# Position-Based Dynamics

Surgical robots need to anticipate how instrument motion will deform tissue when visibility is interrupted, and prior differentiable physics simulation predicted absolute tissue positions, so reconstruction error, initialization, and simulation offsets left the whole surface persistently displaced. The forecast now anchors each tissue point to its last valid observation and predicts only the deformation induced by the known future tool trajectory, using mesh-free position-based dynamics with scene-specific rigidity, attachment, and grasp coupling. Across 12 surgical manipulation clips, the referenced forecast has a median within-clip error ratio of 0.912 against the persistence baseline, 95% interval 0.787–1.070, improving 8 of 12 clips, with the interval including parity.

Surgical robots need to anticipate how instrument motion will deform tissue when visibility is interrupted, and prior differentiable physics simulation predicted absolute tissue positions, so reconstruction error, initialization, and simulation offsets left the whole surface persistently displaced. The forecast now anchors each tissue point to its last valid observation and predicts only the deformation induced by the known future tool trajectory, using mesh-free position-based dynamics with scene-specific rigidity, attachment, and grasp coupling. Across 12 surgical manipulation clips, the referenced forecast has a median within-clip error ratio of 0.912 against the persistence baseline, 95% interval 0.787–1.070, improving 8 of 12 clips, with the interval including parity.