A Nonlinear Framework for Generating Graded Transitional Upper-Limb Motions for Rehabilitation

Generating adaptable and human-like upper-limb motion is a critical challenge in motor rehabilitation and human-machine interaction. Existing computational methods often fail to support smooth, progressive transitions between impaired and healthy motor states, which is essential to prevent maladaptive compensatory strategies during motor learning and recovery. To address this gap, we present a novel, proof-of-concept framework utilizing nonlinear Hénon maps to model and interpolate 2-D inter-joint coordination patterns (shoulder and elbow). Using kinematic recordings from adults performing grasping tasks in both pre-immobilization (i.e., mimicking healthy condition) and post-immobilization (i.e., impaired) states, we developed condition-specific models. By applying a weighted interpolation to the subject-specific model parameters, we synthesized intermediate kinematics that represent a graded continuum between the impaired-like and healthy-like movement profiles. The synthesized trajectories demonstrated high predictive accuracy, yielding low mean squared prediction errors relative to the joint range of motion. Furthermore, robust phase-space and kinematic evaluations revealed no statistically significant differences between the simulated and actual biological movements regarding their nonlinear dynamical complexity—measured via the Lyapunov Exponent and Correlation Dimension—or their movement smoothness, measured via the Normalized Average Rectified Jerk. This computationally efficient approach successfully generates graded transitions between motor states while strictly preserving the biologically realistic dynamics and kinematic smoothness of natural human movement. This framework establishes a robust mathematical foundation for driving personalized, adaptive rehabilitation protocols within Extended Reality (XR) and robotic environments.