Precise contact motion planning for deformable planar curved shapes

• We present an efficient motion planning algorithm for a planar deformable robot.
• We employ KK-contact motion analysis to reduce the degrees of freedom of the robot.
• Our algorithm efficiently finds a feasible path via a graph searching algorithm.

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 C1C1-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)K(=2,3) simultaneous tangential contact points between the robot and the obstacles. The KK-contact motion analysis effectively reduces the degrees of freedom of the robot, which enables a more efficient motion planning. The geometric conditions for the KK-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 KK-contact motions are represented as curves in a 4-dimensional (x,y,θ,t)(x,y,θ,t) space, where x,y,θx,y,θ are the degrees of freedom of the rigid motion and tt is the deformation’s parameter. Using the graph structure of the solution curves for the KK-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.