## 3 Results
### Kinematic Analysis
#### 3.2.2 Non-Linear Analysis  
The non-linear analysis of joint behaviour during the feedforward phase of GI revealed significant differences between the stroke and healthy groups. The stroke group consistently exhibited reduced convergence or greater divergence in movement trajectories, as indicated by less negative or more positive LyE, respectively (detailed information is available in Tables S6 to S10 in the Supplementary Materials). This was accompanied by a marked loss of complexity, reflected in decreased MSE. Head, Pelvis, and Trunk Joints  
In the sagittal plane, the stroke group exhibited less negative and convergent LyE values. For the head, significant differences were observed in POS (\(p\) = 0.004). MSE measures demonstrated significant reductions across all dimensions for both POS (S1: \(p\) = 0.002; S2: \(p\) = 0.009; CI: \(p\) = 0.006) and DISP (S1: \(p\) = 0.009; S2: \(p\) = 0.034; CI: \(p\) = 0.021) (Figure 7). In the frontal plane, the stroke group exhibited less negative LyE values, reflecting reduced convergence. For the head, significant differences were observed in POS (\(p\) = 0.006) and the MSE measures demonstrated significant reductions across all dimensions for POS (S1: \(p\) = 0.023; S2: \(p\) = 0.021; CI: \(p\) = 0.013) and DISP (S1: \(p\) < 0.001; S2: \(p\) = 0.007; CI: \(p\) = 0.006). For the trunk, MSE reductions were significant for POS (S1: \(p\) = 0.007; S2: \(p\) = 0.002; CI: \(p\) = 0.003). For the pelvis, LyE values were significantly less negative for POS (\(p\) = 0.011), while those for MDISPL were less positive, indicating reduced divergence; however, these differences were not statistically significant (\(p\) > 0.05) (Figure 7). In the transverse plane, LyE values in the stroke group exhibited a tendency toward less negative values, indicating reduced convergence, with significantly less negative values for pelvis POS (\(p\) < 0.001). For the head, MSE measures showed significant reductions for POS (S1: \(p\) = 0.009; S2: \(p\) < 0.001; CI: \(p\) = 0.005) and DISP (S1: \(p\) = 0.002; S2: \(p\) = 0.006; CI: \(p\) = 0.005). For the trunk, MSE reductions were significant for POS (S1: \(p\) = 0.021; CI: \(p\) = 0.040), while reductions in DISP were not statistically significant (\(p\) > 0.05). For the pelvis, MSE reductions were significant for POS (S1: \(p\) = 0.002; S2: \(p\) = 0.019; CI: \(p\) = 0.004) and DISP (S1: \(p\) = 0.021; S2: \(p\) = 0.044) (Figure 6). Figure 7: Non-linear analysis of position and mean displacement of head, pelvis, and trunk joints. H: healthy; S: stroke; LyE, largest Lyapunov exponent; S1: Multiscale Entropy Scale 1; S2: Multiscale Entropy Scale 2; CI, Multiscale Entropy Complexity Index; EXT, extension; FLE, flexion; RT, right tilt; LT, left tilt; LR, left rotation: RR, right rotation; RV, retroversion; AV, anteversion; * \(p\)-value \(<\) 0.05: Mann–Whitney test. Lower Limb Joints  
In the sagittal plane, the stroke group exhibited less convergence in LyE values. For the hip, significantly less negative POS values were observed in both the swing (\(p\) = 0.021) and stance (\(p\) = 0.006) limbs and the MSE measures showed significant reductions for POS in the swing limb (S2: \(p\) = 0.026; CI: \(p\) = 0.040). For the knee, DISP LyE values showed contrasting patterns: the healthy group exhibited positive values, indicating divergence, while the stroke group displayed negative values in the swing limb, reflecting convergence. However, these differences were not statistically significant (\(p\) > 0.05). MSE measures for the knee showed a significant reduction for POS in the swing limb (CI: \(p\) = 0.026). For the ankle, the stroke group exhibited significantly less negative LyE values for POS in the stance limb (\(p\) = 0.016) (Figures 8 and 9). In the frontal plane, the stroke group exhibited less convergence in POS LyE values across all joints, though these differences were not statistically significant (\(p\) > 0.05).