A surgical telemanipulator never moves the instrument tip exactly as the surgeon's hand moves. Two corrections sit in the control loop between the master controller and the patient-side instrument:
filtered(t) = filtered(t-1) + α·(raw(t) − filtered(t-1)) [low-pass, α = 1 − filter strength]
tip(t) = filtered(t) / N [N = motion-scaling ratio]
The exponential low-pass filter removes the ~8–12 Hz physiological hand tremor present in every human hand, since a real-time control loop can distinguish "fast, small, oscillatory" tremor from the surgeon's "slow, large, deliberate" intended motion by frequency alone. The motion-scaling divide then shrinks whatever intentional movement survives the filter — a 5 cm hand motion at a 5:1 ratio becomes a 1 cm instrument motion — trading working volume for the sub-millimetre precision needed for micro-suturing and vessel work.
- Motion scaling ratio — how many millimetres of hand motion produce one millimetre of instrument motion; higher ratios give finer control at the cost of needing larger hand movements to cross the same working field.
- Physiological tremor — the amplitude of the surgeon's natural hand tremor before filtering; every human hand has this, it just isn't usually visible at unaided scale.
- Tremor-filter strength — how aggressively the low-pass filter suppresses fast oscillation; too low leaves visible jitter at the tip, too high starts to lag genuine fast intentional moves.
- Show raw master path — overlay the surgeon's unfiltered hand trace to compare against the smoothed, scaled instrument trace.
This is the same architecture used by real robotic-surgery platforms: the surgeon's hands never touch the patient, and everything the instrument does is a filtered, scaled reconstruction of the surgeon's intent, sent from a console to a patient-side manipulator arm.