lucas-vivian / manipulador

Simulation and trajectory control algorithms of the ARM 5E Mini manipulator.

Trajectory Control with 5-DOF Manipulator

This repo contains the simulation and control algorithms of my undergraduate thesis project: Five Degree of Freedom Manipulator Positioning Interface for Subsea Applications, which uses the ARM 5E Mini manipulator from ECA Robotics.

It's composed by three folders:

• Matlab: Theoretical simulations of the manipulator's kinematic model;
• Python: Trajectory control and data send/receive algorithms to/from the manipulator;
• Trajectory Points: Set of points of three different trajectories to be coursed by the manipulator.

Matlab

This folder is divided in Forward and Inverse Kinematics. The FK folder contains four main simulation files: FK_TCC, FK_Workspace, Workspace_TCC and DH_Robot_literal. There's a support file called MGD_DH for the last one. The IK folder has only one main file minsumsquare_test.m and one support file.

Forward Kinematics (FK)

The forward kinematics problem is defined by: ".. determine the position n and orientation of the end effector in terms of joint variables". Using the Denavit-Hartenberg notation, the description of this problem in multiple DOF is simplified.

1. Interactive FK interface with FK_TCC.m

Having determined the DH parameters and the offset of the manipulator, the links are created and the joint limits defined. Using the teach function from Peter Corke toolbox we create an interactive enviroment to solve the forward kinematics problem of the manipulator.

When the program is executed, a new window will appear allowing the user to set angles for each joint showing the three coordinates of the end-effector as result.

2. Generating workspace with Workspace_TCC.m

The workspace of a manipulator is defined by all the points that the end-effector can reach without going over the manipulator's mechanical limits. Knowing the joint limits and using the linspace function, we create a aproximation of all joints' possible values to generate the workspace points through the forward kinematics equations.

Instead of using a for loop to apply each set of angles to each joint individually, we can use the ndgrid function to create a 50x50x50 matrix to each set to then use directly into the equations and then scatter the results.

3. Combining interface with workspace in FK_Workspace.m

Combining the two previous files we get a validation to the equations because it's possible to observe that when sliding the joints, they doesn't exceed workspace plot.

4. Generating Forward Kinematics equations in DH_Robot_literal.m

Inverse Kinematics (IK)

Python

Pontos