• Masato ISHIKAWA, Dr.Eng., Senior Lecturer, Kyoto univ.
• Yasushi IWATANI, Dr.Eng., Associate Professor, Hirosaki univ. (2001-)

• Ichiro MARUTA, JSPS Research Fellow, Kyoto univ. (2009-)
• Takahiro FUJINO, Master course, Kyoto univ. (2008-)
• Yuki MINAMI, JSPS Research Fellow, Kyoto univ. (2005-2006)
• Yusuke KAMIYA & Kazuhito KIMURA, Master course, Kyoto univ. (2005)
• Takahiro IWATAKE, Master course, Tokyo univ. (2003)
• Norihisa SAKAMOTO & Koutarou YOSHIMOTO, Undergraduate course, Tokyo univ. (2003)

• M. Ishikawa, Y. Minami and T. Sugie: Development and Control Experiment of the Trident Snake Robot, IEEE/ASME Transactions on Mechatronics, Vol. 15, No.1, pp. 9-16, 2010, in press. DOI: 10.1109/TMECH.2008.2011985
• M. Ishikawa, P. Morin and C. Samson: Tracking Control of the Trident Snake Robot with the Transverse Function Approach, Proc. of the 48th IEEE Conference on Decision and Control (CDC09), pp. 4137-4143, 2009. 12. (Shanghai, PR China)
• M. Ishikawa, T. Fujino (presented by T. Sugie) : Control of the Double-Linked Trident Snake Robot based on the Analysis of its Oscillatory Dynamics, in IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2009), pp. 1314-1319, 2009.10. (St. Louis, USA)
• Snake Robot and Trident Snake Robot: Control based on Controllability Structure, Journalvol.42, No.7, pp.640-645, 2007 (in Japanese).
• Iwatani and Ishikawa: Snake robot and trident snake robot: control based on controllability analysis, Journal of SICE, vol.42, No.7, pp.620-625, 2006 (in Japanese)
• Locomotion analysis and periodic control of the multi-linked trident snake robot, Trans. of SICE, vol. 42, No.5, 2006 (in Japanese)
• Point-to-point feedback control of trident snake robot, to appear in Trans. of ISCIE, vol. 20, No.2, 2007 (in Japanese, outstanding paper award)
• Motion analysis and control of trident snake robot, Trans. of SICE, vol. 39, No.12, 2003 (in Japanese)
• Motion analysis and control of multi-linked trident snake robot, Proc. of the 3rd SICE Annual Conference on Control Systems, pp.601-606, 2003 (in Japanese, outstanding presentation award)
  Paper (PDF,679KB) Presentation (PDF,700KB)
• Dynamical modeling of the trident snake robot and its periodic feedback control, Proc. of the 4th SICE Annual Conference on Control Systems, pp.503--506, 2004 (in Japanese).
  Paper (PDF,461KB) Presentation (PDF,782KB)
• Trident Snake Robot: Locomotion Analysis and Control, IFAC NOLCOS'04, Stuttgart, 2004.
  Paper (PDF, 347KB) Presentation (PDF, 775KB)
• Development and Control Experiment of the Trident Snake Robot, in Proc. of the 45th IEEE Conference on Decision and Control(CDC'06), submitted to IEEE Trans. Mech.

The basic idea of this invention is based on a purely mathematical interest on nonholonomic systems with multi-generators. In terms of nonlinear controllability, multi-generator systems are structurally different from single-generator systems such as chained systems, which have been comprehensively investigated since early 90's. Control problem for these systems is relatively a new field and is quite complicated as yet; we believe this robot would cast a fascinating stimulation to this field.

On the other hand, research on snake robots traces back to the 70's: Hirose has thoroughly studied the motion mechanism of live snakes and developed world's first robotic snakes (see Hirose'94 and references therein), and established the most fundamental principle of their winding locomotion; to trace the serpenoid curve, or roughly speaking, to control the joint angles according a phase-shifted sinusoidal functions.

• cf. Conventional winding propulsion control based on serpenoid curve principle[1] MPEG(1.5MB)
• See also my alternative approch to snake robot control. ->link

Principle of locomotive control is strongly related to controllability structure. In this research, we first performed modeling and controllability analysis of the trident snake robot, especially for its simplified (1-link or 2-link) models. Grounded on the analysis, we proposed periodic control patterns which generate motion primitives (rotation and translation), in order to clarify the principle just like in the case of conventional snakes.

The Model

The robot is put on a flat plane. In the middle of its body, the robot has a root block; an equilateral triangular plate with three actuated joints at its vertices. The robot has three branch legs as well, which are connected to the root block via the joints. Each branch is composed of serial N links with actuated joints. Each link has a passive wheel on its center, which is assumed not to slip, nor slide sideways.

\phi_ij denotes j-th joint of the i-th branch. The shape vector of the robot is

\phi := (\phi_11, ..., \phi_1N, \phi_21, ..., \phi_2N, \phi_31, ..., \phi_3N )

The position of the robot is represented by the coordinates (x,y) of the center, and its orientation is represented by \theta0. The configuration vector of the robot is

w := (x, y, \theta0)

---

1. Fundamental periodic control of the trident snake based on the holonomy analysis
   • 1-link, rotation control MPEG 1.5MB
   • 1-link, translation control MPEG 2.6MB
   • 2-link, rotation control MPEG 1.8MB
   • 2-link, translation control MPEG 2.0MB

2. Robustification -- stability of periodic locomotion
   While investigating the aforementioned control for the 2-link model, we noticed that the locomotion pattern is not uniquie and its sustainability of locomotion is strongly dependent on the choice of reference shape.

   We then analyzed the invariance of diverse locomotion cycles, and found that invariant cycles are distibuted as a one-dimensional manifold. Moreover, there are some (asymptotically) stable cycles and the others unstable. Choosing an appropriate reference shape corresponding to a stable cycle, we finally achieved robust and sustainable locomotion. (Ishikawa et al., 2004)

   
   

   • 2-link, translation control, the aforesaid method --- may fail to continue the locomotion (bad case) MPEG 2.6MB
   • 2-link, translation control, the improved method --- its motion converges to a stable cycle MPEG 2.3MB
   • 2-link, rotation control, the improved method --- its motion converges to a stable cycle MPEG 2.3MB
   • Combining the translation and rotation controls, it is possible to move around on the field like a swimming stingray! MPEG 3.8MB

Trident snake 0 (LEGO MINDSTORM version)

Trident snake 1 (R/C servo version)

• 1link, rotation control MPEG 5.8MB
• 1link,translation control MPEG 6.8MB

Trident snake 2 (Multi-link, R/C + Position sensor + Manual Controller version)

• 1link, rotation control (clockwise） MPEG 1.6B
• 1link, rotation control (counter-clockwise) MPEG 1.4MB
• 1link, translation control (downward) MPEG 1.3MB
• 1link, translation control (rightward) MPEG 1.2MB

Trident snake 3 (1-link, wireless and light-weight version)

• 1link, rotation control (counter-clockwise)
  (Visit YouTube)

Computation : MaTX and MATLAB(R) / Visualization : Mgtk based on Gtk / Experiment : RTLinux free, Arduino

See Also

• My research on regular snake robot

Acknowledgement

Special thanks to:

• Prof. Shinji HARA, Dept. of Information Physics and Computing, The university of Tokyo
• Prof. Toshiharu SUGIE, Dept. of Systems Science, Kyoto university