A path following feedback control law for a new type of undulatory locomotor: A trident steering walker

This paper presents a path following feedback control law for an undulatory wheeled locomotor referred to as a ldquotrident steering walker.rdquo This undulatory wheeled locomotor makes undulatory locomotion in which it transforms the rotations of its three joints into its movement by using four steering mechanisms. In this feedback control law, we especially replace some mechanical elements of the trident steering walker with virtual mechanical elements and we also provide with additional virtual mechanical elements for it. We prove that, by defining the virtual mechanical elements, it is possible to convert the kinematical equation of the trident steering walker into five-chain, single-generator chained form in a coordinate system where an arbitrary path whose curvature is two times differentiable is one coordinate axis and a straight line perpendicular to the tangent of the path is the other axis. This conversion is more general because it includes a conversion performed in the Cartesian coordinate system where its two axes are straight and they are perpendicular to each other. Based on chained form, we derive a feedback control law which causes the trident steering walker to follow an arbitrary path whose curvature is two times differentiable. We have performed a path following simulation in which the equilateral triangular base of the trident steering walker follows a biquadratic Bezier path and its relative orientation to the tangent of the path converges into a desired angle. The validity of the conversion of the kinematical equation into chained form and the path following feedback control law is verified by computer simulations.