Constraint-Based Motion Planning in Deformable Environments

I present a novel algorithm for motion planning for a deformable robot in a deformable environment. Given the initial and goal configurations of the robot, I use a constraint-based planning approach to simulate deformations to the robot and the environment and compute a physically viable path to the goal. The algorithm takes into account standard geometric constraints like non-penetration and also considers physical constraints such as volume preservation. I. INTRODUCTION The classic motion planning problem considers a rigid robot planning a path through a static, rigid environment. Nevertheless, as the physical modeling of deformable objects has improved, developments in motion planning have followed to allow for motion planning with deformable robots and in deformable environments. There are many situations one can envision where the robot or the environment presented in a motion planning problem are deformable, however, the human body, especially the interior provides a particularly interesting example. Due to the highly deformable nature of the human interior and the need for exact solutions (due to the extremely high risk involved in damaging the interior of the body), it is poorly approximated using rigid models and deformable robots and environments become a necessity. By modeling the organs within the human body as deformable objects, we are able to plan paths that will cause the least damage for the hand or an organ as it is moved through the body cavity during surgery. A. Issues Due to the extremely large number of movable points in the environment (since each vertex of each deformable object must be considered one degree of freedom), standard motion planning algorithms that operate in C-obstacle space become completely intractable. Alternative planning frameworks that operate in the work space must therefore be explored.