Tracking control of the trident snake robot with the Transverse Function approach

The transverse function (TF) approach is applied to the tracking control problem for a specific nonholonomic mechanical system, called the trident snake robot. To this purpose an homogeneous (nilpotent) approximation, also invariant on a Lie group, of the kinematic equations of the system is used. The proposed feedback control automatically generates deformations of the mechanism which simultaneously achieve the practical stabilization of a reference frame with arbitrary position/rotation displacements on the plane and the avoidance of mechanical singularities. Another original contribution concerns the design of the transverse function employed for the control design. This function is here defined on the rotation group SO(3), instead of the torus T³ used in previous works on the TF approach. Beside the conceptual interest associated with this new possibility, and the simplicity of the function itself, improvements in terms of control smoothness and stability can be observed from numerical simulations performed on the trident snake robot, one of which is reported for illustration and visualization purposes.