DJI-Gimbal-FOC/README.md

# DJI Gimbal FOC

The aim of this project is to be able to use the 3-axis DJI gimbal with a custom open source controller like [SimpleFOC](https://docs.simplefoc.com/). This high quality gimbal is very tiny and easy to find as a replacement part which makes it very suitable for DIY projects. 

<img src="https://git.lurenaud.com/lurenaud/DJI-Gimbal-FOC/raw/branch/main/docs/overview.jpg" height=250>
<img src="https://git.lurenaud.com/lurenaud/DJI-Gimbal-FOC/raw/branch/main/docs/working.gif" height=250>

## Pinout identification
The Gimbal is composed of a flex PCB with a main connector and 3 smaller for each motor. The main end connector is a 40-pin mezzanine board to board connectors. In order to work easily I have designed a breakout board which open to a 2.54" header. (Kicad folder)

Here is the strategy I followed to find the pinout:
1. Find all equipotential pins with a multimeter set to continuity tests, and test all the combinations

2. Group remaining pins by motor With the multimeter find all the pins connected to the motor connector. (Reapeat 3 times for the other connectors)

<img src="https://git.lurenaud.com/lurenaud/DJI-Gimbal-FOC/raw/branch/main/Kicad/Breakout_DJI_Gimbal.png" height=400> <img src="https://git.lurenaud.com/lurenaud/DJI-Gimbal-FOC/raw/branch/main/docs/setup.jpg" height=400>

### Open-loop control

Each motor has its own drivers a MP6536. Which makes it easy as no additional hardware is necessary to drive the motors. 
There are 4 pins from the MP6536:
1. PWM1 
2. PWM2 
3. PWM3 
4. Fault : Output. When low, indicates overtemperature, over-current, or under-voltage.

Connected directly to a MCU (here a STM32 Nucleo F401RE) and with the Simple FOC Library, open-loop control works quite well. However due to open-loop control, it cannot know when a "step" is missed so misalignment can occur. Also, the motor tends to become quite hot due to the continuous current sent to the coils.

## Position estimation with the integrated linear hall sensors

### 1. Setup
Each motor is composed of two absolute linear hall sensors. (Texas Instrument DRV5053 Analog-Bipolar Hall Effect Sensor) They are placed at around 120º from each other (eyes measured) and measure the magnetic field of the rotor. 

<img src="https://git.lurenaud.com/lurenaud/DJI-Gimbal-FOC/raw/branch/main/docs/Hallmotor.jpg" height=300> 

Those sensor are absolute, meaning that the output of the measured magnetic field is the same regardless of the power suplly. In this setup, with 5V supply, the output measured is between 520mV and 1.5V, so a 1V amplitude signal. 

### 2. Measures

These oscilloscope traces are the sensor output when rotating the rotor forth and back. (a bit less than 180º on the 3rd motor)
The channel 0 (Yellow) is the Hall 1 and the Channel 1 (Green) is the Hall 2

<img src="https://git.lurenaud.com/lurenaud/DJI-Gimbal-FOC/raw/branch/main/docs/courbes.png" height=250> <img src="https://git.lurenaud.com/lurenaud/DJI-Gimbal-FOC/raw/branch/main/docs/cosSinEncoderDiagram.png" height=250>

We can see that in the first movement (positive rotation), the green is out of phase of π/2.`

### 3. Encoding the position 
1. Get the absolute angle within a period

Since the 2 signals correspond to a cos and sin signals, it is possible to compute the angle inside the period using arctan2 function. However, we have more than one period, it is so necessary to increment a position.

$$\theta= atan2(a,b)$$

2. Incremental position

To increment the position, it is necessary to start from 0 at a known postion. For that the motor is moved in open loop to one end and the position is set to 0.
Then we need to sum all the delta of movement at each measure sample.

$$\phi_t=\phi_{t-1} + (\theta_t - \theta_{t-1})mod(-\pi;\pi)$$

## Coding the solution
1. Get the angle in the perdiod

In order to compute the angle from the cos and sin with atan, it is necessary to remap the values of the analog readings from -1 to 1. 
Beforehand, the maximum and minimum peak of the signals need to be found. It can be done by swiping the motor on startup in open-loop mode.
Then the arctan function can be applied. It is preferable to use arctan2 as it will give an angle within the 4 quadrants (-π,π). Whereas arctan give an angle between (-π/2,π/2). [Wikipedia](https://en.wikipedia.org/wiki/Atan2)

```C++

float LinearHallSensor::Callback()  // Return the estimated position of the sensor
{
    A = norm(analogRead(CH1),minCh1, maxCh1);   //read analog values and normalise between [-1;1]
    B = norm(analogRead(CH2),minCh2, maxCh2);

    theta = atan2(A,B); // Compute the absolute angle in the period

    phi = phi + dist_angle(theta, theta_prev);  // increment the difference

    theta_prev = theta; // save fot nex time

    return phi;
}

float norm(float x, float in_min, float in_max) //return the input value normalised between [-1;1]
{
    return (float)(x + 1.0) * (2.0) / (float)(in_max - in_min) -1.0;
}

float dist_angle(float newAngle, float prevAngle) // return the difference modulo [-pi;pi]
{
    float diff = newAngle - prevAngle;
    while (diff < (-M_PI))
        diff += 2 * M_PI;
    while (diff > M_PI)
        diff -= 2 * M_PI;
    return diff;
}

``` 

## Tuning the PIDs
To achive position control it is necessary to have first, a velocity controller well tuned, as they are in cascade. (SimpleFOC implementation and diagram) 
![Closed loop position diagram from SimpleFOC](docs/angle_loop_v.png)

However, the motors of the gimbal have hard stop and can only rotate of around a half turn. It was so necessary to remove these  mecanical stops. I drilled with a 1.6mm drill the two little holes to remove it. Then the motor was able to rotate freely and PID can be tuned.

<img src="https://git.lurenaud.com/lurenaud/DJI-Gimbal-FOC/raw/branch/main/docs/drilling.jpg" height=250> <img src="https://git.lurenaud.com/lurenaud/DJI-Gimbal-FOC/raw/branch/main/docs/freeturn.gif" height=250>