Revise paste Model Predictive Controller

#include <ArduinoMPC.h>

// Define system parameters
const int numInputs = 2; // Number of control inputs (e.g., torques for each joint)
const int numOutputs = 2; // Number of system outputs (e.g., joint angles)
const int horizon = 10; // Prediction horizon

// MPC object
MPC mpc(numInputs, numOutputs, horizon);

// Define system model matrices (A, B, C, etc.)
// These matrices need to be tailored to your specific robotic arm model
float A[2] = {1.0, 0.0}; // State transition matrix (simplified)
float B[2] = {0.1, 0.1}; // Control input matrix (simplified)
float C[2] = {1.0, 1.0}; // Output matrix (simplified)
float Q[2] = {1.0, 1.0}; // State cost matrix
float R[2] = {0.1, 0.1}; // Control cost matrix

void setup() {
  Serial.begin(115200);
  
  // Initialize MPC with model parameters
  mpc.setModelMatrices(A, B, C);
  mpc.setCostMatrices(Q, R);
  
  // Set constraints for joint movements (example constraints)
  mpc.setInputConstraints(-10, 10); // Example input constraints for joint torques
}

void loop() {
  // Read current system state (e.g., joint angles)
  float currentState[numOutputs] = {readJointAngle(0), readJointAngle(1)};
  
  // Define desired setpoint (target joint angles)
  float setpoint[numOutputs] = {1.0, 1.0}; // Example setpoints in radians
  
  // Compute optimal control inputs
  float optimalInputs[numInputs];
  mpc.computeOptimalInputs(currentState, setpoint, optimalInputs);
  
  // Apply control inputs to actuators (e.g., motors controlling the joints)
  applyControlInputs(optimalInputs);
  
  // Print the results
  Serial.print("Optimal Inputs: ");
  for (int i = 0; i < numInputs; i++) {
    Serial.print(optimalInputs[i]);
    Serial.print(" ");
  }
  Serial.println();
  
  delay(100); // Loop delay
}

float readJointAngle(int joint) {
  // Implement function to read joint angles from sensors
  // For example, use an analog sensor or an encoder
  return analogRead(joint); // Placeholder, replace with actual sensor reading
}

void applyControlInputs(float* inputs) {
  // Implement function to send control inputs to motors
  // For example, use PWM to control motor torques
  analogWrite(LED_BUILTIN, inputs[0]); // Example: use control input for joint 1
  analogWrite(LED_BUILTIN + 1, inputs[1]); // Example: use control input for joint 2
}