Collision-free path planning method for digital orthodontic treatment

The rapid evolution of digital orthodontics has highlighted a critical need for automated treatment planning systems that balance computational efficiency with clinical reliability. However, existing methods still suffer from several limitations, including excessive clinician involvement (accounting for over 35% of treatment planning time), reliance on empirically defined key frames, and limited biomechanical plausibility, particularly in cases of severe dental crowding. This paper proposes a novel collision-free optimization framework to address these issues simultaneously. Our method defines a total movement energy function evaluated over each tooth’s pose at intermediate time frames. This energy is minimized iteratively using a steepest descent strategy. A rollback mechanism is employed: if inter-tooth penetration is detected during an update, the step size is halved repeatedly until collisions are eliminated. The framework allows flexible control over the number of intermediate frames to enforce a strict constraint on per-tooth displacement, limiting it to 0.2 mm translation or $2°$ rotation every 10 to 14 days. Clinical evaluations show that the proposed algorithm can generate desirable and clinically valid tooth movement plans, even in complex cases, while significantly reducing the need for manual intervention.