The reintegration of people in the workplace after an upper-limb injury is often a long process. Collaborative robots and humanoids operating in shared workspaces must adapt their behavior to the physical capabilities of their human partners. Achieving this requires robots to autonomously estimate task-relevant human mobility during interaction, without relying on external clinical assessments. In this work, we formulate the estimation of upper-limb functional mobility as an active perception problem. We model task-available upper-limb functional ranges of motion through impairment coefficients that parameterize reductions of healthy joint limits, and integrate this representation into a human model used by the robot during interaction. Based on this formulation, we propose an online active perception pipeline in which the robot actively probes the user through repeated handover requests while progressively updating a Bayesian belief over the impairment coefficients. This enables the robot to continuously refine its internal model of the user's joint-level capabilities through interaction rather than passive observation. The proposed framework was evaluated through simulation studies and a proof-of-concept physical validation with a robotic platform and enacted human impairments, demonstrating that the pipeline can accurately recover the impairment coefficients during real human-robot handovers.

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