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ARllCLES LEGGED ROBOTS Research on legged machines can lead to the construction of useful legged vehicles and help us to understand legged locomotion in animals. MARC H. RAIBERT LEGGED MACHINES? run, there are two serious reasons for ex- the use of legs for locomotion. One is mobil- WHY STUDY Aside from the sheer thrill of creating machines that actually ploring ity: There is a need for vehicles that can travel in difficult terrain, where existing vehicles cannot go. Wheels excel on prepared surfaces such as rails and roads, but perform poorly where the terrain is soft or uneven. Because of these limitations, only about half the earth’s landmass is accessible to existing wheeled and tracked vehicles, whereas a much greater area can be reached by animals on foot. It should be possible to build go to the places that animals can now reach. legged vehicles that can One reason legs provide better mobility in rough is that they can use isolated footholds that terrain optimize support and traction, whereas a wheel re- quires a continuous path of support. As a conse- quence, a legged system can choose among the best footholds in the reachable terrain; a wheel must ne- gotiate the worst terrain. A ladder illustrates point: Rungs provide footholds that enable the as- cent of legged systems, but the spaces between the rungs prohibit the ascent of wheeled systems. this With the exception of a few modifications. Legged Robofs sion of the author and The MIT Press. tl~of Balance. 0 1986 by Marc H. Raibert. Reprinted by permis- this article is excerpted from Another advantage of legs is that they provide an active suspension that decouples the path of the body from the paths of the feet. The payload is free to travel smoothly despite pronounced variations in the terrain. A legged system can also step over obsta- cles. In principle, the performance of legged vehicles can, to a great extent, be independent of the detailed roughness of the ground. footholds, sense the terrain The construction of useful legged vehicles de- pends on progress in several areas of engineering and science. Legged vehicles will need systems that control joint motions, sequence the use of legs, mon- itor and manipulate balance, generate motions to use known to find good foot- holds, and calculate negotiable foothold sequences. Most of these tasks are not well understood yet, but research is under way. If this research is successful, it will that travel efficiently and quickly in terrain where softness, grade, or obstacles make existing vehicles ineffective. Such vehicles will be useful in indus- trial, agricultural, and military applications. lead to the development of legged vehicles The second reason for exploring legged machines is to gain a better understanding of human and ani- mal locomotion. Slow-motion replays re- veal to us the large variety and complexity of ways athletes can carry, swing, toss, glide, and otherwise television june 1986 Volume 29 Number 6 Communications of the ACM 499

Articles is equally propel their bodies through space, maintaining orientation, balance, and speed as they go. Such per- to professional athletes; be- formance is not limited impressive havior at the local playgroun’d from a mechanical engineering, sensory-motor inte- gration, or computational point of view. Animals also demonstrate g.reat mobihty and agility. They use their legs to move quickly and reliably through forest, swamp, marsh, and jungle, and from tree to tree. Sometimes thsey move with great speed, often with great efficiency. is to build for animal locomotion locomotion the control prmciples Despite the skill we apply in using our own legs for locomotion, we are still at a primitive stage in understanding that underlie walking and running. What control mechanisms do animals use? One way to learn more about plausible mechanisms legged machines. To the extent that an animal and a ma- chine perform similar tasks, their control systems and mecha.nical structures must solve simi- lar problems. By building machines, we can gain new insights into these problems, and learn about possible solutions. Of particul.ar value is the rigor required that actually work. The concrete theories and algorithms devel- oped for such machines can guide biological search by suggesting specific models for experimen- tal testing and verification. This sort of interdisci- plinary approach is already becoming popular in other areas where biology and robotics have a com- mon ground, such as vision, speech, and manipula- tion. to build p:hysical machines re- ON LEGGED MACHINES RESEARCH The scientific study of legged locomotion began just over a century ago when Leland Stanford, then gov- ernor of California, commissioned Eadweard Muy- bridge to find out whether or not a trotting horse left the ground with all four feet at the same time. See Table I for milestones in the development of legged robots. Stanford had wagered that it never did. After Muybridge proved him wrong with a set of stop- motion photographs ican in 1878, Muybridge went on to document walking and rurming behavior of over 40 mammals, including humans still of considerable value and survive as a landmark in locomotion that appeared in Scientific Amer- [24, 251. His photographic data are the research. The study of machines that walk also had its ori- gin in Muybridge’s time. An early walking model appeared in about 1870 [13]. It used a linkage to move the body along a straight horizontal path while the feet moved up and down to exchange support during stepping (see Figure 1). The linkage was origi- TABLE 1. Milestones in the Development of Legged Robots 1850 Chebyshev 1872 Muybridge : 1893 Rygg 1946 ’ Wallace 1961 Space General 1963 Cannon, Higdon, and Schaefer Daaigns linkage usad in early walking mechanism [13]. lkaS stop-motion photography to document running animals. Patents human-powered mechanical horse. Patents hopping tank with reaction wheals that provide : stability. Eight-legged kinematic machine walks in outdoor terrain [21]. i=ontrot system balances single, j double, and limber inverted -pendulums. 1968 Frank and h&Ghea simple digital logii controls walking of Phony Pony. 1968 Mosher 1969 Bucyrus-Erie Co. i977 kAcGhee 1977 Gurfinkel 1977 McMahon and Greene . 1980 Hfrose and Vrnetani 1980 Kate 1980 Matsuoka 1981 Miura and Shimoyama 1983 Gumerland 1983 Odetics fSE quadruped truck climbs railroad ties under control of human driver. Big Muskie, a 15,000-ton walking dragline, is used for strip mining. ft moves in soft terrain at a speed of 900 ft./h. [35]. Digital computer coordinates leg motions of hexapod walking machine. Hybrid computer controls hexapod walker in USSR. fluman runners set new speed records on tuned track at ; Harvard. I& compliance is ; adjusted to mechanics of .& human leg. &adrupad machina climbs stairs and climbs over obstacles [ using simple sensors. The leg mechanism simplifies control. fiydraulic biped walks with quasi- ‘ dynamic gait. Mechanism balances in the plane while hopping on one leg. Walking biped balances actively in three-dimensional space. pexapod carries human rider. Computer, hydraulics, and human share computing task. &alf-contained hexapod lifts and moves back end of pickup i +ruck [31]. the 80 or nally designed by the famous Russian mathemati- cian Chebyshev some years earlier. During the task of 90 years that followed, workers viewed building walking machines as the task of designing linkages that would generate suitable stepping mo- tions when driven by a source of power. Many de- signs were proposed (e.g., [l, 21, 34, 36, 38]), but the performance of such machines was limited by their fixed patterns of motion, since they could not adjust to variations in the terrain by placing the feet on the 500 Communications of the ACM lune 1986 Volume 29 Number 6

best footholds (see Figure 2, page 502). By the late 195Os, it had become clear that linkages providing fixed motion would not suffice and that useful walk- ing machines would need control [ll]. truck at General Electric One approach to control was to harness a human. Ralph Mosher used this approach in building a four- legged walking in the mid 1960s [12]. The project was part of a decade-long campaign to build advanced teleoperators, capable of providing better dexterity through high-fidelity force feedback. The machine Mosher built stood 11 feet tall, weighed 3000 pounds, and was powered hydraulically. It is shown in Figure 3, page 503. Each of the driver’s limbs was connected to a handle or pedal that controlled one of the truck’s four legs. Whenever the driver caused a truck leg to push against an obstacle, force feedback let the driver feel the obstacle as though it were his or her own arm or leg doing the pushing. After about 20 hours of training, Mosher was able to handle the machine with surprising agility. Films of the machine operating under his control show it ambling along at about 5 MPH, climbing a stack of CD=AD=DM=2 3 + v7 4+J7 Bc = 3 When the input crank AB rotates, the output point M moves along a straight path during one part of the cycle and an arched path during the other part. Two identical linkages are arranged to operate out of phase so at least one provides a straight motion at all times. The body is always supported by feet connected to the straight-moving linkage. Linkages of this sort, consisting of pivots and rigid members, are a sim- ple means of generating patterned motion. After Lucas [ 131. FIGURE 1. Linkage Used in an Early Walking Machine Articles ties, pushing a foundered railroad jeep out of the mud, and maneuvering a large drum onto some hooks. Despite its dependence on a well-trained man for control, mark in legged technology. this walking machine was a land- hu- Computer control became an alternative to human in the 1970s. Robert task was to solve kinematic equa- the 18 electric motors control of legged vehicles McGhee’s group at the Ohio State University was the first to use this approach successfully [16]. In 1977 they built an insectlike hexapod that could walk with a number of standard gaits, turn, walk sideways, and negotiate simple obstacles. The com- puter’s primary tions in order to coordinate driving the legs. This coordination ensured that the machine’s center of mass stayed over the polygon of support provided by the feet while allowing the legs to sequence through a gait (Figure 4, page 504). The machine traveled quite slowly, covering several yards per minute. Force and visual sensing provided a measure of terrain accommodation in later devel- opments. to pursue his earlier The hexapod provided McGhee with an excellent findings opportunity on the combinatorics and selection of gait [lo, 15, 181. The group at Ohio State is currently building a much larger hexapod (about 3 tons), which tended to operate on rough terrain with a high de- gree of autonomy theoretical is in- [40]. Gurfinkel and his co-workers in the USSR built a machine with characteristics and performance quite similar used a hybrid computer of analog computation to McGhee’s at about the same time [3]. It for control, with heavy use for low-level functions. the control of locomotion and [6, 71. The leg was a three- that translated Hirose realized that linkage design and computer control were not mutually exclusive. His experience had built with clever and unusual mechanisms-he seven kinds of mechanical snakes-led to a special leg that simplified could improve efficiency dimensional pantograph of each actuator into a pure Cartesian translation of the foot. With the ability translations of each foot by merely choosing an ac- tuator, the control computer was freed from the ar- duous task of performing kinematic solutions. The mechanical to perform the calculations needed for locomotion. The linkage was efficient because the actuators performed only positive work in moving the body forward. linkage was actually helping to generate x, y, and z the motion Hirose used this leg design to build a small quad- ruped, about one yard long. It was equipped with touch sensors on each foot and an oil-damped pen- dulum attached to the body. Simple algorithms used June 1986 Volume 29 Number 6 Communications of the ACM 501

This device was patented by Lewis A. Rygg in 1893. The stirrups double as pedak so the rider can power the stepping motions. The reins move the head and forelegs from side to side for steer- ing. Apparently this machine was never built. Articles 110 Yew.) - L. A. BYQQ. YEOEANIOAL H018E. No. 49X, 7, ?A Patented Feb. 14, L&n. FIGURE 2. Mechanical Horse the sensors to control the actions of the feet. For instance, if a touch sensor indicated contact while the foot was moving forward, the leg would move backward a little b:it, move upward a little bit, then resume its forward motion. If the foot had not cleared the obstacle, the cycle would repeat. The use of several simple algorithms Hirose’s machine negotiate other obstacles without human interven- tion [6]. to climb up and down stairs and to like this one permitted 502 Communications of the ACM lune 1986 Volume 29 Number 6

These three walking machines, McGhee’s, Gurfin- kel’s, and Hirose’s, represent a class called static crawlers. Each differs in the details of construction and in the computing technology used for control, but shares a common approach to balance and sta- bility. Enough feet are kept on the ground to guaran- tee a broad base of support at all times, and the body and legs move to keep the center of mass over this broad support base. The forward velocity ficiently ured into the stability calculation. Each of these ma- chines has been used to study rough terrain locomo- tion in the laboratory through experiments on ter- rain sensing, gait selection, and selection of foothold sequences. Several other machines that fall into this class have been studied in the intervening years, for example, see [31] and [3i’]. low so that stored energy need not be fig- is kept suf- Articles AND BALANCE the behavior of a dynamic system, we In order to predict DYNAMICS IMPROVE MOBILITY We now consider the study of dynamic machines that balance actively. This means that the legged systems studied operate in a regime where the ve- locities and kinetic energies of the masses are impor- tant determinants of behavior. and influence must consider the energy stored in each mass and spring as well as the geometric structure and config- uration of the mechanism. Geometry and configura- tion taken alone do not provide an adequate model when a system moves with substantial speed or has large mass. Consider, for example, a fast-moving ve- hicle with feet: It would its center of mass too close to the front tip over if it stopped suddenly. The exchange of energy among its various forms is This vehicle was developed by Ralph Mosher at General Electric in about 1966. The human driver controlled the machine with four handles and pedals that were hy- draulically connected to the four legs. Photograph cour- tesy of General Electric Re- search and Development Center. FIGURE 3. Walking Truck ]une 1986 Volume 29 Number 6 Communications of the ACM 503

Articles Left rear Left front Right rear 1 Right front \-- \ \ 0-o \ 5 6 7 a The diagram shows the sequence of support patterns pr& vided by the feet of a quadruped walking with a crawlfng gait. The body and legs move to keep the projeotfon of the center of mass within the polygon defined by the feet. A supporting foot is located at each vertex. The dot indicates the projection of the center of mass. Adapted from McGhee and Frank [17]. FIGURE 4. Statically Stable Gait mals sometimes use this sort of balance when they move slowly, but they usually balance actively. A legged system that balances actively can tolerate departures from static equilibrium. Unlike a stati- cally balanced system, which must always operate in or near equilibrium, an actively balanced system is permitted to tip and accelerate for short periods of time. The control system manipulates body and leg motions to ensure that each tipping is brief and that each tipping motion compensated by a tipping motion direction. An effective base of support is thus main- tained over time. A system that balances actively can also tolerate vertical acceleration, such as the ballistic running. is in the opposite flight and bouncing that occur during interval in one direction in the dynamics of legged locomotion. also important For example, there is a cycle of activity in running that changes the form of the stored energy several times: The body’s potential energy of elevation changes into kinetic energy during strain energy when parts of the leg deform elasti- cally during rebound with the ground, then into ki- netic energy again as the body accelerates upward, and finally back into potential energy of elevation. This sort of dynamic exchange is central to an un- derstanding of legged locomotion. then into falling, Dynamics also plays a role in giving legged sys- to balance actively. A statically bal- tems the ability anced system avoids tipping and the ensuing hori- zontal accelerations by keeping its center of mass over the polygon of support formed by the feet. Ani- Cannon and his students built machines that balanced inverted pendulums on a moving cart. They balanced two pendulums side by side, ohe pendulum on top of an- other, and a long limber in- verted pendulum. Only one input, the force driving the cart horizontally, was avail- able for control. Adapted from Schaefer and Cannon 1321. FIGURE 5. Balancing Inverted Pendulums 504 Communications of the ,4CM Iune 1986 Volume 29 Number 6

This machine eling at about ftom right to 11 made by light tached to the cate paths of the hip. is shown trav- I .75 MPH eft. Lines sources at- machine indi- the foot and The control s to regulate hr forward vekx posture. Top ning speed v\I 4.8 MPH. )ystem operates opping height, :ity, and body recorded run- ras about FIGURE 6. Planar Hopping Machine FIGURE 7. Three-Dimensional Hopping Machine ]une 1986 Volume 29 Number 6 Communications of the ACM 505

Articles Two hydraulic cylin- ders at 90” control hip angles; servo -, valves used for pre- cise positroning Springs augment 7 lifting force and min- imize loading on knee components Hydraulic accumula- tor reduces pres- sure fluctuations and minimizes re- quired size of sup- Ben Brown and 1 had this early concept for a one legged hopping machine that was to operate in three dimensions. The design never left the drawing board. cylin- Hydraulic/air der acts in series with spring to extend le Valve for exten- Pivot for lateral Wires/cables hold knee “vertical” Gears in knee joint keep angles legs ual for upper and lower Tapered for minimum weight (stepped) leg FIGURE 8. Design for Three-Dimensional Hopping Machine The ability of an actively balanced system to de- relaxes the rules gov- part from static equilibrium erning how legs can be used for support, which in turn leads to improved mobihty. For example, if a legged system can tolerate tipping, then it can posi- tion its feet far from the center of mass in order to use widely separated or erratically placed footholds. If it can remain upright with a small base of support, then it can travel where obstructions are closely spaced or where the path of firm support is narrow. support also con- The ability tributes to mobility by allowing a system to move all its legs to new footholds at one time, to jump onto or over obstacles, and to use short periods of ballistic flight narrow-base and intermittent crease the types of terrain a legged system can nego- tiate. Animals travel quickly on di.fficult will have to balance actively, move with animallike mobility and speed. routinely exploit active balance to legged vehicles to use support generally for increased speed. These abilities to tolerate intermittent too, if they are to terrain; in- BALANCE RESEARCH ON ACTIVE The first machines that balanced actively were auto- matically controlled knows that a human can balance a broom on a finger with relative ease. Why not use automatic inverted pendulums. Everyone the first to do so. In to build a broom that can balance itself? control Claude Shannon was probably 1951 he used the parts from an erector set to build a machine that balanced an inverted pendulum atop a small powered truck. The truck drove back and forth in response to the tipping movements of the pendulum, as sensed by a pair of switches at its base. In order to move from one place to another, the truck first had to drive away from the goal to unbalance toward the goal; in order to balance again at the destination, past the destination until upright with no forward velocity, to the goal. the pendulum was again then moved back the truck moved the pendulum At Shannon’s urging, Robert Cannon and two of his students at Stanford University set about demon- strating controllers that balanced two pendulums at once. In one case, the pendulums were mounted side by side on the cart, and in the other, they were mounted one on top of the other (Figure 5, page 504). Cannon’s group was interested in the single-input multiple-output problem and in the limitations of achievable balance: How could they use the single force that drove the cart’s motion to control the angles of two pendulums as well as the position of the cart? How far from balance could the system deviate before it was impossible to to return Communications of the ACM /we 1986 Volume 29 Number 6

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