trajectory-simulation-pelican-robot

Trajectory simulation of the Pelican Prototype Robot of the CICESE Research Center, Mexico. The position control used was PD control with gravity compensation and the 4th order Runge-Kutta method.

Project maintained by JCLArriaga5 Hosted on GitHub Pages — Theme by mattgraham

Pelican Experimental Robot Trajectory Simulation

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Trajectory simulation of the Pelican Prototype Robot of the CICESE Research Center, Mexico. The position control used was PD control with gravity compensation and the 4th order Runge-Kutta method.

Use the repository

$ git clone https://github.com/JCLArriaga5/trajectory-simulation-pelican-robot.git

Enter the path where the repository was cloned and install the dependencies with the following command:

$ pip install -r requirements.txt

Simulation

You can review the simulation carried out in a Colab notebook using the functions created in probot, by clicking here:

or use the shell/command prompt for run simulation in probot Python File:

:~/trajectory-simulation-pelican-robot$ cd pelcnrbt/
:~/trajectory-simulation-pelican-robot/pelcnrbt$ python probot.py

The simulation must be in order:

# Desired position
pd = [0.26, 0.13]
# Gains
kp = [[30.0, 0.0],
      [0.0, 30.0]]
kv = [[7.0, 0.0],
      [0.0, 3.0]]
# Initial values of angles and velocities
qi = [0.0, 0.0]
vi = [0.0, 0.0]
ti = 0.0
tf = 1.0

sim = pelican_robot(pd, kp, kv, control_law='PD-GC')
qsf, qpsf = sim.run(ti, qi, vi, tf)

Kp, Kv are symmetric positive definite and selected by the designer and are commonly referred to as position gain and velocity (or derivative) gain, respectively. In form:

Kp = diag{kp} = diag{30, 30} [Nm/rad]
Kv = diag{kv} = diag{7, 3} [Nm/rad]

the qi angles were set to zero to start from home position in this case, if you want it to start from another position you can use the inverse_k function in utils.py which is the robot inverse kinematics which returns the values of q1 and q2 for the position you want:

from utils import inverse_k

qi = inverse_k(px, py)
# px is the desired x-coordinate
# py is the desired y-coordinate

Once the simulation values have been generated by run you can use the functions to graph the results.

Images for desired position (0.26, 0.13)

Graph of error: The graph shows how the error of the angles for the desired position was reduced by the controller. The errors shown in the graph are a product of the friction phenomenon that has not been included in the dynamics of the robot.

sim.plot_q_error()

Graph of velocities behavior: The graph shows how the speed of each link behaved until reaching the desired position

sim.plot_velocity_bhvr()

Graph of desired position trajectory

sim.plot_trajectory(50)

Simulation Animated

If you want to see the animation of the trajectory to the desired position and the behavior of the error during the set time, use the parameter display=True in the RK4 function, as shown:

Note: Once the simulation values have been generated, inside sim.run code when the number of total iterations done, there will get values and show animation.

Note: Animation is not showing in Google Colab

sim = pelican_robot(pd, kp, kv, control_law='PD-GC')
qsf, qpsf = sim.run(ti, qi, vi, tf, display=True)

References

Kelly, R., Davila, V. S., & Perez, J. A. L. (2006). Control of robot manipulators in joint space. Springer Science & Business Media.

“Case Study: The Pelican Prototype Robot.” Control of Robot Manipulators in Joint Space, Springer-Verlag, 2005, pp. 113–32. DOI.org (Crossref), https://doi.org/10.1007/1-85233-999-3_6.