If the shape of the object is known, then a rolling tactile finger can detect its location on the object boundary, in other words, localize itself with respect to the object (before, say, manipulating it). In this case, the finger needs to detect only two or three contact locations at different time instants. During a period of rolling, the contact traces out a segment on the object boundary. The length of this segment is equal to the length of the segment traced out by the contact on the finger (which is known to the tactile sensor). The rotation of the curve tangent as the contact moves from one endpoint of the segment to the other endpoint can also be determined from the finger's self-rotation and the corresponding tangent rotation on the finger.

This reduces the localization problem into finding all segments on a closed simple parametric curve that satisfy given arc length and total curvature requirements. I recently developed a numerical algorithm to solve this localization problem. The algorithm slides an imaginary segment along the object boundary curve by alternatively marching its two endpoints forward, stretching or contracting it if necessary. Through a curvature-based analysis I established the global convergence of the algorithm to every feasible location of such a desirable segment and also derived the local converence rate. The algorithm runs in time linear in the size of the discretized curve domain. It has been tested on various closed and open curves.

I have designed a 2-axis force/torque sensor for contact sensing and the localization of 2-D curved shapes. The sensor is an aluminum piece attached with two ``chip sensors'', each a half-bridge circuit consisting of two strain gauges. It functions like a ``wrist'' which uses the two chip sensors to detect bending and twisting moments, respectively. When an external force is exerted on a jaw mounted with the F/T sensor, the point of force application is linearly related to the ratio between the reading variations from the chip sensors. This principle is used for determining contact locations on the jaw after calibration. A simple strategy is later described to control the jaw to roll on a motionless 2-D object while estimating the movement of contact. Given its shape, the object's position and orientation relative to the jaw are estimated during the rolling motion by the localization algorithm. Experiments have been conducted with an Adept Cobra 600 manipulator.

A 2-axis F/T sensor for contact detection. It consists of two chip sensors, each a half-bridge of two strain gauges with electrical resistance of 900+-150 ohm. To localize the jaw on a part, the jaw makes some intial contact (a*), rolls along the part boundary before stopping at an intermediate point (b*), then rolls again and finally stops at a third point (c*). Jaw placement is computed based on the arc length estimates from a* to b* to c*, as well as the corresponding turnning angles.

Related publications:

• Localization of curved parts through continual touch [Abstract] (317K, 9 pages). IEEE Transactions on Robotics, vol. 21, no. 4, pp. 726-733, 2005.

• Contact sensing for parts localization: sensor design and experiments [Abstract, Slides] (330K). In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Las Vegas, NV, Oct 27-31, 2003.

• Localization on curved objects using tactile information [Abstract, Slides] (184K). In Proceedings of the IEEE/RSJ International Conferences on Intelligent Robots and Systems, pp. 701-706, Maui, HI, Oct 29 - Nov 3, 2001.

• Grasping curved objects through rolling [Abstract , Slides] (140K). In Proceedings of the IEEE International Conference on Robotics and Automation, pp. 377-382, San Francisco, CA, April 2000.