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https://github.com/wissem01chiha/robotic-arm-manipulator

mini palletizing 4 dof robot drafting arm project
https://github.com/wissem01chiha/robotic-arm-manipulator

arduino control-systems drafting industrial inverse kinematics matlab robotics simulation

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mini palletizing 4 dof robot drafting arm project

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README 

        
 



## Industrial Palletizing Robot Arm ABB  Project 

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### Table of Contents

- [Introduction](#introduction)

- [Project Structure](#project-struture)

- [Methodology](#methodology)

- [Kinematic Problem](#kinematic-problem)

- [Inverse Kinamatic Problem](#inverse_kinematic_problem)

- [Control Schema](#control_schema)

- [Experimentation](#experimentation)

- [Referances](#referances)

- [Contributing](#contributing)

- [License](#license)  



### Introduction 

Welcome to my Industrial Palletizing Robot Arm project! Explore my journey of designing, building, and programming this complex robot and how I transformed it into a 2D drafting machine. Discover its kinematics, control systems, and more exciting features.



### Project Structure

The project is organized in the flowwing tree: 

    

  •  Figures include simulation images and illustration graphics.

    • 

  •  Demo comprises demonstration videos and GIFs.  

    • 

  •  Datasheets consist of hardware component datasheets.

    • 

  •  Scripts encompass MATLAB calculus and command scripts. 

    • 

 

 



### Methodology

Regarding the complexity of the robot's kinematic chain, the equations I derived differ from the approach described in the following sections. I worked in cylindrical coordinates $(r, \rho, z)$ while keeping the base rotation of the robot fixed. I employed classical rigid body mechanics through closed-chain formulas.



### Kinematic Problem

 



  




 

The Denavit-Hartenberg Representation of our robot is described as follows:



$$A=

\begin{bmatrix}

c_{\theta_{i}} & -s_{\theta_{i}}c_{\alpha_{i}} &s_{\theta_{i}}s_{\alpha_{i}} & a_{i}c_{\theta_{i}} \\

s_{\theta_{i}}& c_{\theta_{i}}c_{\alpha_{i}}& -c_{\theta_{i}}s_{\alpha_{i}}& a_{i}s_{\theta_{i}} \\

0&s_{\alpha_{i}}& c_{\alpha_{i}}& d_{i}&\\

0 & 0 & 0 & 1\\

\end{bmatrix}

$$ 



The robot input parameters consist of three rotation angles denoted as $(q_1, q_2, q_3)$.



#### Main kinematic Chain

Link | $a_{i}$  |$\alpha_{i}$|$d_{i}$|$\theta_{i}$  

---|---         |---         |---    |---

1  | $a_{1}$    | 0          |$d_{1}$     | $q_{1}$

2  | $a_{2}$    | $90°$     | 0     | $q_{2}$

3  |  $a_{3}$ |0           |  0  |$q_{3}$

4  | $a_{4}$    | 0          |0     | $\theta$



We use the real dimensions provided in the official robot datasheet, even though our prototype model is a smaller kit. 



Since joint 3 is passive, the value of $\theta$ will be determined by the second chain with respect to the main chain.



$T_{0}^{4}(q_{1},q_{2},q_{3},\theta)= A1 * A2 * A3 * A4$

 

We obtain the position of the end effector from the fourth column of the matrix T :



$$P(q_{1},q_{2},q_{3},\theta)=

\begin{bmatrix}

p_{x}(q_{1},q_{2},q_{3},\theta)\\

p_{y}(q_{1},q_{2},q_{3},\theta)\\

p_{z}(q_{1},q_{2},q_{3},\theta)

\end{bmatrix}$$



#### Parallel Kinematic chain 

The parameter $\theta$ is controlled by the second chain, which also depends on the position of the main chain, specifically the variable positions of the joint centers $O_3$ and $O_4$ in the base frame $(x_0, y_0, z_0)$. By applying parallelogram angles properties, we can assume that the joint variable $\theta$ satisfies the following property:
  

$\theta=f(q_{3},q_{2})=4\pi/3+2\gamma-q_{3}-q_{2}-\beta$



We can observe that the system's forward kinematics are highly nonlinear, making traditional solving methods time-consuming. To simplify the equations, I propose changing the system's coordinate system into a cylindrical system. 

### Inverse Kinematic Problem

Given an initial position of the robot defined by $P_0(q_1, q_2, q_3)$, if we introduce an infinitesimal variation in each joint variable, the end effector moves to position $P$. The error is given by:



$$ \Delta P(q_{1},q_{2},q_{3})=P-P_{0}=\begin{bmatrix}

p_{x}(q_{10}+\delta q_{1},q_{2}+\delta q_{2},q_{3}+\delta q_{3})-p_{x}(q_{1},q_{2},q_{3})\\

p_{y}(q_{1}+\delta q_{1},q_{2}+\delta q_{2},q_{30}+\delta q_{3})-p_{y}(q_{1},q_{2},q_{3})\\

p_{z}(q_{10}+\delta q_{1},q_{2}+\delta q_{2},q_{3}+\delta q_{3})-p_{z}(q_{1},q_{2},q_{3})

\end{bmatrix}=

[J].

\begin{bmatrix}

  \delta q_{1} \\

  \delta q_{2}\\

  \delta q_{3}

\end{bmatrix}=

[J][\Delta q]$$



where  $[J]$ is a $3 \times 3$ matrix 



To compute the inverse Jacobian, we need to invert the matrix $[J]$. Therefore, we obtain:



$$[\Delta q]=[J]^{-1} [\Delta P]=[J(q_{1},q_{2},q_{3})]^{-1}

\begin{bmatrix} 

\Delta x ,\Delta y, \Delta z 

\end{bmatrix}$$



The $[\Delta P]$ vector results from the discretization of the robot end-effector trajectory. In my case, I use a fixed step workspace grid, and I determine the joint limits and workspace dimensions from experimenting with the robot's limit configurations.

### Control Schema

For the control part, I employ the classical Inverse Jacobian Algorithm. Since we work in 2D, it's essential to maintain $\Delta z = 0$ to ensure contact of the end effector with the paper surface. We can achieve this by incorporating an additional prismatic joint.






### Prototyping & Experimentation 

The project implementation took me more than 2 months, during which I encountered significant technical challenges. I can summarize my journey in the following main steps:

    

  •  I began by repairing and assembling the robot from scratch, using the minimal tools available in our club.

    • 



    

  •  I initiated my initial tests using unipolar stepper motors (28YBJ-48). However, their torque couldn't support the heavy load of the manipulator, and they would overheat.

    • 

  • 

    I switched to NEMA17 bipolar stepper motors, but without the appropriate driver and a 12V DC power supply, it was quite chaotic.

    • 



    

  • Eventually, I resolved the issues by using MG995 servo motors, and I started determining my workspace dimensions while developing the theoretical study. I used an Arduino Mega 2560 board, which I controlled through MATLAB, although the algorithm's high computational complexity strained the hardware's capabilities. 

    • 



    

  •  Finally, I set up the code to create basic shapes like letters "H" and "I," as well as geometric shapes such as rectangles and lines..
    

    I use an arduino Mega 2560 board wich i controlled it thought MATLAB , regarding the hight computation complexity of the algorthim  which The harware cannot support.

    • 



    

     



 

 ### Results :






Here are the best results we obtained in some of our tests:






### Referaneces

    

  •  Robotics: Modelling Planning and Control Bruno-Siciliano-2010

    • 

  •  Robotics, Vision and Control - Peter Corke-2020

    • 

  



### Contributing 

I would be happy to welcome anyone willing to contribute or support this project.

### Licence 

The project is licensed under the GNU license. For more details, please refer to the License file.