Precise contact motion planning for deformable planar curved shapes. (January 2016) - Kim, Yong-Joon; Elber, Gershon; Kim, Myung-Soo
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.