Snake Robots

The figure illustrates a simple 3-link snake robot model. (we only consider its kinematic behavior, neglecting dynamic one).It is composed of three rigid links with two joints.

Each link has a passive wheel on its center, which does not slip nor slide sideways. Let (x,y,θ)(x,y,θ) denote its head position and orientation, and (q1,q2)(q1,q2) denote joint angles. We also assume that the joint angular velocities are given as the control input u=q˙u=q˙. This 2-input 5-state system is an example of nonholonomic system with *two generators*, which is structurally distinguished from those with single generator, convertible to well-known *chained form systems* [2]. Its controllability Lie algebra is expressed as {g1, g2, [g1,g2], [g1,[g1,g2]], [g2,[g1,g2]]}. The ball-plate manipulation problem[5-7] is also categorized into the same class.

An illusrative demonstration — pararrel driving of the snake along “y”-axis. In this case, the snake is tracking a moving target specified as (x,y+0.8), where the current position is (x,y). Please look with keen interest that the *snake is moving in the direction perpendicular to its body*! This motion is essentially artificial, different from those obtained from bio-mimetic approaches.

- Initial head position = (0,0)[m] / orientation = 0 [rad]
- Desired head position = (0,5.0)[m] / orientation = 0 [rad]

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- Control of nonholonomic drift-free systems by iterative curvature feedback, the 3rd IFAC workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control (LHMNLC’06), 2006.

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