## Abstract

This work presents a closed-loop strategy for 3D online motion planning of beveled steerable needles using duty-cycled rotation. The algorithm first selects an entry point that minimizes a multi-criteria cost function and then combines an RRT-based path planner with an intraoperative replanning algorithm and workspace feedback information to constantly update the needle inputs and adjust the trajectory. Simulations in a workspace based on a typical prostate needle steering scenario show that the algorithm is robust against disturbances and model uncertainties and can provide online trajectories to avoid obstacles even under the presence of physiological motion.

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## Notes

- 1.
Although we use here the expression “input,” one should notice that we do not refer to the needle actuation inputs \(\omega \) and \(\nu \), but to pure geometrical parameters used to expand the RRT tree. The insertion and velocity actuation inputs are actually a consequence of the planned path formed by the concatenation of arcs obtained from such geometrical parameters.

- 2.
For videos, see the first part of Online Resource 1.

- 3.
For videos, see the second part of Online Resource 1.

## References

Abolhassani, N., Patel, R., & Moallem, M. (2007). Needle insertion into soft tissue: A survey.

*Medical Engineering and Physics*,*29*, 413–431.Alterovitz, R., & Goldberg, K. (June 2007). The stochastic motion roadmap: A sampling framework for planning with markov motion uncertainty. In

*Proceedings of the Robotics: Science and Systems Conference*, Atlanta, GA, pp. 1–8.Alterovitz, R., Branicky, M., & Goldberg, K. (2008). Motion planning under uncertainty for image-guided medical needle steering.

*The International Journal of Robotics Research*,*2*(11–12), 1361–1374.Alterovitz, R., Goldberg, K., & Okamura, A. (2005). Planning for steerable bevel-tip needle insertion through 2D soft tissue with obstacles. In

*Proceedings of the IEEE International Conference on Robotics and Automation*, pp. 1640–1645.Bernardes, M. C., Adorno, B. V., Poignet, P., & Borges, G. A. (2012). Semi-automatic needle steering system with robotic manipulator. In

*Proceedings of the IEEE International Conference on Robotics and Automation*, pp. 1595–1600.Bernardes, M. C., Adorno, B. V., Poignet, P., Zemiti, N., & Borges, G. A. (2011). Adaptive path planning for steerable needles using duty-cycling. In

*Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems*, pp. 2545–2550.Duindam, V., Alterovitz, R., Sastry, S., & Goldberg, K. (2010). Three-dimensional motion planning algorithms for steerable needles using inverse kinematics.

*The International Journal of Robotics Research*,*29*(7), 789–800.Fichtinger, G., Kazanzides, P., Okamura, A. M., Hager, G. D., Whitcomb, L. L., & Taylor, R. H. (2008). Surgical and Interventional Robotics: Part II. In

*IEEE Robotics and Automation Magazine*, pp. 94–102.Hauser, K., Alterovitz, R., Chentanez, N., Okamura, A., & Goldberg, K. (June 2009). Feedback control for steering needles through 3D deformable tissue using helical paths. In

*Proceedings of the Robotics: Science and Systems Conference*, Seattle, WA, pp. 1–8.Kuffner, J. J., & LaValle, S. M. (2000). RRT-connect: An efficient approach to single-query path planning. In

*Proceedings of the IEEE International Conference on Robotics and Automation*, pp. 995–1001.LaValle, S. M., & Kuffner, J. J. (1999). Randomized kinodynamic planning. In

*Proceedings of the IEEE International Conference on Robotics and Automation*, pp. 473–479.Lobaton, E., Zhang, J., Patil, S., & Alterovitz, R. (2011). Planning curvature-constrained paths to multiple goals using circle Sampling. In

*Proceedings of the IEEE International Conference on Robotics and Automation*, pp. 1463–1469.Minhas, D., Engh, J., Fenske, M., & Riviere, C. (2007). Modeling of needle steering via duty-cycled spinning. In

*Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society*, pp. 2756–2759.Mittal, S., & Deb, K. (2007). Three-dimensional offline path planning for UAVs using multiobjective evolutionary algorithms. In

*Proceedings of the IEEE Congress on Evolutionary Computation*, pp. 3195–3202.Park, W., Kim, J., Zhou, Y., Cowan, N. J., Okamura, A., & Chirikjian, G. (2005). Diffusion-based motion planning for a nonholonomic flexible needle model. In

*Proceedings of the IEEE International Conference on Robotics and Automation*, pp. 4611–4616.Patil, S., & Alterovitz, R. (2010). Interactive motion planning for steerable needles in 3D environments with obstacles. In

*Proceedings of the IEEE/RAS-EMBS International Conference on Biomedical Robotics and Biomechatronics*, pp. 893–899.Patil, S., van den Berg, J. P., & Alterovitz, R. (2011). Motion planning under uncertainty in highly deformable environments. In

*Proceedings of the Robotics: Science and Systems Conference*.van den Berg, J. P., Patil, S., & Alterovitz, R. (2010). LQG-based planning, sensing, and control of steerable needles. In

*Proceedings of the International Workshop on the Algorithmic Foundations of Robotics*, pp. 373–389.Vancamberg, L., Sahbani, A., Muller, S., & Morel, G. (2010). Needle path planning for digital breast tomosynthesis biopsy. In

*Proceedings of the IEEE International Conference on Robotics and Automation*, pp. 2062–2067.Vancamberg, L., Sahbani, A., Muller, S., & Morel, G. (2011). Needle path planning for digital breast tomosynthesis biopsy using a heterogeneous model. In

*Proceedings of the IEEE International Conference on Robotics and Automation*, pp. 5749–5755.Webster III, R. J., Kim, J., Cowan N. J., Chirikjian, G., & Okamura, A. (2006). Nonholonomic modeling of needle steering.

*The International Journal of Robotics Research*,*25*(5–6), 509–525.Xu, J., Duindam, V., Alterovitz, R., & Goldberg, K. (2008). Motion planning for steerable needles in 3D environments with obstacles using rapidly-exploring Random Trees and backchaining. In

*Proceedings of the IEEE International Conference on Automation Science and Engineering*, pp. 41–46.

## Acknowledgments

This work was supported by Coordenaç\({\tilde{a}}\)o de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), and by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq).

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## Appendix

### Appendix

A quaternion \(\mathbf {h}\) consists of a real component plus an imaginary part composed of three quaternionic units \(\hat{\imath },\hat{\jmath },\hat{k}\); that is, \(\mathbf {h}=a+b\hat{\imath }+c\hat{\jmath }+d\hat{k}\), where \(a,b,c,d\in \mathbb {R}\), \(\hat{\imath }^{2}=\hat{\jmath }^{2}=\hat{k}^{2}=-1\), and \(\hat{\imath }\hat{\jmath }\hat{k}=-1\). Its conjugate is given by \(\mathbf {h^{*}}=a-b\hat{\imath }-c\hat{\jmath }-d\hat{k}\).

A rotation composed of a rotation angle \(\phi \) around the axis \(\mathbf {n}=n_{x}\hat{\imath }+n_{y}\hat{\jmath }+n_{z}\hat{k}\) is given by the quaternion \(\mathbf {r}=\cos (\phi /2)+\sin (\phi /2)\mathbf {n}\).

A translation \(\mathbf {p}\) is represented by a pure quaternion; that is, a quaternion where the real part is equal to zero. Thus, \(\mathbf {p}=p_{x}\hat{\imath }+p_{y}\hat{\jmath }+p_{z}\hat{k}\).

The rigid motion is then completely represented by the dual quaternion \(\underline{\mathbf {q}}=\mathbf {r}+\epsilon \frac{1}{2}\mathbf {p}\mathbf {r}\), where \(\epsilon \) is Clifford’s dual unit, which is nilpotent; that is, \(\epsilon \ne 0\) but \(\epsilon ^{2}=0\).

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Bernardes, M.C., Adorno, B.V., Borges, G.A. *et al.* 3D Robust Online Motion Planning for Steerable Needles in Dynamic Workspaces Using Duty-Cycled Rotation.
*J Control Autom Electr Syst* **25, **216–227 (2014). https://doi.org/10.1007/s40313-013-0104-4

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### Keywords

- Medical robotics
- Needle steering
- Motion planning