= Swing phase
The <swing phase> of a robot leg is the interval in which its foot moves between ground contacts without providing the intended ground support. It complements the <stance phase>. In a periodic <gait> with period $T$ and contact <duty cycle> $\beta$, its duration is $(1-\beta)T$. The leg can still require substantial actuator effort: moving its own mass and controlling its <trajectory> are different from supporting the robot through ground contact.
An original planar foot path gives an explicit design example. Let $s=t/T_w\in[0,1]$ parameterize a swing of duration $T_w$, horizontal travel $L$ and desired <swing-foot clearance> $h$ over a flat reference plane. Choose
$$
x(s)=x_0+L(3s^2-2s^3),\qquad z(s)=h\sin^2(\pi s).
$$
Both components have zero endpoint velocity. At mid-swing the foot has moved halfway horizontally and reaches height $h$. The maximum horizontal and vertical speed magnitudes are
$$
\max|\dot x|=\frac{3L}{2T_w},\qquad
\max|\dot z|=\frac{\pi h}{T_w}.
$$
For $L=0.20\,\mathrm m$, $h=0.040\,\mathrm m$ and $T_w=0.40\,\mathrm s$, these are $0.75\,\mathrm{m\,s^{-1}}$ and about $0.314\,\mathrm{m\,s^{-1}}$. Halving the available swing time doubles the path's speed requirements and quadruples its acceleration requirements. A contact schedule can therefore be feasible in timing arithmetic but too demanding for the actual leg.
The path is only a foot-level specification. <Inverse kinematics> must find joint configurations that realize it, and joint motion, collision and actuator constraints must also hold. Zero endpoint velocity does not guarantee continuous acceleration when this segment is joined to another trajectory. An uncertain or uneven ground height changes the actual clearance and contact time.
The primary contact-planning treatment distinguishes choosing contacts from moving through <configuration space> between them.<Robotic Systems by Kris Hauser>[Chapter 12, Manipulation planning and locomotion planning and Multi-modal motion planning]{ref} A proposed robot test measures the foot path, the contact transition and joint response while changing swing duration or clearance. Calibrated <sensors> can distinguish premature ground contact from a trajectory-tracking error. The example above is an original motion prescription; it is not a measured gait or a complete stability controller.
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