The Trident Snake Robot project

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The trident snake is a three-headed snake robot, proposed by the authors as an entirely new locomotive mechanism. It is composed of three branches of serial links and a root block, where the three branches are connected to the root block at center like a three-pointed star. Each branch is the same as a conventional snake robot; i.e., every link has a passive wheel and all the joints are actuated. (see

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.

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

  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)


Recent Movies

Trident snake 0 (LEGO MINDSTORM version)

Developed by: N. Sakamoto and K. Yoshimoto
Technical notes for LEGO MINDSTOM (in Japanese)

Trident snake 1 (R/C servo version)

Staffs: Y. Minami, Y. Kamiya and K. Kimura

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

Developed by: Y. Minami

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

Developed by: I. Maruta

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

See Also


This research is partially supported by the Ministry of Education, Culture, Sports, Science and Technology, Grant-in-Aid for Young Scientists, No.14750361.

Special thanks to: