ADVISOR: Taskin Padir, Ph.D.
Collaborated with team members to design and develop an algorithm in MATLAB to control a high-speed robotic convoy over rough terrain.
Made use of a POTENTIAL FIELDS ALGORITHM in order to control a convoy, while generating a trajectory reference for the robots to follow. By possessing priori kinetic models of the other vehicles in the convoy, the followers are able to determine the intended trajectory of their leader without the use of explicit communication.
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POTENTIAL FIELDS ALGORITHM: Control of a high-speed robotic convoy over rough terrain (Investigation Project)
1. Control of a
high-speed robotic
convoy over rough
terrain
RBE595
Final Project
Prof Padir
April-19-2012
Michael Audi
Aaron Fineman
Yifan Li
Michael Raineri
Annette M Rivera Courtesy of http://simhqcom/forum/ubbthreadsphp/topics/2122888html
2. Introduction:
Commonly seen in military convoy driving
Vehicles must:
follow each other while
maintaining a safe and constant
distance
avoid obstacles that the preceding
vehicle failed to detect
continue unimpeded, rather than
become trapped waiting for the
leader to continue
Inspired by searching for ways to control full-
scale convoys
Courtesy of http://simhqcom/forum/ubbthreadsphp/topics/2122888html
24/17/2012RBE595 - Final Presentation
3. Purpose/Goal:
To apply various high-level control algorithms, in
particular potential field based methods, for use in
robotic convoys driving at high speed over rough
terrain
34/17/2012RBE595 - Final Presentation
4. Related Work:
Robotic convoying
Significant research problem in mobile robotics
Addressed from different points of view, eg, artificial vision, control theory,
artificial intelligence, etc [1]
Most existing mobile robot systems still involve a single robot working alone,
while there is a wide range of potential applications for robots acting in
concert
Potential Fields
Assisting a robot to move from one initial configuration to a desired
final configuration without colliding with any obstacles
Car Models
Dynamics of a vehicle system
typically modeled as a quarter car, a half car, and a full car
44/17/2012RBE595 - Final Presentation
5. Robotic convoying:
Following Robot Imitates its lead robot
Each of the following robots track the angular and linear velocity of
its lead robot.
Courtesy of Belkhouche and Belkhouche (August 2005)
54/17/2012RBE595 - Final Presentation
Convoy with constant distance
between robots
Constant Distance Between Robots
with
Velocity Pursuit
Deviated Pursuit
Proportional Navigation
Modeling and Controlling a Robotic Convoy Using Guidance Laws Strategies
Fethi Belkhouche, Member, IEEE, and Boumediene Belkhouche, Member, IEEE
IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART B:
CYBERNETICS, VOL. 35, NO. 4, AUGUST 2005 (p.813-825)
6. Potential Fields:
Additive Attractive/Repulsive
Potential Functions
attracting the robot to the goal position
while repelling the robot from the
obstacles by superposing these two
effects into one resultant force applied on
the robot.
𝑭 𝒒 = −𝛁 𝑼 𝒂 𝒒 + 𝑼 𝒓 𝒒
Courtesy of Firat Uyanik (n.d.)
64/17/2012RBE595 - Final Presentation
Additive attractive/repulsive
potential function
A study on Artificial Potential Fields
Kadir Firat Uyanik
KOVAN Research Lab. Dept. of Computer Eng.
Middle East Technical Univ. Ankara, Turkey
7. Car Models:
𝑀 𝐱 + 𝑏 𝐱 + 𝑘 𝐱 = 𝐅
Courtesy of Jazar (2009)
Quarter Car Half Car
Full Car
74/17/2012RBE595 - Final Presentation
Courtesy of Jazar (2009)
Courtesy of Jazar (2009)
8. Procedure:
A version of the potential fields control method was
implemented in MATLAB This program was then used to
directly control three Khepera III's utilizing a serial over
Bluetooth link
84/17/2012RBE595 - Final Presentation
9. Procedure:
The potential field models are governed by the following
characteristic equation:
𝐹 𝑞 = −𝛻 𝑈 𝑎𝑡𝑡𝑟𝑎𝑡𝑖𝑣𝑒 𝑞 + 𝑈𝑟𝑒𝑝𝑢𝑙𝑠𝑖𝑣𝑒 𝑞
Figure:
Potential field shape
The characteristic shape used for
our potential fields is
demonstrated in Figure
94/17/2012RBE595 - Final Presentation
10. Robot Following Simulation (Fixed Offset)
Leading Robot:
𝑞 𝑛 = 𝑞 + −𝐾 ∗ 𝐹 𝑞 𝑞
Sequential Following Robots:
𝑞 𝑛 𝑟 = 𝑞(𝑟+1) − 𝑜
4/17/2012 10RBE595 - Final Presentation
12. Hardware Implementation
Khepera 3 Robots
Potential Field Implementation
Controlled by Matlab
Almost Completed
4/17/2012 12RBE595 - Final Presentation
13. Procedure:
2D (half) and 3D (full) car models were implemented in
MATLAB showing the forward dynamics of the system,
which takes on the following characteristic form:
𝑀 𝐱 + 𝑏 𝐱 + 𝑘 𝐱 = 𝐅
(m being the mass coefficients, b being the damping coefficients, k being
the spring coefficients)
Figure:
2D (half) car model
Figure
Courtesy of Jazar (2009)
134/17/2012RBE595 - Final Presentation
14. Procedure:
𝑀 𝐱 + 𝑏 𝐱 + 𝑘 𝐱 = 𝐅
144/17/2012RBE595 - Final Presentation
% Mass Matrix
m = [ms 0 ;
0 mu];
% Damper matrix
b = [bs -bs ;
-bs (bs+bu)];
% Spring matrix
k = [ks -ks ;
-ks (ks+ku)];
Figure:
Quarter car model
Courtesy of Jazar (2009)
Quarter Car
16. Procedure:
The inverse dynamic models were then implemented in
MATLAB These simulate a following vehicle with perfect
virtual sensors measuring the changes in the center of the
leading vehicle so that the road disturbances may be
estimated
𝑀 𝐱 + 𝑏 𝐱 + 𝑘 𝐱 = 𝐅
Courtesy of Jazar (2009)
164/17/2012RBE595 - Final Presentation
17. Procedure:
4/17/2012 17RBE595 - Final Presentation
Use the last measurement for the position,
velocity, and input force to calculate the current
acceleration
The assumption made here is the acceleration for the current time
is approximately equal to the acceleration for the last point in time
A(t) = A(t-1) = M-1 * (F(t-1) – B*V(t-1) – K*X(t-1))
Using the estimated acceleration, the input force
matrix was calculated for the current instance in
time
F(t) = M*A(t) + B*V(t) + K*X(t)
The force matrix contains the input ground disturbance
18. Simulations:
Response to a 2 cm bump:
Position
Velocity
Error
Courtesy of Spenko, Iagnemma, Dubowsky (nd)
184/17/2012RBE595 - Final Presentation
25. Summary:
Modeled the car dynamics of the robots as Linear
models.
254/17/2012RBE595 - Final Presentation
Technologies Rating
Bluetooth
MATLAB
Khepera III's
Potential Fields for
Path and Trajectory
Planning in a convoy.
Used a control algorithm to
compensate for obstacle
avoidance.