Research Papers

Joint Angle Measurement Using Strategically Placed Accelerometers and Gyroscope

[+] Author and Article Information
Vishesh Vikas

Center of Intelligent Machines
and Robotics (CIMAR),
Department of Mechanical and
Aerospace Engineering,
University of Florida,
Gainesville, FL 32611
e-mail: vishesh.vikas@gmail.com

Carl D. Crane, III

Center of Intelligent Machines
and Robotics (CIMAR),
Department of Mechanical and
Aerospace Engineering,
University of Florida,
Gainesville, FL 32611
e-mail: carl.crane@gmail.com

1Current affiliation: Postdoctoral Researcher, Neuromechanics and Biomimetic Devices Laboratory, Tufts University, Meford MA 02155.

Manuscript received November 26, 2014; final manuscript received July 25, 2015; published online November 24, 2015. Assoc. Editor: Jaydev P. Desai.

J. Mechanisms Robotics 8(2), 021003 (Nov 24, 2015) (7 pages) Paper No: JMR-14-1328; doi: 10.1115/1.4031299 History: Received November 26, 2014; Revised July 25, 2015; Accepted July 26, 2015

Optical and magnetic encoders are widely used to measure joint angles. These sensors are required to be installed at the axes of rotation (joint centers). However, microelectromechanical system (MEMS) accelerometer and gyroscope-based joint angle measurement sensors possess the advantage of being flexible with regard to the point of installation. Inertial measurement units (IMUs) are capable of providing orientation and are also used for joint angle estimation. They conventionally fuse gyroscope and accelerometer data using Kalman filter-like algorithm to estimate the joint angles. This research presents a novel approach of measuring joint parameters—joint angles, angular velocities, and accelerations, of two links joined by revolute or universal joint. The gravity-invariant vestibular dynamic inclinometer (VDI) and planar VDI (pVDI) are used on each link to measure the joint parameters of links joined by revolute and universal joints, respectively. The VDI consists of two dual-axis accelerometers and an uniaxial gyroscope, while the pVDI consists of four strategically placed dual-axis accelerometers and a triaxial gyroscope. The measurements of joint parameters using the presented algorithms are independent of integration errors/drift, do not require knowledge of robot dynamics, and are computationally less burdensome.

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Cheng, P. , and Oelmann, B. , 2010, “ Joint-Angle Measurement Using Accelerometers and Gyroscopes—A Survey,” IEEE Trans. Instrum. Meas., 59(2), pp. 404–414. [CrossRef]
Tong, K. , and Granat, M. , 1999, “ A Practical Gait Analysis System Using Gyroscopes,” Med. Eng. Phys., 21(2), pp. 87–94. [CrossRef] [PubMed]
Williamson, R. , and Andrews, B. , 2001, “ Detecting Absolute Human Knee Angle and Angular Velocity Using Accelerometers and Rate Gyroscopes,” Med. Biol. Eng. Comput., 39(3), pp. 294–302. [CrossRef] [PubMed]
Willemsen, A. , Van Alste, J. , and Boom, H. , 1990, “ Real-Time Gait Assessment Utilizing a New Way of Accelerometry,” J. Biomech., 23(8), pp. 859–863. [CrossRef] [PubMed]
Miyazaki, S. , 1997, “ Long-Term Unrestrained Measurement of Stride Length and Walking Velocity Utilizing a Piezoelectric Gyroscope,” IEEE Trans. Biomed. Eng., 44(8), pp. 753–759. [CrossRef] [PubMed]
Moe-Nilssen, R. , 1998, “ A New Method for Evaluating Motor Control in Gait Under Real-Life Environmental Conditions. Part 1—The Instrument,” Clin. Biomech., 13(4–5), pp. 320–327. [CrossRef]
Moe-Nilssen, R. , and Helbostad, J. , 2002, “ Trunk Accelerometry as a Measure of Balance Control During Quiet Standing,” Gait Posture, 16(1), pp. 60–68. [CrossRef] [PubMed]
Pappas, I. , Popovic, M. , Keller, T. , Dietz, V. , and Morari, M. , 2001, “ A Reliable Gait Phase Detection System,” IEEE Trans. Neural Syst. Rehabil. Eng., 9(2), pp. 113–125. [CrossRef] [PubMed]
Kurata, S. , Makikawa, M. , Kobayashi, H. , Takahashi, A. , and Tokue, R. , 1998, “ Joint Motion Monitoring by Accelerometers Set at Both Near Sides Around the Joint,” 20th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEMBS), Hong Kong, Oct. 29–Nov. 1, Vol. 4, pp. 1936–1939.
Ghassemi, F. , Tafazoli, S. , Lawrence, P. , and Hashtrudi-Zaad, K. , 2007, “ Design and Calibration of an Integration-Free Accelerometer-Based Joint-Angle Sensor,” IEEE Trans. Instrum. Meas., 57(1), pp. 150–159. [CrossRef]
Ghassemi, F. , Tafazoli, S. , Lawrence, P. , and Hashtrudi-Zaad, K. , 2002, “ An Accelerometer-Based Joint Angle Sensor for Heavy-Duty Manipulators,” IEEE International Conference on Robotics and Automation (ICRA '02), Washington, DC, May 11–15, Vol. 2, pp. 1771–1776.
Willemsen, A. , Frigo, C. , and Boom, H. , 2002, “ Lower Extremity Angle Measurement With Accelerometers-Error and Sensitivity Analysis,” IEEE Trans. Biomed. Eng., 38(12), pp. 1186–1193. [CrossRef]
King, A. , 1998, “ Inertial Navigation-Forty Years of Evolution,” GEC Rev., 13(3), pp. 140–149, available at: http://www.imar-navigation.de/downloads/papers/inertial_navigation_introduction.pdf
Vaganay, J. , Aldon, M. , and Fournier, A. , 1993, “ Mobile Robot Attitude Estimation by Fusion of Inertial Data,” IEEE International Conference on Robotics and Automation (ICRA), Atlanta, GA, May 2–6, pp. 277–282.
Foxlin, E. , 1996, “ Inertial Head-Tracker Sensor Fusion by a Complementary Separate-Bias Kalman Filter,” IEEE Virtual Reality Annual International Symposium (VRAIS), Santa Clara, CA, Mar. 30–Apr. 3, pp. 185–194.
Luinge, H. , and Veltink, P. , 2005, “ Measuring Orientation of Human Body Segments Using Miniature Gyroscopes and Accelerometers,” Med. Biol. Eng. Comput., 43(2), pp. 273–282. [CrossRef] [PubMed]
Luinge, H. , and Veltink, P. , 2004, “ Inclination Measurement of Human Movement Using a 3-D Accelerometer With Autocalibration,” IEEE Trans. Neural Syst. Rehabil. Eng., 12(1), pp. 112–121. [CrossRef] [PubMed]
Roetenberg, D. , 2006, “ Inertial and Magnetic Sensing of Human Motion,” Ph.D. thesis, University of Twente, Enschede, The Netherlands.
Baerveldt, A. , and Klang, R. , 1997, “ A Low-Cost and Low-Weight Attitude Estimation System for an Autonomous Helicopter,” IEEE International Conference on Intelligent Engineering Systems (INES '97), Budapest, Sept. 15–17, pp. 391–395.
Nebot, E. , and Durrant-Whyte, H. , 1999, “ Initial Calibration and Alignment of Low-Cost Inertial Navigation Units for Land Vehicle Applications,” J. Rob. Syst., 16(2), pp. 81–92. [CrossRef]
Algrain, M. , and Saniie, J. , 1991, “ Estimation of 3D Angular Motion Using Gyroscopes and Linear Accelerometers,” IEEE Trans. Aerosp. Electron. Syst., 27(6), pp. 910–920. [CrossRef]
Laurens, J. , and Droulez, J. , 2007, “ Bayesian Processing of Vestibular Information,” Biol. Cybernet., 96(4), pp. 389–404. [CrossRef]
Bachmann, E. R. , 2000, “ Inertial and Magnetic Tracking of Limb Segment Orientation for Inserting Humans Into Synthetic Environments,” Ph.D. thesis, Naval Postgraduate School, Monterey, CA.
Tahboub, K. , 2008, “ Optimal Estimation of Body Angular Velocity Based on Otolith-Canal Interaction,” 16th Mediterranean Conference on Control and Automation (MED), Ajaccio, France, June 25–27, pp. 848–853.
Veltink, P. , Luinge, H. , Kooi, B. , Baten, C. , Slycke, P. , Olthuis, W. , and Bergveld, P. , 2001, “ The Artificial Vestibular System-Design of a Tri-Axial Inertial Sensor System and Its Application in the Study of Human Movement,” Symposium of the International Society for Postural and Gait Research (ISPG 2001), Maastricht, The Netherlands, June 23–27.
Patane, F. , Laschi, C. , Miwa, H. , Guglielmelli, E. , Dario, P. , and Takanishi, A. , 2004, “ Design and Development of a Biologically-Inspired Artificial Vestibular System for Robot Heads,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2004), Sendai, Japan, Sept. 28–Oct. 2, Vol. 2, pp. 1317–1322.
Xsens , 2011, “ MVN Biomech,” Xsens North America, Inc., Culver City, CA, http://www.xsens.com
Vikas, V. , and Crane, C. D. , 2011, “ Inclination Parameter Estimation for Manipulator and Humanoid Robot Links,” ASME Paper No. DETC2011-48221.
Vikas, V. , and Crane, C. , 2015, “ Bioinspired Dynamic Inclination Measurement Using Inertial Sensors,” Bioinspiration Biomimetics, 10(3), p. 036003. [CrossRef] [PubMed]
Vikas, V. , and Crane, C. D. , 2010, “ Inclination Estimation and Balance of Robot Using Vestibular Dynamic Inclinometer,” 10th IEEE/RAS International Conference on Humanoid Robots (Humanoids), Nashville, TN, Dec. 6–8, pp. 245–250.
Vikas, V. , and Crane, C. D. , 2013, “ Measurement of Robot Link Joint Parameters Using Multiple Accelerometers and Gyroscopes,” ASME Paper No. DETC2013-12741.
Murray, R. M. , and Sastry, S. S. , 1994, A Mathematical Introduction to Robotic Manipulation, CRC Press, Boca Raton, FL.
Frosio, I. , Pedersini, F. , and Borghese, N. , 2009, “ Autocalibration of MEMS Accelerometers,” IEEE Trans. Instrum. Meas., 58(6), pp. 2034–2041. [CrossRef]


Grahic Jump Location
Fig. 1

Mechanism comprises rigid links where each link has an inertial sensor combination attached onto it at some location. (a) Two links i, j are joined at point Oi,j. The joint Oi,j may be modeled as a revolute (joint angle between links) or universal joint (Euler joint angles between links). (b) The base link is in contact with the ground surface with acceleration g at one end (Ob). The base angle(s) represent the angle(s) between g and the link b.

Grahic Jump Location
Fig. 2

The VDI is comprised of two accelerometers (L, R) and a gyroscope (G). Three different designs for placement of the accelerometers are possible: (a) accelerometers are symmetrically placed at distance d/2 about point P along axis e1. (b) Here the accelerometers are placed symmetrically along axis e3. (c) Design of VDI where the accelerometers are nonsymmetrically placed about point P.

Grahic Jump Location
Fig. 3

The VDI and pVDI sensors can be concisely presented as a function which, when given the location of the sensor from the joints (rPi/Oh,i, rPi/Oi,j), calculates the linear acceleration of the two joints (aOh,i, aOi,j), angular velocity (ωLI) and acceleration (αLI) of the link

Grahic Jump Location
Fig. 4

The design of the pVDI consists of a triaxial gyroscope (G) and four symmetrically placed accelerometers along e1 and e2 directions about point P. Hollow arrows indicate the direction of the required measurements.

Grahic Jump Location
Fig. 5

Other possible variations in the pVDI sensor design. The two different planes that the accelerometers may be placed symmetrically are the (a) {e2,e3} or (b) {e3,e1} plane. The hollow arrows indicate the measurement directions of the dual-axis linear accelerometers.

Grahic Jump Location
Fig. 6

Modeling of the joint as a universal joint (Euler 2-1 angles): (a) the base and link joined at point O and (b) links i, j joined at point Oi,j

Grahic Jump Location
Fig. 7

Experimental setup of two links (L1, L2) joined by an universal joint. Each link has a pVDI sensor (pVDI1, pVDI2) strapped onto it which consists of four symmetrically placed MEMS accelerometers and a MEMS gyroscope.

Grahic Jump Location
Fig. 8

Experimental setup of the pVDI sensor consisting of four symmetrically placed linear MEMS accelerometers at a distance of 6 cm from the centerline and one MEMS gyroscope

Grahic Jump Location
Fig. 9

Comparison plot of angular acceleration of link 1 obtained from the pVDI sensor with differentiated values from smooth gyroscope readings

Grahic Jump Location
Fig. 10

Plot of angular acceleration of link 2 obtained from the pVDI sensor. The values are compared against differentiated gyroscope readings.

Grahic Jump Location
Fig. 11

Comparison of Euler 2-1 angles of the universal joint with the readings from the magnetic encoder




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