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A portable system for in-situ re-calibration of force platforms: Experimental validation
Gait & Posture 29 (2009) 449–453
Contents lists available at ScienceDirect
Gait & Posture journal homepage: www.elsevier.com/locate/gaitpost
A portable system for in-situ re-calibration of force platforms: Experimental validation Andrea Cedraro, Angelo Cappello *, Lorenzo Chiari Biomedical Engineering Group, Department of Electronics, Computer Science and Systems, University of Bologna, Bologna, Italy
A R T I C L E I N F O
A B S T R A C T
Article history: Received 28 March 2008 Received in revised form 26 September 2008 Accepted 4 November 2008
A system for the in-situ re-calibration of six-component force platforms is presented. The system consists of a device, a data-acquisition procedure and an algorithm. The device, simple and lightweight, is composed of a high-precision, 3-D load cell, loaded through a triangular stage, and precisely positioned on the force platform under re-calibration by means of a template. The data-acquisition procedure lasts about 1 h and requires up to 13 measurements consisting of manual positioning the load cell on the force platform, and then having the operator exerting loads on both load cell and force platform by his/her body movement. As a result, the procedure makes use of loads in the same range of posture and gait tests. The algorithm estimates the local or global six-by-six re-calibration matrix of the force platform through a least-squares optimization, and is presented in detail in a separate paper [Cedraro A, Cappello A, Chiari L. A portable system for in-situ re-calibration of force platforms: Theoretical validation. Gait Posture 2008;28:488–94]. The system was validated on four commercial force platforms (Amti OR6, Bertec 4060–08, Bertec 4080–10, and Kistler 9286A). The average accuracy in the measurement of the center of pressure were 2.3 1.4 mm, 2.6 1.5 mm, 11.8 4.3 mm, 14.0 2.5 mm before re-calibration, 1.1 0.6 mm, 1.8 1.1 mm, 1.0 0.6 mm, 3.2 1.1 mm after global re-calibration, and 0.7 0.4 mm, 0.8 0.5 mm, 0.5 0.3 mm, 2.0 1.2 mm after local re-calibration (results presented in random order). The force platform re-calibration influenced the value, sign, and timing of net joint moments, estimated during a gait task through an inverse dynamics approach. ß 2008 Elsevier B.V. All rights reserved.
Keywords: Force platform Re-calibration matrix Inverse dynamics Movement analysis Error propagation
1. Introduction Force platforms, FPs, are precision instruments used in human movement analysis to measure the ground reaction force, GRF, and the center of pressure, COP. From the FP data, other kinetic quantities are calculated, such as: (i) the location of the body center-of-mass [1]; (ii) energy quantities, such as work or power [2]; and (iii) net joint forces and moments, determined from kinetic and kinematic data through an inverse dynamics approach [3,4]. Due to in-situ installation procedures, usage and aging, the accuracy of the FP data may decrease [5]. This lack of accuracy may propagate to calculated kinetic quantities [6]. Some groups developed systems to assess the accuracy of the FP data, using ad hoc designed devices comprising: instrumented poles [7,8], a framework-attached pendulum [9], a passive
* Corresponding author at: Dipartimento di Elettronica, Informatica e Sistemistica, Universita` di Bologna, Viale Risorgimento, 2, I-40136 Bologna, Italy. Tel.: +39 051 2093097; fax: +39 051 2093073. E-mail address: [email protected] (A. Cappello). 0966-6362/$ – see front matter ß 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.gaitpost.2008.11.004
moveable plate [10], rectangular steel feet [11], or orthogonal rails and trolleys [12]. Morasso et al. [13] developed a system, comprising two metal masses manually set in rotation. This system minimized COP errors by a linear transformation that compensated FP anisotropy. Hall et al. [14] developed a system, comprising orthogonal rails and pulleys. This system estimated the six-by-six re-calibration matrix, C, by an algorithm based on static 2-D loads that required accurate alignment with the FP axes. Recently, Cappello et al. [15] presented an iterative, weightedleast-squares algorithm that estimated C with time-varying 2-D loads laying on planes approximately aligned with the FP axes and perpendicular to the FP itself. More recently, in the first paper of this series, Cedraro et al. [16] revised the Cappello et al. algorithm [15] with the aim of developing a simple and robust re-calibration device and an associated data-acquisition procedure. The main advantage of the revised algorithm is that it is based on time-varying 3-D loads, without any alignment restrictions. In this paper, we present the design and the experimental validation of the new system, which consists of the re-calibration
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device and the data-acquisition procedure, to efficiently implement the algorithm presented in [16]. 2. Materials and methods 2.1. Revised algorithm The first article in this series [16] provides a detailed description of the revised algorithm that we proposed for the estimation of the re-calibration matrix C. The main diagonal elements of matrix C quantify the sensitivities of the FP signals and the off-diagonal elements quantify the crosstalk between any couple of FP output signals. The algorithm estimates C using 5 or more measurement sites. Each measurement consists of data coming from the simultaneous loading of the FP and a triaxial load cell, LC, by a force in sites of known coordinates. For each measurement, the LC reference frame is re-aligned to the FP reference frame by a proper rotation matrix, estimated by minimizing the difference between the LC and FP output signals. If the sites chosen for the re-calibration cover an area smaller than the entire FP surface, the corresponding C may be defined ‘‘local’’, since the elements of C reflect the mechanical properties of the loaded FP area. If the sites chosen cover most of the FP surface, the corresponding C may be instead defined ‘‘global’’. Local and global C can be useful to quantify the FP non-linearity. 2.2. Re-calibration device The re-calibration device (Fig. 1) consists of 3 major components: a custom triaxial load cell, a triangular stage, and a template. The load cell is made of aluminum and steel (Laumas Elettronica, Italy). Technical specifications follow: full scale (FS) 500 N for shear forces and 1000 N for vertical force; hysteresis 0.06% FS; non-linearity 0.05% FS. The load cell works with 3 Wheatstone bridges, each one sensitive mainly to the force applied along the relevant axis of an orthogonal reference frame, TLN (T = transverse, L = longitudinal; N = normal). The load cell was calibrated with the assistance of a metrological center (Cermet, certificate number: 0709020FRI) using precision weights, ranging up to 600 N for vertical force and from 150 N to 150 N for shear forces. The metrological center ran single and multi-axis calibrations to characterize the non-linear behavior of the LC, assuming a quadratic calibration model: F i ¼ ATi V þ VT Bi V
simulation (Visual Nastran, MNC), in which the LC was loaded at its top with a horizontal force up to 200 N while the LC basement was blocked. The maximal COP displacement induced was less than 0.14 mm. This uncertainty on COP position was considered negligible, based on tests in which the LC bending was included in a simulated re-calibration procedure. The LC output voltages were amplified by three customized voltage-amplifiers and then A/D converted using a NI-DAQPad6020E (National Instruments) acquisition board. 2.3. Data-acquisition procedure The data-acquisition procedure is summarized as follows: (1)
Both FP and LC electrical hardware are turned on, and a warm-up time is waited according to manufacturers’ specifications. (2) The template is manually positioned on the FP surface. (3) The LC is manually placed in one of the measurement sites. The placement of the template and of the LC causes a static offset in the FP output. Both FP and LC outputs are zeroed before proceeding. (4) The stage is placed as shown in Fig. 1: the socket is placed on the LC top and the feet are placed outside the FP surface. (5) The operator stands on the stage and sways his/her body with circular movements with rapid changes in his/her rotational speed, generating a timevarying 3-D load. (6) The LC and FP output are acquired for 30 s. The LC and FP acquisition systems are not synchronized and work independently. (7) Steps 3/6 are repeated for all the chosen measurement sites. (8) After data-acquisition, the LC and FP signals are off-line synchronized, by finding the best cross-correlation between the vertical forces measured by the LC and FP. The a-posteriori time-synchronization error corresponds, at worst, to half of the sampling period. By keeping a sampling frequency 1000 Hz, such error is negligible (as proven by a simulation test). (9) After synchronization, C can be estimated by the algorithm described in [16]. (10) The FP output vector L is then calibrated by: LC ¼ CL
(2)
(1)
where Fi = FT, FL, FN and V = [VT VL VN]T is the LC output voltage. Vectors Ai (3 1) and matrices Bi (3 3) were estimated by a least-squares method from LC outputs and the applied loads. The load cell has a circular base of support (Ø = 100 mm) to reduce inaccuracies caused by FP deformation, due to a point source loading [11,17,18]. A steel cone is screwed on the LC top. The triangular stage is equilateral with a 600 mm side and a 16 mm thickness. It consists of an aluminum plate with a honeycomb internal structure and results lightweight (2 kg), easy to move, but suitably rigid to support the operator’s weight. In this way, the FP is loaded in or near its usual working range. Two feet, made of commercial-grade steel and brass, are screwed on two corners of the stage. The feet terminate with ball bearings, to concentrate shear force transmission to the LC. In the third corner of the stage there is a steel, conical socket that easily joins with the LC top. The vertex of the LC top is the only point of contact with the socket; hence, the vertex is the point of force transfer to the FP (COP). The torque applied to the LC can be considered negligible, since it was minimized by the mechanical uncoupling between the stage and the LC. The template is a 400 mm 600 mm sheet of plastic, placed on the FP during the data-acquisition procedure, and used to locate easily and precisely the LC on the FP. The template has 13 holes (Ø = 100 mm) centered at the measurement sites and distributed on the whole surface. The minimum number and minimum reciprocal distance of the measurement sites to be used for re-calibration were determined via a simulation approach in the first paper [16]. The load cell bends when loaded, causing a variation in the COP coordinates. We determined the maximal LC flexion that we may expect by using a finite element
2.4. Experimental tests and outcome measures The new system was tested on 4 commercial FPs, three of which were straingauge FPs: AMTI OR6, size 464 mm 508 mm (Advanced Medical Technology Inc., Watertown, MA, USA), Bertec 4060–08, size 400 mm 600 mm, and 4080–10, size 400 mm 800 mm (Bertec Corporation, Columbus, OH, USA); one FP was piezoelectric: Kistler 9286A, size 400 mm 600 mm (Kistler Instrumente AG, Winterthur, CH). These FPs were routinely used in clinical and research laboratories for gait and balance analysis and the FPs signals were calibrated by the manufacturers’ calibration matrix. The FPs age was 5 3 years. Due to the different factor-form and size of the FPs, we chose partially different placement and number of the measurement sites, as reported in the following. We kept the reciprocal distance between each couple of sites greater than the minimum distance of 100 mm identified in [16]. AMTI OR6 X COP ¼ ð0; 70; 70; 70; 70; 0; 0; 140; 140; 194; 194; 194; 194Þ mm Y COP ¼ ð0; 120; 120; 120; 120; 182; 182; 0; 0; 182; 182; 182; 182Þ mm (3) Bertec 4060 08 Kistler 9286A X COP ¼ ð0; 70; 70; 70; 70; 0; 0; 140; 140; 140; 140; 140; 140Þmm Y COP ¼ ð0; 120; 120; 120; 120; 240; 240; 0; 0; 240; 240; 240; 240Þmm (4) Bertec 4080 fBertec 4060 08 COPsg þ
Fig. 1. View of the re-calibration device.
X COP ¼ ð70; 70; 70; 70Þ mm Y COP ¼ ð340; 340; 340; 340Þ mm
(5)
For all the measurements, ZCOP = 124 mm, that corresponds to the height of the LC. In the following, the FP manufacturers are omitted, since no comparison between the manufacturers was intended, also due to different age, usage and installation of the FPs, that prevent any possibility to draw general conclusions from this limited sample. Each FP will be addressed by a unique identifier such as FP#1, #2, #3, and #4. The forces used in re-calibrating all the FPs ranged from 80 N to 80 N for the horizontal components and from 200 N to 600 N for the vertical component. The above described range was defined in a separate test, where a calibration procedure was performed on FP#2 with forces ranging 200 N (horizontal) and 400/ 1000 N (vertical). Then, global re-calibration matrices were estimated using only the
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acquired samples in which the forces were below two varying threshold limits, one for the horizontal and one for the vertical force. The matrix estimation stabilized using the following values: 80 N for the horizontal and 550 N for the vertical force. Hence, using 80 N and 600 N as maximum values the estimation was considered as satisfactory. For all the FPs, the algorithm estimated 5 local C using different subsets of 5 sites each: one subset relative to the FP center, and four relative to the FP quadrants. For all the FPs, the algorithm estimated one global C, using all the available measurement sites. Finally, we calculated difference matrices, DC, as the difference between the estimated C (local or global) and the six-by-six identity matrix, I, which was assumed to be the template of a perfectly calibrated FP (LC = L ) C = I). We considered the percentage difference DC% as an index of FP functionality and the standard deviation of the values of DC%, computed for the global and the 5 local C matrices, as an index of FPs non-linearity. The effectiveness of the new system was verified by measuring the COP accuracy, before and after re-calibration, when loading the FP in different, known COPs. For each local re-calibration, the COPs were distributed only in the FP area used for the recalibration procedure. The mean value of the COPs, before and after re-calibration, was subtracted from the actual COPs. The distance between the measured and actual COPs was considered as residual error in the COP measurement. To assess how the re-calibration process propagated to the estimates of kinetic quantities, such as joint net moments, we performed a gait analysis test on a young healthy subject (age: 28, body weight: 76 kg, height: 1.86 m) who gave his informed consent. A set of 12 reflective markers was used to measure the subject’s kinematics, according to the Davis protocol [19], using a Vicon 460 system and FP#4 measured his GRF. The net joint moments were estimated, using a bottom-up inverse dynamics approach [3] with adapted, inertial parameters [20,21]. The subject was modeled as a multilink with 3 joints (ankle–knee–hip). The centers of the ankle and knee joints were located at the midpoint between the lateral and medial malleoli and epicondyles, respectively. The center of the hip joint was calculated from the ASIS and PSIS makers, as described in [22]. The marker trajectories were acquired with a frequency of 100 Hz and filtered through a Woltring filter with MSE = 10. We calculated the joint moments using the FP data before and after re-calibration. The FP data were re-calibrated using the local C relative to the portion of the FP loaded during the gait trial. The differences between the joint moments, before and after re-calibration, were considered as an estimate of the propagation error due to the FP miscalibration.
deviation of the elements of DC% obtained from the global and the 5 local matrices. FP#1 and #2 reported an average value for the global DC% <1%, while FP#3 and #4 reported an average value for the global DC% > 1%. FP#1 and #3 reported an average value of the standard deviation DC% < 1% while FP #2 and #4 reported an average value of the standard deviation DC% > 1%. Table 2 shows the residual error in the COP measurement before re-calibration and after global and local re-calibration. Before re-calibration, the average value of COP-measurement error for FP#1 and #2 was <10 mm, while for FP#3 and #4, the error was >10 mm. After re-calibration, the COP-measurement error was always smaller after a local re-calibration than after a global recalibration. For all the FPs, the COP-measurement error was not homogeneous on the FP surface, thus revealing non-linearity in the FP functioning. The FP non-linearity is evident in Fig. 2 where representative results from FP#3 are shown: the error was greater near the FP corners than in its center. Fig. 2 also compares the COPmeasurement error for the local and global re-calibration processes. This result is consistent with Table 2 since the COPmeasurement error was smaller after a local re-calibration than after a global re-calibration. The propagation of the FP re-calibration results on the net joint moments is shown in Fig. 3. The difference between the curves, before and after re-calibration, was comparable to the intrasubject variability typically observed in a movement analysis
COP accuracy [mm]
FP #1
FP #2
FP #3
FP #4
3. Results
Before
2.3 1.4
2.6 1.5
11.8 4.3
14.0 2.5
After global After local(s)
1.1 0.6 0.7 0.4
1.8 1.1 0.8 0.5
1.0 0.6 0.5 0.3
3.2 1.1 2.0 1.2
For each one of the FPs under test, Table 1 shows the percentage difference, DC%, computed for the global matrix, and the standard
Table 2 Error in the COP measurement. Results are shown for the tested force platforms, before and after re-calibration, for both global and local re-calibration. The errors (mean std) are expressed in mm.
Table 1 Percentage difference between the estimated re-calibration matrix and the identity matrix, for the tested force platforms. The numbers in bold refer to the global recalibration matrix; those in brackets refer to the standard deviation resulting from the local and global re-calibration matrices. The shaded numbers reflect the change in the FP sensitivity elements, while the off-diagonal numbers reflect the change in the crosstalk elements.
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The FP re-calibration results propagated to the estimation of net joint moments, in particular they changed sign and the transition time between flexion and extension. This influence could be critical since the estimated joint moments are often the basis for clinical decision, e.g. when planning a treatment or a surgical procedure in orthopedics. The range of the forces used during all the data-acquisition procedures was comparable to the typical range for posture and normal-speed gait studies [23]. Therefore, a re-calibration performed by the new system is maximally effective for these types of test. All the data-acquisition procedures lasted less than 1 h, hence, the disturbances in the work routine of a laboratory was minimized. Based on our experience, we would suggest performing a recalibration procedure every six months for FPs used in balance tests, and more often for FPs used in gait tests or when the FP is intensely loaded, as in sports or in dynamic posturography tests.
Fig. 2. Error in the COP measurement (in mm), before re-calibration (A) and after recalibration (B) for force platform #3. The black lines represent isolevel lines of COP error in the case of global re-calibration. The shaded area (panel B) reflects the results of one of the five local re-calibration processes.
setting [23]. Further, the sign of the knee moment, as well as the transition time of hip moment from flexion to extension, changed during the stance phase. 4. Discussion In this paper we presented a new system for the in-situ recalibration of a six-component FP. The effectiveness of the new system was verified and quantified by testing it on 4 commercial FPs. The index DC% quantified the changes in the sensitivity and crosstalk elements of the FPs functioning: all these changes were below the thresholds defined in the FP user manuals, with the only exception of the first force component of FP#4. These changes may be due to aging, usage and in-situ installation of the FPs, and caused a lack of accuracy in the FPs data. For all the tested FPs, the recalibration matrix C estimated by the new system (Table 1) compensated this lack of accuracy, and resulted in a smaller COPmeasurement error (Table 2). Local re-calibration increased the FP accuracy more than global re-calibration, this outcome was more effective for FP#2 and #4. Given the complexity of the re-calibration matrix, an essentially arbitrary threshold of 1% is proposed to discriminate between small or large lack of accuracy or non-linearity. This threshold is substantiated by the results, in facts, regarding the lack of accuracy, we could associate a value <1% (>1%), as reported in Table 1, to an error in the COP measurement <10 mm (>10 mm), as shown in Table 2 Regarding the non-linearity, a value <1% (>1%) reflected in a difference between local and global re-calibrations <10 mm (>10 mm) for estimated COP coordinates. Depending on the degree of the FP non-linearity and on its usage, a local re-calibration may hence be preferable to a global one. A local re-calibration may better compensate the FP non-linearity since it is relative to a smaller area on the FP surface.
Fig. 3. Influence of the re-calibration of FP#4 on the net joint moments estimated by an inverse dynamics approach. Net joint moments estimated before re-calibration (thin, black line) and after re-calibration (thick, grey line). This FP showed the largest lack-of-calibration, with the antero-posterior force component exceeding manufacturer’s specifications before re-calibration.
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The over-time stability of a FP can be controlled by performing two re-calibration procedures with a reasonable time spacing: a FP could be considered stable when the estimated C differ by less than 1%; larger differences may indicate that significant changes have occurred in the mechanics or electronics of the FP. 5. Conclusions The post-calibration residual error in the COP measurement obtained with the aid of the new system presented in this paper was comparable to the FP sensitivity threshold, as described in the FPs datasheet. We conclude that the new system optimized the FPs functioning. The new system was designed for non-technical persons to evaluate the accuracy of the FP in the working environment where routinely used. The new system does not require any hardware interface with the FP acquisition system. Further, the system is composed by few elements resulting lightweight (about 5 kg) and portable; and the re-calibration procedure consists of few, simple steps. Finally, the new system uses a range of input loads that are commonly used in balance and gait experiments. Conflict of interest statement We have disclosed all financial support for our work and other potential conflicts of interest. No work resembling the enclosed article has been published or is being submitted for publication elsewhere. We certify that each of us has made a substantial contribution to qualify for authorship and agreed with the typescript. Each author was involved in the design of the study, interpretation of the data, writing of the manuscript, and has read and concurs with the content in the manuscript. Acknowledgements This study was supported by the project Strategic neTwork for Assistive and Rehabilitation Technologies in Emilia/Romagna (StartER). The authors are grateful to Dr. Giovanni Ferraresi for evaluating our results from a clinical perspective, Dr. Sandra Oster for editing the text, Dr. Marco Chiossi for assisting the authors with the finite element simulation, and Drs. Maurizio Lannocca and Andrea Sabbioni for helping in the hardware construction.
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References [1] Lenzi D, Cappello A, Chiari L. Influence of body segment parameters and modelling assumptions on the estimate of center of mass trajectory. J Biomech 2003;36:1335–41. [2] Meichtry A, Romkes J, Gobelet C, Brunner R, Mueller R. Criterion validity of 3D trunk accelerations to assess external work and power in able-bodied gait. Gait Posture 2007;25:25–32. [3] Cappozzo A. Gait analysis methodology. Hum Mov Sci 1984;2:27–50. [4] Winter DA. Biomechanics and motor control of human gait. University of Waterloo Press; 1991. [5] Chockalingam N, Giakas G, Iossifidou A. Do strain gauge force platforms need in situ correction? Gait Posture 2002;16:233–7. [6] Mc Caw ST, De Vita P. Errors in alignment of center of pressure and foot coordinates affect predicted lower extremity torques. J Biomech 1995;28: 985–8. [7] Holden JP, Selbie WS, Stanhope SJ. A proposed test to support the clinical movement analysis laboratory accreditation process. Gait Posture 2003;17(3): 205–13. [8] Lewis A, Stewart C, Postans N, Trevelyan J. Development of an instrumented pole test for use as a gait laboratory quality check. Gait Posture 2007;26(2): 317–22. [9] Fairburn PS, Palmer R, Whybrow J, Fielden S, Jones S. A prototype system for testing force platform dynamic performances. Gait Posture 2000;12:25–33. [10] Browne J, O’Hare N. A quality control procedure for force platform. Physiol Meas 2000;21(11):515–24. [11] Middleton J, Sinclair P, Patton R. Accuracy of centre of pressure measurement using a piezoelectric force platform. Clin Biomech 1999;14(5):357–60. [12] Gill HS, O’Connor JJ. A new testing rig for force platform calibration and accuracy tests. Gait Posture 1997;5:228–32. [13] Morasso PG, Re C, Casadio M. Spotcheck and recalibration of stabilometric platforms 2004;12:293–304. [14] Hall MG, Fleming HE, Dolan MJ, Millbank SF, Paul JP. Static in situ calibration of force plates. J Biomech 1996;29(5):659–65. [15] Cappello A, Lenzi D, Chiari L. Periodical in-situ re-calibration of force platforms: a new method for the robust estimation of the calibration matrix. Med Biol Eng Comput 2004;42:350–5. [16] Cedraro A, Cappello A, Chiari L. A portable system for in-situ re-calibration of force platforms: theoretical validation. Gait Posture 2008;28:488–94. [17] Bobbert MF, Schamhardt HC. Accuracy of determining the point of force application with piezoelectric force plates. J Biomech 1990;23:701–5. [18] Schmiedmayer HB, Kastner J. Enhancements in the accuracy of the center of pressure (COP) determined with piezoelectric force plates are dependent on the load distribution. J Biomech Eng 2000;122:523–7. [19] Davis RB, Ounpuu S, Tyburski D, Gage JR. A gait data collection and reduction technique. Hum Mov Sci 1991;10:575–87. [20] de Leva P. Adjustments to Zatsiorsky-Seluyanov’s segment inertia parameters. J Biomech 1996;29:1223–30. [21] Zatsiorsky V, Seluyanov V, Chugunova L. In vivo body segment inertial parameters determination using gamma scanner method. In: Berme N, Cappozzo A, editors. Biomechanics of human movement, applications in rehabilitation. Sports and Ergonomics; 1990. [22] Shea KM, Lenhoff MW, Otis JC, Backus SI. Validation of a method for location of the hip joint centre. Gait Posture 1997;5:157–8. [23] Benedetti MG, Catani F, Leardini A, Pignotti ESG. Data management in gait analysis for clinical applications. Clin Biomech 1998;13(3):204–15.
Contents lists available at ScienceDirect
Gait & Posture journal homepage: www.elsevier.com/locate/gaitpost
A portable system for in-situ re-calibration of force platforms: Experimental validation Andrea Cedraro, Angelo Cappello *, Lorenzo Chiari Biomedical Engineering Group, Department of Electronics, Computer Science and Systems, University of Bologna, Bologna, Italy
A R T I C L E I N F O
A B S T R A C T
Article history: Received 28 March 2008 Received in revised form 26 September 2008 Accepted 4 November 2008
A system for the in-situ re-calibration of six-component force platforms is presented. The system consists of a device, a data-acquisition procedure and an algorithm. The device, simple and lightweight, is composed of a high-precision, 3-D load cell, loaded through a triangular stage, and precisely positioned on the force platform under re-calibration by means of a template. The data-acquisition procedure lasts about 1 h and requires up to 13 measurements consisting of manual positioning the load cell on the force platform, and then having the operator exerting loads on both load cell and force platform by his/her body movement. As a result, the procedure makes use of loads in the same range of posture and gait tests. The algorithm estimates the local or global six-by-six re-calibration matrix of the force platform through a least-squares optimization, and is presented in detail in a separate paper [Cedraro A, Cappello A, Chiari L. A portable system for in-situ re-calibration of force platforms: Theoretical validation. Gait Posture 2008;28:488–94]. The system was validated on four commercial force platforms (Amti OR6, Bertec 4060–08, Bertec 4080–10, and Kistler 9286A). The average accuracy in the measurement of the center of pressure were 2.3 1.4 mm, 2.6 1.5 mm, 11.8 4.3 mm, 14.0 2.5 mm before re-calibration, 1.1 0.6 mm, 1.8 1.1 mm, 1.0 0.6 mm, 3.2 1.1 mm after global re-calibration, and 0.7 0.4 mm, 0.8 0.5 mm, 0.5 0.3 mm, 2.0 1.2 mm after local re-calibration (results presented in random order). The force platform re-calibration influenced the value, sign, and timing of net joint moments, estimated during a gait task through an inverse dynamics approach. ß 2008 Elsevier B.V. All rights reserved.
Keywords: Force platform Re-calibration matrix Inverse dynamics Movement analysis Error propagation
1. Introduction Force platforms, FPs, are precision instruments used in human movement analysis to measure the ground reaction force, GRF, and the center of pressure, COP. From the FP data, other kinetic quantities are calculated, such as: (i) the location of the body center-of-mass [1]; (ii) energy quantities, such as work or power [2]; and (iii) net joint forces and moments, determined from kinetic and kinematic data through an inverse dynamics approach [3,4]. Due to in-situ installation procedures, usage and aging, the accuracy of the FP data may decrease [5]. This lack of accuracy may propagate to calculated kinetic quantities [6]. Some groups developed systems to assess the accuracy of the FP data, using ad hoc designed devices comprising: instrumented poles [7,8], a framework-attached pendulum [9], a passive
* Corresponding author at: Dipartimento di Elettronica, Informatica e Sistemistica, Universita` di Bologna, Viale Risorgimento, 2, I-40136 Bologna, Italy. Tel.: +39 051 2093097; fax: +39 051 2093073. E-mail address: [email protected] (A. Cappello). 0966-6362/$ – see front matter ß 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.gaitpost.2008.11.004
moveable plate [10], rectangular steel feet [11], or orthogonal rails and trolleys [12]. Morasso et al. [13] developed a system, comprising two metal masses manually set in rotation. This system minimized COP errors by a linear transformation that compensated FP anisotropy. Hall et al. [14] developed a system, comprising orthogonal rails and pulleys. This system estimated the six-by-six re-calibration matrix, C, by an algorithm based on static 2-D loads that required accurate alignment with the FP axes. Recently, Cappello et al. [15] presented an iterative, weightedleast-squares algorithm that estimated C with time-varying 2-D loads laying on planes approximately aligned with the FP axes and perpendicular to the FP itself. More recently, in the first paper of this series, Cedraro et al. [16] revised the Cappello et al. algorithm [15] with the aim of developing a simple and robust re-calibration device and an associated data-acquisition procedure. The main advantage of the revised algorithm is that it is based on time-varying 3-D loads, without any alignment restrictions. In this paper, we present the design and the experimental validation of the new system, which consists of the re-calibration
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device and the data-acquisition procedure, to efficiently implement the algorithm presented in [16]. 2. Materials and methods 2.1. Revised algorithm The first article in this series [16] provides a detailed description of the revised algorithm that we proposed for the estimation of the re-calibration matrix C. The main diagonal elements of matrix C quantify the sensitivities of the FP signals and the off-diagonal elements quantify the crosstalk between any couple of FP output signals. The algorithm estimates C using 5 or more measurement sites. Each measurement consists of data coming from the simultaneous loading of the FP and a triaxial load cell, LC, by a force in sites of known coordinates. For each measurement, the LC reference frame is re-aligned to the FP reference frame by a proper rotation matrix, estimated by minimizing the difference between the LC and FP output signals. If the sites chosen for the re-calibration cover an area smaller than the entire FP surface, the corresponding C may be defined ‘‘local’’, since the elements of C reflect the mechanical properties of the loaded FP area. If the sites chosen cover most of the FP surface, the corresponding C may be instead defined ‘‘global’’. Local and global C can be useful to quantify the FP non-linearity. 2.2. Re-calibration device The re-calibration device (Fig. 1) consists of 3 major components: a custom triaxial load cell, a triangular stage, and a template. The load cell is made of aluminum and steel (Laumas Elettronica, Italy). Technical specifications follow: full scale (FS) 500 N for shear forces and 1000 N for vertical force; hysteresis 0.06% FS; non-linearity 0.05% FS. The load cell works with 3 Wheatstone bridges, each one sensitive mainly to the force applied along the relevant axis of an orthogonal reference frame, TLN (T = transverse, L = longitudinal; N = normal). The load cell was calibrated with the assistance of a metrological center (Cermet, certificate number: 0709020FRI) using precision weights, ranging up to 600 N for vertical force and from 150 N to 150 N for shear forces. The metrological center ran single and multi-axis calibrations to characterize the non-linear behavior of the LC, assuming a quadratic calibration model: F i ¼ ATi V þ VT Bi V
simulation (Visual Nastran, MNC), in which the LC was loaded at its top with a horizontal force up to 200 N while the LC basement was blocked. The maximal COP displacement induced was less than 0.14 mm. This uncertainty on COP position was considered negligible, based on tests in which the LC bending was included in a simulated re-calibration procedure. The LC output voltages were amplified by three customized voltage-amplifiers and then A/D converted using a NI-DAQPad6020E (National Instruments) acquisition board. 2.3. Data-acquisition procedure The data-acquisition procedure is summarized as follows: (1)
Both FP and LC electrical hardware are turned on, and a warm-up time is waited according to manufacturers’ specifications. (2) The template is manually positioned on the FP surface. (3) The LC is manually placed in one of the measurement sites. The placement of the template and of the LC causes a static offset in the FP output. Both FP and LC outputs are zeroed before proceeding. (4) The stage is placed as shown in Fig. 1: the socket is placed on the LC top and the feet are placed outside the FP surface. (5) The operator stands on the stage and sways his/her body with circular movements with rapid changes in his/her rotational speed, generating a timevarying 3-D load. (6) The LC and FP output are acquired for 30 s. The LC and FP acquisition systems are not synchronized and work independently. (7) Steps 3/6 are repeated for all the chosen measurement sites. (8) After data-acquisition, the LC and FP signals are off-line synchronized, by finding the best cross-correlation between the vertical forces measured by the LC and FP. The a-posteriori time-synchronization error corresponds, at worst, to half of the sampling period. By keeping a sampling frequency 1000 Hz, such error is negligible (as proven by a simulation test). (9) After synchronization, C can be estimated by the algorithm described in [16]. (10) The FP output vector L is then calibrated by: LC ¼ CL
(2)
(1)
where Fi = FT, FL, FN and V = [VT VL VN]T is the LC output voltage. Vectors Ai (3 1) and matrices Bi (3 3) were estimated by a least-squares method from LC outputs and the applied loads. The load cell has a circular base of support (Ø = 100 mm) to reduce inaccuracies caused by FP deformation, due to a point source loading [11,17,18]. A steel cone is screwed on the LC top. The triangular stage is equilateral with a 600 mm side and a 16 mm thickness. It consists of an aluminum plate with a honeycomb internal structure and results lightweight (2 kg), easy to move, but suitably rigid to support the operator’s weight. In this way, the FP is loaded in or near its usual working range. Two feet, made of commercial-grade steel and brass, are screwed on two corners of the stage. The feet terminate with ball bearings, to concentrate shear force transmission to the LC. In the third corner of the stage there is a steel, conical socket that easily joins with the LC top. The vertex of the LC top is the only point of contact with the socket; hence, the vertex is the point of force transfer to the FP (COP). The torque applied to the LC can be considered negligible, since it was minimized by the mechanical uncoupling between the stage and the LC. The template is a 400 mm 600 mm sheet of plastic, placed on the FP during the data-acquisition procedure, and used to locate easily and precisely the LC on the FP. The template has 13 holes (Ø = 100 mm) centered at the measurement sites and distributed on the whole surface. The minimum number and minimum reciprocal distance of the measurement sites to be used for re-calibration were determined via a simulation approach in the first paper [16]. The load cell bends when loaded, causing a variation in the COP coordinates. We determined the maximal LC flexion that we may expect by using a finite element
2.4. Experimental tests and outcome measures The new system was tested on 4 commercial FPs, three of which were straingauge FPs: AMTI OR6, size 464 mm 508 mm (Advanced Medical Technology Inc., Watertown, MA, USA), Bertec 4060–08, size 400 mm 600 mm, and 4080–10, size 400 mm 800 mm (Bertec Corporation, Columbus, OH, USA); one FP was piezoelectric: Kistler 9286A, size 400 mm 600 mm (Kistler Instrumente AG, Winterthur, CH). These FPs were routinely used in clinical and research laboratories for gait and balance analysis and the FPs signals were calibrated by the manufacturers’ calibration matrix. The FPs age was 5 3 years. Due to the different factor-form and size of the FPs, we chose partially different placement and number of the measurement sites, as reported in the following. We kept the reciprocal distance between each couple of sites greater than the minimum distance of 100 mm identified in [16]. AMTI OR6 X COP ¼ ð0; 70; 70; 70; 70; 0; 0; 140; 140; 194; 194; 194; 194Þ mm Y COP ¼ ð0; 120; 120; 120; 120; 182; 182; 0; 0; 182; 182; 182; 182Þ mm (3) Bertec 4060 08 Kistler 9286A X COP ¼ ð0; 70; 70; 70; 70; 0; 0; 140; 140; 140; 140; 140; 140Þmm Y COP ¼ ð0; 120; 120; 120; 120; 240; 240; 0; 0; 240; 240; 240; 240Þmm (4) Bertec 4080 fBertec 4060 08 COPsg þ
Fig. 1. View of the re-calibration device.
X COP ¼ ð70; 70; 70; 70Þ mm Y COP ¼ ð340; 340; 340; 340Þ mm
(5)
For all the measurements, ZCOP = 124 mm, that corresponds to the height of the LC. In the following, the FP manufacturers are omitted, since no comparison between the manufacturers was intended, also due to different age, usage and installation of the FPs, that prevent any possibility to draw general conclusions from this limited sample. Each FP will be addressed by a unique identifier such as FP#1, #2, #3, and #4. The forces used in re-calibrating all the FPs ranged from 80 N to 80 N for the horizontal components and from 200 N to 600 N for the vertical component. The above described range was defined in a separate test, where a calibration procedure was performed on FP#2 with forces ranging 200 N (horizontal) and 400/ 1000 N (vertical). Then, global re-calibration matrices were estimated using only the
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acquired samples in which the forces were below two varying threshold limits, one for the horizontal and one for the vertical force. The matrix estimation stabilized using the following values: 80 N for the horizontal and 550 N for the vertical force. Hence, using 80 N and 600 N as maximum values the estimation was considered as satisfactory. For all the FPs, the algorithm estimated 5 local C using different subsets of 5 sites each: one subset relative to the FP center, and four relative to the FP quadrants. For all the FPs, the algorithm estimated one global C, using all the available measurement sites. Finally, we calculated difference matrices, DC, as the difference between the estimated C (local or global) and the six-by-six identity matrix, I, which was assumed to be the template of a perfectly calibrated FP (LC = L ) C = I). We considered the percentage difference DC% as an index of FP functionality and the standard deviation of the values of DC%, computed for the global and the 5 local C matrices, as an index of FPs non-linearity. The effectiveness of the new system was verified by measuring the COP accuracy, before and after re-calibration, when loading the FP in different, known COPs. For each local re-calibration, the COPs were distributed only in the FP area used for the recalibration procedure. The mean value of the COPs, before and after re-calibration, was subtracted from the actual COPs. The distance between the measured and actual COPs was considered as residual error in the COP measurement. To assess how the re-calibration process propagated to the estimates of kinetic quantities, such as joint net moments, we performed a gait analysis test on a young healthy subject (age: 28, body weight: 76 kg, height: 1.86 m) who gave his informed consent. A set of 12 reflective markers was used to measure the subject’s kinematics, according to the Davis protocol [19], using a Vicon 460 system and FP#4 measured his GRF. The net joint moments were estimated, using a bottom-up inverse dynamics approach [3] with adapted, inertial parameters [20,21]. The subject was modeled as a multilink with 3 joints (ankle–knee–hip). The centers of the ankle and knee joints were located at the midpoint between the lateral and medial malleoli and epicondyles, respectively. The center of the hip joint was calculated from the ASIS and PSIS makers, as described in [22]. The marker trajectories were acquired with a frequency of 100 Hz and filtered through a Woltring filter with MSE = 10. We calculated the joint moments using the FP data before and after re-calibration. The FP data were re-calibrated using the local C relative to the portion of the FP loaded during the gait trial. The differences between the joint moments, before and after re-calibration, were considered as an estimate of the propagation error due to the FP miscalibration.
deviation of the elements of DC% obtained from the global and the 5 local matrices. FP#1 and #2 reported an average value for the global DC% <1%, while FP#3 and #4 reported an average value for the global DC% > 1%. FP#1 and #3 reported an average value of the standard deviation DC% < 1% while FP #2 and #4 reported an average value of the standard deviation DC% > 1%. Table 2 shows the residual error in the COP measurement before re-calibration and after global and local re-calibration. Before re-calibration, the average value of COP-measurement error for FP#1 and #2 was <10 mm, while for FP#3 and #4, the error was >10 mm. After re-calibration, the COP-measurement error was always smaller after a local re-calibration than after a global recalibration. For all the FPs, the COP-measurement error was not homogeneous on the FP surface, thus revealing non-linearity in the FP functioning. The FP non-linearity is evident in Fig. 2 where representative results from FP#3 are shown: the error was greater near the FP corners than in its center. Fig. 2 also compares the COPmeasurement error for the local and global re-calibration processes. This result is consistent with Table 2 since the COPmeasurement error was smaller after a local re-calibration than after a global re-calibration. The propagation of the FP re-calibration results on the net joint moments is shown in Fig. 3. The difference between the curves, before and after re-calibration, was comparable to the intrasubject variability typically observed in a movement analysis
COP accuracy [mm]
FP #1
FP #2
FP #3
FP #4
3. Results
Before
2.3 1.4
2.6 1.5
11.8 4.3
14.0 2.5
After global After local(s)
1.1 0.6 0.7 0.4
1.8 1.1 0.8 0.5
1.0 0.6 0.5 0.3
3.2 1.1 2.0 1.2
For each one of the FPs under test, Table 1 shows the percentage difference, DC%, computed for the global matrix, and the standard
Table 2 Error in the COP measurement. Results are shown for the tested force platforms, before and after re-calibration, for both global and local re-calibration. The errors (mean std) are expressed in mm.
Table 1 Percentage difference between the estimated re-calibration matrix and the identity matrix, for the tested force platforms. The numbers in bold refer to the global recalibration matrix; those in brackets refer to the standard deviation resulting from the local and global re-calibration matrices. The shaded numbers reflect the change in the FP sensitivity elements, while the off-diagonal numbers reflect the change in the crosstalk elements.
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The FP re-calibration results propagated to the estimation of net joint moments, in particular they changed sign and the transition time between flexion and extension. This influence could be critical since the estimated joint moments are often the basis for clinical decision, e.g. when planning a treatment or a surgical procedure in orthopedics. The range of the forces used during all the data-acquisition procedures was comparable to the typical range for posture and normal-speed gait studies [23]. Therefore, a re-calibration performed by the new system is maximally effective for these types of test. All the data-acquisition procedures lasted less than 1 h, hence, the disturbances in the work routine of a laboratory was minimized. Based on our experience, we would suggest performing a recalibration procedure every six months for FPs used in balance tests, and more often for FPs used in gait tests or when the FP is intensely loaded, as in sports or in dynamic posturography tests.
Fig. 2. Error in the COP measurement (in mm), before re-calibration (A) and after recalibration (B) for force platform #3. The black lines represent isolevel lines of COP error in the case of global re-calibration. The shaded area (panel B) reflects the results of one of the five local re-calibration processes.
setting [23]. Further, the sign of the knee moment, as well as the transition time of hip moment from flexion to extension, changed during the stance phase. 4. Discussion In this paper we presented a new system for the in-situ recalibration of a six-component FP. The effectiveness of the new system was verified and quantified by testing it on 4 commercial FPs. The index DC% quantified the changes in the sensitivity and crosstalk elements of the FPs functioning: all these changes were below the thresholds defined in the FP user manuals, with the only exception of the first force component of FP#4. These changes may be due to aging, usage and in-situ installation of the FPs, and caused a lack of accuracy in the FPs data. For all the tested FPs, the recalibration matrix C estimated by the new system (Table 1) compensated this lack of accuracy, and resulted in a smaller COPmeasurement error (Table 2). Local re-calibration increased the FP accuracy more than global re-calibration, this outcome was more effective for FP#2 and #4. Given the complexity of the re-calibration matrix, an essentially arbitrary threshold of 1% is proposed to discriminate between small or large lack of accuracy or non-linearity. This threshold is substantiated by the results, in facts, regarding the lack of accuracy, we could associate a value <1% (>1%), as reported in Table 1, to an error in the COP measurement <10 mm (>10 mm), as shown in Table 2 Regarding the non-linearity, a value <1% (>1%) reflected in a difference between local and global re-calibrations <10 mm (>10 mm) for estimated COP coordinates. Depending on the degree of the FP non-linearity and on its usage, a local re-calibration may hence be preferable to a global one. A local re-calibration may better compensate the FP non-linearity since it is relative to a smaller area on the FP surface.
Fig. 3. Influence of the re-calibration of FP#4 on the net joint moments estimated by an inverse dynamics approach. Net joint moments estimated before re-calibration (thin, black line) and after re-calibration (thick, grey line). This FP showed the largest lack-of-calibration, with the antero-posterior force component exceeding manufacturer’s specifications before re-calibration.
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The over-time stability of a FP can be controlled by performing two re-calibration procedures with a reasonable time spacing: a FP could be considered stable when the estimated C differ by less than 1%; larger differences may indicate that significant changes have occurred in the mechanics or electronics of the FP. 5. Conclusions The post-calibration residual error in the COP measurement obtained with the aid of the new system presented in this paper was comparable to the FP sensitivity threshold, as described in the FPs datasheet. We conclude that the new system optimized the FPs functioning. The new system was designed for non-technical persons to evaluate the accuracy of the FP in the working environment where routinely used. The new system does not require any hardware interface with the FP acquisition system. Further, the system is composed by few elements resulting lightweight (about 5 kg) and portable; and the re-calibration procedure consists of few, simple steps. Finally, the new system uses a range of input loads that are commonly used in balance and gait experiments. Conflict of interest statement We have disclosed all financial support for our work and other potential conflicts of interest. No work resembling the enclosed article has been published or is being submitted for publication elsewhere. We certify that each of us has made a substantial contribution to qualify for authorship and agreed with the typescript. Each author was involved in the design of the study, interpretation of the data, writing of the manuscript, and has read and concurs with the content in the manuscript. Acknowledgements This study was supported by the project Strategic neTwork for Assistive and Rehabilitation Technologies in Emilia/Romagna (StartER). The authors are grateful to Dr. Giovanni Ferraresi for evaluating our results from a clinical perspective, Dr. Sandra Oster for editing the text, Dr. Marco Chiossi for assisting the authors with the finite element simulation, and Drs. Maurizio Lannocca and Andrea Sabbioni for helping in the hardware construction.
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