# 2009 Research Summary

## 3D Motion Planning for Steerable Needles Using Inverse Kinematics and Numerical Optimization

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Vincent Duindam, Ron Alterovitz, Xu Jijie, Hauser Kris, S. Shankar Sastry and Ken Goldberg

National Institutes of Health R01 EB006435 and Netherlands Organization for Scientific Research

We are developing algorithms to compute optimal trajectories for steerable needles in a 3D environment with obstacles. A first algorithm [1] is based on optimization of a cost function that numerically quantifies the planning objective, and uses a suitable discretization of the control space to quickly compute a needle path with minimal cost. A second algorithm [2] relies on an explicit expression of the inverse kinematics of the needle to generate a range of valid needle paths from start to target, from which the best solution can be selected. We envision these algorithms to be components in a larger path planning system that guarantees global optimality.

Figure 1: System setup with steerable needle, start and target locations, and obstacles

Figure 2: Graphical user interface for the various motion planning algorithms implemented in C++. An example of a solution path is shown.

- [1]
- V. Duindam, R. Alterovitz, S. Sastry, and K. Goldberg, "Screw-based Motion Planning for Bevel-Tip Flexible Needles in 3D Environments with Obstacles,"
*Proceedings of the IEEE International Conference on Robotics and Automation,*May 2008, pp. 2483-2488. - [2]
- V. Duindam, J. Xu, R. Alterovitz, S. Sastry, and K. Goldberg, "3D Motion Planning Algorithms for Steerable Needles Using Inverse Kinematics,"
*International Workshop on the Algorithmic Foundations of Robotics,*December 2008 (to appear).