Kinematic Convex Combinations of Multiple Poses of a Bounded Planar Object Based on an Average-Distance Minimizing Motion Sweep

Abstract

Abstract. This article deals with the computational kinematic geometry of bounded planar objects rather than that of infinitely large moving spaces. In this article, we present a new formulation for kinematic convexity based on an average-distance minimizing motion sweep of a bounded planar object. The resulting single-degree-of-freedom (DOF) motion sweep between two planar poses is represented as a convex combination in the configuration space defined by (x,y,z) where (x,y) is associated with the location of the centroid of the planar object and z=sinθ with θ being the angle of rotation. For three poses, a 2DOF motion sweep is developed that not only minimizes the combined average squared distances but also attains a convex combination representation so that existing algorithms for convex hull of points can be readily applied to the construction and analysis of kinematic convex hulls. This results in a new type of convex hull for planar kinematics such that its boundaries are defined by the average-distance minimizing sweeps of the bounded planar object.