Feedback control of a wheeled snake mechanism with the Transverse Function approach

The Transverse Function (TF) approach is applied to the tracking control problem for a nonholonomic three-segments/snake-like wheeled mechanism similar to a planar low-dimensional version of Hirose´s Active Cord Mechanism (ACM). Unlike earlier studies devoted to this type of serpentine mechanism and based on the computation and sequential application of a discrete number of open-loop control primitives, the proposed control design yields smooth (nonlinear) feedbacks in the spirit, and prolongation, of Linear Control Theory. It is also supported by a rigorous stability analysis, and it further includes a solution to the delicate -often overlooked-problem of mechanical singularities avoidance. Another asset of the approach is that the ultimate boundedness of the tracking errors, with arbitrary tracking precision obtained via the tuning of the considered transverse function parameters, is achieved for any motion of the reference frame used to specify the desired gross motion of the mechanism. These properties are illustrated by simulation results. The fact that the TF approach involves periodic functions with time-derivatives depending on frequencies used as extra control variables points out connections between this approach and biologically inspired Central Pattern Generators (CPG) often evoked in the literature on systems exhibiting internal oscillatory behavior.