Three simulated image-guided needle insertion procedures from a fixed starting point with needle motion uncertainty standard deviations of σi = 5° during insertion and σr = 20° during direction changes. After each insertion distance δ we assume the needle tip is localized in the image and identified using a dot. Based on the DP look-up table, the needle is either inserted (small dots) or a direction change is made (larger dots). The effect of uncertainty can be seen as deflections in the path, i.e., locations where the tangent of the path abruptly changes. Since σr > σi, deflections are more likely to occur at points of direction change. In all cases, ps = 72.35% at the initial state. In (c), multiple deflections and the nonholonomic constraint on needle motion prevent the needle from reaching the target.