Control of A New Type of Undulatory Wheeled Locomotor: A Trident Steering Walker Based on Chained Form

摘要

This paper introduces and describes a new type of undulatory wheeled locomotor, which we refer to as a "trident steering walker." The wheeled locomotor is a nonholonomic mechanical system, which consists of an equilateral triangular base, three joints, three links and four steering systems. The equilateral triangular base has a steering system at its center of mass. At each apex of the base is a joint which connects the base and a link. The link has a steering system at its midpoint. The wheeled locomotor transforms driving the three joints into its movement by operating the four steering systems. This means that the wheeled locomotor achieves undulatory locomotion in which changes in its own shape are transformed into its net displacement. We assume that there is a virtual joint at the end of the first link. The virtual joint connects the first link and a virtual link which has a virtual axle at its midpoint and a virtual steering system at its end. We prove that, by assuming the presence of such 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 mathematical framework, differential geometry. Based on chained form, we derive a path following feedback control method which causes the trident steering walker to follow a straight path. We also define a performance index of propulsion of the trident steering walker to design its control parameters. The validity of the mechanical design of the trident steering walker, the conversion of its kinematical equation into chained form, the straight path following feedback control method, and the design of the control parameters reflecting the performance index of propulsion has been verified by computer simulations.