Domains of Mobility for a Planar Body Moving Among Obstacles

Abstract

A formulation is presented for defining domains of mobility for a planar convex body moving with three degrees-of-freedom among convex planar obstacles. Applications included are determination of areas of a factory floor or material storage facility in which objects can he manipulated without impacting fixed obstacles. Mobility of the moving body is defined to encompass (1) dexterous mobility of the body; i.e., points that can be reached by a reference point on the body and at which the body can be rotated through a specified range of admissible orientations without penetrating any stationary obstacle, and (2) limited mobility of the body; i.e., points that can be reached by the reference point and at which the body does not penetrate any stationary obstacle, for some admissible orientation. Analytical criteria for points on boundaries of domains of mobility are derived and numerical methods suitable for mapping these boundaries are summarized. An elementary example involving a moving and a stationary ellipse, with and without orientation restrictions, is solved analytically to illustrate the method. A more general application with one moving body and three stationary obstacles is solved numerically.