Robot motion control strategies generally center around trajectory planning schemes which are point-to-point. This paper explores the problem of planning robot trajectories which sweep an area in a two-link robot's work space. A diffeomorphism which transforms the linear coordinates of Euclidean space to the non-linear angular coordinates which represent the displacements of the joint motors is developed. It is used to determine the distortion of an object's area at different locations in the robot's work space and for different robot link length geometries. Study of such distortions may lead to an optimization scheme by which the placement of the object in the work space and/or choice of a robot link length ratio will lead to enhanced performance of the robot.
Gallagher, Justin, "Robot Space Coordinate Representation of Objects in Euclidean Space" (1994). Mathematical Sciences Technical Reports (MSTR). 124.