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.
\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)
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)
Computation : MaTX and MATLAB(R) / Visualization : Mgtk based on Gtk / Experiment : RTLinux free, Arduino
Special thanks to: