Screw-Based Motion Planning for Bevel-Tip Flexible Needles in 3D Environments with Obstacles
Vincent Duindam, Ron Alterovitz, S. Shankar Sastry and Ken Goldberg
As part of an NIH-funded project on flexible needle steering in soft tissue, we consider motion planning of a steerable, flexible, bevel-tip needle in a 3D environment with obstacles. The needle has two control inputs: (1) a torque around the needle's main axis, and (2) a forward pushing force which, due to the asymmetric forces on the tip, results in motion along a circle. Together, these inputs generate helical needle motions.
The objective of the path-planning algorithm is to find control inputs that steer the needle from a starting configuration (location and orientation) to a goal configuration in an optimal way, while avoiding impenetrable and sensitive areas. We formulate this objective as a minimization problem, with cost determined by the deviation from the goal, penetration of obstacles, path length, and required control effort. We use screw-theory to describe the kinematics of the needle, resulting in fast optimization of the cost function, a few seconds on a standard PC for typical 3D environments with obstacles.
Figure 1: Path planning objective: control the forward and twisting speed of the bevel-tip needle such that it moves from start to goal, avoiding obstacles and using minimal control effort
Figure 2: Optimal 3D paths around obstacles from one starting position to different goal positions
- V. Duindam, R. Alterovitz, S. Sastry, and K. Goldberg, "Screw-Based Motion Planning for Bevel-Tip Flexible Needles in 3D Environments with Obstacles," IEEE International Conference on Robotics and Automation, 2008 (submitted).