Robot automation and motion planning has been inseparable since very first robot. There has been lots of interest in motion planning, especially in methods that utilize the probabilistic roadmap methods. It is a common practice to represent robots as rigid objects or a series of links each of which is a rigid object. Although this is a realistic situation, there may be cases where a more flexible representation, such as the one proposed in this work, of the robot would be preferred.

In our approach, we first find a path which requires the robot to deform in order to follow it. The path may contain collisions for the rigid (undeformed) version of the robot. Note that there is a direct relation between collision volume and the energy that we need to deform the robot to a collision-free shape. We associate this volume with the deformation energy. Since we don't know the energy priory and collision volume is hard to get, we used the parameters returned from our feasibility metrics as the approximate energy. These parameters are the size of the shrunk robot with respect to the original robot and the value of penetration for each configuration found. Following figure shows roadmap generated by these methods.

Left : roadmap generated by shrunk robot. Right : roadmap generated by enabling penetration.

After finding such path, we employ two different methods, bounding box deformation or geometric deformation to deform the robot to avoid collisions. Our approach deforms the robot only in necessary conditions (if there is a collision). It is our observation that the robot is deformed only if it has intersection with obstacles. Deformation can be divided into deformer and deformable object. Deformer pushes part of deformable object to collision free state and deformable object then changes shape according to external forces. We can see from following pictures that obstacles are made as deformer which pushes deformable object into collision-free configuration.

Left : Bounding Box Deformation. Using modified ChainMail3D and FFD. Right : Geometric Deformation.

We study the following examples: