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Intelligent Sensing with Inertial Sensors

Mechanically, the human body displays a remarkable quality of maintaining equilibrium for a body that is in a state of unstable equilibrium (biped stance). I take inspiration from the human vestibular system to answer "what is the equilibrium position?" and build orientation sensors using multiple inertial sensors.

Dynamic Equilibrium Axis - The axis along which the human body (modeled as an inverted pendulum) is at equilibrium. It is parallel to the direction of the resultant acceleration of the surface of contact. It helps to explain the tendency of the human body to lean backward, forward or sideways to align themselves to equilibrium position in acceleration varying environments. It also explains the surface-normal human posture when standing on a flat surface but not on an incline (gravity-aligned). Most importantly, the equilibrium position ceases to exist in space (zero gravity) as the resultant acceleration of the surface of contact is zero. [DOI:10.1088/1748-3190/10/3/036003][DOI:10.1109/ICHR.2010.5686299]

Figure IS-1 : What is the equilibrium position in humans? The equilibrium position is the surface-normal when standing on a non-accelerating flat-surface, however, this position changes while standing on a non-accelerating incline. The body aligns itself along the gravity (solid arrow), not the surface normal (dotted line). For non-static surfaces like an accelerating or de-accelerating bus, the Dynamic Equilibrium Axis (DEA) changes and the body tends to bend backward on an accelerating bus and lean forward for a de-accelerating bus to align itself along this equilibrium axis. Similarly, the equilibrium axis changes when turning right or left on a curve (left or right respectively). For the cases of space, the equilibrium axis ceases to exist as the body is always in equilibrium and does not need to align itself along any axis.

Bioinspired Inertial Sensing

Non-contact orientation sensors comprising of multiple inertial sensors - Measure orientation from the equilibrium position. The sensor are able to measure joint angles and angular accelerations.[DOI:10.1115/1.4031299]
Figure IS-2 :  The non-contact sensors inclination sensors (VDI and pVDI) allow measurement of joint parameters - joint angles, angular velocity and acceleration of the rigid links. The two sensors are the Vestibular Dynamic Inclinometer (VDI) and planar Vestibular Dynamic Inclinometer (pVDI) which comprise of one tri-axial gyroscope combined with strategically placed two or four bi-axial accelerometers.

Software Gyroscope (Gyro-Free IMU) - Four non-coplanarly placed accelerometers can measure angular acceleration and velocity without the drift in bias resulting from MEMS gyroscope. [DOI:10.1115/DETC2014-35360]

Figure IS-3 : (a) Four or more non-coplanarly placed tri-axial accelerometers are sufficient to determine linear acceleration of any point on a given body, angular acceleration and second order angular velocity of the body. (b) Combining four or more accelerometers with magnetometers - unique rotation matrix between two different coordinate systems can be determined.


  1. V. Vikas and C. D. Crane III, "Joint angle measurement using strategically placed accelerometers and gyroscope", Journal of Mechanisms and Robotics, July 2015. [DOI:10.1115/1.4031299]
  2. V. Vikas and C. D. Crane III, "Dynamic Inclination measurement using multiple accelerometers and gyroscope", Bioinspiration and Biomimetics, April 2015. [DOI:10.1088/1748-3190/10/3/036003]
  3. V. Vikas and C. D. Crane III, "Gyroscope-free link parameter measurement using accelerometers and magnetometer", ASME International Design Engineering Technical Conference, Aug 2014. [DOI:10.1115/DETC2014-35360]
  4. V. Vikas and C. D. Crane III, "Measurement of robot link joint parameters using multiple accelerometers and gyroscopes", ASME International Design Engineering Technical Conference, Aug 2013. [DOI:10.1115/DETC2013- 12741]
  5. V. Vikas and C. D. Crane III, "Dynamic Inclination Measurement for five degrees-of-freedom robots", The 2nd IASTED International Conference on Robotics, Nov 2011. [DOI:10.1115/DETC2011-48221]
  6. V. Vikas and C. D. Crane III, "Inclination Parameter Estimation for Manipulator and Humanoid Robot Links", ASME International Design Engineering Technical Conference, Aug 2011. [DOI:10.2316/P.2011.752-021]
  7. V. Vikas, S. Ridgeway and C. D. Crane III, "Interpretation of Time-Varying Actions for Behavior Learning in Autonomous Vehicles", Florida Conference on Recent Advances in Robotics, May 2011. 
  8. V. Vikas and C. D. Crane III, "Inclination Estimation and Balance of Robot using Vestibular Dynamic Inclinometer", IEEE-RAS International Conference on Humanoid Robots, pp. 245-250, Dec 2010. [DOI:10.1109/ICHR.2010.5686299]
  9. V. Vikas and C. D. Crane III, "Robot Inclination Estimation using Vestibular Dynamic Inclinometer", IASTED International Conference Robotics and Applications, Vol. 706, Nov 2010. [DOI:10.13140/RG.2.1.5062.3524]
  10. V. Vikas, J. Godowski and C. D. Crane III, "Balancing Static Robots using Vestibular Dynamic Inclinometer", Florida Conference on Recent Advances in Robotics, May 2010. [DOI:10.13140/RG.2.1.2810.0006]