 + Alpha_2;
Theta_3 = (acos((pow(Femur, 2) + pow(Tibia, 2) - pow(R, 2)) / (2 * Femur * Tibia))) * (180.00 / Pi);
}
else if (Z_2 < 0.00) {
D = sqrt(pow(X_2, 2) + pow(Z_2, 2));
Theta_1 = 90.00 + (90.00 - fabs((atan(X_2 / Z_2)) * (180.00 / Pi)));
d = D - Coxa;
Y_Offset = G_C - Y_2;
R = sqrt(pow(d, 2) + pow(Y_Offset, 2));
Alpha_1 = (acos(Y_Offset / R)) * (180.00 / Pi);
Alpha_2 = (acos((pow(Femur, 2) + pow(R, 2) - pow(Tibia, 2)) / (2 * Femur * R))) * (180.00 / Pi);
Theta_2 = Alpha_1 + Alpha_2;
Theta_3 = (acos((pow(Femur, 2) + pow(Tibia, 2) - pow(R, 2)) / (2 * Femur * Tibia))) * (180.00 / Pi);
}
}
void Rumus_IK_3() {
if (Z_3 > 0.00) {
D = sqrt(pow(X_3, 2) + pow(Z_3, 2));
Theta_1 = (atan(X_3 / Z_3)) * (180.00 / Pi);
d = D - Coxa;
Y_Offset = G_C - Y_3;
R = sqrt(pow(d, 2) + pow(Y_Offset, 2));
Alpha_1 = (acos(Y_Offset / R)) * (180.00 / Pi);
Alpha_2 = (acos((pow(Femur, 2) + pow(R, 2) - pow(Tibia, 2)) / (2 * Femur * R))) * (180.00 / Pi);
Theta_2 = Alpha_1 + Alpha_2;
Theta_3 = (acos((pow(Femur, 2) + pow(Tibia, 2) - pow(R, 2)) / (2 * Femur * Tibia))) * (180.00 / Pi);
}
else if (Z_3 == 0.00) {
D = sqrt(pow(X_3, 2) + pow(Z_3, 2));
Theta_1 = 90.00;
d = D - Coxa;
Y_Offset = G_C - Y_3;
R = sqrt(pow(d, 2) + pow(Y_Offset, 2));
Alpha_1 = (acos(Y_Offset / R)) * (180.00 / Pi);
Alpha_2 = (acos((pow(Femur, 2) + pow(R, 2) - pow(Tibia, 2)) / (2 * Femur * R))) * (180.00 / Pi);
Theta_2 = Alpha_1 + Alpha_2;
Theta_3 = (acos((pow(Femur, 2) + pow(Tibia, 2) - pow(R, 2)) / (2 * Femur * Tibia))) * (180.00 / Pi);
}
else if (Z_3 < 0.00) {
D = sqrt(pow(X_3, 2) + pow(Z_3, 2));
Theta_1 = 90.00 + (90.00 - fabs((atan(X_3 / Z_3)) * (180.00 / Pi)));
d = D - Coxa;
Y_Offset = G_C - Y_3;
R = sqrt(pow(d, 2) + pow(Y_Offset, 2));
Alpha_1 = (acos(Y_Offset / R)) * (180.00 / Pi);
Alpha_2 = (acos((pow(Femur, 2) + pow(R, 2) - pow(Tibia, 2)) / (2 * Femur * R))) * (180.00 / Pi);
Theta_2 = Alpha_1 + Alpha_2;
Theta_3 = (acos((pow(Femur, 2) + pow(Tibia, 2) - pow(R, 2)) / (2 * Femur * Tibia))) * (180.00 / Pi);
}
}
void Rumus_IK_4() {
if (Z_4 > 0.00) {
D = sqrt(pow(X_4, 2) + pow(Z_4, 2));
Theta_1 = (atan(X_4 / Z_4)) * (180.00 / Pi);
d = D - Coxa;
Y_Offset = G_C - Y_4;
R = sqrt(pow(d, 2) + pow(Y_Offset, 2));
Alpha_1 = (acos(Y_Offset / R)) * (180.00 / Pi);
Alpha_2 = (acos((pow(Femur, 2) + pow(R, 2) - pow(Tibia, 2)) / (2 * Femur * R))) * (180.00 / Pi);
Theta_2 = Alpha_1 + Alpha_2;
Theta_3 = (acos((pow(Femur, 2) + pow(Tibia, 2) - pow(R, 2)) / (2 * Femur * Tibia))) * (180.00 / Pi);
}
else if (Z_4 == 0.00) {
D = sqrt(pow(X_4, 2) + pow(Z_4, 2));
Theta_1 = 90.00;
d = D - Coxa;
Y_Offset = G_C - Y_4;
R = sqrt(pow(d, 2) + pow(Y_Offset, 2));
Alpha_1 = (acos(Y_Offset / R)) * (180.00 / Pi);
Alpha_2 = (acos((pow(Femur, 2) + pow(R, 2) - pow(Tibia, 2)) / (2 * Femur * R))) * (180.00 / Pi);
Theta_2 = Alpha_1 + Alpha_2;
Theta_3 = (acos((pow(Femur, 2) + pow(Tibia, 2) - pow(R, 2)) / (2 * Femur * Tibia))) * (180.00 / Pi);
}
else if (Z_4 < 0.00) {
D = sqrt(pow(X_4, 2) + pow(Z_4, 2));
Theta_1 = 90.00 + (90.00 - fabs((atan(X_4 / Z_4)) * (180.00 / Pi)));
d = D - Coxa;
Y_Offset = G_C - Y_4;
R = sqrt(pow(d, 2) + pow(Y_Offset, 2));
Alpha_1 = (acos(Y_Offset / R)) * (180.00 / Pi);
Alpha_2 = (acos((pow(Femur, 2) + pow(R, 2) - pow(Tibia, 2)) / (2 * Femur * R))) * (180.00 / Pi);
Theta_2 = Alpha_1 + Alpha_2;
Theta_3 = (acos((pow(Femur, 2) + pow(Tibia, 2) - pow(R, 2)) / (2 * Femur * Tibia))) * (180.00 / Pi);
}
}
// ----- Setup and Main Loop -----
void setup() {
Serial.begin(9600);
Wire.begin();
pwm.begin();
pwm.setPWMFreq(60); // Set frequency to 60 Hz
// ---- Initial (Stance) Position ----
// Leg 1 (Channels: Coxa_1=0, Femur_1=1, Tibia_1=2)
{
X_1 = 70.00;
Y_1 = 0.00;
Z_1 = 40.00;
Rumus_IK_1();
setServo(0, Theta_1);
setServo(1, Theta_2);
setServo(2, Theta_3);
}
// Leg 2 (Channels: Coxa_2=3, Femur_2=4, Tibia_2=5)
{
X_2 = 70.00;
Y_2 = 0.00;
Z_2 = -40.00;
Rumus_IK_2();
setServo(3, Theta_1);
setServo(4, 180.00 - Theta_2);
setServo(5, 180.00 - Theta_3);
}
// Leg 3 (Channels: Coxa_3=6, Femur_3=7, Tibia_3=8)
{
X_3 = 70.00;
Y_3 = 0.00;
Z_3 = 0.00;
Rumus_IK_3();
setServo(6, 180.00 - Theta_1);
setServo(7, 180.00 - Theta_2);
setServo(8, 180.00 - Theta_3);
}
// Leg 4 (Channels: Coxa_4=9, Femur_4=10, Tibia_4=11)
{
X_4 = 70.00;
Y_4 = 0.00;
Z_4 = 0.00;
Rumus_IK_4();
setServo(9, 180.00 - Theta_1);
setServo(10, Theta_2);
setServo(11, Theta_3);
}
}
void loop() {
// Use millis() to pace the motions
unsigned long currentMillis = millis();
if (currentMillis - previousMillis >= interval) {
// ---- Leg 3 Movement ----
// 1. Lift leg 3 (increasing Y)
Y_3 = 0.00;
do {
X_3 = 70.00;
Z_3 = 0.00;
Y_3 += 0.2;
Rumus_IK_3();
setServo(6, 180.00 - Theta_1);
setServo(7, 180.00