Local and Global Isotropy Analysis of Mobile Robots with Three Active Caster Wheels

Abstract

In the near future, personal service robots are expected to come into human daily life as supporters in education, leisure, house care, health care, and so on. Most of them are built on an omnidirectional mobile robot so as to navigate in an environment restricted in space and cluttered with obstacles. Caster wheels have been chosen for the development of an omnidirectional mobile robot, as reported in (Holmberg, 2000), among several omnidirectional wheel mechanisms, including universal wheels, Swedish wheels, orthogonal wheels, and ball wheels. This is because caster wheels can operate without additional peripheral rollers or support structure, and maintain good performance even though payload or ground condition changes. There have been several works on the kinematics of a caster wheeled omnidirectional mobile robot (COMR), including the kinematic modeling, the design and control, the isotropy analysis, as reported in (Holmberg, 2000; Muir & Neuman, 1987; Campion et al., 1996; Kim & Kim, 2004; Park et al., 2002; Kim & Moon, 2005; Oetomo et al., 2005; Kim & Jung, 2007). Previous isotropy analysis, as reported in (Kim & Kim, 2004; Park et al., 2002; Kim & Moon, 2005; Oetomo et al., 2005), has been made only for a COMR in which the steering link offset is equal to the wheel radius, except our recent work, as reported in (Kim & Jung, 2007). It was found that such a restriction is necessary to have globally optimal isotropic characteristics of a COMR, as reported in (Park et al., 2002; Kim & Moon, 2005; Oetomo et al., 2005). Nevertheless, many practical COMR's in use take advantage of the steering link offset which is different from the wheel radius, mainly for improved tipover stability, as reported in (McGhee & Frank, 1968; Papadopoulos & Rey, 1996). The tipover stability becomes critical when a COMR makes a rapid turn or sudden external forces are applied to a COMR. The accuracy of the velocity kinematics of a robotic system depends on the condition number of the Jacobian matrix involved. Based on the Euclidean norm, the condition number of a matrix can be defined as the ratio of the largest to smallest singular values of the matrix, as reported in (Strang, 1988), whose value ranges from unity to infinity. For a given linear system b Ax = , the condition number of A represents the amplification of the