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A gait is a pattern of coordinated limb motion and contact used in locomotion. In a periodic gait, the order of foot contacts, their relative timing and the duration of each contact characterize a cycle. A quadrupedal robot can change gait without changing the number of legs or their basic mechanical arrangement.

For a repeated foot motion with period $T$, the stance phase is the interval during which that foot contacts the ground; the swing phase moves it between contacts. If stance lasts $T_s$, its contact duty cycle is $\beta =T_s/T$. Relative phase specifies how one leg's cycle is shifted from another's. Equal duty cycles do not determine a unique gait because those phase shifts can differ.

For an original four-leg schedule, take front-left, front-right, hind-left and hind-right phases $(0,1/2,3/4,1/4)$ with $\beta =3/4$. Apart from transition instants, three feet contact the floor. A second constructed schedule takes phases $(0,1/2,1/2,0)$ and $\beta =1/2$: diagonal pairs contact together and alternate every half-cycle, illustrating a trot. The first schedule has total contact-time sum $4\beta T=3T$ per cycle; the second has $2T$. Summing leg contact times does not mean a stride itself lasts three or two periods.

A real dynamic apparatus illustrates why timing must connect to forces. The 2015 MIT Cheetah demonstration adjusted approach strides and motor forces to execute a running jump; its account describes bounding as successive small jumps.^[ref] The numerical schedules above are not measurements from that experiment.

A support polygon is useful for a stipulated static contact model, but a contact schedule alone does not establish static or dynamic feasibility. Friction, joint motion, actuator capability and angular momentum can matter. Measuring foot-contact times alongside body motion and ground reactions tests whether a planned gait is actually realized. Nonperiodic transitions, starts and obstacle maneuvers additionally require more than one fixed repeating cycle.

The stance phase of a robot leg is the portion of a gait during which its foot is in the intended ground contact. It permits force transfer between the robot and its surroundings. Contact can occur with little load, and contact alone does not imply that the foot remains fixed without slipping. The swing phase instead transfers the foot toward another contact.

In an ideal rigid, nonadhesive contact model, let $g$ be the foot's normal gap above the ground and $F_n$ its normal contact force. The conditionsexclude penetration and tensile ground reaction. An open gap requires zero normal reaction; a zero gap permits a compressive reaction but does not require it to be strictly positive. The primary contact model distinguishes these unilateral constraints from the force/torque equations for equilibrium.^[ref]

For an original level-ground example, take a $20\mathrm{kg}$ robot supported by two stance feet, neglecting other external vertical forces. Newton's second law giveswhere $g_0=9.81\mathrm{m}{\mathrm{s}}^{-2}$ is gravitational acceleration and $a_z$ is upward center of mass acceleration. With equal sharing and $a_z=0$, each foot carries $98.1\mathrm{N}$. With $a_z=2\mathrm{m}{\mathrm{s}}^{-2}$, each carries $118.1\mathrm{N}$. Equal sharing is an additional symmetry assumption, not a consequence of knowing there are two contacts.

A simple Coulomb friction model constrains tangential force by $|F_t|\le \mu F_n$. At zero vertical acceleration and $\mu =0.3$, the two feet's combined horizontal-force capacity is at most $0.3m{g}_0=58.86\mathrm{N}$ in this planar model. Accelerating the body horizontally at $4\mathrm{m}{\mathrm{s}}^{-2}$ would require $80\mathrm{N}$ and violate that bound. A stance-time schedule alone cannot remove this force limit. Individual contact geometry and torque balance can impose further constraints even when the combined bound passes.

For a periodic cycle, contact duration $T_s$ gives duty cycle $\beta =T_s/T$. A proposed test records stance timing and forces separately, using calibrated sensors under the contacts together with body-motion measurements. It checks load transfer and slipping as well as touch timing. A support polygon is useful in an explicitly static planar model; dynamic stance additionally requires the changing force and momentum balance.

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.

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. ChooseBoth 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 areFor $L=0.20\mathrm{m}$, $h=0.040\mathrm{m}$ and $T_w=0.40\mathrm{s}$, these are $0.75\mathrm{m}{\mathrm{s}}^{-1}$ and about $0.314\mathrm{m}{\mathrm{s}}^{-1}$. 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.^[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.

A trot in a quadrupedal robot coordinates diagonal leg pairs: front-left with hind-right, and front-right with hind-left. The two pairs alternate their stance phases and swing phases. The pairing and relative timing define the pattern; the fraction of each cycle spent in contact can vary.

For an original periodic model, take cycle period $T$ and normalized cycle phase $u=t/T(\mathrm{mod}1)$. Let the front-left/hind-right pair have phase zero and the other pair have phase $1/2$. Each foot remains in stance phase for fraction $\beta$ of the cycle. At $\beta =1/2$, one diagonal pair contacts while the other swings, apart from the idealized transition instants.

The contact-time consequences follow directly. For $\beta <1/2$, the diagonal-pair contacts do not overlap, and the fraction of the cycle with no foot contact isFor $\beta >1/2$, the intervals overlap, and the fraction with all four feet in contact is $2\beta -1$. Thus $\beta =0.4$ gives 20% no-contact time, while $\beta =0.6$ gives 20% four-foot overlap. The average number of contacting feet is $4\beta$ in either case, but an average does not describe the instantaneous support.

For stipulated $T=0.5\mathrm{s}$ and $\beta =0.6$, each foot's stance lasts $0.3\mathrm{s}$ and swing lasts $0.2\mathrm{s}$. Each pair overlaps the other for $0.05\mathrm{s}$ at each exchange, totaling $0.1\mathrm{s}$ per cycle. These are constructed timings, not measurements of a particular machine.

Two ideal diagonal point contacts have a support polygon reduced to a line segment. Static balance would require the projected center of mass to lie on that segment under the usual horizontal-plane assumptions, leaving no area margin to lateral disturbance. Dynamic motion additionally involves contact forces, angular momentum, friction and actuator limits. The contact and equilibrium models in the primary robotics text explain why a geometric schedule alone is insufficient.^[ref]

A proposed robot trial records all foot-contact events, body motion and ground contact forces while commanding the diagonal pattern. It checks whether the planned duty fraction and phase offsets are realized and whether motion remains feasible. Contact timing identifies the gait; the force and motion records test its execution.