Adaptive Optimal Control for Avatar-Guided Motor Rehabilitation in Virtual Reality

TL;DR

The paper tackles barriers to post-stroke rehabilitation by proposing a home VR platform where an autonomous avatar provides adaptive, interpretable motor guidance. It uses a multi-objective finite-horizon optimal control driven by Hogan's minimum-jerk reference and introduces an ability index to tailor assistance across sessions. Validation comprises simulations and preliminary tests with healthy participants, demonstrating co-adaptive avatar behavior and potential for scalable remote physiotherapy with clinician oversight. Limitations include validation only on a 1-DOF task and the need for clinical trials with stroke patients, with future work aiming at multi-joint models and rigorous clinical validation.

Abstract

A control-theoretic framework for autonomous avatar-guided rehabilitation in virtual reality, based on interpretable, adaptive motor guidance through optimal control, is presented. The framework faces critical challenges in motor rehabilitation due to accessibility, cost, and continuity of care, with over 50% of patients inability to attend regular clinic sessions. The system enables post-stroke patients to undergo personalized therapy in immersive virtual reality at home, while being monitored by clinicians. The core is a nonlinear, human-in-the-loop control strategy, where the avatar adapts in real time to the patient's performance. Balance between following the patient's movements and guiding them to ideal kinematic profiles based on the Hogan minimum-jerk model is achieved through multi-objective optimal control. A data-driven "ability index" uses smoothness metrics to dynamically adjust control gains according to the patient's progress. The system was validated through simulations and preliminary trials, and shows potential for delivering adaptive, engaging and scalable remote physiotherapy guided by interpretable control-theoretic principles.

Figures (7)

• Figure 1: Motor task used in the design of the rehabilitation platform.(a) Illustration representing a human performing the reaching task at the beginning and at the end of the task. Blue circle represents the start angle position, whereas the red circle represents the final angle position. A dashed arrow indicates the trajectory that the human has to follow. (b) Real scenario in which human is asked to move the forearm in an angular motion assisted by the clinician.
• Figure 2: Control architecture designed for the assisting avatar. The Inner Dynamics block constraints the behavior of avatar, while the the Temporal Correspondence Control block minimizes the position error between the avatar and the human, The Reference Signal and the Reference Control blocks confer a desired kinematic features to the virtual agent. $\theta,\dot{\theta}$ are angular position and angular velocity of the avatar, whereas $\theta_P, \dot{\theta}_P$ are measured angular position and estimated angular velocity of the human partner; $\dot{\theta}_H$ is the angular velocity signal reference generated by the Hogan model; $u$ is the control input.
• Figure 3: System Architecture. Conceptual diagram of the system architecture. Hand movements are tracked using Meta Quest controllers and transmitted via Quest Link to the rendering engine (Unreal Engine) hosted on a dedicated computer. A TCP/IP communication protocol allows data exchange between the Unreal Engine front-end and a MATLAB back-end responsible for avatar motion computation. This setup facilitates flexible prototyping of control algorithms
• Figure 4: User interface in virtual reality. In the virtual environment, the user is prompted to grab the object on the right, follow the yellow trace, and reach the target location. Simultaneously, an autonomous avatar powered by our optimal control strategy on the other side of the table performs the same exercise, adapting its behavior (according to the methodology presented in Section \ref{['sec:architecture_avatar']}) to guide human subject physiotherapy session via visual feedback.
• Figure 5: Mathematical simulation of the rehabilitation process assisted by the avatar. Mathematical simulation of the rehabilitation process showing the patient (in blue) assisted by the avatar (in red) during the phases of Awing and Pawing. (a)-(d) Position and velocity time series of the patient (in red) and the avatar (in blue) are reported for an Awing trial having the maximum angle set at $90$ degrees. The patient was simulated to have two hesitations during the task ($m=3$ in Eq. \ref{['eq:patient_simulation']}). (b)-(e) Position and velocity time series are reported for a Pawing trial that goes from $0$ to $90$ degree. The patient was simulated to have only one hesitation ($m=2$ in Eq. \ref{['eq:patient_simulation']}). (c)-(f) Position and velocity time series are reported for a Pawing trial simulating the patient with no hesitation ($m=1$ in Eq. \ref{['eq:patient_simulation']}). Furthermore, for each trial the weight of the avatar's control law $\alpha_p$ and the index of ability $I_A$ are reported showing that while one decreases the other one increases simulating the progresses of the patient.