initial velocity control loop

Achieved with a PI controller checking the current velocity as output by the motors. Since I'm
using stepper motors, the angular velocity is exact (if the motors are not skipping steps) and does not need encoders on the
motors.

TODO: add a little deadzone either on the setpoint or on the velocity, to prevent
oscillations when around the equilibrium point.

selfbalance-madgwick/imu.ino

@@ -4,7 +4,7 @@
 
 //#define PRINT_ANGLES
 //#define PRINT_QUAT
-#define PERFORM_CALIBRATION //Comment to disable startup calibration
+// #define PERFORM_CALIBRATION //Comment to disable startup calibration
 
 #define IMU_ADDRESS 0x68    //Change to the address of the IMU
 MPU6050 IMU;               //Change to the name of any supported IMU!

selfbalance-madgwick/selfbalance-madgwick.ino

@@ -22,18 +22,25 @@ constexpr double KP = 42;
 constexpr double KI = KP * 10.8852;
 constexpr double KD = 0.3; 
 
-// IMU little bit tilted
-// TODO: Implement an outer control loop for angular velocity. But that requires encoders on the motors
-// TODO: try to achieve it crudely by just using a PI controller on the velocity given by the PID balance controller
+// PI constants for outer velocity control loop
+constexpr double KP_vel = 0.0025;
+constexpr double KI_vel = 0.0005;
+
 float setpoint = 0.0;
 float output = 0;
 float input = 0;
 
+float vel_setpoint = 0.0;
+float vel_input = 0.0;
+
+
 float yaw{ 0 }, pitch{ 0 }, roll{ 0 };
 
 
 
 QuickPID pitchCtrl(&input, &output, &setpoint, KP, KI, KD, pitchCtrl.pMode::pOnError, pitchCtrl.dMode::dOnMeas, pitchCtrl.iAwMode::iAwCondition, pitchCtrl.Action::reverse);
+// TODO: a little deadzone when the input is almost 0, just to avoid unnecessary "nervous" control and eventual oscillations
+QuickPID velCtrl(&output, &setpoint, &vel_setpoint, KP_vel, KI_vel, 0, velCtrl.pMode::pOnMeas, velCtrl.dMode::dOnMeas, velCtrl.iAwMode::iAwCondition, velCtrl.Action::direct);
 
 void setup() {
   Serial.begin(9600);
@@ -57,6 +64,10 @@ void setup() {
   pitchCtrl.SetMode(pitchCtrl.Control::automatic);
   pitchCtrl.SetSampleTimeUs(1000);
 
+  velCtrl.SetOutputLimits(-0.15, 0.15);
+  velCtrl.SetMode(velCtrl.Control::automatic);
+  velCtrl.SetSampleTimeUs(10000);
+
   digitalWrite(LED_BUILTIN, LOW);
 }
 
@@ -117,13 +128,17 @@ uint32_t current_time = millis(), last_time = millis();
 void loop() {
   update_imu();
 
+  velCtrl.Compute();
+
   input = pitch;
-  //if(abs(input -setpoint) <= 0.01) input = setpoint;
+
+  Serial.println(setpoint);
   
   // I also modified the ArduPID library to use compute as a boolean. If calculations were done, it returns true. If not enough time has elapsed, it returns false
   if(pitchCtrl.Compute()){
 
     double tvelocity = output;
+    
     tvelocity = tvelocity / WHEEL_RADIUS * 180 / PI;
     frequency = tvelocity *  0.1125;
     half_period0 = 1000000 / (2*frequency);