[SOLVED] CS7639 Project 1-Robotarium and Feedback Control

The Robotarium is an open access, remotely accessible robotics testbed housed at
Georgia Tech, which was designed with the purpose of enabling robotics research by
providing users with free, remote access to state of the art hardware and
infrastructure. It consists of a large planar arena, occupied by dozens of small
differential drive robots, called GRITSBots. After prototyping their algorithms in the
provided simulator, users take control of the robots by submitting their code online.
The Robotarium web site is www.robotarium.gatech.edu.
The purpose of this first project is to help you learn the basics of how to operate
individual robots with various levels of accuracy, and to stress the knowledge you
have acquired during the first few lectures (from introduction to low-level/mid-level
designs).
The GRITSBot is controlled using unicycle dynamics,
�
� = 𝑣
𝜔 = 𝑥
𝜃
where 𝜃 is the angle of the body frame of the robot with respect to the frame
defined on the testbed. The units of the velocity inputs 𝑣 and 𝜔 are m/s and rad/s
respectively.
Figure 1. The GRITSBot X (the bigger one on the left).
Figure 2. Drawing of the arena.
An overhead sensor is used to return pose data for the robot,
�
�
𝑝 = 𝑦 .
�
�
The position coordinates (x, y) are given in meters and 𝜃 is in radians, with a range
of [-pi, pi].
can
The Robotarium simulator, along with more information on the GRITSBot X and
testbed
be
found
on
(https://www.robotarium.gatech.edu/faq).
Modeling the Kinematics of the Robots
the
Robotarium
website
1. Learn how to perform basic operations on the robots (e.g. move from base to
a point with a given orientation, return to a base point etc.) on the
Robotarium simulation.
a. Find out the equation describing the relationship between the rpm of
the wheels, 𝜔wheel, and the forward velocity of the robot, v, with the
given parameters. The radius of the wheels is 1.5cm.
b. Find out the relationship between the translational velocity of the
wheels, vwheel, and the angular velocity of the robot, 𝜔, assuming the
wheels are rotating in opposite directions and with the same speed.
2. Describe the feedback control loop for controlling the orientation, 𝜃, of the
robots along a path used in the Robotarium using a block diagram. That is, a
desired orientation is commanded and thus should be your input. Make sure
to start with the input and end with the output in order to have a complete
diagram.
This could be helpful: https://en.wikipedia.org/wiki/Control_theory
Make sure to label each block as sensor/controller/actuator and label on
each line what variable is passed to the next block. An open loop block
diagram of the robot is like this:
3. Give brief descriptions of the sensor, actuator and controller. What do they do?
Relate these components to the actual relevant functions in the code.
Simulation Activities
Note: Do NOT use any pre-defined functions in the Robotarium simulator (/
examples and /utilities).
Prepare a script for your robot to do the following list of tasks:
1. Open the file, Template_Project_1.py, which contains two 3×1 pose vectors (i.e.
[𝑥; 𝑦; 𝜃]) with the names target1 and target2.
2. Command one robot to target1.
3. Once Task 2 is completed, command the robot to target2, with constant
velocity 8 cm/s and no angular velocity (open loop control). This can be done
by first pointing the robot to a desired direction at its current location, and
then calculating the theoretical number of iterations needed to reach
target2 at the given speed. The controller is running at 30 Hz (i.e. one
iteration corresponds to about 0.033 seconds).
4. Command the robot to target1.
5. Command the robot to target2 with constant 8 cm/s and a feedback strategy
where the angular velocity is adjusted (closed loop control) based on the
angular deviation from the direction to the target position. Stop the
experiment when the robot reaches the target position, within 1 cm and 0.1
radian accuracy. The feedback strategy can be expressed like the following:
𝜔 =𝑘(𝜃
where k is a gain value of 1.
−𝜃
),
6. Command the robot to target1.
Submit Your Experiment
Once you are satisfied with the simulation, submit the script,
Template_Project_1.py, to the Robotarium through your account. Data will be
accessible in several days.
Data Analysis
1. Plot the experimental position data of Task 3 and Task 5 on the same Y vs X
plot.
2. Plot the distance to the target position of Task 3 and Task 5 against the
number of iterations (normalized from 0) on the same plot.
3. Discuss and explain what you see in the plots.
Report and Grading
All the tasks are accomplished by the robot. (50 pts)
In your report, please do the following:
1. Answer the 3 questions in the Modeling section. (30 pts)
2. Indicate the theoretical number of iterations needed in Simulation Task 3. (5 pts)
3. Include 2 plots and the discussion from the Data Analysis section. (15 pts)
Submissions
P1 Attempt 1 & 2: The simulation .mat file (renamed simulation.mat) and
source .py file from your simulation. From robotarium your public experiment
link and .mat file (renamed experiment.mat) all submitted to Canvas.
*P1 Attempt 2 is optional if you do not like your score or need to make
modifications to your P1 Attempt 1. The best of the two scores will be used.
P1 Report: A final report (pdf) on Canvas by the submission
deadline.
Python Installation
Python is restricted to 3.5.x+
https://github.com/robotarium/robotarium_python_simulator