Forward Dynamics of UR5 Robot
Robot dynamics is the study of the motion of a robot, taking into account the forces and torques that cause it. The forward dynamics of a robot arm consists in finding the joint accelerations caused by the set of torques applied to the joints and the force applied by the end-effector (i.e. when grasping an object).
Here, I wrote a program that implements forward dynamics of the UR5 robot from Universal Robots, to simulate the motion .
First, it takes as input the initial the vector of joint coordinates, the vector of joint speeds, the input joint torques and end-effector wrench, where a wrench is a representation of a force acting on a point, and the moment it generates.
Then, it calculates the joint accelerations from the mass matrix, velocity quadratic forces, gravity forces and end-effector wrench. Finally, these joint accelerations are integrated over time to get the joint angle configurations. The motion is shown in the simulation videos.
The first case corresponds to an initial vector of joint coordinates of (0,0,0,0,0,0), and the second case corresponds to an initial vector of joint coordinates of (0,-1,0,0,0,0) radians. For both cases, all initial joint speeds and accelerations are zero, there are no forces acting at the end-effector (wrenches), the input joint torques is zero, which means, only gravity is the acting force.
Simulation 1
Simulation 2
© 2015 by Marissa G. Campa. Created with Wix.com
I used Python 3.7 to develop this program, with the libraries numpy and csv. I also used the library 'modern_robotics' provided in the Modern Robotics wiki website.
http://hades.mech.northwestern.edu/index.php/Modern_Robotics
For the simulations, I used the software V-REP EDU PRO software.
I followed the assignments in the Course 3: Robot Dynamics, which is part of the online specialization Modern Robotics: Mechanics, Planing and Control, offered by Nortwestern University and Coursera.
