TL;DR:
A gait is a repeating pattern of which feet are on the ground and when. The duty factor is the fraction of the cycle each foot spends on the ground.
A walk keeps at least three feet down and is statically stable, a trot lifts diagonal pairs together, and a bound swings front and rear pairs.
Faster gaits have shorter ground contact and need active balance control.
Watch a dog walk slowly, then trot, then run. Its legs do the same job each time, but the order in which they touch the ground changes. A four-legged robot needs a rule for that order, and the rule is called a gait.
What a gait is
A gait is a repeating cycle. In each cycle every leg spends some time on the ground, the stance phase, pushing the body along, and some time in the air, the swing phase, moving forward to the next foothold. The gait specifies when each leg starts its stance relative to the others.
The key number is the duty factor, the fraction of the cycle that a foot is on the ground:
duty factor β = stance time / cycle time
A high duty factor means feet are on the ground most of the time and several legs support the body at once. A low duty factor means feet are on the ground briefly and sometimes none are.
The three gaits
Walk. Legs move one at a time, in a sequence such as left-hind, left-front, right-hind, right-front. The cycle is offset by a quarter between legs. Three or four feet are always down.
Trot. Diagonal pairs move together: the front-left and rear-right legs, then the front-right and rear-left legs. At any moment two feet are down, and in a fast trot there is a brief moment when none are.
Bound. The two front legs move together, then the two rear legs. The body flexes forward and back like a rabbit or a galloping dog.
Worked example: which legs move together in each gait
Take a cycle time of 0.8 s for a walk. Call the legs LH, LF, RH, RF (left or right, hind or front).
Walk. Each leg starts its stance a quarter of a cycle after the previous one in the order LH, LF, RH, RF: offsets 0, 0.2, 0.4, 0.6 s. With a duty factor of 0.75, each foot is down for 0.75 × 0.8 = 0.6 s and up for 0.2 s. So at any instant, three feet are on the ground (and for a brief moment all four). Check: four legs, each with 0.75 of the cycle down, gives an average of 4 × 0.75 = 3 feet on the ground.
Trot. Use a cycle of 0.5 s with a duty factor of 0.5. Each foot is down for 0.25 s and up for 0.25 s. The diagonal pairs alternate exactly, so exactly two feet are down at any time: 4 × 0.5 = 2. The support polygon is only a line between the two diagonal feet.
Bound. A cycle of 0.4 s, with a duty factor of 0.5: front pair down for 0.2 s, then the rear pair down for 0.2 s. There are always two feet down (a front pair or a rear pair), or none during flight if the duty factor drops below 0.5.
Now compare speed. Speed equals stride length divided by cycle time. If each stride covers 0.40 m:
Walk:
0.40 / 0.8 = 0.50 m/s.Trot:
0.40 / 0.5 = 0.80 m/s.Bound:
0.40 / 0.4 = 1.0 m/s.
(These strides are examples. Real stride length also grows with speed.)
Static versus dynamic stability
The rule of thumb for a quadruped is that a walk with a duty factor of at least 0.75 can keep three feet down at all times, so the robot can in principle stop in mid-stride without falling, as long as it keeps its center of mass inside the triangle of support (see how a quadruped robot keeps its balance). That is static stability.
The trot and the bound have fewer than three feet down at times, so the support polygon is a line or is missing. The robot stays upright because it keeps moving, with each foot landing where it is needed. That is dynamic stability, and it requires fast feedback from the IMU and the joint encoders.
Trade-offs
Speed. Lower duty factors allow faster motion.
Efficiency. At higher speeds a trot or a bound can store and return energy in the legs, which saves power, but it needs more care with the mechanics.
Terrain. A slow walk lets the robot test each foothold, which suits rough or unknown ground. A trot suits smoother ground.
Control effort. A walk is easier to program: one leg moves at a time. A trot or bound needs timing control and balance feedback.
Impacts. Fast gaits have harder foot impacts, which wear gears and can break parts.
Where it goes wrong
Phase errors. If two legs that should be a half cycle apart drift together, the robot lurches. Use one clock for all legs.
Foot slip. A foot that slides during stance wastes energy and upsets balance.
Changing gait suddenly. Switching from a walk to a trot in one step can leave the robot with no feet down. Transition gradually, using intermediate timing.
Overloaded motors. In a trot, each stance leg carries about half the robot's weight, instead of about a third in a walk. For a 10 kg robot the weight is
10 × 9.8 = 98 N, so each of two feet carries about 49 N at rest, and more when it lands with speed. Check that the leg motors can hold that.
Safety: A legged robot's legs swing fast and its joints pinch. Do not stand in front of or behind a robot that is trotting, because a stumble can send it forward. Test at slow speed and low gait frequency first, hold the robot on a stand or a safety line when you change gaits, and keep a switch to cut motor power in reach.
How real robots use gaits
Quadruped robots switch between a slow, stable walk and a quicker trot depending on the speed asked for, and some add a bound for speed. Controllers define the gait as a table of stance and swing times for each leg, and a stepping plan builds on it. The same ideas appear in six-legged and two-legged walkers. The related question of why a robot falls over at all is explored in center of mass and why robots tip over.
Try it yourself
Take a toy with four legs, or use four fingers on a table, and act out each gait: walk (one at a time), trot (diagonal pairs) and bound (front pair, then rear pair). Time each with a stopwatch. Write the cycle time, the duty factor and the number of feet on the table at each moment. Then work out how many feet are down on average and check it against 4 × β.
Frequently asked questions
What does duty factor tell me?
It is the fraction of the cycle a foot is on the ground. Multiply by the number of legs to get the average number of feet down at any time.
Why not trot all the time?
A trot needs fast balance control and gives a small support polygon. A walk is slower but more stable on rough ground.
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