README.md

Industrial Palletizing Robot Arm ABB Project

Table of Contents

• Introduction
• Project Structure
• Methodology
• Kinematic Problem
• Inverse Kinamatic Problem
• Control Schema
• Experimentation
• Referances
• Contributing
• 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.