Research
My MS thesis advisor is Dr Krovi, our research focus on motion-planning for multiple wheeled mobile robots using potential field approaches.
My thesis title is "Decentralized Motion Planning Within a Artificial Potential Framework (APF) for Cooperative Payload Transport by Multi-robot Collectives".
As such, the two main issues in my research are:
1. What kind of potential field function is best for mobile-robot's motion planning? and;
2. How to maintain formation with the use of potential field approach?
Here, I provide movies that I created using Matlab to demonstrate some of the ideas in my thesis. Detailed mathematics formulation can be found in my thesis, available to download below:
Download:
1. Thesis - Download. [PDF ver. size: 7.15MB]
2. Presentation - Download. [.rar File Size: 24.67MB]
3. Navigarion Function Standalone GUI ver 0.1 - Download [File Size: 143.MB]
Note:
1. The presentation compressed file contain movies files. Use Winrar to extract the files.
2. The Standalone GUI contain MATLAB Component Runtime installer (size 149MB). You can run the GUI without MATLAB installed. Please read the README.txt file to set up the GUI.
I have recently upload most of the video here to YouTube. By doing so, it avoid a lot of issues regarding the video codec to play the movie files. Please visit my YouTube page at: YouTube.
'Watch' my thesis presentation:
Chap. 1 & 2
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Chapter 1: Intoduction & Chapter 2: Background [3:25min] -Chapter 1 includes motivation, overview, scope of the research, and organization of the thesis. -Chapter 2 provides an overview on motion planning for mobile robots, noting the distinctions with respect to control. We will however restrict ourselves to focus to the motion planning problem and explore some of the differences between explicit motion planning and implicit motion planning. -View it on: YouTube. |
Chap. 3
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Chapter 3: Local Potential Field Approaches. [2:15min] -In Chapter 3, we introduce some of the most commonly used local potential functions within the class of implicit motion planning approaches. These include Harmonic Potential, Superquadric Potential, etc. -We also highlight the benefits and limitations of such local potential field approaches. -View it on: YouTube. |
Chap. 4
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Chapter 4: Global Potential Approach - The Navigation Function. [2:58min] -Chapter 4 focuses on navigation functions which are a class of potential fields that may be constructed with a unique global minimum. We begin by reinvestigating the steps to create a potential field that has only a unique minimum at the target position for a workspace with arbitary shaped obstacles. -View it on: YouTube. |
Chap. 5
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Chapter 5: Robots Kinematics & Dynamics Formulation. [4:34min] -Chapter 5 presents the kinematic and dynamic formulations for single robot module and robot collective without formation constraints, which are then used to generate motion plans for the robot together with the potential field approaches described in Chapter 3 and Chapter 4. -View it on: YouTube. |
Chap. 6
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Chapter 6: Dynamic Formulation for a Group of Robots. [3:46min] -Chapter 6 introduces the concept of constraint dynamics and formulates the dynamics for groups of robots with formation constraint within a potential framework. Three methods were introduced to solve the constrained dynamics formulations – i.e. Method I, direct Lagrange multiplier elimination method, Method II, penalty formulation method, and Method III, constraint manifold projection method. -View it on: YouTube. |
Chap. 7A
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Chapter 7: Simulations and Results (part 1)[4:48min] -Chapter 7 presents simulation results for various interesting cases studies using the dynamic equation formulated in Chapter 6. In particular, four case studies were performed. The first two case studies pertain to the performance of each of the three methods in maintaining rigid formation, and the other two case studies evaluate their proformance when the robots undergo formation changes. -View it on: YouTube. |
Chap. 7B
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Chapter 7: Simulations and Results (part 2)[5:25min] -Chapter 7 presents simulation results for various interesting cases studies using the dynamic equation formulated in Chapter 6. In particular, four case studies were performed. The first two case studies pertain to the performance of each of the three methods in maintaining rigid formation, and the other two case studies evaluate their proformance when the robots undergo formation changes. -View it on: YouTube. |
Chap. 7 full
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Chapter 7: Simulation and Results (full) [9:28min] -Chapter 7 presents simulation results for various interesting cases studies using the dynamic equation formulated in Chapter 6. In particular, four case studies were performed. The general characteristics of each method are also discussed base on the simulation results we obtained from these case studies. -View it on: YouTube. |
Brief Introduction:
Potential Field Approach.
| - Potential field approach is a widely used method for collision avoidance for robot manipulators
since it was introduced in the Mid 80's by Khatib. Since then, it has been used for many researchers
simply because of its mathematical elegance.
However, some limitations were discovered. Among them, local minimum problems seem to be the most disaster one. Potential Field approach, where obstacles in the workspace are modeled as high potential field (Repulsive Potential) and target is model as the lowest potential, the (Attractive Potential) point in a workspace, when we force the robot to follow the negative gradient (Toward lowest point) of the potential, the robot will eventually converge to the target point. |
[view larger screen on:YouTube.] |
| [View it on: YouTube.] | One can think of this situation as a placing a ball in a surface, the ball will roll
until it reach the lowest point of the given surface. As shown in the animation at the left. View other
version of the simulations on YouTube: [Ver1.0], [
Ver2.0], [
Ver3.0]
The total potential of a workspace is obtained by adding the Repulsice potential and the Attractive potential field. In this way, local minimum may occurred due to some arrangement of the obstacles. If local minimum exist in a workspace, the robot may trapped in the local minimum and never reach the target. |
...
Please read my thesis for more detailed explanation.
Note: If you want to use any of the materials on this site, please kindly send me an email. =)
Graphs :
3D Graphs2D Graphs |
Here are some of the 3D and 2D plots used in my thesis, and presentation. Click on the graph to play the slide show. Note: For detailed information on these graphs, please download the presentation file. |
Movies:
PART I: Visualization.
Visual 01
| 1. Visualization of Navigation Function. v1.0
- FileSize: 344KB[download]. - See how the shape of the potential field created using navigation function of a workspace with 4 obstacles changes as the control value kappa changes. - View it on: YouTube. - View other versions on YouTube: [ v0.1],[ v0.3],[ v0.5]. |
Visual 02
| 2. Visualization: 3 Balls Rolling, without formation constraint. v2.0
- FileSize: 867KB [download] - As 3 balls rolling down a surface without formation constraint, they collide into each other. - View it on: YouTube. - View other version on YouTube: [ v1.0] |
Visual 03
| 3. Visualization: 3 Balls Rolling, with formation constraint. v2.0
- FileSize: 897KB [download] - With formation constraint, three ball maintained a formation while rolling down the surface. - View it on: YouTube. - View other version on YouTube: [ v1.0] |
Visual 04
| 4. Visualization: APF approach-ball rolling down a surface. v3.0
- FileSize: 1.76MB [download] - Following the negative gradient of a potential surface, a robot (ball) rolls down the surface. - View it on: YouTube. - View other versions on YouTube: [ v1.0],[ v2.0]. |
Visual 05
| 5. Visualization: Simulated real workspace-Motion planning of single robot.
- FileSize: 1.49MB [download] - In this simulation, I tried to create a 3D workspace in MATLAB that shows obstacles (cylinder tubes), the robot (shown as a ball) and show the resulting motion plan of single robot using potential field method. - View it on: YouTube. |
Visual 06
| 6. Visualization of Navigation Function (Contour plot).
- FileSize: 6.36MB [download] - Visualization of the contour plot of the potential of a workspace with four obstacles generated using Navigation Function. See how the shape of the potential field created using navigation function of a workspace with 4 obstacles changes as the control value kappa changes. - View it on: YouTube. |
PART II: Single Robot Module Simulation.
Case 01
| 1. Single Robot, One Obstacle, FIRAS Function.
- Motion Planning of single robot in workspace with one obstacle, potential created using FIRAS Function. - FileSize: 4.32MB [download]. - View it on: YouTube. |
Case 02
| 2. Single Robot, two obstacles, Ge's new potential.
- Motion Planning of single robot in workspace with two obstacle, potential created using FIRAS Function. - FileSize: 7.77MB [download] - View it on: YouTube. |
Case 03
| 3. Single Robot, four obstacles, Navigation Function.
- Motion Planning of single robot in workspace with two obstacle, potential created using Navigation Function. - FileSize: 1.46MB [download] - View it on: YouTube. |
Case 04
| 4. Single NH-Wheeled Mobile Robot, four obstacles, Navigation Function.
- Motion Planning of single Nonholonomic (NH) Wheeled Mobile Robot in workspace with four obstacles, potential created using navigation function. - FileSize: 2.89MB [download] - View it on: YouTube. |
PART III: Robots in Group Simulation. (still under construction...)
Case 01
| 1. 3 Robots in quadratic field, with formation constraint.
- Case study performed in my thesis, shown here is motion planning solved uising Method I. - Download avi: [Method I], [Method II], [Method III]. - View it on YouTube: [Method I], [Method II], [Method III]. |
Case 02
| 2. 3 Robots with one obstacle, with formation constraint.
- Case study performed in my thesis, shown here is motion planning solved using Method II. - Download avi: [Method I], [Method II], [Method III]. - View it on YouTube: [Method I], [Method II], [Method III]. |
Case 03
| 3. 3 Robots in quadratic field, with formation expansion.
- Case study performed in my thesis. Shown here is Motion Planning solved using Method III. - Download avi: [Method I], [Method II], [Method III]. - View it on YouTube: [Method I], [Method II], [Method III]. |
Case 04
| 4. 3 Robots in quadratic field, with formation shape change.
- Case study performed in my thesis. Shown here is Motion Planning solved using Method II. - Download avi: [Method II], [Method III]. - View it on YouTube: [Method II], [Method III]. |
Case 05
| 5. 10 Robots in quadratic field, with formation constraint.
- Simulation of 10 robots in a quadratic potential field with formation constraint. - Download avi: [Method I], [Method II], [Method III]. - View it on YouTube: [Method I], [Method II], [Method III]. |
Case 06
| 6. 10 Robots with one obstacle, with formation constraint.
- Simulation of 10 robots with formation constraint in a workspace with one obstacle, potential field created using navigation function. - Download avi: [Method I], [Method II], [Method III]. - View it on YouTube: [Method I], [Method II], [Method III]. |
Note: Some links in Part III still not ready. For now, these links will connect to my YouTube channel.