michaelnaps / donald

Repository for the development of a personal robot project, Donald.

Path-following robot: Donald

This repository serves as the testing grounds for functions and classes that will be used for the development of my personal robot, Donald.

State/Model Selection:

$$ x = \left[ \begin{matrix} x \\ y \\ \theta \end{matrix} \right] $$

$$ \dot{x} = \left[ \begin{matrix} \dot x_1 \\ \dot x_2 \\ \dot x_3 \end{matrix} \right] = \left[ \begin{matrix} \dot{x} \\ \dot{y} \\ \dot{\theta} \end{matrix} \right] = \left[ \begin{matrix} \textrm{cos} (x_3) (u_1 + u_2) \\ \textrm{sin} (x_3) (u_1 + u_2) \\ \frac{1}{R} (u_1 - u_2) \end{matrix} \right] $$

This can then be converted to the discrete function form using a sufficiently small step-size parameter, $\Delta t$.

$$ x^+ = x + \Delta t \cdot \dot{x} $$