Precise contact motion planning for deformable planar curved shapes

Yong-Joon Kim, Gershon Elber, Myung-Soo Kim

Research output: Contribution to journalArticlepeer-review

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 C1-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.

Original languageEnglish
Pages (from-to)126-133
Number of pages8
JournalComputer-Aided Design
Volume70
DOIs
StatePublished - 1 Jan 2016

Keywords

  • B-spline curves
  • Configuration spaces
  • Deformable robots
  • Freeform geometric models
  • Multivariate algebraic constraints

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering

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