Precise contact motion planning for deformable planar curved shapes. (January 2016)

• Record Type: Journal Article
• Authors: Kim, Yong-Joon; Elber, Gershon; Kim, Myung-Soo
• Is Part Of: Computer aided design. Volume 70(2016)
• Page Start: 126
• Page End: 133
• Publication Date: 2016-01
• Subjects: Configuration spaces -- Multivariate algebraic constraints -- Freeform geometric models -- B-spline curves -- Deformable robots; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2015.06.015
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: We present a precise contact motion planning algorithm for a deformable robot in a planar environment with stationary obstacles. The robot and obstacles are both represented with C 1 -continuous implicit or parametric curves. The robot is changing its shape using a single degree of freedom (via a one-parameter family of deformable curves). In order to reduce the dimensionality of the configuration space, geometrically constrained yet collision free contact motions are sought, that have K ( = 2, 3 ) simultaneous tangential contact points between the robot and the obstacles. The K -contact motion analysis effectively reduces the degrees of freedom of the robot, which enables a more efficient motion planning. The geometric conditions for the K -contact motions can be formulated as a system of non-linear polynomial equations, which can be solved precisely using a multivariate equation solver. The solutions for K -contact motions are represented as curves in a 4-dimensional ( x, y, θ, t ) space, where x, y, θ are the degrees of freedom of the rigid motion and t is the deformation's parameter. Using the graph structure of the solution curves for the K -contact motions, our algorithm efficiently finds a feasible path connecting two configurations via a graph searching algorithm, whenever available. We demonstrate the effectiveness of the proposed approach using several examples. Highlights: We present an efficient motion planning algorithm for a planar deformable robot. We employ K -contact motion analysis to reduce the degrees of freedom of the robot. Our algorithm efficiently finds a feasible path via a graph searching algorithm.