Surgical and Medical Robots

In keyhole surgery, long thin instruments pass through small cuts in the body. The instrument must pivot exactly at the cut, the remote center of motion, so it never tears the tissue around it. Surgical robots like the da Vinci system enforce that pivot mechanically, scale large hand motions into tiny tip motions, and filter out the natural tremor of the surgeon's hand.

Motion scaling (hand to tip) Hand tremor Filter out the tremor

Remote center of motion

The instrument shaft must always pass through the incision point $\mathbf{c}$. Only its angle and how far it is pushed in can change, so the tip position is

$$\mathbf{p}_{\text{tip}} = \mathbf{c} + d\,\hat{\mathbf{u}}(\theta), \qquad \Delta\mathbf{p}_{\text{tip}} = s\,\Delta\mathbf{p}_{\text{hand}}$$

with insertion depth $d$, shaft direction $\hat{\mathbf{u}}$, and motion scaling factor $s$. Hand tremor, typically 8 to 12 Hz, is removed with a low-pass filter, since intended motions are much slower.

What to notice

The shaft always crosses the skin at the same spot, while the tip moves freely inside. Scaling down to 0.3 turns a 3 cm hand motion into a 9 mm tip motion, which makes fine work like stitching easier. With the filter off, the tremor shows up in the tip path. With it on, the tip path is smooth, at the cost of a small lag. These systems are teleoperated: the surgeon always decides, and the robot makes the motion steadier and more precise.