Control of a four-steering, planar five-bar linkage-walker

This paper introduces and describes a new type of wheeled locomotor referred to as a "four-steering, planar five-bar linkage-walker." This wheeled locomotor is a nonholonomic mechanical system that consists of five links, five rotational joints, and four steering systems. The five links coupled by the five joints form a closed-loop. The four steering systems are attached to four of the five links. Each of the four links has its own steering system at its middle point. The wheeled locomotor transforms the rotations of the five joints into movement by using the four steering systems. This means that the wheeled locomotor performs undulatory locomotion in which it transforms a change in its internal shape into the generation of its net displacement. In addition, a virtual joint is added to one of the ends of the first link. The virtual joint couples the first link and a virtual link which has a virtual axle at its middle point and a virtual steering system at its end. It is proven that, by assuming the presence of such virtual mechanical elements, it is possible to convert the kinematic equation of the wheeled locomotor into a five-chain, single-generator chained form in differential geometry. Based on chained form, a path-following feedback control method that enables the wheeled locomotor to follow a straight line is derived. The validity of the mechanical design of the wheeled locomotor, the transformation of its kinematic equation into chained form, and the path-following feedback control method is verified by computer simulation.