1. MAE505: Robotics Final Project – Papers Review.
Main Topic: Nonholonomic-Wheel Mobile Robot (WMR). Sub-Topics: Modeling, Redundancies, & Motion Control.
Presented By:
Tao Gan
Advisor: Dr. Venkat Krovi.

2. Focus on two papers:
1. “Nonholonomic Mobile Manipulators: Kinematics, Velocities and Redundancies,”
- Journal of Intelligent and Robotic Systems Volume 36 , Issue 1 (January 2003) Pages: 45 – 63.
- Authors: B. Bayle, J-Y. Fourquet and M. Renaud.
- Present by: Leng-Feng Lee.
2. “Coordinating Locomotion and Manipulation of a Mobile Manipulator”
-IEEE Transactions on Automatic Control, Vol. 39, No. 6, June 1994, pp
- Authors: Yoshio Yamamoto and Xiaoping Yun.
- Present by: Tao Gan.

3. Organization of Presentation:
In each paper, we will present the following:
- Introduction of the paper.
- Formulation of the problem using an example.
- Simulation setting used.
- Simulation Result.
- Discussion of the Simulation Result.

4. 2nd paper: “Coordinating Locomotion and Manipulation of a Mobile Manipulator”
Introduction:
When a person writes across a board, he/she positions his/her arm in a comfortable writing configuration by moving his/her body rather than reaching out the arm.
-The same situation happens in many case such as people transporting a heavy object cooperatively.
Therefore, when a mobile manipulator performs a manipulation task, it is desirable to bring the manipulator into certain preferred configurations by appropriately planning the motion of the mobile platform.

5. Modeling: Using an Example
2nd paper: “Coordinating Locomotion and Manipulation of a Mobile Manipulator”
Modeling: Using an Example
Arial View
Modeling

6. 2nd paper: “Coordinating Locomotion and Manipulation of a Mobile Manipulator”
Modeling:
State Variables:
Three variables describe the position and orientation of the platform
Two variables specify the angular positions for the driving wheels

7. 2nd paper: “Coordinating Locomotion and Manipulation of a Mobile Manipulator”
Modeling:
Adding Nonholonomic Constraints
No.1 constraint is that the platform must move in the direction of the axis of symmetry (holonomic).
stop
No.2,3 C
No.2,3 constraints are the rolling constraints, i.e. the driving wheels do not slip(nonholonomic).
No. 1 C

8. 2nd paper: “Coordinating Locomotion and Manipulation of a Mobile Manipulator”
Modeling:
Three Constraints
According to the q, the three constraints can be written in the form of
where

9. 2nd paper: “Coordinating Locomotion and Manipulation of a Mobile Manipulator”
Modeling:
State Space Representation
The Mobile plateform’s equation of motion are described by
N x N inertia matrix
N x 1 vector of position and velocity dependent forces
N x r input transformation matrix
r-dimensional input vector

10. 2nd paper: “Coordinating Locomotion and Manipulation of a Mobile Manipulator”
Modeling:
Dynamic Equations
N x N inertia matrix

11. 2nd paper: “Coordinating Locomotion and Manipulation of a Mobile Manipulator”
r-dimensional input vector
Modeling:
Dynamic Equations
N x 1 vector of position and velocity dependent forces
N x r input transformation matrix

12. 2nd paper: “Coordinating Locomotion and Manipulation of a Mobile Manipulator”
Modeling:
Dynamic Equations
Constraints matrix
S(q) are in the null space of A(q).

13. 2nd paper: “Coordinating Locomotion and Manipulation of a Mobile Manipulator”
Differentiate and replace the one in the
Premultiply by

14. 2nd paper: “Coordinating Locomotion and Manipulation of a Mobile Manipulator”
Using state-space vector
linearize
Suppose there is input u
What is u?

15. 2nd paper: “Coordinating Locomotion and Manipulation of a Mobile Manipulator”
Differentiate it.
Decoupling Matrix
Differentiate it again.
This is u.

16. We can know every state variables in the system.
2nd paper: “Coordinating Locomotion and Manipulation of a Mobile Manipulator”
Since we know u
We can know every state variables in the system.

17. 2nd paper: “Coordinating Locomotion and Manipulation of a Mobile Manipulator”
Simulation:
Simulation Setting
1. Time Span: 0 – 60 sec
2. Path Trace: x = 6, y = t
3. Velocity: x_dot = 0,
y_dot = 1
4. Length of Link 1 = 5/sqrt(2),
Link 2= 5/sqrt(2),

18. 2nd paper: “Coordinating Locomotion and Manipulation of a Mobile Manipulator”
Simulation:
Simulation Setting
1. Time Span: 0 – 60 sec
2. Path Trace: x = t, y = t+t
3. Velocity: x_dot = 1,
y_dot = 1
4. Length of Link 1 = 5/sqrt(2),
Link 2= 5/sqrt(2),

20. 2nd paper: “Coordinating Locomotion and Manipulation of a Mobile Manipulator”
Simulation:
Simulation Result (case i)
Notice:
-Control of WMR with Nonholonomic Constraints with Error Correction.
-The velocity of point Po are shown.

21. 2nd paper: “Coordinating Locomotion and Manipulation of a Mobile Manipulator”
Simulation:
Simulation Result (case i)
Notice:
-It indicates that the mobile platform moved backward for a short period of time at the very beginning to achieve the needed heading angle.

22. 2nd paper: “Coordinating Locomotion and Manipulation of a Mobile Manipulator”
Simulation:
Simulation Result (case ii)

24. 2nd paper: “Coordinating Locomotion and Manipulation of a Mobile Manipulator”
Simulation:
Simulation Result (case ii)
Notice:
-Control of WMR with Nonholonomic Constraints with Error Correction.
-The velocity of point Po are shown.

25. 2nd paper: “Coordinating Locomotion and Manipulation of a Mobile Manipulator”
Simulation:
Simulation Result (case ii)
Notice:
-It indicates that the mobile platform moved backward for a short period of time at the very beginning to achieve the needed heading angle.

26. 2nd paper: “Coordinating Locomotion and Manipulation of a Mobile Manipulator”
Simulation:
Simulation Result (case ii)

27. 2nd paper: “Coordinating Locomotion and Manipulation of a Mobile Manipulator”
Conclusion:
-The second paper introduce a method of using Manipulability Measure of the Mobile Manipulator as the potential function included in the motion control of the WMR.
-We verified the effectiveness of the method by simulations on two representative trajectories