simulations of a three degree of freedom brachiating y-bot robot

8/15/2019 Simulations of a Three Degree of Freedom Brachiating Y-Bot Robot

1/23

1

Simulations of a Three Degree of Freedom Brachiating Y-Bot Robot

by

Alexander Breton

Submitted to theDepartment of Mechanical Engineering

in Partial Fulfillment of the Requirements for the Degree of

Bachelor of Science in Mechanical Engineering

at the

Massachusetts Institute of Technology

May 2016

© 2016 Massachusetts Institute of Technology. All rights reserved.

Signature of Author:

Alexander G. BretonDepartment of Mechanical Engineering

May 16, 2016

Certified by:

Sangbae Kim

Associate Professor of Mechanical EngineeringThesis Supervisor

Accepted by:

Anette Hosoi

Professor of Mechanical EngineeringUndergraduate Officer


2/23

2

Simulations of a Three Degree of Freedom Brachiating Y-Bot Robot

by

Alexander Breton

Submitted to the Department of Mechanical Engineeringon May 16, 2016 in Partial Fulfillment of the

Requirements for the Degree of

Bachelor of Science in Mechanical Engineering

ABSTRACT

Brachiation is a means of locomotion for lightweight apes like gibbons. It involves the animalswinging its arms to gain moment and swing forward. A large amount of research has been done

studying a simplified two-link two DOF robot, named “acrobot” by Mark Spong. While the

problems of this robot have been studied extensively, it’s functionality is quite limited. This paper studies a three-link three DOF brachiating robot, dubbed “Y-bot”. The goal of adding the

extra link is to add functionality.

Simulations of a model were run in Matlab taking advantage of Russ Tedrake’s toolbox Drake,which was designed to solve optimization problems of underactuated systems. The main method

used in the trajectory optimization was direct collocation. The task of the robot in the simulationswas to swing from a one “branch” point to another. The trajectories of two Y-bot modelsswinging from rest were optimized. Furthermore, the gait of one of the models was examined,

and a beneficial state for the second swing of a gait was suggested. A method to optimizing the

gait of a model was proposed. A linear relationship between the total trajectory time and thescale of the model was defined.

The paper suggests a physical model of the Y-bot could be constructed using Saito’s two DOF

brachiating robot as a benchmark. The problems of gait optimization and payload transportationwere mentioned as future work to be done.

Thesis Supervisor: Sangbae KimTitle: Associate Professor of Mechanical Engineering


3/23

3

Table of Contents

Abstract 2

Table of Contents 3

List of Figures 4

List of Tables 5

1. Introduction 6

1.1 Brachiation Description 6

1.2 Previous Work 6

1.3 3 DOF Brachiation Robot 8

2. Set Up 9

2.1 Model 9

2.2 Nonlinear Optimal Trajectory Planning Problem 10

2.2.1. Direct Linear Collocation 10

2.2.2. Implementation in Matlab through Drake 11

3. Simulation and Results 13

3.1 Characteristics of the Equilink Model 13

3.1.1. Continuous Brachiation 13

3.2 Body Link as Smaller Acrobot 18

3.3 Optimal Trajectory Time as a Function of Length 18

4. Conclusion 20

4.1 Open Problems 20

4.2 Future Steps 20

5. Bibliography 22


4/23

4

List of Figures

Figure 1.1: Diagram of Gibbon Brachiating 6

Figure 1.2: Diagram of 2 DOF brachiating robot 7

Figure 1.3: Schematic of Saito’s physical model 7

Figure 2.1: Diagram of Y-bot 9

Figure 2.2: Y-bot at problem’s initial position 12

Figure 3.1: Passive trajectories of acrobot and Y-bot 13

Figure 3.2: Optimized trajectory of equilink simulation from rest 14

Figure 3.3: Optimized trajectory of equilink simulation of the second swing of a gait 15

Figure 3.4: Trajectory of body link after swing 16

Figure 3.5: Total times of 2nd swings 17

Figure 3.6: Total sum of impulses of 2nd swings 17

Figure 3.7: Optimized trajectory of Y-bot with an acrobot body link 18

Figure 3.8: Optimal trajectory times of equilink models of different scales 19

Figure 3.9: Optimal trajectory times vs scales of equilink models 19


5/23

5

List of Tables

TABLE 3.1: Parameters of equilink model 16


6/23


7/23


8/23


9/23


10/23


11/23


12/23


13/23


14/23


15/23


16/23


17/23


18/23


19/23


20/23


21/23


22/23

6. Bibliography

[1] O'Neill, Dennis. "The Primates: Apes." The Primates: Apes. Palomar College, n.d. Web.3 Apr. 2016.

[2] Gibbon Swinging through the Trees Very Fast. Youtube . N.p., 13 Feb. 2011. Web.

[3] Saito, Fuminori, Toshio Fukuda, and Fumihito Arai. "Swing and Locomotion Control for

a Two-Link Brachiation Robot." IEEE Control Systems Magazine, 12:5-12, February

1994.

[4] Gibbons Swinging. Digital image. Locomotion. Gibbon Research Lab,. Web.

[5] Saito, Fominori. , “Motion control of the brachiation type of mobile robot,” Ph.D.

dissertation (in Japanese), Nagoya Univ., Nagoya, Japan, Mar. 1995.

[6] Nakanishi, J., Fukuda, T., and Koditschek, D.E. "Preliminary studies of a second

generation brachiation robot controller". April 1997.

[7] Spong, M. “The swing up control problem for the acrobot.” IEEE Control Systems

Magazine, 15:49-55, February 1995.

[8] Nakanishi, Jun. Thesis. Nagoya University, 2000.

[9] V. M. de Oliveira and W. F. Lages, "Predictive Control of an Underactuated Brachiation

Robot," IFAC Proceedings Volumes, 8th IFAC Symposium on Robot Control , 2006, pp.

19-24.

[10] V. M. de Oliveira and W. F. Lages, "Control of a brachiating robot for inspection ofaerial power lines," Applied Robotics for the Power Industry (CARPI), 2010 1st

International Conference on, Montreal, QC, 2010, pp. 1-6.

[11] Fukuda, Toshio, Tadayoshi Aoyama, Yasuhisa Hasegawa, Kosuke Sekiyama, and

Shigetaka Kojima. "PDAC-Based Control for the Multi-Locomotion Robot." (2009): n.

pag. Web.

[12] Askeland, Stian Hjellvik. "Stabilization of Brachiation Locomotion in a Monkey Robot."

Thesis. Norwegian University of Science and Technology, 2012. Stabilization of

Brachiation Locomotion in a Monkey Robot . June 2012. Web.

[13] Tedrake, Russ. Drake: A Planning, Control, and Analysis Toolbox for Nonlinear

Dynamical Systems" Computer software. Vers. 0.9.11. 2014. Web.

[14] Tedrake, R. Underactuated Robotics: Algorithms for Walking, Running, Swimming, Flying, and Manipulation (Course Notes for MIT 6.832). Downloaded on 3/20/16 from

http://underactuated.mit.edu/

[15] C. R. Hargraves and S. W. Paris. Direct trajectory optimization using nonlinear

programming and collocation. J Guidance, 10(4):338-342, July-August 1987.

[16] Gede, Gilbert. "The Direct Collocation Method for Optimal Control." UC Davis. 26 May2011. Lecture.


23/23

[17] Gill, Philip E., Elizabeth Wong, and Michael Saunders. SNOPT . Computer software.

Vers. 7.5. Web.

simulations of a three degree of freedom brachiating y-bot robot

Documents