Robotic Surgery Teleoperation: Motion Scaling & Tremor Filtering

Console Link

Motion scaling ratio 3.0 : 1

Hand tremor amplitude 1.2 mm

Tremor-filter time constant 150 ms

Console path speed 1.0×

Live Readouts

Tip precision (RMS)

0.00 mm

Tremor rejected

Instrument tip speed

0.00 mm/s

How it works

A tele-operated surgical robot never drives the instrument at 1:1 with the surgeon's console handle. Two signal-processing stages sit between hand and tip:

h(t)  = path(t) + tremor(t)            raw console handle position
f(t) += (h(t) - f(t)) * (1 - e^(-dt/τ)) exponential low-pass filter
p(t)  = f(t) / N                        instrument tip = filtered / scale N

The filter f(t) is a single-pole exponential moving average with time constant τ: physiological hand tremor lives at 8–12 Hz, well above the 1–2 Hz surgical intent the surgeon is actually steering, so a few hundred milliseconds of smoothing removes most of the tremor energy while barely lagging the intended path.

The motion-scaling ratio N then divides that filtered displacement down: at 5:1, a 25 mm hand sweep becomes a 5 mm instrument sweep, trading console workspace for sub-millimetre precision at the tip — exactly the mechanism systems like da Vinci use to make a human hand tremor-free and precise enough for micro-suturing.

Scaling ratio — higher N means the instrument moves less per unit of hand motion (more precision, less reach).
Tremor amplitude — the raw physiological shake injected into the console path before filtering.
Filter time constant τ — 0 ms disables filtering entirely (tremor passes straight through, scaled); higher τ rejects more tremor but adds lag.
Network delay — toggles a fixed signal-transport lag, as in remote/telesurgery, to show how latency (not tremor) becomes the dominant error source at large τ.
Tremor rejected — rolling comparison of the raw vs. filtered high-frequency residual, as a percentage removed.

Console handle (surgeon hand) Instrument tip (filtered + scaled) Ideal scaled path (target)

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