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 language | English |
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Pages (from-to) | 126-133 |
Number of pages | 8 |
Journal | Computer-Aided Design |
Volume | 70 |
DOIs | |
State | Published - 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