Human Joint Trajectory Tracking with Patient-Specific Range-of-Motion Constraints for Robotic Rehabilitation

Abstract End-effector-based robotic systems represent a promising solution for upper-limb rehabilitation due to their mechanical simplicity, adaptability and ease of use. Since the interaction with the patient occurs only at the end-effector, however, reproducing a desired Cartesian trajectory does not guarantee that the patient's joints evolve as intended. The Human Joint Trajectory Tracking (HJTT) framework addresses this limitation by generating robot trajectories that minimize the discrepancy between a reference joint configuration and the one induced in the patient. The reference motion is recorded from a therapist whose mobility is unimpaired. When the patient's range of motion (ROM) is restricted, reproducing it faithfully may therefore require joint excursions beyond those that the patient can safely achieve, with possible discomfort or injury. The objective of this thesis is to adapt the trajectory to the ROM of the individual patient. The adaptation is formulated as an optimization problem in the human joint space, in which the original tracking objective is combined with logarithmic barrier terms associated with the ROM boundaries. The formulation supports simultaneous constraints on several joints and accounts for differences between their admissible ranges. Reference trajectories are acquired with the Xsens MVN Awinda inertial motion capture system, and the adapted motions are executed on a Franka Emika Panda collaborative robot. For each reference trajectory, the algorithm computes the robot joint trajectory while simulating the corresponding evolution of the human joint configuration. The predicted human joint trajectories remained within the prescribed ROM limits throughout the adapted motions. The resulting trajectories were then executed by the robot with a single healthy subject under imposed ROM limits. The experimental measurements showed the intended reduction in joint excursion on the constrained joints, with a corresponding deviation from the reference. The resulting framework extends HJTT toward safer and more patient-specific end-effector-based rehabilitation, while retaining the joint-space tracking formulation of the original method.