Create LorenzAttractor_ESP32.ino

examples/LorenzAttractor/LorenzAttractor_ESP32.ino

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+//
+// Lorenz Attractor Data Generator (Fixed-Point Arithmetic)
+//
+// Author: Alex Spataru
+//
+// This program is specifically designed for the ESP32 microcontroller and simulates
+// the Lorenz system using fixed-point arithmetic. The Lorenz system is a set of
+// three chaotic differential equations, and the program transmits the generated
+// data (x, y, z) over the serial port. The output is ideal for visualizing the 
+// Lorenz attractor in real-time using tools like Serial Studio.
+//
+// Lorenz System Parameters:
+// - σ (sigma): 10.0      (controls the rate of rotation in the attractor)
+// - ρ (rho):   28.0      (sets the "height" of the attractor)
+// - β (beta):  8.0 / 3.0 (controls the damping)
+//
+// How It Works:
+// - The program calculates the Lorenz attractor using the Euler method, updating
+//   the x, y, and z values at each step based on the Lorenz equations.
+// - It uses fixed-point arithmetic for precise calculations, which is necessary
+//   due to the ESP32's 32-bit floating-point limitations.
+// - The ESP32's FreeRTOS capabilities are leveraged to separate simulation and
+//   serial transmission tasks for optimal performance.
+// - The data is transmitted asynchronously at regular intervals for visualization.
+//
+// Required Tools:
+// - ESP32 microcontroller (e.g., ESP32 DevKit, NodeMCU ESP32, etc.)
+// - Serial Studio or any serial plotting tool to visualize the data.
+//
+// Baud Rates:
+// - Serial Studio: 115200 baud
+//
+// Notes:
+// - This program is optimized for the ESP32 and may require modifications to work
+//   on other platforms due to its use of FreeRTOS and ESP32-specific features.
+// - Ensure your ESP32 board is correctly connected and configured for the Arduino IDE.
+//
+// How to Run:
+// - Load this program onto an ESP32 using the Arduino IDE or similar tool.
+// - Connect to the ESP32 via Serial Studio or another serial plotting tool.
+// - Observe the real-time Lorenz attractor visualization.
+//
+
+#include <Arduino.h>
+
+// Parameters for the Lorenz system (scaled by 1000 for fixed-point arithmetic)
+const int32_t sigma = 10000;  // σ: 10.0 scaled by 1000
+const int32_t rho = 28000;    // ρ: 28.0 scaled by 1000
+const int32_t beta = 2666;    // β: 8/3 scaled by 1000
+
+// Initial conditions (scaled by 1000)
+int32_t x = 100;  // Initial X value (0.1 scaled by 1000)
+int32_t y = 0;    // Initial Y value
+int32_t z = 0;    // Initial Z value
+
+// Time step (scaled by 1000)
+const int32_t dt = 10;  // 0.01 scaled by 1000
+
+// Interval between data transmissions (microseconds)
+const unsigned long transmissionInterval = 1000;
+
+// Queue for asynchronous data transmission
+QueueHandle_t dataQueue;
+
+///
+/// Task to calculate the Lorenz system state
+///
+void simulationTask(void *param) {
+  while (true) {
+    // Calculate the derivatives (scaled by 1000)
+    int32_t dx = ((sigma * (y - x)) / 1000) * dt / 1000;
+    int32_t dy = (((x * (rho - z)) / 1000 - y) * dt) / 1000;
+    int32_t dz = (((x * y) / 1000 - (beta * z) / 1000) * dt) / 1000;
+
+    // Integrate the derivatives to update the system's state
+    x += dx;
+    y += dy;
+    z += dz;
+
+    // Send data to the queue
+    int32_t data[3] = {x, y, z};
+    xQueueSend(dataQueue, &data, portMAX_DELAY);
+
+    // Maintain consistent time step
+    vTaskDelay(pdMS_TO_TICKS(1));
+  }
+}
+
+///
+/// Task to transmit Lorenz system data over Serial
+///
+void serialTask(void *param) {
+  while (true) {
+    int32_t data[3];
+    if (xQueueReceive(dataQueue, &data, portMAX_DELAY)) {
+      // Convert data back to float for serial output
+      Serial.print(data[0] / 1000.0, 6);
+      Serial.print(",");
+      Serial.print(data[1] / 1000.0, 6);
+      Serial.print(",");
+      Serial.println(data[2] / 1000.0, 6);
+    }
+  }
+}
+
+///
+/// Configures the ESP32, initializes the serial port, and creates tasks
+///
+void setup() {
+  // Initialize Serial communication
+  Serial.begin(115200);
+  while (!Serial);
+
+  // Create a queue to hold Lorenz system data
+  dataQueue = xQueueCreate(10, sizeof(int32_t[3]));
+
+  // Create tasks for simulation and data transmission
+  xTaskCreate(simulationTask, "SimulationTask", 4096, NULL, 1, NULL);
+  xTaskCreate(serialTask, "SerialTask", 2048, NULL, 1, NULL);
+}
+
+///
+/// The main loop is empty; tasks handle simulation and data transmission
+///
+void loop() {
+  // Do nothing
+}