ZED tracking coordinate-based kart control

[arya1106]

Use the information provided by #6 and a series of target points to plan and follow a given path. Output control values of:

• Braking
• Steering
• Throttle

[arya1106]

Discord Channel

[arya1106]

Planning to use LQR implementation with forward kinematics from here. Another example implementation. Simulation code here.

[arya1106]

Symbol definitions:

$x$ – x-coordinate relative to world frame
$\dot{x}$ – x-coordinate change
$y$ – y-coordinate relative to world frame
$\dot{y}$ – y-coordinate change
$\theta$ – yaw in degrees relative to world frae
$\dot{\theta }$ – change in yaw
$\varphi$ – current steering angle of car
$\dot{\varphi }$ – current steering angle of car
$t_0$ – current time
$t_1$ – time we are trying to predict
$dt$ – discrete time step
$\beta$ – Brake (0-255)
$\tau$ – Throttle (0-255)
$\pi$ – Steering Angle (0-255)
$u_1$ - velocity of kart
$u_2$ - turning rate of kart

What we get from the kart:

$x,y,\theta$ – Coordinates from #6
$\varphi$ - Control memory

Forward kinematics

State vector

$$\left[\begin{array}{c}x\\ y\\ \varphi \\ \theta \end{array}\right]$$

Inputs:

• $u_1$
• $u_2$

Software (us) Controls (inputs):

• $\beta$
• $\tau$
• $\pi$

Conversions:

$u_1$ = $c_1\beta +c_2\tau$
$u_2$ = $\frac{\pi -\varphi }{dt}$

$c_1$ and $c_2$ to be found experimentally.

Differential State Matrix

$$\left[\begin{array}{c}\dot{x}\\ \dot{y}\\ \dot{\varphi }\\ \dot{\theta }\end{array}\right]=\left[\begin{array}{c}{u}_1\cos \theta \\ u_1\sin \theta \\ u_2\\ u_1\cdot \frac{1}{L}\cdot \tan \varphi \end{array}\right]$$

State prediction

$$\left[\begin{array}{c}{x}_t\\ y_t\\ {\varphi }_t\\ {\theta }_t\end{array}\right]+\left[\begin{array}{c}\dot{x}\\ \dot{y}\\ \dot{\varphi }\\ \dot{\theta }\end{array}\right]=\left[\begin{array}{c}{x}_{t+1}\\ y_{t+1}\\ {\varphi }_{t+1}\\ {\theta }_{t+1}\end{array}\right]$$

[arya1106]

Just found this....

Worth a try to implement ourselves for the challenge, but we can use the reference here if we struggle.