Robot locomotion

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Robot locomotion is the collective name for the various methods that robots use to transport themselves from place to place.

Contents

Wheeled robots are typically quite energy efficient and simple to control. However, other forms of locomotion may be more appropriate for a number of reasons, for example traversing rough terrain, as well as moving and interacting in human environments. Furthermore, studying bipedal and insect-like robots may beneficially impact on biomechanics.

A major goal in this field is in developing capabilities for robots to autonomously decide how, when, and where to move. However, coordinating numerous robot joints for even simple matters, like negotiating stairs, is difficult. Autonomous robot locomotion is a major technological obstacle for many areas of robotics, such as humanoids (like Honda's Asimo).

Types of locomotion

Walking

Klann linkage walking motion F4-motion.gif
Klann linkage walking motion

Walking robots simulate human or animal gait, as a replacement for wheeled motion. Legged motion makes it possible to negotiate uneven surfaces, steps, and other areas that would be difficult for a wheeled robot to reach, as well as causes less damage to environmental terrain as wheeled robots, which would erode it. [1]

Hexapod robots are based on insect locomotion, most popularly the cockroach [2] and stick insect, whose neurological and sensory output is less complex than other animals. Multiple legs allow several different gaits, even if a leg is damaged, making their movements more useful in robots transporting objects.

Examples of advanced running robots include ASIMO, BigDog, HUBO 2, RunBot, and Toyota Partner Robot.

Rolling

In terms of energy efficiency on hard, flat surfaces, wheeled robots are the most efficient. This is because an ideal, non-deformable rolling (but not slipping) wheel loses no energy. This is in contrast to legged robots which suffer an impact with the ground at heel strike and lose energy as a result.

Segway in the Robot museum in Nagoya Segway 01.JPG
Segway in the Robot museum in Nagoya

For simplicity, most mobile robots have four wheels or a number of continuous tracks. Some researchers have tried to create more complex wheeled robots with only one or two wheels. These can have certain advantages such as greater efficiency and reduced parts, as well as allowing a robot to navigate in confined places that a four-wheeled robot would not be able to.

Examples: Boe-Bot, Cosmobot, Elmer, Elsie, Enon, HERO, IRobot Create, iRobot's Roomba, Johns Hopkins Beast, Land Walker, Modulus robot, Musa, Omnibot, PaPeRo, Phobot, Pocketdelta robot, Push the Talking Trash Can, RB5X, Rovio, Seropi, Shakey the robot, Sony Rolly, Spykee, TiLR, Topo, TR Araña, and Wakamaru.

Hopping

Several robots, built in the 1980s by Marc Raibert at the MIT Leg Laboratory, successfully demonstrated very dynamic walking. Initially, a robot with only one leg, and a very small foot, could stay upright simply by hopping. The movement is the same as that of a person on a pogo stick. As the robot falls to one side, it would jump slightly in that direction, in order to catch itself. [3] Soon, the algorithm was generalised to two and four legs. A bipedal robot was demonstrated running and even performing somersaults. [4] A quadruped was also demonstrated which could trot, run, pace, and bound. [5]

Examples:

Metachronal motion

Coordinated, sequential mechanical action having the appearance of a traveling wave is called a metachronal rhythm or wave, and is employed in nature by ciliates for transport, and by worms and arthropods for locomotion.

Slithering

Several snake robots have been successfully developed. Mimicking the way real snakes move, these robots can navigate very confined spaces, meaning they may one day be used to search for people trapped in collapsed buildings. [8] The Japanese ACM-R5 snake robot [9] can even navigate both on land and in water. [10]

Examples: Snake-arm robot, Roboboa, and Snakebot.

Swimming

Brachiating

Brachiation allows robots to travel by swinging, using energy only to grab and release surfaces. [11] This motion is similar to an ape swinging from tree to tree. The two types of brachiation can be compared to bipedal walking motions (continuous contact) or running (ricochetal). Continuous contact is when a hand/grasping mechanism is always attached to the surface being crossed; ricochetal employs a phase of aerial "flight" from one surface/limb to the next.

Hybrid

Robots can also be designed to perform locomotion in multiple modes. For example, the Reconfigurable Bipedal Snake Robot [12] can both slither like a snake and walk like a biped robot.

Biologically inspired locomotion

The desire to create robots with dynamic locomotive abilities has driven scientists to look to nature for solutions. Several robots capable of basic locomotion in a single mode have been invented but are found to lack several capabilities, hence limiting their functions and applications. Highly intelligent robots are needed in several areas such as search and rescue missions, battlefields, and landscape investigation. Thus robots of this nature need to be small, light, quick, and possess the ability to move in multiple locomotive modes. As it turns out, multiple animals have provided inspiration for the design of several robots. Some such animals are:

Pteromyini (flying squirrels)

Illustrative image of the flying squirrel (Pteromyini) Oggetto MuSe 020.JPG
Illustrative image of the flying squirrel (Pteromyini)

Pteromyini (a tribe made up of flying squirrels) exhibit great mobility while on land by making use of their quadruped walking ability with high-degrees of freedom (DoF) legs. In air, flying squirrels glide through by utilizing lift forces from the membrane between their legs. They possess a highly flexible membrane that allows for unrestrained movement of the legs. [13] They use their highly elastic membrane to glide while in air and demonstrate lithe movement on the ground. In addition, Pteromyini are able to exhibit multi-modal locomotion due to the membrane that connects the fore and hind legs which also enhances their gliding ability. [13] It has been proven that a flexible membrane possesses a higher lift coefficient than rigid plates and delays the angle of attack at which stall occurs. [13] The flying squirrel also possesses thick bundles on the edges of its membrane, wingtips and tail which helps to minimize fluctuations and unnecessary energy loss. [13]

Image showing the location of the uropatagium Platyrrhinus helleri2.jpg
Image showing the location of the uropatagium

Pteromyini are able to boost their gliding ability due to the numerous physical attributes they possess.

The flexible muscle structure serves multiple purposes. For one, the plagiopatagium, which serves as the primary generator of lift for the flying squirrel, is able to effectively function due to its thin and flexible muscles. [14] [15] The plagiopatagium is able to control tension on the membrane due to contraction and expansion. Tension control can ultimately help in energy savings due to minimized fluttering of the membrane. Once the squirrel lands, it contracts its membrane to ensure that the membrane does not sag when it is walking. [15]

The propatagium and uropatagium serve to provide extra lift for Pteromyini. [15] While the propatagium is situated between the head and forelimbs of the flying squirrel, the uropatagium is located at the tail and hind limbs and these serve to provide the flying squirrel with increased agility and drag for landing. [15]

Additionally, the flying squirrel possesses thick rope-like muscle structures on the edges of its membrane to maintain the shape of the membranes. [15] These muscular structures called platysma, tibiocarpalis, and semitendinosus, are located on the propatagium, plagiopatagium and uropatagium respectively. [15] These thick muscle structures serve to guard against unnecessary fluttering due to strong wind pressures during gliding hence minimizing energy loss. [15]

The wingtips are situated at the forelimb wrists and serve to form an airfoil which minimizes the effect of induced drag due to the formation of wingtip vortices. [14] The wingtips dampen the effects of the vortices and obstruct the induced drag from affecting the whole wing. Flying squirrels are able to unfold and fold their wingtips while gliding by using their thumbs. This serves to prevent undesired sagging of the wingtips. [14]

The tail of the flying squirrel allows for improved gliding abilities as it plays a critical role. As opposed to other vertebrates, Pteromyini possess a tail that is flattened to gain more aerodynamic surface as they glide. [16] [17] This also allows the flying squirrel to maintain pitch angle stability of its tail. This is particularly useful during landing as the flying squirrel is able to widen its pitch angle and induce more drag so as to decelerate and land safely. [15]

Furthermore, the legs and tail of Pteromyini serve to control their gliding direction. Due to the flexibility of the membranes around the legs, the chord angle and dihedral angle between the membrane and coronal plane of the body is controlled. [13] This allows the animal to create rolling, pitching, and yawing movements which in turn control the speed and direction of the gliding. [18] [19] During landing, the animal is able to rapidly reduce its speed by increasing drag and changing its pitch angle using its membranes and further increasing air resistance by loosening the tension between the membranes of its legs. [18] [19]

Desmodus Rotundus (vampire bat)

Image showing the Desmodus Rotundus (vampire bat) Desmodus rotundus 1.jpg
Image showing the Desmodus Rotundus (vampire bat)

The common vampire bats are known to possess powerful modes of terrestrial locomotion, such as jumping, and aerial locomotion such as gliding. Several studies have demonstrated that the morphology of the bat enables it to easily and effectively alternate between both locomotive modes. [20] The anatomy that aids in this is essentially built around the largest muscle in the body of the bat, pectoralis profundus (posterior division). [20] Between the two modes of locomotion, there are three bones that are shared. These three main bones are integral parts of the arm structure, namely the humerus, ulna, and radius. Since there already exists a sharing of components for both modes, no additional muscles are needed when transitioning from jumping to gliding. [20]

Image showing the schistocerca gregaria (desert locust) Schistocerca gregaria - normal.jpg
Image showing the schistocerca gregaria (desert locust)

A detailed study of the morphology of the shoulder of the bat shows that the bones of the arm are slightly sturdier and the ulna and the radius have been fused so as to accommodate heavy reaction forces from the ground [20]

Schistocerca gregaria (desert locust)

The desert locust is known for its ability to jump and fly over long distances as well as crawl on land. [21] A detailed study of the anatomy of this organism provides some detail about the mechanisms for locomotion. The hind legs of the locust are developed for jumping. They possess a semi-lunar process which consists of the large extensor tibiae muscle, small flexor tibiae muscle, and banana-shaped thickened cuticle. [22] [23] When the tibiae muscle flexes, the mechanical advantage of the muscles and the vertical thrust component of the leg extension are increased. [24] These desert locusts utilize a catapult mechanism wherein the energy is first stored in the hind legs and then released to extend the legs. [25]

In order for a perfect jump to occur, the locust must push its legs on the ground with a strong enough force so as to initiate a fast takeoff. The force must be adequate enough in order to attain a quick takeoff and decent jump height. The force must also be generated quickly. In order to effectively transition from the jumping mode to the flying mode, the insect must adjust the time during the wing opening to maximize the distance and height of the jump. When it is at the zenith of its jump, the flight mode becomes actuated. [22]

Multi-modal robot locomotion based on bio-inspiration

Modeling of a multi-modal walking and gliding robot after Pteromyini (flying squirrels)

Following the discovery of the requisite model to mimic, researchers sought to design a legged robot that was capable of achieving effective motion in aerial and terrestrial environments by the use of a flexible membrane. Thus, to achieve this goal, the following design considerations had to be taken into account:

1.       The shape and area of the membrane had to be consciously selected so that the intended aerodynamic capabilities of this membrane could be achieved. Additionally, the design of the membrane would affect the design of the legs since the membrane is attached to the legs. [13]

2.       The membrane had to be flexible enough to allow for unrestricted movement of the legs during gliding and walking. However, the amount of flexibility had to be controlled due to the fact that excessive flexibility could lead to a significant loss of energy caused by the oscillations at regions of the membrane where strong pressure occur. [13]

3.       The leg of the robot had to be designed to allow for appropriate torques for walking as well as gliding. [13]

In order to incorporate these factors, close attention had to be paid to the characteristics of the flying squirrel. The aerodynamic features of the robot were modeled using dynamic modeling and simulation. By imitating the thick muscle bundles of the membrane of the flying squirrel, the designers were able to minimize the fluctuations and oscillations on the membrane edges of the robot, thus reducing needless energy loss. [13] Furthermore, the amount of drag on the wing of the robot was reduced by the use of retractable wingtips thereby allowing for improved gliding abilities. [14] Moreover, the leg of the robot was designed to incorporate sufficient torque after mimicking the anatomy of Pteryomini's leg using virtual work analysis. [13]

Following the design of the leg and membrane of the robot, its average gliding ratio (GR) was determined to be 1.88. The robot functioned effectively, walking in several gait patterns and crawling with its high DoF legs. [13] The robot was also able to land safely. These performances demonstrated the gliding and walking capabilities of the robot and its multi-modal locomotion

Modeling of a multi-modal jumping and gliding robot after the Desmodus Rotundus (vampire bat)

The design of the robot called Multi-Mo Bat involved the establishment of four primary phases of operation: energy storage phase, jumping phase, coasting phase, and gliding phase. [20] The energy storing phase essentially involves the reservation of energy for the jumping energy. This energy is stored in the main power springs. This process additionally creates a torque around the joint of the shoulders which in turn configures the legs for jumping. Once the stored energy is released, the jump phase can be initiated. When the jump phase is initiated and the robot takes off from the ground, it transitions to the coast phase which occurs until the acme is reached and it begins to descend. As the robot descends, drag helps to reduce the speed at which it descends as the wing is reconfigured due to increased drag on the bottom of the airfoils. [20] At this stage, the robot glides down.

The anatomy of the arm of the vampire bat plays a key role in the design of the leg of the robot. In order to minimize the number of Degrees of Freedom (DoFs), the two components of the arm are mirrored over the xz plane. [20] This then creates the four-bar design of the leg structure of the robot which results in only two independent DoFs. [20]

Modeling of a multi-modal jumping and flying robot after the Schistocerca gregaria (desert locust)

The robot designed was powered by a single DC motor which integrated the performances of jumping and flapping. [23] It was designed as an incorporation of the inverted slider-crank mechanism for the construction of the legs, a dog-clutch system to serve as the mechanism for winching, and a rack-pinion mechanism used for the flapping-wing system. [20] This design incorporated a very efficient energy storage and release mechanism and an integrated wing flapping mechanism. [20]

A robot with features similar to the locust was developed. The primary feature of the robot's design was a gear system powered by a single motor which allowed the robot to perform its jumping and flapping motions. Just like the motion of the locust, the motion of the robot is initiated by the flexing of the legs to the position of maximum energy storage after which the energy is released immediately to generate the force necessary to attain flight. [20]

The robot was tested for performance and the results demonstrated that the robot was able to jump to an approximate height of 0.9m while weighing 23g and flapping its wings at a frequency of about 19 Hz. [20] The robot tested without flapping wings performed less impressively, showing about 30% decrease in jumping performance as compared to the robot with the wings. [20] These results are quite impressive[ editorializing ] as it is expected that the reverse be the case since the weight of the wings should have impacted the jumping.

Approaches

Notable researchers in the field

See also

Related Research Articles

<span class="mw-page-title-main">Bipedalism</span> Terrestrial locomotion using two limbs

Bipedalism is a form of terrestrial locomotion where a tetrapod moves by means of its two rear limbs or legs. An animal or machine that usually moves in a bipedal manner is known as a biped, meaning 'two feet'. Types of bipedal movement include walking or running and hopping.

<span class="mw-page-title-main">Walking</span> Gait of locomotion among legged animals

Walking is one of the main gaits of terrestrial locomotion among legged animals. Walking is typically slower than running and other gaits. Walking is defined by an "inverted pendulum" gait in which the body vaults over the stiff limb or limbs with each step. This applies regardless of the usable number of limbs—even arthropods, with six, eight, or more limbs, walk. In humans, walking has health benefits including improved mental health and reduced risk of cardiovascular disease and death.

<span class="mw-page-title-main">Jumping</span> Form of movement in which an organism or mechanical system propels itself into the air

Jumping or leaping is a form of locomotion or movement in which an organism or non-living mechanical system propels itself through the air along a ballistic trajectory. Jumping can be distinguished from running, galloping and other gaits where the entire body is temporarily airborne, by the relatively long duration of the aerial phase and high angle of initial launch.

<span class="mw-page-title-main">Gait</span> Pattern of movement of the limbs of animals

Gait is the pattern of movement of the limbs of animals, including humans, during locomotion over a solid substrate. Most animals use a variety of gaits, selecting gait based on speed, terrain, the need to maneuver, and energetic efficiency. Different animal species may use different gaits due to differences in anatomy that prevent use of certain gaits, or simply due to evolved innate preferences as a result of habitat differences. While various gaits are given specific names, the complexity of biological systems and interacting with the environment make these distinctions "fuzzy" at best. Gaits are typically classified according to footfall patterns, but recent studies often prefer definitions based on mechanics. The term typically does not refer to limb-based propulsion through fluid mediums such as water or air, but rather to propulsion across a solid substrate by generating reactive forces against it.

<span class="mw-page-title-main">Flying squirrel</span> Tribe of mammals

Flying squirrels are a tribe of 50 species of squirrels in the family Sciuridae. Despite their name, they are not in fact capable of full flight in the same way as birds or bats, but they are able to glide from one tree to another with the aid of a patagium, a furred skin membrane that stretches from wrist to ankle. Their long tails also provide stability as they glide. Anatomically they are very similar to other squirrels with a number of adaptations to suit their lifestyle; their limb bones are longer and their hand bones, foot bones, and distal vertebrae are shorter. Flying squirrels are able to steer and exert control over their glide path with their limbs and tail.

<span class="mw-page-title-main">Rectilinear locomotion</span> Mode of locomotion associated with snakes

Rectilinear locomotion or rectilinear progression is a mode of locomotion most often associated with snakes. In particular, it is associated with heavy-bodied species such as terrestrial African adders, pythons and boas; however, most snakes are capable of it. It is one of at least five forms of locomotion used by snakes, the others being lateral undulation, sidewinding, concertina movement, and slide-pushing. Unlike all other modes of snake locomotion, which include the snake bending its body, the snake flexes its body only when turning in rectilinear locomotion.

<span class="mw-page-title-main">Animal locomotion</span> Self-propulsion by an animal

In ethology, animal locomotion is any of a variety of methods that animals use to move from one place to another. Some modes of locomotion are (initially) self-propelled, e.g., running, swimming, jumping, flying, hopping, soaring and gliding. There are also many animal species that depend on their environment for transportation, a type of mobility called passive locomotion, e.g., sailing, kiting (spiders), rolling or riding other animals (phoresis).

<span class="mw-page-title-main">Fish locomotion</span> Ways that fish move around

Fish locomotion is the various types of animal locomotion used by fish, principally by swimming. This is achieved in different groups of fish by a variety of mechanisms of propulsion, most often by wave-like lateral flexions of the fish's body and tail in the water, and in various specialised fish by motions of the fins. The major forms of locomotion in fish are:

<span class="mw-page-title-main">Flying and gliding animals</span> Animals that have evolved aerial locomotion

A number of animals are capable of aerial locomotion, either by powered flight or by gliding. This trait has appeared by evolution many times, without any single common ancestor. Flight has evolved at least four times in separate animals: insects, pterosaurs, birds, and bats. Gliding has evolved on many more occasions. Usually the development is to aid canopy animals in getting from tree to tree, although there are other possibilities. Gliding, in particular, has evolved among rainforest animals, especially in the rainforests in Asia where the trees are tall and widely spaced. Several species of aquatic animals, and a few amphibians and reptiles have also evolved this gliding flight ability, typically as a means of evading predators.

<span class="mw-page-title-main">Terrestrial locomotion</span> Ability of animals to travel on land

Terrestrial locomotion has evolved as animals adapted from aquatic to terrestrial environments. Locomotion on land raises different problems than that in water, with reduced friction being replaced by the increased effects of gravity.

A facultative biped is an animal that is capable of walking or running on two legs (bipedal), as a response to exceptional circumstances (facultative), while normally walking or running on four limbs or more. In contrast, obligate bipedalism is where walking or running on two legs is the primary method of locomotion. Facultative bipedalism has been observed in several families of lizards and multiple species of primates, including sifakas, capuchin monkeys, baboons, gibbons, gorillas, bonobos and chimpanzees. Several dinosaur and other prehistoric archosaur species are facultative bipeds, most notably ornithopods and marginocephalians, with some recorded examples within sauropodomorpha. Different facultatively bipedal species employ different types of bipedalism corresponding to the varying reasons they have for engaging in facultative bipedalism. In primates, bipedalism is often associated with food gathering and transport. In lizards, it has been debated whether bipedal locomotion is an advantage for speed and energy conservation or whether it is governed solely by the mechanics of the acceleration and lizard's center of mass. Facultative bipedalism is often divided into high-speed (lizards) and low-speed (gibbons), but some species cannot be easily categorized into one of these two. Facultative bipedalism has also been observed in cockroaches and some desert rodents.

<span class="mw-page-title-main">Legged robot</span> Type of mobile robot

Legged robots are a type of mobile robot which use articulated limbs, such as leg mechanisms, to provide locomotion. They are more versatile than wheeled robots and can traverse many different terrains, though these advantages require increased complexity and power consumption. Legged robots often imitate legged animals, such as humans or insects, in an example of biomimicry.

<span class="mw-page-title-main">Origin of avian flight</span> Evolution of birds from non-flying ancestors

Around 350 BCE, Aristotle and other philosophers of the time attempted to explain the aerodynamics of avian flight. Even after the discovery of the ancestral bird Archaeopteryx which lived over 150 million years ago, debates still persist regarding the evolution of flight. There are three leading hypotheses pertaining to avian flight: Pouncing Proavis model, Cursorial model, and Arboreal model.

<span class="mw-page-title-main">Human skeletal changes due to bipedalism</span> Evoltionary changes to the human skeleton as a consequence of bipedalism

The evolution of human bipedalism, which began in primates approximately four million years ago, or as early as seven million years ago with Sahelanthropus, or approximately twelve million years ago with Danuvius guggenmosi, has led to morphological alterations to the human skeleton including changes to the arrangement, shape, and size of the bones of the foot, hip, knee, leg, and the vertebral column. These changes allowed for the upright gait to be overall more energy efficient in comparison to quadrupeds. The evolutionary factors that produced these changes have been the subject of several theories that correspond with environmental changes on a global scale.

<span class="mw-page-title-main">Leg</span> Weight bearing and locomotive anatomical structure

A leg is a weight-bearing and locomotive anatomical structure, usually having a columnar shape. During locomotion, legs function as "extensible struts". The combination of movements at all joints can be modeled as a single, linear element capable of changing length and rotating about an omnidirectional "hip" joint.

<span class="mw-page-title-main">Comparative foot morphology</span> Comparative anatomy

Comparative foot morphology involves comparing the form of distal limb structures of a variety of terrestrial vertebrates. Understanding the role that the foot plays for each type of organism must take account of the differences in body type, foot shape, arrangement of structures, loading conditions and other variables. However, similarities also exist among the feet of many different terrestrial vertebrates. The paw of the dog, the hoof of the horse, the manus (forefoot) and pes (hindfoot) of the elephant, and the foot of the human all share some common features of structure, organization and function. Their foot structures function as the load-transmission platform which is essential to balance, standing and types of locomotion.

Role of skin in locomotion describes how the integumentary system is involved in locomotion. Typically the integumentary system can be thought of as skin, however the integumentary system also includes the segmented exoskeleton in arthropods and feathers of birds. The primary role of the integumentary system is to provide protection for the body. However, the structure of the skin has evolved to aid animals in their different modes of locomotion. Soft bodied animals such as starfish rely on the arrangement of the fibers in their tube feet for movement. Eels, snakes, and fish use their skin like an external tendon to generate the propulsive forces need for undulatory locomotion. Vertebrates that fly, glide, and parachute also have a characteristic fiber arrangements of their flight membranes that allows for the skin to maintain its structural integrity during the stress and strain experienced during flight.

<span class="mw-page-title-main">Bio-inspired robotics</span>

Bio-inspired robotic locomotion is a fairly new subcategory of bio-inspired design. It is about learning concepts from nature and applying them to the design of real-world engineered systems. More specifically, this field is about making robots that are inspired by biological systems, including Biomimicry. Biomimicry is copying from nature while bio-inspired design is learning from nature and making a mechanism that is simpler and more effective than the system observed in nature. Biomimicry has led to the development of a different branch of robotics called soft robotics. The biological systems have been optimized for specific tasks according to their habitat. However, they are multifunctional and are not designed for only one specific functionality. Bio-inspired robotics is about studying biological systems, and looking for the mechanisms that may solve a problem in the engineering field. The designer should then try to simplify and enhance that mechanism for the specific task of interest. Bio-inspired roboticists are usually interested in biosensors, bioactuators, or biomaterials. Most of the robots have some type of locomotion system. Thus, in this article different modes of animal locomotion and few examples of the corresponding bio-inspired robots are introduced.

<span class="mw-page-title-main">Arm swing in human locomotion</span>

Arm swing in human bipedal walking is a natural motion wherein each arm swings with the motion of the opposing leg. Swinging arms in an opposing direction with respect to the lower limb reduces the angular momentum of the body, balancing the rotational motion produced during walking. Although such pendulum-like motion of arms is not essential for walking, recent studies point that arm swing improves the stability and energy efficiency in human locomotion. Those positive effects of arm swing have been utilized in sports, especially in racewalking and sprinting.

<span class="mw-page-title-main">Walking vehicle</span> Vehicles that use legs rather than wheels, wings or hulls, for land locomotion

A walking vehicle is a vehicle that moves on legs rather than wheels or tracks. Walking vehicles have been constructed with anywhere from one to more than eight legs. There are many designs for the leg mechanisms of walking machines that provide foot trajectories with different properties.

References

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  9. ↑ ACM-R5 Archived 2011-10-11 at the Wayback Machine
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  18. 1 2 Bishop, Kristin L. (2006-02-15). "The relationship between 3-D kinematics and gliding performance in the southern flying squirrel, Glaucomys volans". Journal of Experimental Biology. 209 (4): 689–701. doi: 10.1242/jeb.02062 . ISSN   0022-0949. PMID   16449563.
  19. 1 2 Bishop, Kristin L. (2007-08-01). "Aerodynamic force generation, performance and control of body orientation during gliding in sugar gliders (Petaurus breviceps)". Journal of Experimental Biology. 210 (15): 2593–2606. doi: 10.1242/jeb.002071 . ISSN   0022-0949. PMID   17644674.
  20. 1 2 3 4 5 6 7 8 9 10 11 12 13 Woodward, Matthew A.; Sitti, Metin (2014-09-04). "MultiMo-Bat: A biologically inspired integrated jumping–gliding robot". The International Journal of Robotics Research. 33 (12): 1511–1529. doi:10.1177/0278364914541301. ISSN   0278-3649. S2CID   206500583.
  21. ↑ Rillich, Jan; Stevenson, Paul A.; Pflueger, Hans-Joachim (2013-05-09). "Flight and Walking in Locusts–Cholinergic Co-Activation, Temporal Coupling and Its Modulation by Biogenic Amines". PLOS ONE. 8 (5): e62899. Bibcode:2013PLoSO...862899R. doi: 10.1371/journal.pone.0062899 . ISSN   1932-6203. PMC   3650027 . PMID   23671643.
  22. 1 2 "How Grasshoppers Jump". www.st-andrews.ac.uk. Retrieved 2019-11-04.
  23. 1 2 Truong, Ngoc Thien; Phan, Hoang Vu; Park, Hoon Cheol (2019-03-13). "Design and demonstration of a bio-inspired flapping-wing-assisted jumping robot". Bioinspiration & Biomimetics. 14 (3): 036010. Bibcode:2019BiBi...14c6010T. doi:10.1088/1748-3190/aafff5. ISSN   1748-3190. PMID   30658344. S2CID   58665597.
  24. ↑ Burrows, M. (1995-05-01). "Motor patterns during kicking movements in the locust". Journal of Comparative Physiology A. 176 (3): 289–305. doi:10.1007/BF00219055. ISSN   1432-1351. PMID   7707268. S2CID   21759140.
  25. ↑ Burrows, Malcolm; Sutton, Gregory P. (2012-10-01). "Locusts use a composite of resilin and hard cuticle as an energy store for jumping and kicking". Journal of Experimental Biology. 215 (19): 3501–3512. doi: 10.1242/jeb.071993 . ISSN   0022-0949. PMID   22693029.
  26. ↑ Kajita, Shuuji, et al. Biped walking pattern generation by using preview control of zero-moment point. Proceedings of the IEEE International Conference on Robotics and Automation. Volume 2. IEEE, 2003. ISSN   1050-4729. doi : 10.1109/ROBOT.2003.1241826.
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