The trident-snake is a nonholonomic wheeled mechanism imagined by Dr. Ishikawa from the University of Osaka to test nonlinear control design methods and techniques. It is composed of a triangular-shaped body at the summits of which three limbs equipped with non-actuated wheels at their extremities are attached via rotary actuated joints. The mechanism moves on a planar surface by modifying the angles between the limbs and the body. The kinematics of this mechanism can be modelled as a 6-dimensional control system with 3 control inputs.

In the video, the blue frame is the reference frame whose motion is specified by the user without taking the mechanism’s motion limitations into account, and the red frame is a frame attached to the trident-snake’s body.
The control objective is to have the red frame track the blue one, both in position and orientation.

Click here to watch the video.