Calibrated 2D Angular Kinematics by Single-Axis Accelerometers: From Inverted Pendulum to ${\rm N}$-Link Chain

A new method for the estimation of multi-link angular kinematics in the sagittal plane, using one single-axis accelerometer (SAA) per segment, is presented in this paper. A preliminary calibration, using SAAs and a reference system (encoder or stereo-photogrammetry), allows the estimation of sensors position and orientation and segment lengths. These parameters are then used to predict the chain kinematics using the SAAs only. To evaluate the method, the algorithm is first tested on a mechanical arm equipped with a reference encoder. A general method for estimating the kinematics of an N-link chain is also provided. Finally, a three-link biomechanical model is applied to a human subject to estimate the joint angles during squat tasks; a stereo-photogrammetric system is used for validation. The results are very close to the reference values. Mean descriptive (predictive) root mean squared error (RMSE) is 0.15
^°
(0.16
^°
) for the inverted pendulum, and 0.39
^°
(0.59
^°
) for the shank, 0.82
^°
(1.06
^°
) for the thigh, 0.87
^°
(1.09
^°
) for the HAT (head-arm-trunk) in the three-link model. The mean value of RMSE without calibration is 1.02
^°
for the inverted pendulum, and 11.01
^°
(shank), 11.39
^°
(thigh) and 12.21
^°
(HAT) in the three-link model. These results suggest that, after the calibration procedure, one SAA per segment is enough to estimate 2D joint angles accurately in a kinematic chain of any number of links.