LocomotionCSE169: Computer AnimationInstructor: Steve RotenbergUCSD, Winter 2008Legged LocomotionMuybridge Eadweard Muybridge “Animal Locomotion” - 1887 “Animals in Motion” - 1899 “The Human Figure in Motion” - 1901Gaits A gait refers to a particular sequence of lifting and placing the feet during legged locomotion (gallop, trot, walk, run…) Each repetition of the sequence is called a gait cycle The time taken in one complete cycle is the gaitperiod The inverse of the period is the gait frequency(1/period) Normally, in one gait cycle, each leg goes through exactly one complete step cycleGait Phase We can think of the gait phase a value that ranges from 0 to 1 as the gait cycle proceeds We can choose 0 as being any arbitrary point within the cycle (such as when the back left foot begins its step) The phase is like a clock that keeps going round and round (0…1, 0…1, 0…1) For a particular gait, the stepping of the legs and all other motion of the character can be described relative to the gait phaseStep Cycle In one gait cycle, each individual leg goes through a complete step cycle Each leg’s step cycle is phase shifted relative to the main gait cycle The step cycle is broken into two main stages Support stage (foot on ground) Transfer stage (foot in the air) The amount of time a leg spends in the support stage is the support duration (& likewise for transfer duration)GaitPeriodrationTransferDuationSupportDur=+Duty Factor The relative amount of time a foot spends on the ground is called the duty factor For a human walking, the duty factor will be greater than 0.5, indicating that there is an overlap time when both feet are on the ground For a run, the duty factor is less than 0.5, indicating that there is a time when both feet are in the air and the body is undergoing ballistic motionGaitPeriodationSupportDurDutyFactor =Step Phase The step phase is a value that ranges from 0 to 1 during an individual leg’s step cycle We can choose 0 to indicate the moment when the foot begins to lift (i.e., the beginning of the transfer phase) The foot contacts the ground and comes to rest when the phase equals 1 minus the duty factorStep Trigger Each leg’s step cycle is phase shifted relative to the main gait cycle This phase shift is called the step trigger The trigger is the phase within the main gait cycle where a particular leg begins its step cycle.0Biped Walk.5Locomotion Terminology Gait Gait cycle Gait period Gait frequency Gait phase Stepping Step cycle Step phase Support stage, support duration Transfer stage, transfer duration Duty factor Step triggerGait Description A simple description of the timing of a particular gait requires the following information Number of legs Gait period Duty factor & step trigger for each legAnimal GaitsAncestral Tetrapods All land based vertebrates evolved from an original ‘tetrapod’ ancestor The tetrapod was like a primitive reptile- closer to a fish The 4 legs were adaptations of swimming fins and the creature moved on land by a combination of ‘paddling’with its legs and ‘swimming’ with it’s spine All present day quadruped vertebrates are based on the same underlying construction, but with various adaptations Even snakes, birds, dolphins, and whales evolved from the ancestral tetrapod and still show many similaritiesQuadruped Construction Arms Clavicle Scapula Humerus Radius/Ulna Carpals Metacarpals Phalanges Legs Pelvis Femur Tibia/Fibula Tarsals Metatarsals PhalangesQuadrupedsStances Some animals, such as humans and bears walk flat footed (palmate) Some, like horses and cattle walk more on their fingers (digitate) Smaller or stockier animals sometimes walk with wide stances (sprawling gaits) (these include insects, many reptiles, and some small mammals) Larger animals tend to walk with straighter legsQuadruped Gaits Quadruped: 4 legs Muybridge showed that almost all quadrupeds use one or more of the following gaits Walk Amble Trot Rack/Pace Gallop (rotary & transverse) CanterQuadruped Walk.0.25.5.75Walk The basic slow gait of most quadrupeds is the walk Very slow walks may involve 3-4 legs on the ground, but normal walks involve 3 legs on the ground with a brief moment with only 2 The duty factor is therefore relatively high (.6 ~ .8) Actual timing of walk gaits may vary from the diagramWalksAmble.0.2.5.7Amble Ambles are like a quicker version of the walk, but are also associated with larger, slow moving quadrupeds The duty factor is often in the .5 ~ .7 range, but some horses amble at even lower duty factors Elephants use the amble gait exclusively. The front and back legs are often very close in phase (shifted by around .1 or so) The gait often involves a noticeable swinging of the body from left to rightTrot.0.5.5.0Trot The trot is a medium paced gait where alternate diagonal legs step nearly in sync (though often slightly led by the forefoot) The duty factor is usually relatively low (<.4) and there are moments where all 4 legs are off the ground (actually, cats sometimes trot at a higher duty factor…) Before Muybridge, most horse trainers believed a trotting horse always had at least one foot on the groundPace / Rack.0.0.5.5Pace / Rack The rack or pace has similar qualities to the trot, but horses are rarely trained to perform this gait This gait is considered to be the least comfortable for a rider, but supposedly offers better traction than the trot Most camels use this as their primary gaitCanter.0.7.3.0Canter Unlike the first 4 quadruped gaits we looked at, the canter is asymmetrical The canter is a medium speed gait, but a bit irregular and not usually used for long intervals Some horses canter as they slow down from a gallop Sometimes, the timing of the canter is more like .6, .0, .0, .1, with 3 legs stepping in rapid succession, alternating with the 4th legTransverse Gallop.0.5.1.6Transverse Gallop The gallop is the fastest quadruped gait The gallop involves an alternation between the front and back pairs of legs, but slightly out of sync There are several subtle variations on gallops, but they are generally separated into transverse and rotary gallops Horses tend to prefer the transverse gallop, as do most