Continuous Estimation of the Lower-Limb Multi-Joint Angles Based on Muscle Synergy Theory and State-Space Model

Continuous joint angle estimation is essential for enhancing man-machine collaboration performance. However, it is challenging to estimate the complex multi-joint angle of the lower limb accurately. First, a nonredundant feature extraction algorithm for muscle synergy was proposed. The nonnegative matrix factorization (NMF) algorithm was used to extract the muscle activation coefficient matrix, and the muscle activation coefficient matrix was divided into nonredundant and redundant feature vectors. Then, a state-space frame model with nonredundant features as input and redundant features as measurement output to reduce system error was proposed. The square root unscented Kalman filter (SRUKF) algorithm was used to estimate the multi-joint angle of lower limbs. We recruited ten subjects to participate in seven daily activities, including going upstairs (US), downing stairs (DS), going uphill (UH), going downhill (DH), and walking at three speeds of 0.6, 1.0, and 1.4 m/s. The results showed that the average root mean square error (RMSE) of the proposed approach for estimating hip and knee joint angles was 0.44 ± 0.1 and 0.73 ± 0.5, respectively, which was significantly smaller than the common neural networks ( ${p} < 0.05$ ). Particularly, the anti-interference performance of the proposed model was tested. Meanwhile, the adaptability test was carried out through the developed lower-limb multi-joint angle estimation verification system, which proved that the proposed approach could provide accurate and stable estimation results by making full use of redundant features. It can improve the safety of online applications for surface electromyography (sEMG) auxiliary equipment.