An ISB-consistent upper limb model based on the Denavit-Hartenberg convention for joint angle estimation during prolonged rehabilitation exercises

Abstract

An accurate and robust joint kinematics description is a crucial prerequisite for the development of tele- rehabilitation applications. Miniaturized wearable sensors (IMUs), along with the use of efficient sensor fusion algorithms, represent a suitable solution. However, orientation drift can affect real-time joint kinematics over prolonged acquisition. In this work, we proposed an optimization kinematics framework which exploits a Denavit-Hartenberg (DH) model of the upper limbs, compliant with the guidelines of the International Society of Biomechanics. The accuracy of the estimated 3D shoulder and elbow kinematics was evaluated using data recorded by two IMUs attached to a robotic arm during a 20- minute planar exercise and compared with the errors obtained using a model-free approach. The upper limb was modelled as a three-segment chain including trunk, upper arm (UA), and the forearm (FA) (Fig. 1). Shoulder and elbow joints were modelled with three (φ1, φ2, φ3) and two degrees of freedom (φ4, φ6), respectively. The carrying angle (φ5) was introduced as a fixed subject-specific parameter to describe the physiological abduction of the FA with respect to the UA. The joint angles were computed in an optimization process which minimizes at each time step the difference between the orientation predicted using the DH model and the corresponding orientation estimated by a sensor fusion algorithm without the magnetometer [1]. In addition, joint angle constraints were set based on the maximum angular velocity, the physiological angular limits, and the specific range of movement when known a-priori . To validate the methods, two IMUs (Xsens – MTw) were attached to the UA and FA of a robotic arm (Kinova – Jaco2) programmed to mimic a shoulder flexion-extension (φ1, φ2, φ3), an elbow flexion-extension (φ4), and a forearm prono-supination (φ6), simultaneously, for 20 minutes (~150 cycles) [3]. The φ5 was equal to zero for the robot. IMU and reference data were collected at 100 Hz. The gyroscope offset was computed during a preliminary acquisition and then subtracted from the measurements. The accuracy was evaluated in terms of root mean square difference (RMSD) between the model-based optimized and robot reference joint angles. Furthermore, the RMSD corresponding to the Euler inversion of the FA-to-UA relative orientation (model-free) was also computed. The RMSD (deg) for the joint angles obtained with the optimization (model-free) process amounted to 1 (10.2), 0.4 (0.2), 0.9 (1.4), 3.0 (3.1), 0 (8.2), and 1 (6) for φ1, φ2, φ3, φ4, φ5, φ6, respectively. The proposed methods allowed to reduce joint angles errors of almost a factor 10 over long period compared to model-free approach (1.1 vs 8.9 deg on average). These results if further confirmed on human experiments can contribute to the design of tele-rehabilitation applications relying on the accurate upper limb joint kinematics estimates. Funded by Sardegna Ricerche (POR FESR 2014/2020).