Fig. 9.

(a) The artificial environment for the steerable needle has two narrow passages in a 10 cm × 10 cm × 10 cm box. The goal region (sky blue sphere) is defined in ℝ³ with radius 0.5 cm. (b) The passage between the two red boxes (1.2 cm) is wider than the passage between the yellow box and the middle red box (1.0 cm). The goal is closer to the narrower passage. (c) For highest probability of success, HFR guided the needle to pass through the wider passage in order to acheive a higher probability of success. (d) For minimizing path length with the defined chance constraint, HFR guided the needle to pass through the passage between the yellow box and the middle red box to acheive a shorter path while still satisfying the chance constraint.