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. Author manuscript; available in PMC: 2017 Apr 1.
Published in final edited form as: IEEE Trans Autom Sci Eng. 2016 Jan 27;13(2):437–447. doi: 10.1109/TASE.2016.2517124

Fig. 1.

Fig. 1

We show plans computed by SELQR for needle steering for a liver biopsy with motion uncertainty. The objective is to access the tumor (yellow) while avoiding the hepatic arteries (red), hepatic veins (blue), portal veins (pink), and bile ducts (green). The smooth trajectories explicitly consider uncertainty and minimize the a priori expected value of a cost function that considers obstacle avoidance and path length.