"In the first [exercise](https://git.rwth-aachen.de/introduction-to-robotics-course/introduction-to-robotics-2023/-/tree/main/01_IntroductionToPython) you got introduced to the fundamentals of `Python` (variables, data types, operators, decision structures, loops, functions and modules). In order to consolidate and extend the knowledge aquired, the following tutorial tasks should be solved / implemented.\n",
"\n",
"## Task 1.1\n",
"\n",
"The **forward_kinematics** function from the [forward_kinematics module](https://git.rwth-aachen.de/introduction-to-robotics-course/introduction-to-robotics-2023/-/blob/main/01_IntroductionToPython/forward_kinematics.py) is implemented for an manipulator of **n links** and **n+1 revolute joints** that starts from an **initial position** with all joint rotations $\\theta=0$.\n",
"\n",
"Implement a function named **fk_task_1** inside the [forward_kinematics module](https://git.rwth-aachen.de/introduction-to-robotics-course/introduction-to-robotics-2023/-/blob/main/01_IntroductionToPython/forward_kinematics.py) that ***returns*** a list which contains for each time step all joint coordinates $x_i$ and $y_i$ for a manipulator (**n links** and **n+1 revolute joints**) with an initial joint rotation that is described by the current rotations $\\theta_{i,0}$ and the desired incremental joint rotations at time t $\\Delta\\theta_{i,t}$ for joint i. The base link is rotating around the given point $[x_0 = 0, y_0 = 1]$. \n",
"\n",
"Test the implemented function inside this jupyter notebook in the following cells. Use the given structure to\n",
"\n",
"1. **Import** necessary modules.\n",
"2. **Define** the **parameters** needed to test the 'fk_task_1' function.\n",
" - base link coordinates $x_0$ and $y_0$\n",
" - link lengths $a_i=[1,1,1,1,1]$\n",
" - initial joint roations $\\theta_{i,t=0}=[90,0,0,0,0]$ in degree\n",
" - incremental change of joint rotation $\\Delta\\theta_{i,t=1} = [0,0,90,-30,45]$\n",
"3. **Call** the 'fk_task_1' **function** and save the return values under appropriate named variables.\n",
"4. **Create** a **plot** containing the initial manipulator position (red) and the position after incremental rotation (green).\n",
"\n",
"**Hint:** Use the the data type [array](https://numpy.org/doc/stable/reference/arrays.ndarray.html) from the [numpy package](https://numpy.org/doc/stable/) to define define the variables which contains sequence of values. That allows you to use arithmetic operators directly on the variables.\n"
]
},
{
"cell_type": "code",
"execution_count": 54,
"id": "59a9ad77-e04e-40ac-83d6-2e379901020f",
"metadata": {
"vscode": {
"languageId": "python"
}
},
"outputs": [],
"source": [
"# Use this cell to import the necessary modules"
]
},
{
"cell_type": "code",
"execution_count": 122,
"id": "2e47f84e-0363-4a6c-a148-41a4ef2614ea",
"metadata": {
"vscode": {
"languageId": "python"
}
},
"outputs": [],
"source": [
"# Use this cell to define the gemoetry and rotation parameters"
]
},
{
"cell_type": "code",
"execution_count": 124,
"id": "22db17d3-491b-480d-87ac-eff27acb3712",
"metadata": {
"vscode": {
"languageId": "python"
}
},
"outputs": [],
"source": [
"# Use this cell to call the function 'fk_task_1'"
"# Use this cell to plot the initial maniplator position and the position after incremental rotation"
]
},
{
"cell_type": "markdown",
"id": "6b0921a2-a094-429c-84f6-405e62f53c6b",
"metadata": {},
"source": [
"## Task 1.2\n",
"\n",
"After implementing the **fk_task_1** function and teststing it for one time step, respectiveley one increment, test the function now for several time steps. The goal is now to reach the rotation position $\\theta_i$ from **Task 1.1** in 5 evenly spaced steps and generate one plot which contains the resulting configuration of the arm manipulator for all time steps. \n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "9dfed8f7",
"metadata": {
"vscode": {
"languageId": "python"
}
},
"outputs": [],
"source": [
"# Calculation of the incremental rotation steps to reach the final rotation position"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1716ad7e",
"metadata": {
"vscode": {
"languageId": "python"
}
},
"outputs": [],
"source": [
"# Use this cell to call the function 'fk_task_1'"
In the first [exercise](https://git.rwth-aachen.de/introduction-to-robotics-course/introduction-to-robotics-2023/-/tree/main/01_IntroductionToPython) you got introduced to the fundamentals of `Python` (variables, data types, operators, decision structures, loops, functions and modules). In order to consolidate and extend the knowledge aquired, the following tutorial tasks should be solved / implemented.
## Task 1.1
The **forward_kinematics** function from the [forward_kinematics module](https://git.rwth-aachen.de/introduction-to-robotics-course/introduction-to-robotics-2023/-/blob/main/01_IntroductionToPython/forward_kinematics.py) is implemented for an manipulator of **n links** and **n+1 revolute joints** that starts from an **initial position** with all joint rotations $\theta=0$.
Implement a function named **fk_task_1** inside the [forward_kinematics module](https://git.rwth-aachen.de/introduction-to-robotics-course/introduction-to-robotics-2023/-/blob/main/01_IntroductionToPython/forward_kinematics.py) that ***returns*** a list which contains for each time step all joint coordinates $x_i$ and $y_i$ for a manipulator (**n links** and **n+1 revolute joints**) with an initial joint rotation that is described by the current rotations $\theta_{i,0}$ and the desired incremental joint rotations at time t $\Delta\theta_{i,t}$ for joint i. The base link is rotating around the given point $[x_0 = 0, y_0 = 1]$.
Test the implemented function inside this jupyter notebook in the following cells. Use the given structure to
1.**Import** necessary modules.
2.**Define** the **parameters** needed to test the 'fk_task_1' function.
- base link coordinates $x_0$ and $y_0$
- link lengths $a_i=[1,1,1,1,1]$
- initial joint roations $\theta_{i,t=0}=[90,0,0,0,0]$ in degree
- incremental change of joint rotation $\Delta\theta_{i,t=1} = [0,0,90,-30,45]$
3.**Call** the 'fk_task_1' **function** and save the return values under appropriate named variables.
4.**Create** a **plot** containing the initial manipulator position (red) and the position after incremental rotation (green).
**Hint:** Use the the data type [array](https://numpy.org/doc/stable/reference/arrays.ndarray.html) from the [numpy package](https://numpy.org/doc/stable/) to define define the variables which contains sequence of values. That allows you to use arithmetic operators directly on the variables.
After implementing the **fk_task_1** function and teststing it for one time step, respectiveley one increment, test the function now for several time steps. The goal is now to reach the rotation position $\theta_i$ from **Task 1.1** in 5 evenly spaced steps and generate one plot which contains the resulting configuration of the arm manipulator for all time steps.
%% Cell type:code id:9dfed8f7 tags:
``` python
# Calculation of the incremental rotation steps to reach the final rotation position
