An automatic atherectomy system uses a rotary burr at the tip of a catheter as a sensing device, in order to measure both electrical conductivity and permittivity of surrounding tissue at multiple frequencies. From these parameters it is determined which tissue lies in different directions around the tip. A servo system steers the catheter tip in the direction of the tissue to be removed. In non-atherectomy applications the rotary burr can be replaced with any desired tool and the system can be used to automatically steer the catheter to the desired position. The steering may be done hydraulically, by pressurizing miniature bellows located near the catheter tip.