Reconstructing trajectory during an upper limb functional task: A single IMU optimization approach. = Ricostruzione della traiettoria durante lo svolgimento di un esercizio funzionale per l'arto superiore: Un approccio di ottimizzazione con singolo IMU.

This thesis examines trajectory reconstruction during a drinking task, a common rehabilitation exercise used to assess upper limb functionality, using a single inertial unit (IMU) worn on the wrist. Compared to other human motion capture methods, inertial measurements are a cheaper and more ergonomic alternative, but they are prone to noise and drift errors that by accumulating over time, lead to an inaccurate estimation. The aim of this work is to develop an optimization-based method to enhance trajectory reconstruction accuracy when using a single wrist-mounted IMU within a structured protocol. The proposed method is validated against a stereophotogrammetric gold standard. This approach has potential applications in telerehabilitation by enabling objective clinical assessments of functional tasks with minimal setup, making it accessible for remote use by non-experts. To evaluate IMU performance, an initial analysis was conducted on uniaxial movements using a double integration approach. For this purpose, a custom-built workbench was designed, featuring a sliding cart on which the IMU was mounted to test controlled slide distance trajectory reconstruction. A simple double integration approach was applied to assess errors when integration was performed directly without precautions. To identify start and end points for integration, a template-matching method was developed, averaging multiple slide trials to generate a reference template for precise segmentation. Results indicate an absolute error of approximately 1 ± 0.5 cm per axis over a 15 cm slide, corresponding to 6% of the total movement. Following this preliminary analysis, the same IMU was then tested on a drinking task (R2G) involving 11 subjects. Trajectories were reconstructed using direct double integration and the zero-velocity update (ZUPT) technique. A statistical algorithm, DynAMoS, was employed to detect static periods, which were then used to apply ZUPT. Additionally, an optimization method was developed to refine trajectory estimation based on expected movement characteristics. Results indicate that applying ZUPT to the dynamic phases identified by DynAMoS reduces trajectory reconstruction mean absolute errors compared to double integration by more than 40% of the range of motion along each axis in most subjects. However, an error of approximately 20% of range of motion still remains relative to the gold standard. After optimization, the trajectory reconstruction mean absolute error improves to less than 2cm on all axes for most subjects, with a normalized error relative to the movement’s range of motion of less than 10% for x-axis and around 5% on other axes. These findings suggest that accurate trajectory estimation can be achieved using minimal anthropometric data and a single IMU, with errors remaining below 10% of the range of motion (ROM). However, this error is higher compared to more complex approaches, such as multi-IMU kinematic models, which achieve errors in the 1–2% range. Despite this limitation, the proposed approach represents a viable solution for telerehabilitation due to its ease of setup and minimal measurement requirements. Future research should explore its effectiveness in clinical populations, particularly in patients with motor impairments. Additionally, incorporating new functional cost terms may further reduce errors and improve overall accuracy.