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Locating arteries hidden beneath superficial tissue can be a difficult task in minimally invasive surgery. This paper reports the development of a system that finds the paths of arteries using tactile sensing. The surgeon begins by using the surgical robot to place the tactile sensor instrument on a known artery location. Signal processing algorithms locate the artery from its pulsatile pressure variation. An adaptive extrapolation algorithm then generates predicted locations for the artery based on previous measurements. After moving to the predicted location, if the artery is not located then a backtracking mechanism moves the sensor towards previously detected locations. Tests with model arteries show good tracking ability for circular arcs with curvatures as small as 80 mm, although problems with compliance in the system result in occasional loss of the artery path. Preliminary tests demonstrate the ability to transcutaneously track the radial artery in the human wrist.