Precise contact motion planning for deformable planar curved shapes

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 oneparameter 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, theta, t) space, where x, y, theta 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. (C) 2015 Elsevier Ltd. All rights reserved.N