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.

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. 1326-1332. - Authors: Yoshio Yamamoto and Xiaoping Yun. - Present by: Tao Gan.

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.

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.

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

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

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

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

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

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

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

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).

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

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

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

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.

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),

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),

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.

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.

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

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.

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.

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

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