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Miniature Low-Power Inertial Sensors: Promising Technology for Implantable Motion Capture Systems Joris M. Lambrecht and Robert F. Kirsch, Member, IEEE

Abstract—Inertial and magnetic sensors are valuable for untethered, self-contained human movement analysis. Very recently, complete integration of inertial sensors, magnetic sensors, and processing into single packages, has resulted in miniature, low power devices that could feasibly be employed in an implantable motion capture system. We developed a wearable sensor system based on a commercially available system-in-package inertial and magnetic sensor. We characterized the accuracy of the system in measuring 3-D orientation—with and without magnetometer-based heading compensation—relative to a research grade optical motion capture system. The root mean square error was less than 4 in dynamic and static conditions about all axes. Using four sensors, recording from seven degrees-of-freedom of the upper limb (shoulder, elbow, wrist) was demonstrated in one subject during reaching motions. Very high correlation and low error was found across all joints relative to the optical motion capture system. Findings were similar to previous publications using inertial sensors, but at a fraction of the power consumption and size of the sensors. Such ultra-small, low power sensors provide exciting new avenues for movement monitoring for various movement disorders, movement-based command interfaces for assistive devices, and implementation of kinematic feedback systems for assistive interventions like functional electrical stimulation. Index Terms—Implantable sensors, inertial measurement unit (IMU), inertial sensors motion capture, neuroprosthesis.

I. INTRODUCTION

I

N THE last decade or so, inertial sensors have become a popular method of quantifying human movement because they provide an opportunity for untethered measurements in an unlimited workspace. An inertial measurement unit (IMU) uses three orthogonal gyroscopes in combination with three orthogonal accelerometers. Gyroscopes provide an accurate measure of angular velocity but small velocity errors result in a measured orientation drift overtime. Under conditions of no linear acceleration, accelerometer data allows determination of the absolute tilt of the sensor with respect to gravity which can correct the Manuscript received September 06, 2013; revised March 26, 2014; accepted May 09, 2014. Date of publication May 16, 2014; date of current version November 13, 2014. This work was supported in part by the U.S. Army Medical Research and Materiel Command, TATRC, under Grant W81XWH-07-2-0044. J. M. Lambrecht is with the Department of Biomedical Engineering, Case Western Reserve University, Cleveland, OH 44106 USA (e-mail: joris. [email protected]). R. F. Kirsch is with the Department of Biomedical Engineering, Case Western Reserve University, Cleveland, OH 44106, USA, and also with the Louis Stokes Cleveland VA, FES Center of Excellence, Cleveland, OH 44106 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TNSRE.2014.2324825

drift except about the vertical axis. Luinge et al. demonstrated the ability to measure the orientation of human body segments using IMUs [1], [2], but reported the necessity for additional sensors or assumptions in applications where heading—rotation about the vertical axis—information is important. A magnetic, angular rate, and gravity (MARG) sensor [3]—or attitude and heading reference system (AHRS) in aerospace terminology—combines a three-axis magnetometer with an IMU to determine the absolute heading with respect to earth’s magnetic field. Magnetometers suffer from distortions in the magnetic field due to nearby ferrous metal objects. However magnetic compensation algorithms have successfully been built into Kalman filters that “fuse” the various sensor data [4], [5]. Initially, IMUs required up to six distinct microelecto-mechanical-system (MEMS) components. Miniaturization and combinations of these sensors into single chips—primarily for mobile phones and other consumer electronics—has resulted in IMUs so small and low-power that their use in implantable devices can now be considered. Accelerometers have been used in pacemakers to adjust pacing rate for over 30 year by providing an estimate of activity level [6]. Tse, et al. used torso inclination—estimated from accelerometers only—to detect supine to standing transitions [7]. However, an IMU to detect the 3-D orientation of a body segment has not been implanted to date. Such information could be highly useful for implanted neuroprosthetic and prosthetic applications for a variety of movement disorders. For example, the paralysis resulting from a high-level spinal cord injury (SCI) leaves individuals with very little function to perform activities of daily living. functional electrical stimulation (FES) can be used to restore movement via coordinated stimulation of appropriate muscles via implanted stimulators [8], [9]. However, determining user intent to coordinate the movement of multiple degrees-of-freedom without significant cognitive burden is a challenging problem. Wearable orientation sensors have been used as command sources for persons with paralyzed [10] or prosthetic arms [11]. Orientation sensors could also provide feedback information to a neuroprosthetic controller [12] to offload some of the control burden from the user or make automatic corrective actions to perturbations [13]. For prosthetic applications, knowledge of arm orientation can improve pattern recognition accuracy [14]. Measures of activity over time could be used to control the release of pharmacological agents from implanted pumps or to adjust the stimulation patterns of brain stimulation used in Parkinson’s disease or other movement disorders. In an implanted FES system, an implanted network of IMUs would provide many advantages over an externally mounted

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LAMBRECHT AND KIRSCH: MINIATURE LOW-POWER INERTIAL SENSORS: PROMISING TECHNOLOGY FOR IMPLANTABLE MOTION CAPTURE SYSTEMS

Fig. 1. Photograph of the wearable IMU sensor pair. Larger sensor unit (A) and contains a microcontroller and an MPU-9150 measures orientation sensor chip. The smaller sensor unit (B) measures and houses a second MPU-9150. Cable exiting the frame provides power and a serial communication link to other devices.

sensor network. The sensors would not require donning/doffing by a caretaker, they could be available for measurement as soon as the system was turned on (if calibration is not required), and they would not affect cosmesis or interfere with clothing. Furthermore, sensors could be implanted close to the bone or even attached to the bone to minimize soft tissue artifact, maintaining a constant orientation with respect to the body segment. The Networked Neuroprosthetic System [15] being developed by the Cleveland FES Center is an ideal platform for implementing such a sensor system because it already provides the power, communication, and processing capability to implanted modules in various anatomic segments. However, the accuracy of these ultra small and low power sensors has not previously been determined. In this paper, we characterize the accuracy of a small, lowpower, external and wearable IMU with magnetometer-based heading compensation for measuring independent 3-D orientation and relative orientation between body segments. We discuss the implications of our results for the development of an implantable motion capture system. II. MATERIALS AND METHODS A. Sensor System We developed an ultra-small and low-power wearable sensor system based on the MPU-9150 (InvenSense Inc., Sunnyvale, CA, USA) system-in-a-package (SiP) orientation sensor. Fig. 1 shows a photograph of the packaged sensor system. The MPU-9150 combines a three-axis gyroscope, three-axis accelerometer, three-axis magnetometer, and digital motion processor (DMP) in a single package, with a total current consumption of 4.25 mA when all sensors are active. Our wearable sensor system consists of two MPU-9150 SiPs and a single MSP430G2553 (Texas Instruments Inc., Dallas, TX, USA) microcontroller (MCU) that communicate on an bus. The MCU was selected for its low power and

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to demonstrate the ability to achieve full orientation sensing with limited processing capability. The contributions of the MCU, two MPU-9150 chips, and a personal computer (PC) in executing the various processing steps is summarized in Fig. 2. The DMP application provided by InvenSense (within Embedded Motion Driver v5.1) outputs a quaternion that is generated from accelerometer and gyroscope data using a proprietary algorithm, but does not utilize magnetometer data. Therefore, raw magnetometer data is queried from the MPU-9150 along with the “6-axis” quaternion to generate a heading-corrected “9-axis” quaternion within our custom code on the MCU. The nomenclature “6-axis” and “9-axis” is used by InvenSense and refers to the number of raw sensor axes used to generate the output; in both cases the quaternion is a standard four parameter unit quaternion describing the 3-D orientation with respect to a North-East-Down coordinate system. InvenSense does not yet provide a DMP application or source code for implementing the heading compensation, so custom code is required for obtaining the “9-axis” quaternion. The raw accelerometer and gyroscope data are sampled at 200 Hz within the DMP, and generate the “6-axis quaternion” at 50 Hz. The “6-axis” quaternion is sampled at 50 Hz and the raw magnetometer values are sampled at 10 Hz by the custom code on the MCU. The formulas for the heading fusion algorithm we developed are provided in the Appendix and are summarized in Fig. 2. The “Hard Iron Offset” is calibrated offline on a PC by fitting raw magnetometer data to a sphere as the sensor is rotated. The vector offset to bring the center of the sphere to the origin is stored in Flash on the MCU and added to the raw magnetometer values. The adjusted magnetometer values are then tilt-compensated using tilt values obtained from the “6-axis” quaternion using a method similar to that described in [16]. After tilt compensation, the heading from the magnetometer is acquired and compared to the heading obtained from the “6-axis” quaternion. The difference, or heading offset, is heavily rate-limited to eliminate fast changes due to noise in the magnetometer data. Assuming the magnetometer data is accurate, the heading offset is simply a measure of the z-axis gyro drift, and is therefore only expected to change at a rate of a few degrees per minute or less. Inaccurate magnetometer data is detected if the z-component of the tilt-compensated magnetometer data is not within its expected range, which is also stored in Flash on the MCU and must be calibrated as described below. On startup, the rate-limiter gradually reduces the allowed maximum rate, such that the sensor quickly ( 5 s) converges to a stable, accurate, Earth-referenced heading. The heading offset is applied to the “6-axis” quaternion each time-step via a simple quaternion product, to generate the “9-axis” quaternion without the need to obtain the heading and tilt values at each time-step (the magnetometer data is sampled at 1/5 the rate of the “6-axis” quaternion). The Hard Iron distortion is dependent on the circuit layout and any magnetic materials that are rigidly joined with the sensor causing a permanent bias in sensor outputs. Calibration of these parameters is only necessary once after the sensor has been packaged. “Soft Iron” distortion, which causes the recorded raw magnetometer data to fall on a rotated ellipsoid rather than a sphere, was not found to be a problem. The tilt-compensated z-component of the magnetometer data—used

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Fig. 2. Functional block diagram for each component of the IMU sensor system with magnetometer-based heading adjustment.

within the magnetic field distortion correction—is dependent only on the magnetic field strength and magnetic inclination as is shown in the Appendix. Both field strength and inclination vary by geographic location and change slowly over time. For example, in Cleveland, OH, USA, field strength changes about 0.2% annually and inclination changes about 0.1% annually [17]. Over a change in latitude and longitude for our location (roughly a distance of 140 km), field strength varies 1.1% and inclination varies 1.3% [17]. The expected range for the tilt-compensated magnetometer z-component value is calculated using the same data as for the hard iron offset calibration. The minimum and maximum were set to the 5th and 95th percentile of the tilt-compensated z-component values recorded during the calibration procedure. Because this calibration is valid for a long time period (years) and a large geographic region (many km), daily recalibration will typically not be necessary. The algorithm described above was programmed in C using Code Composer Studio 5.2, (Texas Instruments, Dallas, TX, USA). Because the MCU does not have a floating point unit, trigonometric, inverse trigonometric, and square root functions were implemented using the CORDIC method [18]. The MCU runs at 8 MHz, and uses approximately 9 KB of Flash and 248 bytes of RAM out of 16 KB and 512 bytes available, respectively. Data is sent to a PC serial port at 50 Hz via UART ( baud). B. Sensor Accuracy To determine the accuracy of the sensor system, we utilized an active-marker motion capture system, Optotrak Certus (Northern Digital Inc., Waterloo, ON, Canada) as a “gold standard.” We mounted the sensor system to a rigid aluminum cube with 16 infrared emitting diodes (IRED). The global coordinate system of the Optotrak system was aligned with a wooden table, such that the cube’s local coordinate system could easily

be aligned with the global coordinate system by resting it on the table. The axes of each sensor pair were aligned as closely as possible to the corresponding axes of the cube. Three sensor pairs were tested independently in each of the three testing paradigms. 1) The cube was placed in a new static configurations every 10 s for 2 min. Only 4 s of each configuration was included in the dataset to ignore the dynamic transitions between configurations. 2) The cube was rotated arbitrarily about all axes at a slow to moderate rate for 2 min. 3) The cube was hung from a string and allowed to swing freely for 20 min to assess long-term gyro drift. Every 2 min, the cube was nudged to keep the cube moving. For both the static and dynamic trials, for the first and last 10 s, the cube was aligned with the global coordinate system. The orientation of the sensor was computed relative to its starting orientation in all trials. Before being tested, each sensor pair was calibrated with hard iron offsets and initial gyro biases. A tilt correction was also applied to the sensor output to account for inaccuracies in the orientation of each sensor chip relative to the packaging. This correction factor is simply the relative orientation between the measured orientation—with the sensor package resting on a flat surface—and an orientation with an identical yaw but zero pitch and roll. The sensors were not recalibrated between the different testing paradigms, although it is possible that the gyro biases changed, as these are automatically adjusted within the proprietary DMP algorithm after 8 s of no motion. The orientations of the sensors were collected at 50 Hz via serial ports on a PC running the xPC Target real-time operating system (The MathWorks Inc., Natick, MA, USA). Optotrak data were also recorded at 50 Hz using the First Principles Software (Northern Digital Inc., Waterloo, ON, Canada) on a separate PC. Optotrak data collection was initiated by an external hardware

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TABLE I CALCULATING JOINT ANGLES

Fig. 3. Joint angle definitions. Local anatomic coordinate systems are defined using bony landmarks.

trigger generated by the xPC Target computer in order to synchronize the two data sets. Offline, statistics were performed in MATLAB (The MathWorks Inc., Natick, MA, USA). C. Upper Limb Kinematics To demonstrate the applicability towards an implanted motion capture system, we measured seven degrees-of-freedom (dof) upper limb kinematics from one able-bodied subject during normal reaching movements. The subject gave informed consent for the experimental procedure as approved by the MetroHealth Medical Center Institutional Review Board. IRED clusters were mounted to the sternum, upper arm, distal forearm, and hand. Similarly we used two sensor pairs, attaching each sensor unit to the corresponding rigid body segment or the IRED cluster itself. The orientation of the sensor units and IRED clusters relative to the anatomical segments was arbitrary. We assume that there was no motion between an IRED cluster and the corresponding inertial/magnetic sensor. The Optotrak data were sampled at 30 Hz, while the inertial and magnetic (IMU+mag) sensor data were sampled at 50 Hz. Quaternions from both data sets were then down sampled to a matching 10 Hz. The same software, computers, and synchronization methods were used as described previously. The orientation of the anatomic segments was obtained at time zero using positions of bony landmarks recommended by the ISB [19]—located using the Optotrak digitizing probe—and the coordinate system definitions shown in Fig. 3. Since the IRED clusters and sensor orientations were also known at time zero, fixed relationships between the anatomic segments and IRED clusters, and sensors, could be obtained. Joint angles were then calculated using the method shown in Table I. III. RESULTS A representative static and dynamic trial is shown in Fig. 4. In the top three panels of each, the Euler angles are

Method for calculating joint angles from sensor (or IRED cluster) is the quaternion inverse of and is orientations. Note that constant (measured at time zero).

plotted for the Optotrak, IMU, and IMU+mag. The bottom panel shows the error—relative to the Optotrak—for both IMU and IMU+mag. This error is calculated by converting the relative orientation to axis-angle format and ignoring the axis component. The increased error at the end of the trial for the IMU (in yaw and the scalar error) could be attributed to the uncorrected heading drift. However, in some trials, the error was greater at the end of the trial for the IMU+mag than for IMU. Fig. 5 shows the summary of the errors for each sensor for the static and dynamic trials. Since both sensors belonging to a pair (e.g., 1a and 1b) measured the same movement, the relative error between pairs is also shown. Error bars show one standard deviation. We performed a three-way ANOVA to determine if there were statistically significant differences in the sensor error with and without heading compensation, in static or dynamic conditions, and whether the intra-sensor-pair error (A versus B) was different from the error relative to the Optotrak. All interaction terms were found to be insignificant . Means and multicomparison pairwise 95% confidence intervals are shown in Fig. 6. Static errors were lower than dynamic errors as expected . There were no significant differences in performance with and without heading compensation within the 2 min static or dynamic trials. There was also no significant difference found between the Intra-sensor-pair errors and the error relative to the Optotrak . Fig. 7(a) shows the long term heading error from the IMU with the magnetometer-based heading offset overlaid. It is clear that heading can drift significantly within a few minutes although there is substantial variability between the sensors. The heading offset predicted by the magnetometer follows the heading drift quite well. Fig. 7(b) shows the mean errors in the last minute of the 20 min trial. It is immediately evident that the heading compensation improves long term usability of the sensor even for those sensors with minimal drift.

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Fig. 4. Representative 2 min (A) static and (B) dynamic trial. Bottom panel in each shows the error between the IMU+mag and IMU relative to the Optotrak. Note that when Pitch approaches , Yaw and Roll become synonymous (i.e., the apparent large error at 90 s is an artifact of the Euler angle representation and results in only a small difference in orientation as is evident in the scalar error measure, which is unaffected by this singularity). Also the Yaw and Roll angles wrap at which accounts for the apparent discontinuities in the Euler Angles.

Fig. 8 illustrates the effectiveness of the sensors as a 7-dof motion capture system when compared to the Optotrak system during a 50 s reaching trial. The accuracy in each joint angle trajectory was quantified with root mean square error (RMSE) and a correlation coefficient (R). The average correlation coefficient across all joints was 0.988 0.019. The average RMSE across all joints was . During data streaming over UART, the MCU is active 38% of the time. When not streaming, the MCU is still computing heading-adjusted quaternions, but is only active 18% of the time. The total sensor system power consumption is 35 mW when streaming or 31 mW when not (both 3.3 V supply). IV. DISCUSSION A. Implications We characterized the accuracy of a low power and ultra-miniature inertial sensor with and without magnetometer-based heading correction and demonstrated the feasibility of recording the motions of a 7-dof upper limb using four such sensors. There was very high correlation and low error with respect to the same motions recorded using a research-grade visual motion capture system. Other studies have shown similarly high correlation and low RMSE for joint

Fig. 5. Mean scalar angular error during 2-min trials. Error bars are one standard deviation. Three pairs of sensors were tested in static and dynamic conditions with and without heading compensation. Both sensors belonging to a pair were subjected to the identical movements and could therefore also be compared (A versus B)

Fig. 6. Mean scalar angular errors under different conditions. Error bars are 95% confidence intervals in the difference between the means. Intra-pair error is the error between two sensors that were subject to the identical movements (A versus B). Optotrak error is the error between the sensor (A or B) and the “gold standard” visual motion capture system.

angle tracking using inertial and magnetic sensors [20]–[22], but used traditional—larger, nonlow-power—commercially available inertial sensors. Table II shows the RMSE (measured across all IMU+mag sensors relative to Optotrak) for yaw and pitch/roll separately alongside the specifications for five commercially available orientation sensors. Roetenberg et al. reported slightly lower errors of 1.4 static and 2.6 dynamic using an MT9-A (XSens Technologies BV, Enschede, The Netherlands) [5]. Surprisingly, the Pitch/Roll static errors are greater than the Yaw static errors in our sensor. This could be an artifact of recording a limited

LAMBRECHT AND KIRSCH: MINIATURE LOW-POWER INERTIAL SENSORS: PROMISING TECHNOLOGY FOR IMPLANTABLE MOTION CAPTURE SYSTEMS

number of static orientations. It could also be an indication that sensor fusion performed by the proprietary DMP algorithms is not as effective as other Kalman Filter methods in eliminating gyro drift around the nonvertical axes. Crago et al., suggested required resolutions of 5 , 3 , and 5 for hip, knee, and ankle sensors, respectively, used in walking applications [23]. In our upper limb demonstration, the RMSE across all joints was less than 4 . Accuracy would be expected to be similar in the lower limb suggesting that the accuracy of the tested sensors may be sufficient for some feedback or control applications in FES systems. To get a better idea of whether or not the level of accuracy is sufficient for a given application we ran both the Optotrak and IMU+mag calculated joint angles from Fig. 7 into a simple forward kinematics model using the joint axes presented in Fig. 3. Assuming an upper limb length of 34.1 cm and forearm length of 26.5 cm [24], the mean distance between the wrist position approximated by the Optotrak and by the IMU+mag (both via the forward kinematic model) was 4.4 1.3 cm. If a kinematic feedback system for an upper extremity (shoulder, elbow, wrist) FES system could control the wrist position to within a few cm of its intended target, it is expected that a user’s voluntary function (limited trunk and scapular movement) could make up the difference. The required accuracy for command sources and other movement monitoring will vary depending on the application. While the MPU-9150-based IMU+mag is not as accurate as the high-end sensors, it has similar performance to the lower-end devices and is much smaller and draws less power (see Table II). A single MPU-9150-based sensor consumes about 18 mW ( 8% of any other devices shown). Further power savings could be achieved by reducing the operating voltage. In addition during periods of inactivity the sensors can be put into a standby mode, where only the accelerometer is active at a much reduced sampling frequency. If the accelerometer detects an above-threshold input, it interrupts the MCU and then resumes full power orientation sensing. The gyroscope is responsible for about 80% of the total power consumption, accelerometer 5%, magnetometer 7%, and DMP 8% [25], [26]. For slow quasi-static movements, an accelerometer and magnetometer could provide sufficient information for certain applications, which would drastically reduce power requirements. The small size and power consumption of the IMUs presented here compared to traditional—discrete component—IMUs is likely of interest in many applications where unobtrusive measurement is desirable and worth a small decrease in accuracy (e.g., sports, animation). In addition, the small size and power consumption lends itself to implanted applications that would have been impractical previously. Implant-grade rechargeable batteries range in capacity from less than 1 mAh to nearly 1 Ah [27]–[29]. Assuming a large capacity battery of 650 mAh [28], depth of discharge of 70% and a required runtime of 2 h, a system with four MPU-9150 (4.25 mA each) sensors would consume roughly 8% of the power budget. With traditional IMUs, power consumption would be more than a factor of 10 higher resulting in complete utilization of the power budget. This would not allow any other activity—electrical stimulation, drug delivery pumps, telemetery, etc.—to occur without significantly

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reducing the operating time, reducing the number of sensors, combining batteries into impractically large battery packs, or using other power sources. The networked neuroprosthestic system (NNPS), in development by the Cleveland FES Center, consists of remote myoelectric sensing and stimulation modules networked together to a single implanted power module that contains a 600 mAh rechargeable battery pack and wireless communication link [15]. Each module contains a 3-axis accelerometer that could provide rudimentary posture information or activity-level monitoring of the body segment in which it is implanted. The remote modules are small and intended to be implanted within the arm, leg, or trunk segments in which the muscles are to be stimulated or recorded. The processor in each module would be sufficient to perform the heading compensation algorithm used in this study. With minimal further development, the accelerometer could be replaced with a SiP inertial/magnetic sensor that would provide accurate and responsive body segment orientation. This information could be used as command sources or as a feedback to the neuroprosthetic control system. The Cleveland FES Center previously developed a 2-dof implanted joint angle transducer (IJAT) using Hall effect sensors and a permanent magnet [30], [31] for command and feedback applications for neuroprostheses with a best case resolution of 3 . The IJAT is limited by the surgical procedure needed to accurately place the permanent magnet and sensor within the bone. Unlike the IJAT, the orientation sensors would already be within the remote modules, and therefore would not require additional surgical procedures. Additionally, placement within the body segment can be arbitrary as long as it does not change relative to the segment. The IJAT was pulse powered to achieve a power consumption less than 15 mW [32] slightly higher than the power consumption of a single MPU-9150 operating constantly. The IJAT was used with an Implantable Stimulator Telemeter that has a maximum power consumption of 120 mW [32]. B. Limitations The method we used to obtain the joint angles requires knowledge of the relative orientation between the anatomic segment and the sensor. We used an Optotrak system to obtain the anatomic segment coordinate systems. For an implanted sensor system, it is assumed that the sensors would never move relative to the anatomic segments, and therefore this procedure would only need to be performed once. For externally worn sensor systems that would be donned and doffed daily, using a visual motion capture system to obtain the anatomic segment axes would be prohibitively expensive and time consuming for most applications. An alternative method is to put the arm in a known posture during a brief calibration routine. The magnetometer-based heading compensation did not statistically improve or worsen the performance of the IMU during 2-min trials. However, it was clear from the long-term trials that the heading compensation would be required if the sensor is to be used for several minutes. In addition, the heading compensation is required if all sensors need to power up with the same reference coordinate system (e.g., for calculating relative rotations

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between multiple sensors without control of the starting orientations). Unfortunately, the magnetometers required for heading compensation are sensitive to local distortions of the magnetic field (e.g., near ferrous metal objects). While, magnetic compensation algorithms are possible, they are only effective if the distortion to the magnetic field is applied over a short period of time (few minutes depending on gyro bias stability), during which the error caused by gyro drift is negligible. El-Gohary et al. proposed a solution to minimizing heading drift without a magnetometer by incorporating physical constraints and range-of-motion information into an unscented or extended Kalman filter [20]. Zhang et al. [22] also demonstrated that using a constrained link structure allowing only 2-dof between upperarm and forearm and incorporating all sensors data into a single Kalman filter improves estimation accuracy over using independent orientations of each rigid body. However, both these methods will limit the application of the particular sensor fusion algorithm to measuring a unique joint. A priori knowledge of the individual’s range of motion may also be needed. We used the independent orientation of each sensor as this can be a universal method for measuring 3-dof between any rigid body segments. Furthermore, it is likely that in the future SiP or SoC (system-on-chip) inertial/magnetic sensors will incorporate all sensor fusion onboard (the MPU-9150 DMP currently fuses accelerometer and accelerometer data, but leaves heading compensation up to an external processor), minimizing the computational requirements of external processors. For applications where small size and low power are essential, the accuracy that could be gained by implementing joint-specific fusion algorithms may not justify the increased processing burden of reading and fusing raw sensor data on an external processor. The reason for the large variability in measured drift is unclear (Fig. 7). Based on previous experiments, we do not think that Sensor 1 was less accurate than the other sensors due to hardware defects. A likely explanation is that the gyro biases were not recalculated as recently as for the other sensors before commencing the 20 min trial. Since both Sensor 1a and Sensor 1b were rigidly attached, they would both undergo a gyro bias update at roughly the same time during periods of no motion. Though the heading compensation algorithm dramatically reduced heading error for sensor 1, there was still a quite large error in the last minute of the 20 min trial (12.0 for sensor 1a, 6.9 for Sensor 1b). Across the other sensors the heading error was smaller . This inability for the heading compensation to keep up with the drift is likely due to an overly aggressive rate limiter within our heading compensation algorithm as we did not expect the gyro to drift as quickly as Sensor 1 (approximately 9 ). By increasing the allowed heading compensation rate, errors due to magnetometer noise will increase somewhat, but we do not expect this increase to be significant. The sensors tested here were hand soldered. Thermal stresses could have affected the accuracy. In addition the packaging may not have adequately prevented movement of the sensor relative to the packaging. We predict that improved manufacturing may further increase the accuracy of the sensors. The kinematic tracking described in this paper measured orientation only, not position. To track position of the hand

Fig. 7. Long-term heading drift. (A) IMU heading error with the magnetometer predicted heading error overlaid. Sensor was nudged every 2 min, resulting in the peak errors (B) Comparison of absolute value of heading error with and without heading compensation.

Fig. 8. Seven degree-of-freedom kinematic tracking. The subject was initially standing with the arm in the anatomical position. At around 16 s, the subject elevated the arm for roughly 8 s and then proceeded to do whole arm reaching motions for the remaining 26 s. Root Mean Square Error and Correlation Coefficient (relative to Optotrak) are shown above each trace. The dotted line indicates 0 .

relative to the shoulder, for instance, knowledge of the upper arm and forearm lengths would be required. An alternative would be to directly calculate position from the inertial sensors

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TABLE II SENSOR COMPARISON

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would be expected to perform adequately for many higher speed applications as well. V. CONCLUSION

RMSE and power consumption (mW) for several commercially available sensors. XSens Technologies BV, Enschede, The Netherlands [38] LORD Microstrain Inc, Williston, VT [39] InterSense Inc, Billerica, MA [40] Motion Workshop, Seattle, WA [41] Movea, Grenoble, France [42]

by double integrating the accelerometer signal after removal of the gravitational component, a method known as dead reckoning. Double integrating accelerometers to get position change has been demonstrated for short (4 s) durations [33]. For longer durations, Roetenberg et al. and Schepers et al. have demonstrated fusion of inertial sensors with pulsed dc electromagnetic tracking. A three-axis magnetic field source can generate pulses—when estimated errors approached a certain threshold—that provide a reference for updating position and orientation measurements [34], [35]. In the presence of the magnetic field, the three-axis magnetometers serve as more than a compass, but use the strength of the measured field to approximate position [34], [35]. The magnetic field source required much less power than in a system that relies only on magnetic sensing because the magnetic field only needed to be pulsed at 1–2 Hz, rather than the desired sampling rate [35]. The sensors described in this paper could be used with such a dc electromagnetic field source replacing the larger inertial and magnetic sensors, with a lower power, smaller, and lower cost alternative. Inertial sensors are temperature dependent [36], [37]. As implanted sensors, we expect the temperature to remain more constant than in external ambulatory applications. We expect that this could eliminate the need for temperature compensation. Inertial sensors vary in their ability to withstand very high accelerations such as during impact. However, the impact tolerance of inertial sensors far exceeds what would be transferred to a sensor implanted in the body without causing serious bodily injury, so this specification is not critical in selecting a sensor for an implanted application. Biocompatibility of the sensor chip is not required assuming it would be contained within a hermetically sealed capsule. Integrated inertial and magnetic sensors, such as the MPU-9150, are less expensive and simpler to incorporate into systems than using discrete components that need to be aligned properly and require a significant programming effort to achieve correctly fused orientation data. We expect trends in MEMS technology to continue, ever reducing size and power consumption while maintaining or improving accuracy in inertial and magnetic sensors, expanding the potential applications of such technology even further. Motions analyzed in this study were limited to slow to moderate speed movements because of the intended use for individuals with SCI or other motor impairments rather than for sports applications. However, the sensors

We have demonstrated the feasibility of using ultra-small inertial and magnetic sensors for measuring joint kinematics at less than 8% of the power consumption previously realized using commercially available sensors. Miniature low-power inertial and magnetic sensors provide expanding opportunities for human movement sensing, including implanted use for a variety of movement disorder applications: movement monitoring, command sources for assistive devices, and kinematic feedback systems for assistive interventions such as functional electrical stimulation. APPENDIX HEADING FUSION ALGORITHM 1) Obtain the heading and tilt angles from the “6-axis” quaternion,

where and are the tilt angles about the x (roll) and y (pitch) axes and is rotation about the z-axis (yaw or heading). The subscript denotes that values are obtained from the inertial sensors only. 2) Calculate the magnetometer-based heading, , as follows:

3) Calculate a new heading offset if no magnetic disturbance is detected. The tilt-compensated z-value of the magnetometer, , is calculated from the raw magnetometer values, , after applying the Hard Iron Offset, , as

where . is expected to be constant, with a value of , where is the local magnetic field strength, and is the local magnetic inclination. If is within its expected range, a new heading offset is computed. Otherwise, the heading offset remains the same, such that magnetic disturbances will not affect the heading

where

and Heading offset at the current timestep. Heading offset at the previous timestep.

The constant, , will force the algorithm to take multiple iterations to reach the actual heading offset based on the current heading offset. and should be chosen such that the rate limiter is just fast enough to keep up with

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the heading drift, taking into account that magnetic disturbances will not allow the system to update the heading offset. 4) Apply the heading offset. To generate the heading adjusted quaternion, , from the received quaternion, , one only needs to store and , and do a few multiplies and additions

where

,

.

ACKNOWLEDGMENT The authors would like to thank Dr. S. Sidik for statistics consultation and the Networked Neural Prosthesis Development Team: J. Buckett, A. Campean, F. Montague, and B. Smith for their assistance. REFERENCES [1] H. J. Luinge, “Inertial sensing of human movement,” thesis, Twente Univ., Enschede, The Netherlands, 2002. [2] H. J. Luinge and P. H. Veltink, “Measuring orientation of human body segments using miniature gyroscopes and accelerometers,” Med. Biol. Eng. Comput., vol. 43, no. 2, pp. 273–282, Mar. 2005. [3] E. R. Bachmann, “Inertial and Magnetic Tracking of Limb Segment Orientation for Inserting Humans into Synthetic Environments,” thesis, Monterey, CA, 2000, Inertial and magnetic tracking of limb segment orientation for inserting humans into synthetic environments. Monterey, CA: Naval Postgraduate School, 2000. [4] D. Roetenberg, C. T. Baten, and P. H. Veltink, “Estimating body segment orientation by applying inertial and magnetic sensing near ferromagnetic materials,” IEEE Trans. Neural Syst. Rehabil. Eng., vol. 15, no. 3, pp. 469–471, Sep. 2007. [5] D. Roetenberg, H. J. Luinge, and C. T. Baten et al., “Compensation of magnetic disturbances improves inertial and magnetic sensing of human body segment orientation,” IEEE Trans. Neural Syst. Rehabil. Eng., vol. 13, no. 3, pp. 395–405, Sep. 2005. [6] N. E. Fearnot, H. J. Smith, and L. A. Geddes, “A review of pacemakers that physiologically increase rate: The DDD and rate-responsive pacemakers,” Prog. Cardiovasc. Dis., vol. 29, no. 2, pp. 145–164, Sep.–Oct. 1986. [7] H. F. Tse, C. W. Siu, and V. Tsang et al., “Blood pressure response to transition from supine to standing posture using an orthostatic response algorithm,” Pacing Clin. Electrophysiol., vol. 28, pp. S242–S245, Jan. 2005, Suppl 1. [8] A. M. Bryden, K. L. Kilgore, and R. F. Kirsch et al., “An implanted neuroprosthesis for high tetraplegia,” Topics Spinal Cord Injury Rehabil., vol. 10, no. 3, pp. 38–52, 2005. [9] P. H. Peckham, M. W. Keith, and K. L. Kilgore et al., “Efficacy of an implanted neuroprosthesis for restoring hand grasp in tetraplegia: A multicenter study,” Arch. Phys. Med. Rehabil., vol. 82, no. 10, pp. 1380–1388, Oct. 2001. [10] M. R. Williams and R. F. Kirsch, “Evaluation of head orientation and neck muscle EMG signals as command inputs to a human-computer interface for individuals with high tetraplegia,” IEEE Trans. Neural Syst. Rehabil. Eng., vol. 16, no. 5, pp. 485–496, Oct. 2008. [11] L. Resnik, M. R. Meucci, and S. Lieberman-Klinger et al., “Advanced upper limb prosthetic devices: Implications for upper limb prosthetic rehabilitation,” Arch. Phys. Med. Rehabil., vol. 93, no. 4, pp. 710–717, Apr. 2012. [12] D. Blana, R. F. Kirsch, and E. K. Chadwick, “Combined feedforward and feedback control of a redundant, nonlinear, dynamic musculoskeletal system,” Med. Biol. Eng. Comput., vol. 47, no. 5, pp. 533–542, May 2009.

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LAMBRECHT AND KIRSCH: MINIATURE LOW-POWER INERTIAL SENSORS: PROMISING TECHNOLOGY FOR IMPLANTABLE MOTION CAPTURE SYSTEMS

Joris M. Lambrecht received the B.S. and M.S. degree in biomedical engineering from Case Western Reserve University, Cleveland, OH, USA, in 2006 and 2007, respectively. He is currently a Research Engineer with the Department of Biomedical Engineering at Case Western Reserve University, Cleveland, OH, USA, since 2007 as part of the Cleveland FES Center. His research interests include biomechanics, command sources and user interfaces for FES systems and upper limb prostheses, and virtual reality simulators for assessment of neuroprosthetic and prosthetic systems.

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Robert F. Kirsch (M’82) received the B.S. degree in electrical engineering from the University of Cincinnati, Cincinnati, OH, USA, in 1982, and the M.S. and Ph.D. degrees in biomedical engineering from Northwestern University, Evanston, IL, USA, in 1986 and 1990, respectively. He was a postdoctoral fellow in the Department of Biomedical Engineering at McGill University, Montréal, QC, Canada, from 1990 to 1993. He is currently a Professor and Chair of the Department of Biomedical Engineering at Case Western Reserve University and Executive Director for the Cleveland VA FES Center. His research focuses on restoring movement to disabled individuals using functional electrical stimulation (FES) and controlling FES actions via natural neural commands. Computer-based models of the human upper extremity are used to develop new FES approaches. FES user interfaces, including ones based on brain recordings, are being developed to provide FES users with the ability to command movements of their own arm.