s  Abstract — This paper presents a method for detecting contact on a compliant link utilizing a method to sense changes in the resonant frequency of the link due to external contact. The approach uses an inexpensive accelerometer mounted on or inside the compliant link and a phase locked loop circuit to oscillate the link at its resonant frequency. Using this approach, we are able to reliably sense contact anywhere on the link with a contact force threshold sensitivity of between 0.05 and 0.15 N depending on the contact location. I. INTRODUCTION OUCH sensing continues to represent one of the most significant challenges to robotic manipulation. Although humans rely heavily on tactile sensing when grasping objects, the majority of robotic manipulators lack significant tactile sensors [1, 2]. Research efforts to develop novel sensors have spanned the range of both intrinsic/proprioceptive sensors and extrinsic/exteroceptive sensors (e.g. [3-7]). In this work, we present a new approach to contact sensing, particularly useful for compliant, underactuated end-effectors such as the SDM Hand [8]. In general, the approach utilizes measurements of the frequency response of the digit in real time, with contact detection based upon a change in the resonant frequency. Unlike many traditional methods of sensing, which rely on expensive and oftentimes fragile custom-made sensors placed at the fingertips (or any surface where sensing is desired) [9], our approach uses a single, inexpensive accelerometer and a phase locked loop integrated circuit to excite the system at its resonant frequency. By sensing changes in this resonant frequency, we are able to detect contact anywhere on the digit. Other researchers have investigated vibration-based contact sensors and applied similar frequency characterization techniques to systems, but have not combined the two in a frequency-based vibrational contact sensor. For example, Motoo et al. implemented an impedance-based contact sensor that consists of a two piezoelectric elements separated by a polymer sheet [3]. One of the piezoelectric elements is driven at a constant frequency while the other is used as a transducer to monitor the system’s response. The signal from the piezoelectric element is used to measure the impedance of the polymer This work was supported in part by the National Science Foundation grant IIS-0953856. S.B. Backus and A.M. Dollar are with the Department of Mechanical Engineering and Materials Science, School of Engineering and Applied Science, Yale University, New Haven, CT USA (e-mail: {spencer.backus, aaron.dollar}@ yale.edu). and contact is detected when the measured mechanical impedance changes. Rudolf and Seemann used a similar actuation scheme and a phase locked loop to oscillate a beam at resonance, but did not include sensing [10]. Imata and Terunuma have developed a closely related sensor for measuring the in vivo stiffness of human tissues[4]. This sensor consists of a piezoelectric driver and sensor mounted on a probe. The system is excited at its resonant frequency by a phase locked loop that tracks the resonant frequency of the probe. Stiffness of the contacted tissue is inferred based on the change in resonant frequency. This sensor has been developed into a commercial product, the Axiom Biosensor (Fukushima-ken, Japan). In this paper, we utilize a similar resonant frequency tracking method in which we utilize an inexpensive accelerometer mounted within the proximal link of a compliant robotic finger (Fig. 1) and a phase locked loop circuit to drive the finger at its resonant frequency with its main flexion actuator. Using the accelerometer, we sense contact anywhere on the finger, detected when the frequency of resonant oscillation rises more than three standard deviations above the mean resonant frequency. We begin this paper with a description of our approach, utilizing a simple beam and elastic contact model to illustrate the concept. Next, we describe our experimental setup and test procedure, followed by an evaluation of the proposed concept in a wide range of contact conditions and locations on the finger. Finally, we discuss issues related to the practical implementation of the approach, including how the results presented here can be extended to additional contact conditions as well as a richer information set about the contact state. Robust, Inexpensive Resonant Frequency Based Contact Detection for Robotic Manipulators Spencer B. Backus, Student Member, IEEE and Aaron M. Dollar, Member, IEEE T Fig. 1. Diagram of Instrumented finger system and test probe. 2012 IEEE International Conference on Robotics and AutomationRiverCentre, Saint Paul, Minnesota, USAMay 14-18, 2012978-1-4673-1405-3/12/$31.00 ©2012 IEEE 1514II. APPROACH Our sensor operates by measuring the frequency response of the digit in real time and detects contact based upon observed changes in the resonant frequency. As shown in the single link and rotational joint example, Fig. 2, if a contact is modeled as a spring and damper in parallel acting at a point on the link, the stiffness and damping of the contact add to the stiffness and damping of the proximal joint and therefore change the overall stiffness of the system. As a result, the resonant frequency of the overall system changes as a function of both the location and stiffness of the contact. The sensor functions by detecting this change and thereby the underlying contact. Although the change in resonant frequency is a function of contact force and position, there is insufficient information to disambiguate which factor is responsible, making the sensor a purely binary measurement. The following two equations represent the angular acceleration of the rotational joint and the resonant frequency of the link/contact system for small angles: 󰇘1󰇡󰇛ℓ󰇜󰇛ℓ󰇜󰇗󰇛󰇜󰇢 12ℓ  where I is the link’s moment of inertia, k1 and c1 are the spring and damping constants of the joint, k2, c2, and l1 are the contact spring and damping constants and the contact location, and u(t) is the excitation input. As expected, the resonant frequency is only a function of the two stiffnesses and the contact location, assuming the object is grounded or has a much higher inertia than the finger. When contact occurs, the contact stiffness term becomes