Abstract
This paper introduces and describes a new type of wheeled locomotor which we refer to as a “four-steering, planar five-bar linkage-walker.” This wheeled locomotor is a nonholonomic mechanical system, and it 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 its movement by using the four steering systems. This means that the wheeled locomotor makes undulatory locomotion in which it transforms the change of its internal shape into the generation of its net displacement. Especially, we assume a virtual joint at 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 which has a virtual steering system at its tip. We prove that, by assuming such virtual mechanical elements, it is possible to convert the kinematical equation of the wheeled locomotor into five-chain, single-generator chained form in differential geometry. Based on chained form, we derive a path following feedback control method which makes the wheeled locomotor follow a straight line. The validity of the mechanical design of the wheeled locomotor, the transformation of its kinematical equation into chained form, and the path following feedback control method is verified by computer simulations.
