Task 1

Create folder and specifies your preferred ROS version and programming language

• ROS version : ROS2 Foxy
• Programming Language : C++

Task 2

$$\begin{aligned} v_r &= \sqrt{ \dot x_r ^2 + \dot y_r ^2 }\\ w_r &= {(\ddot y_r \dot x_r - \ddot x_r \dot y_r) \over (\dot x_r^2 + \dot y_r ^2)} \end{aligned}$$

Task 3

$$\begin{aligned} x_r &= a \cos(bt)\\ \dot x_r &= - a \cdot b \sin (bt)\\ \ddot x_r &= - a \cdot b^2 \cos(bt) \end{aligned}$$

$$\begin{aligned} y_r &= a \sin(bt)\\ \dot y_r &= a \cdot b \cos (bt)\\ \ddot y_r &= - a \cdot b^2 \sin(bt) \end{aligned}$$

Task 4

$$\begin{aligned} x_r &= \bar a \sin(\bar bt)\\ \dot x_r &= \bar a \cdot \bar b \cos (\bar bt)\\ \ddot x_r &= - \bar a \cdot \bar b^2 \sin (\bar bt)\\ \\ y_r &= \bar a \sin(\bar bt) \cos(\bar bt)\\ \dot y_r &= \bar a \bar b \big( \cos ^2 (\bar bt) - \sin^2 (\bar bt) \big)\\ \ddot y_r &= -4 \bar a \bar b^2 \cos(\bar bt) \sin(\bar bt) \end{aligned}$$