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\begin{document}

\title{Fingertip Force Control with Embedded Fiber Bragg Grating Sensors}
%titlerunning{\emph{iSprawl}} %for an abbreviated version of

%Authors
%Yong-Lae Park, Seok Chang Ryu, Richard J. Black, Behzad Moslehi, and Mark R. Cutkosky

\author{Yong-Lae Park\textsuperscript1, \and
Seok Chang Ryu\textsuperscript1, \and
Richard J. Black\textsuperscript2, \and
Behzad Moslehi\textsuperscript2, \and
and Mark R. Cutkosky\textsuperscript1 \\ \vspace{7pt} \textsuperscript1Center for Design Research, Stanford University\\ Stanford, CA 94305-2232, USA\\ \{ylpark, scryu, cutkosky\}@stanford.edu \\ \vspace{7pt} \textsuperscript2Intelligent Fiber Optic Systems Corporation (http://www.ifos.com)\\ 2363 Calle Del Mundo, Santa Clara, CA 95054, USA\\ \{rjb, bm\}@ifos.com}

%School of Engineering Stanford University Stanford, California 94305-2232
%\andName of Author\inst{2}}
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%\institute{Department of Mechanical Engineering,
%Stanford University,
%Stanford, CA 94305}
%\texttt{cutkosky@stanford.edu}}

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\begin{abstract} 

We describe the dynamic testing and control results obtained with an exoskeletal robot finger with embedded fiber optic sensors. The finger is inspired by the designs of arthropod limbs, with integral strain sensilla concentrated near the joints. The use of fiber Bragg gratings (FBGs) allows for embedded sensors with high strain sensitivity and immunity to electromagnetic interference. The embedded sensors are useful for contact detection and for control of forces during fine manipulation. The application to force control requires precise and high-bandwidth measurement of contact forces. We present a nonlinear force control approach that combines signals from an optical interrogator and conventional joint angle sensors to achieve accurate tracking of desired contact forces. 

\end{abstract}

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\section{Introduction}

In several applications, optical fiber sensors have been utilized as an alternative to conventional piezoresistive sensors for robot force sensing and control. The most common uses have been for tactile sensing, where the robustness of optical fibers and the ability to process the information with a CCD or CMOS camera are advantageous \cite{Danisch1999B, Kamiyama2003, Maekawa1997}. Other applications include using optical fibers in which the loss of light is a function of the bending curvature to measure the bending of the fingers of a glove \cite{Hong1989} or other flexible structure \cite{Danisch1999A}. More recently, FBG sensors have been used as a precise optical strain gage for structures \cite{Park2007, Zhang2005}. The FBG sensors produce shifts in the wavelength of reflected light as a local region of the fiber experiences axial strain. Very small strains, on the order of 0.1 $\mu$strain, can be resolved. In comparison to conventional strain gages, this sensitivity allows the sensors to be used in relatively sturdy structures that undergo small stresses and strains under normal loading conditions.

\begin{figure}
	\centering
		\includegraphics[width=.48\textwidth]{Figures/AdeptDexterFSF.pdf}
	\caption{FBG embedded force sensing finger prototypes integrated with Dexter manipulator and Adept robot arm}
	\label{fig:AdeptDexterFSF}
\end{figure}

All of these sensor developments can take advantage of the electromagnetic noise immunity of optical sensors. As a consequence, they are ideally suited for use around industrial robots with large motors under pulse-width modulated control, in space applications and even in magnetic resonance imaging (MRI) machines.
In addition, as demonstrated by Ascari et al. \cite{Ascari2006}, optical communication can be used to provide a high-bandwidth pathway for taking tactile and/or force information down the robot arm, using only a single optical fiber.

For the case of FBG sensors, it is additionally possible to multiplex optically, putting several strain gage sensors along a single fiber and interrogating them with different wavelengths of light.

In a previous paper \cite{Park2007} we reported on the design and fabrication process for creating a lightweight, hollow robotic finger with embedded FBG sensors. We also showed that by placing a small number of FBG strain sensors near a joint, in a design inspired by  arthropod exoskeletons \cite{Barth1976, Blickhan1985}, we could resolve contact locations using intrinsic tactile sensing \cite{Bicchi1993, Bicchi1989}.  In the present paper, we extend this work to address dynamic characterization of the sensorized finger structures and we demonstrate their application in closed-loop force control. Because the finger structures are made of polymers, they are subject to a certain amount of creep and hysteresis. However, by embedding a reinforcing mesh, these effects are reduced and can easily be accommodated in a force control scheme.

We describe the force control scheme that we have implemented for the finger and present results showing that precise control of manipulation forces can be obtained when a hand equipped with such optical FBG sensors is mounted on a large industrial robot that produces considerable electromagnetic noise. Figure \ref{fig:AdeptDexterFSF} shows the integrated robot system for the control experiments. We also describe ongoing work to miniaturize the technology so that multiple optical FBG sensors can be applied to human-scale robotic fingertips or to tools for minimally invasive robotic surgery. At this scale, optical multiplexing is particularly desirable to eliminate bundles of wires that must be routed down the fingers and arm.

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\section{Dynamic Sensor Characterization}

\subsection{Modes of Vibration}
Characterization of the dynamic response of the fingertips was conducted in preparation for setting up a closed-loop force control system. Impulse tests were performed to find modes of vibration of the finger prototype. Figure \ref{fig:ImpulseResponse} shows the impulse (expressed as a change in the wavelength of light reflected by an FBG cell) and its fast Fourier transform (FFT). The impulse was effected by tapping on the finger with a light and stiff object. The FFT shows a dominant frequency around 167 Hz which is a result of the dominant vibration mode. 

\begin{figure} [b!p!]
	\centering
	\includegraphics[width=.48\textwidth]{Figures/ImpulseResponse.pdf}
	\caption{Impulse response (top) of the finger prototype and its fast Fourier transform (bottom)}
	\label{fig:ImpulseResponse}
\end{figure} 

Finite element analysis was also conducted to check the experimental result, as shown in Figure \ref{fig:VibrationMode}. 
The analysis result shows that bending about orthogonal X and Y axes are the dominant modes (modes 1 and 2 in the figure), with nearly equal predicted frequencies of just over 180 Hz. The difference between the computed and measured frequency is due mainly to imperfect modeling of the local stiffness of the polymer/mesh composite, which depends on manufacturing tolerances and especially on where the mesh fibers are actually located within the polymer structure. (A description of the construction of the structure is given in \cite{Park2007}.)

\begin{figure}
	\centering
	\includegraphics[width=.48\textwidth]{Figures/VibrationMode.pdf}
	\caption{Modes of vibration of the finger prototype using finite element analysis (Modes 1 and 2 represent bending in X and Y axes respectively.)}
	\label{fig:VibrationMode}
\end{figure} 

\subsection{Hysteresis Analysis}

Polymer structures in general are subject to a certain amount of creep and hysteresis, which is one reason why they have traditionally been 
avoided for force sensing and control applications. In the present case, these effects are mitigated by embedding a copper mesh within the structure. 

\begin{figure} [b!p!]
	\centering
		\includegraphics[width=.48\textwidth]{Figures/Creep.pdf}
	\caption{Testing the effect of applying a steady load for several seconds and suddenly removing it from the polymer fingertip. Figure \ref{fig:CreepDetails} shows detailed	views of typical loading and unloading periods.}
	\label{fig:Creep}
\end{figure} 

\begin{figure}
	\centering
		\includegraphics[width=.48\textwidth]{Figures/CreepDetail.pdf}
	\caption{Detailed views of the creep under steady loading (left) and of the hysteresis associated with sudden unloading (right).}
	\label{fig:CreepDetails}
\end{figure} 

However, there is still some creep and hysteresis as shown in Figures \ref{fig:Creep} and \ref{fig:CreepDetails}. The plot in Figure \ref{fig:Creep} was produced by applying a moderate load of approximately 1.8 N to the finger for several seconds and then removing it suddenly. Figure \ref{fig:CreepDetails} shows detailed views of loading and unloading periods. The measured force is obtained by optically interrogating the calibrated FBG sensors.

When a steady load is applied for several seconds there is a small amount of creep, part of which also arises from imperfect thermal compensation in the  polymer structure. The effect is relatively small over periods of a few seconds, corresponding to typical grasping durations in a pick-and-place or manipulation task. A more significant effect occurs when the load is released. As the plots indicate, the force quickly drops to a value of approximately 0.1 N and then more slowly approaches zero. To overcome this effect in manipulation tasks a simple strategy was employed. Whenever the force suddenly drops to a small value (less than 0.17 N), we assume that contact has been broken and that the force is actually zero. At this point we reset the zero-offset after a brief time delay. 
As described in the following section, the loss of contact is also a signal to switch the hand from force control to position control.

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\section{Control System Description}

\subsection{Hardware Description}

Figure \ref{fig:HardwareArchitecture} shows the overall architecture of the components and hardware system. The two-fingered hand, Dexter,
is a low-friction, low-inertia device designed for accurate force control. The hand is controlled by a process running under a real-time operating system (QNX) at 1000 Hz, which reads the joint encoders, computes kinematic and dynamic terms and produces voltages for linear current amplifiers that drive the motors. 

A more complete description of the hand is provided in \cite{Griffin2005}. The hand controller also acquires force information, via shared memory, from a process that obtains analog force information at 5 kHz from the I-Sense\textsuperscript T\textsuperscript M optical interrogator that monitors the fiber optic sensors. 

The optical interrogator is based on high-speed parallel processing Wavelength Division Multiplexing (WDM). Multiple FBG sensors are addressed by spectral slicing, with the available source spectrum divided up so that each sensor is addressed by a different part of the spectrum.
The interrogator built for this work uses 16 channels of a parallel optical processing chip with each channel separated by 100 GHz (approximately 0.8 nm wavelength spacing around an operating wavelength of 1550 nm \footnote[1]{Operation is in the 1550-nm wavelength window (centered around C-band) to exploit the greatest availability and price breaks of components from telecom applications.}) so that the total required source bandwidth is 12.8 nm. We describe how this approach can be adapted to support larger numbers of FBG sensors on a single fiber in Appendix.

\begin{figure}
	\centering
		\includegraphics[width=.48\textwidth]{Figures/HardwareArchitecture.pdf}
	\caption{Overall Hardware System Architecture}
	\label{fig:HardwareArchitecture}
\end{figure} 

The Dexter hand is mounted to a commercial AdeptOne-MV 5-axis industrial robot. Communication with the Adept robot is performed using the ALTER software package, which allows new positions to be sent to the robot over an Ethernet connection every 16 ms (62.5 Hz). Due to this limitation, all force control is done within the Dexter hand, and the Adept robot is used only for large motions and to keep the Dexter hand approximately centered in the middle of its workspace.

When the fingers are not in contact with an object, they are operated under computed-torque position control, with real-time compensation for gravity torques and inertial terms. When in contact with an object, they are switched over to a nonlinear force control as described in the next section.

\subsection{Software Description}
All the internal processes are carried out in the QNX OS in real-time. Figure \ref{fig:SoftwareArchitecture} depicts the overall internal process architecture to control different components independently but simultaneously. The figure shows how different processes perform their tasks interacting with other processes in real time. The Driver process, which is the main process, calls each sub-process whenever it is needed. The User input process obtains user inputs for the configuration of the system. The configuration data are stored in Shared Memory. The Adept control process continuously feeds the next position and angular increments in X, Y, Z, Rx, Ry, and Rz axes in every 16 ms.

\begin{figure}
	\centering
		\includegraphics[width=.48\textwidth]{Figures/SoftwareArchitecture.pdf}
	\caption{Overall Internal Process Architecture}
	\label{fig:SoftwareArchitecture}
\end{figure} 

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\section{Contact Force Control}

\begin{figure} [b!p!]
	\centering
		\includegraphics[width=.48\textwidth]{Figures/ForceController.pdf}
	\caption{Position Based Smart Force Control System}
	\label{fig:ForceController}
\end{figure} 

Most applications of  contact force control can be divided into two main categories: impedance control and force control \cite{Zeng1997}. The impedance control \cite{Hogan1985, Kazerooni1986} aims at controlling position and force by establishing desired contact dynamics while the force control \cite{Raibert1981} commands the system to track a force set-point directly. For this work we adopted a class of nonlinear controller presented by H. Seraji \cite{Seraji1998A, Seraji1996, Seraji1998B}. When the system detects contact with the fingertip, it switches to force control as depicted in Figure \ref{fig:ForceController}. The PI force controller is constructed as \[K(s) = k_p  + \frac{{k_i }}{s}\] based on the first-order admittance \[Y(s) = k_p s + k_i\] where $k_p$ and $k_i$ are the proportional and integral force feedback gains respectively. To make the controller simple, we fix the proportional gain $k_p$ to a constant and make the integral gain $k_i$ a nonlinear function of the force error. The nonlinear integral gain is determined by the sigmoidal function \[k_i  = k_0  + \frac{{k_1 }}{{1 + \exp [ - {\mathop{\rm sgn}} (\Delta )k_2 e]}}\] where $e$ is the force error ($F_r-F$), $\Delta = F_r - F_s$, $F_s$ is the steady value of the contact force and $k_0$, $k_1$, and $k_2$ are user-specified positive constants which determine the minimum value, the range of variation, and the rate of variation of $k_i$ respectively. The value of ${\mathop{\rm sgn}} (\Delta )$ is +1 when $F_r > F_s$, and -1 when $F_r < F_s$.

We can achieve fast responses and small oscillations in control with this nonlinear gain since the nonlinearity provides high gains with large errors and low gains with small errors.

\subsection{Results of Experiments}

In this section we present the results of two experiments that assess the accuracy of control achieved with the prototype finger. The first experiment shows how accurately the manipulator maintains a desired force during a contact by comparing the force data from the finger prototype with that from a commercial 6-axis force-torque sensor (ATI-Nano25  from ATI Industrial Automation). The second experiment shows the force control during manipulation tasks including linear and rotational motions of the hand while grasping an object. 

\begin{figure} [b!p!]
	\centering
		\includegraphics[width=.48\textwidth]{Figures/ExperimentResult1.pdf}
	\caption{(Top) Adept robot motion, (Middle) Joint angle change of Dexter manipulator, (Bottom) Force data from load cell and FBG embedded robot finger prototype; (A) Robot makes a contact, (B) Robot starts retreat, (C) Robot loses the contact.}
	\label{fig:ExperimentResult1}
\end{figure}

\subsubsection{Experiment 1 (Force Setpoint Tracking)}
The Adept arm moves in one direction until the fingertip touches an object, which happens to be a commercial load cell. As soon as the finger detects contact, the Adept stops and the Dexter hand switches to force control. After a period of time the Adept moves away from the object and the hand switches back to position control. Figure \ref{fig:ExperimentResult1} shows the horizontal motion of the Adept arm in parallel with the joint rotation of the distal joint of the Dexter hand and the force data from the fingertip and the commercial load cell. The result shows the two sets of force data almost exactly match over the several seconds of the experiment. As the finger breaks contact, there is a small amount of slippage reflected in the mirror-image dynamic force signals reported by the finger and load cell, respectively.

We note also that to produce this plot it was necessary to carefully shield and ground all wires emanating from the commercial load cell due to the large magnetic fields produced by the industrial robot. 

\subsubsection{Experiment 2 (Force Control during Manipulation)}

Experiment 2 concerns the ability of the hand to maintain a desired grasp force while being subjected to motions in a manipulation task. For the results shown in Figure \ref{fig:ExperimentResult2}, the robot was commanded to lift the grasped object weighing 100 grams, move it horizontally a distance of approximately 30 cm, rotate it about the Z and Y axes, return to the original location, and replace the object. The magnitude of combined (x, y, and z) acceleration of the manipulator is plotted in parallel with the measured grasp force. Disturbances associated with the accelerations and decelerations along the path can be observed in the force data. However, in every case the controller returns to the desired force within 0.01 seconds.

\begin{figure} [b!p!]
	\centering
		\includegraphics[width=.48\textwidth]{Figures/ExperimentResult2.pdf}
	\caption{Force control data during a manipulation task (bottom). Magnitude of combined (x, y, and z) acceleration of the robot is plotted along with the grasp force measured by a finger with FBG sensors (Top).}
	\label{fig:ExperimentResult2}
\end{figure}

%mrc OMIT until we can do an experiment where we know the magnitude and frequency content of the applied disturbance.
%\begin{figure} [b!p!]
%	\centering
%		\includegraphics[width=.48\textwidth]{Figures/ExperimentResult3.pdf}
%	\caption{Force Data showing Disturbance Rejection}
%	\label{fig:ExperimentResult3}
%\end{figure}

%\subsubsection{Experiment 3 (Disturbance Rejection)}
%This Experiment is to check the ability of disturbance rejection during force control. The task procedure was almost the same as that of the experiment 1 except the introduction of a perturbation. A perturbation was given during the force control as shown in Figure \ref{fig:ExperimentResult3}. The result shows the system can reject the perturbation and re-stabilize. 

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\section{Conclusions and Future Work}

We have presented the application of robotic fingers with embedded FBG sensors for force control in a robot hand. The fingers are made in the form
of a hollow shell with a hexagonal grid pattern for strength and light weight. The material is a urethane polymer with embedded optical fibers and an embedded copper mesh to reduce creep and provide some thermal shielding. Although any such polymer composite structure will exhibit more hysteresis than a machined metal part, we demonstrate in the experiments in this paper that the effects are small over short periods of a few seconds or less and do not compromise the ability of the hand to maintain control of the grasp force during manipulation tasks.

The hand is operated in a hybrid control scheme that switches between computed-torque position control and nonlinear force control when contact is sensed.
The finger sensors are capable of resolving small forces and are immune to electromagnetic disturbances so that the system can be mounted on a large industrial robot, or in other applications where large magnetic fields are present, without concern for shielding and grounding. In addition, as multiple FBG sensors can be placed along a single fiber and multiplexed optically, it suffices to route a single optical fiber down the robot arm.

The next steps are to miniaturize the technology and provide larger numbers of sensors on a structure. The motivation is to produce human-scale robotic fingertips for robots designed for human interaction in space applications and to produce sensorized end-effectors suitable for robot-assisted minimally invasive surgery. By using versions of fingertips with no metal components, manipulation applications within MRI devices could also be addressed.

\begin{figure} [b!p]
	\centering
		\includegraphics[width=.48\textwidth]{Figures/MiniFinger.pdf}
	\caption{Miniaturized polyurethane finger prototype fabricated as a hollow shell composed of several curved ribs that are connected
	at the base by a circular ring and meet at the apex. Optical fibers with FBG sensors are embedded in the ribs.}
	\label{fig:MiniFinger}
\end{figure}

Figure  \ref{fig:MiniFinger} shows a prototype of a small fingertip with an embedded optical fiber containing FBG strain sensors. For this application, 80-$\mu$m diameter bend-tolerance optical fibers from OFS were selected. These fibers tolerate comparatively tight bending radii of approximately 7.5 mm.  Tests on the new fingertip are underway.

In parallel, we are adapting the optical fiber interrogator \cite{Chau2007, Lopatin2007, Moslehi2003} to support larger numbers of sensors - see Appendix for practical sensor numbers. In our parallel processing architecture using a broad-band source, the speed is mainly limited by the electronics used and the required resolution. This is in contrast to interrogators based on tunable sources or tunable filters where the tuning speed provides the limitation. We are presently developing electronics to support more wavelength channels and make use of a larger portion of the available source spectrum, thus enabling more sensors to be supported.

\section*{Appendix}

For the range of broadband light sources that we use, the available source bandwidth is between 40 nm and 100 nm. Thus, if we make use of the entire available source spectrum, we can support 20-50 sensors on a single fiber. This number can be further increased by using multiple fibers. In particular, the number of sensors $N_{sensors}$ that can be supported on a single fiber is related to the source bandwidth $\delta \lambda _{source}$ divided by the bandwidth required for each sensor $\delta \lambda _{sensor}$. Further $\delta \lambda _{sensor}$ is given by the maximum strain-dependent wavelength shift $\delta \lambda _{{\rm strain -  max}}$ and the sensor wavelength separation to avoid crosstalk (i.e., to keep it below "tolerable" level) $\delta \lambda _{{\rm c}ross - talk}$. Thus,

\[N_{sensors}  = \frac{{\delta \lambda _{source} }}{{\delta \lambda _{{\rm strain -  max}} {\rm  } + {\rm  }\delta \lambda _{{\rm c}ross - talk} }}.\]

The wavelength separation to avoid crosstalk, $\delta \lambda _{{\rm c}ross - talk}$, will depend on both the FBG spectrum and the parallel spectral processor, but is typically on the order of wavelength channel separation 0.8 nm. Table \ref{tab:table1} summarizes the possible numbers of sensors for different source bandwidths and maximum strain-dependent wavelength shifts assuming $\delta \lambda _{{\rm c}ross - talk}$ = 0.8 nm.

\begin{table} [h!b!p!]
	\caption{Typical sensor numbers that can be supported for a range of spectral characteristics and strain requirements}
	\centering
	\begin{tabular}{ccc}
		\hline
		\hline
		$\delta \lambda _{source}$&$\delta \lambda _{{\rm strain -  max}}$&$N_{sensors}$\\
		\hline
		100 nm&1.2 nm ($\to$1200 $\mu$strain)&50\\
		&9.2 nm ($\to$9200 $\mu$strain)&10\\
		\hline
		40 nm&1.2 nm&20\\
		&9.2 nm&4\\
		\hline
		\hline
	\end{tabular}
	\label{tab:table1}
\end{table}


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\section*{Acknowledgment}

The authors thank the National Aeronautics and Space Administration (NASA) for financial support for this research through the grant from SBIR contract of NNJ06JA36C to IFOS and subcontract to Stanford's Center for Design Research, and the NASA technical monitor Toby Martin for his support and feedback.
Special thanks are also due to the late Dr. Homayoun Seraji of NASA's Jet Propulsion Laboratory (JPL) for his interaction in the early stages of this project and the use of his nonlinear control algorithm.

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