Joint angle estimation using accelerometer arrays and model-based filtering

Measurement of joint angles is an important element for the control of robotic systems and monitoring human gait. This has been traditionally approached through the use of contact sensors, e.g., optical or magnetic encoders, and inertial measurement units (IMUs). IMUs fuse data from accelerometers, gyroscopes, and magnetometers to estimate the orientation of the body. However, microelectromechanical system (MEMS) gyroscopes are prone to drift, and magnetometers are susceptible to electromagnetic interference. In contrast, MEMS accelerometers have stable bias and are resilient to external electromagnetic disturbances. Consequently, an all-accelerometer noncontact sensor can mitigate these problems. In the context of two links connected at a joint, the acceleration at this common point is equivalent irrespective of the coordinate system of either of the links. The research presents the use of an array of two or more accelerometers (noncontact sensors) and the knowledge of the acceleration equivalence at the joint to construct a dynamic model where the states correspond to angular velocities of the joints and the joint angle. The joint angle is estimated using three approaches—analytical, the extended Kalman filter (EKF), and the unscented Kalman filter (UKF). The analytical approach estimates the joint angle, while the model-based filtering approaches (EKF and UKF) also estimate the link angular velocities. Simulations are performed using two to ten accelerometers on each link to compare the performances of the three methods and investigate the placement of accelerometers along the links. The simulation results indicate superior performance of the model-based filtering approaches over the analytical. The analysis also concludes that the best physical placement of the accelerometers is toward the ends of the link for minimizing estimation error. In addition, the lower bound of the estimation error is dictated by the maximum ratio of mean to relative accelerometer length between the two links. The algorithms are experimentally validated using three different accelerometers: ADXL345, ADXL357, and BNO055. Four different canonical movements of slow and fast periodic, ramp, and impulse are examined. The experiment results corroborate the better performance of the model-based filters over the analytical approach.