 Swing-foot clearance

Swing-foot clearance is the separation between a robot's swinging foot and the terrain or obstacles it must pass. It concerns the whole swing phase, not just the maximum foot height. For a finite foot, use the relevant lowest material surface or full collision geometry; the height of a chosen ankle coordinate can differ from actual clearance.

An original point-foot model isolates vertical geometry. Let a planned foot position be $(x(s),z(s))$ and terrain height be $H(x)$, with swing parameter $s\in [0,1]$. DefineGround contact at the beginning and end normally gives zero endpoint clearance, so a positive lower bound must be assigned to the obstacle-crossing part of the path rather than incorrectly demanded throughout the closed contact-to-contact interval.

Use the constructed pathSuppose a flat-topped obstacle of height $15\mathrm{mm}$ occupies the horizontal range corresponding to $s\in [1/4,3/4]$, namely $31.25$ to $168.75\mathrm{mm}$. With $h=40\mathrm{mm}$, the lowest foot height over this interval is $h/2=20\mathrm{mm}$, attained at its edges. The minimum nominal obstacle clearance is therefore only $5\mathrm{mm}$ even though peak foot height is $40\mathrm{mm}$.

A robust swing-foot clearance margin includes specified error bounds. If actual foot height can be $3\mathrm{mm}$ below its plan and actual obstacle height $4\mathrm{mm}$ above the model, the guaranteed clearance is at leastThus the nominally clear path permits collision within those bounds. Guaranteeing at least $5\mathrm{mm}$ above this obstacle under the same errors requiresThe bounds add because both deviations can reduce clearance at once; they are deterministic limits, not independent standard uncertainties to combine by root-sum-square.

Greater height changes the leg's motion requirements. For a fixed swing duration $T_w$, this path has maximum vertical speed $\pi h/T_w$ and accelerations proportional to $h/T_w^2$. Clearance, timing, inverse kinematics and actuator constraints must therefore be checked together. A terrain discontinuity, horizontal position error or non-point foot additionally requires the corresponding geometry rather than just this vertical formula.

The primary planning text treats clearance as a possible planning objective and distinguishes local geometric constraints from dynamic ones.^[ref] A proposed robot test measures the foot surface and obstacle geometry in a shared reference frame, records the trajectory throughout the crossing, and compares the minimum separation with the stated bounds. Observing a high midpoint alone does not test the minimum-clearance claim.