Bipedal Balance
Thomas A Easton
Box 705, RFD 2
Belfast. Maine 04915
A basic problem in the design of any legged walking machine is equilibrium, or balance. When searching for solutions to this problem, it is worthwhile to consider how living bipeds manage to stay on their feet. Then perhaps we can design a machine that works as well as a human, and in at least some of the same ways.
For machines with four or more legs, the usual approach to balance is to program the leg movements so that three or more feet always remain on the ground. There can then always be a "polygon of support" enclosing the projection of the machine's center of gravity on the ground. As long as this projection stays within the polygon of support, no matter how it wavers, the machine cannot tip over. Only when the polygon disappears-as it does in the faster gaits which put fewer than three feet on the ground at a time-must the machine use other ways to preserve equilibrium.
Bipedal machines cannot always have a polygon of support. Even when merely walking, there must be times when only one foot is on the ground, and never are more than two feet on the ground. This does not mean that the machine must balance on one or two points. The feet can be flat and broad to provide a large supportive area. The machine must, however, keep the projection of its center of gravity within the limited "area of support" stamped out by one or two feet.
This constraint is too limiting. Random disturbances inevitably shift the center of gravity out of the stable area. But more importantly, the center of gravity is forced to shift outside the stable area of support each time the machine shifts its weight from one foot to the other. The machine necessarily experiences tipping moments. How then can it stay upright?
Animals commonly anticipate imbalances. That is, each footfall in a gait counteracts a tipping moment. This produces a dynamic equilibrium, rather than a static equilibrium. Bipedal animals rely even more on corrective movements. They constantly counteract tipping moments, either by moving their feet or by shifting their centers of gravity. They do both so skillfully and smoothly that the corrective movements are rarely noticeable. Bipedal machines do neither very well. They seem limited to slow, careful, deliberate movements. Some must even keep both feet on the ground at all times, their motion limited to a slow, shuffling gait.
A number of researchers are working on giving machines the capability for lifelike corrections and balance. Marc Raibert and his colleagues at the Robotics Institute of Carnegie-Mellon University in Pittsburgh have built a computerized pogo stick powered by compressed air. This onelegged "walking" machine hops all over their lab, and it keeps its balance quite successfully. Each time it lands, its computer measures just how far out of balance the machine is. A servo then corrects any tipping moments with countertorques, taking advantage of friction between foot and floor. Some imbalances can be corrected by placing the foot out of the line of motion-by "propping" against a lean or spin.
Animals use both methods to correct their imbalances, but they don't use a central computer to calculate and command corrective actions. Instead, they use a form of distributed control. They do not use the thinking or other high-level parts of the brain. They use reflexes, automatic motor responses to specific sensory stimuli, which are wired into low-level parts of the central nervous system. Many reflexes do not involve the brain at all. Instead, they require only a few nerve cells in the spinal cord, that column of nervous tissue shielded by the backbone.
The simplest reflex is the stretch reflex. It is a biological feedback circuit which holds a muscle at a particular, set length. This results in joints being held at specific angles. The stretch reflex depends on sensors buried deep within muscles. These sensors are the muscle spindles. Each muscle spindle is a bundle of modified muscle fibers enclosed in a tapered sheath. Motor nerves enter the sheath to control the spindle fibers, and sensory nerves leave the sheath to convey signals to the spinal cord.
Motor commands from the spinal cord to a muscle reach both muscle fibers and spindle fibers, so that the two contract in parallel. As long as they remain in parallel, the spindle's sensory nerves carry no signals. The spindle sensor's zero point is set by its own contraction to match the degree of muscle shortening ordered by the nervous system.
However, if the muscle is stretched beyond its "proper,' commanded length, the spindle is stretched beyond its zero point. The spindle then generates signals in its sensory nerves. These spindle signals report the degree and rate of change of the unintended stretch to the spinal cord. Motor cells in the spinal cord then command the muscle to contract further and return to the initially set length. This is what happens in the classic knee-jerk reflex. The doctor's tap on the tendon just below the knee cap stretches the thigh muscle beyond the length set by the nervous system. The thigh muscle's spindles report the deviation to the spinal cord, whose cells then command the thigh muscle to contract. The contraction produces the typical reflex kick.
The same thing happens when someone passes you a book. You hold one hand out, chest-high. When the book lands in your hand, the added weight causes your hand to sag. This motion stretches the biceps muscle which activates the spindles' sensory nerves. The spindles report, and the spinal cord orders the biceps to contract. As a result, your hand rises to its previous position.
The stretch reflex is also involved in maintaining erect posture. It helps the leg muscles keep the legs extended against the pull of gravity and the transient loads induced by the impacts of steps. It helps the muscles of torso and hips correct for sway and lean; it thus helps keep the projection of the body's center of gravity under the feet.
A second important reflex appears in the flexion reflex. In its simplest form, it is a response to sensors in the skin. When these sensors register pain, they report to the spinal cord. Nerve cells there command the muscles that bend or flex the leg to contract. The result is that the pained patch of skin is jerked away from the source of its agony. You see the flexion reflex in action when you step on a tack or touch a hot pot. Your foot or hand jerks away from the pain well before you consciously feel the pain. This demonstrates that the neural circuitry responsible for the reflex is local, in the spinal cord. It does its job while the pain signal is still on its way to the brain.
What help is the flexion reflex in the problem of balance? Because of the way the spinal cord's nerve cells are wired together, the flexion reflex is generally accompanied by the crossed extension reflex. Even as one leg flexes,the other extends or stiffens. As the spinal cord sends commands to the flexor muscles of one leg, it also sends commands to the extensors of the other. It is as if fluid withdrawn from one hydraulic piston were supplied to another, so that the two pistons worked 180 degrees out of phase with each other.
When a biped is standing on two legs, a flexion reflex can yank one foot off the ground. The accompanying crossed extension reflex strengthens the support supplied by the other leg. If the biped is walking, and steps on a stone, the flexion reflex will try to yank the single foot on the ground into the air. The crossed extension reflex will get the other foot down in time to prevent a fall.
Unlike the circuitry of the stretch reflex, where sensory nerves report directly to motor nerve cells, the flexion and crossed extension reflexes involve an intermediate nerve cell. The sensory nerves report to an interneuron, which commands the motor nerve cells to activate the muscles. The existence of this interneuron means that higher levels of the nervous system, such as the brain, may also activate the pair of reflexes.This actually seems to happen during locomotion; as one leg flexes, the other must extend. Reflexes may thus simplify the problem of motor control in general by reducing the number of separate actions the brain must coordinate.
Skin sensors are also involved in the placing reflexes. They help the feet avoid holes and humps and find level ground to rest on. Humans have these reflexes, but they are more apparent in lower animals such as cats. To demonstrate this reflex, blindfold a cat and hold it in the air. Let the edge of one paw gently brush the edge of a table. The cat will lift the paw and place it squarely on the table. The cat does not need the highest levels of its brain to do this, for a cat whose cerebral cortex has been removed still has placing reflexes.
The placing reflexes are well suited to establishing stable footing. The stretch reflex is used to hold a posture once it is set, and for correcting small deviations. The crossed extension reflex seems best for keeping a lurch from turning into a fall. Yet all can fail to keep a biped upright. Other reflexes must come into play. The most important of these other reflexes are the vestibular reflexes, whose sensors lie in the inner ear.
The parts of the inner ear concerned with balance are the semicircular canals, the utricle, and the saccule. The semicircular canals are three hollow hoops set at right angles to each other and filled with fluid. At the base of each hoop is a bulbous ampulla. The ampulla is blocked by a gelatinous cupula in which are embedded the hairlike cilia of the sensory cells. Any rotation of the head in the plane of a hoop sets the fluid in the hoop in motion. The moving fluid deflects the cupula and bends the hairs of the sensory cells. As the hairs bend, the cells generate nerve signals which tell the nervous system which way the head is turning.
The utricle and saccula also contain patches of sensory cells. These cells too have cilia, which are embedded in a gelatinous mass containing granules of calcium carbonate, the statoconia. The utricle and saccule respond to gravity and to linear accelerations, both of which act on the statoconia to bend the sensory cells' cilia. The cells tell the nervous system which way the head is tipping or in which direction it is beginning or ending a movement.
The semicircular canals, utricle, and saccule are all basically accelerometers. They can easily be mimicked in a machine. They work together to maintain balance by triggering reflexes that compensate for leans, tips, spins, and falls.
The vestibular reflexes can be demonstrated in a four-legged animal by standing the animal on a platform that can tip from side to side and from front to back. If the platform tips down in front, the animal's forelegs extend and its hindlegs flex. If the platform tips down in back, the forelegs flex and the hindlegs extend. If the platform tips down to one side, the legs on that side extend and those on the other flex. All these motions tend to keep the body level. Other reflexes, which relate neck bends to vestibular stimuli and to limb flexion and extension, help keep the head level.
The tippable platform is also useful for demonstrating the reflexes in humans. People respond to a sideways tip by flexing the uphill leg and extending the downhill leg. During a forward tip, they lean backward; if the tip is extreme, the person may take a step, setting one leg forward, extended, while the other, now a hind leg, flexes. People respond to a backward tip by leaning forward, or by stepping backward. In each case, the reflex keeps the body straight up and down and balanced on its feet.
Humans also respond with their arms. When they tip to one side, they extend the arm on that side. When they tip forward, they flex both arms, bringing them up in front of the face. When they tip backward, they extend them backward. In each case, the reflex seems to prepare the body to catch itself in case the tip turns into a fall. Here, the reflexes seem to serve self protection more than balance.
Visual reflexes also help bipeds stay upright. The brain compares the visual field against the signals from the vestibular sensors and from pressure sensors in the soles of the feet. The brain can detect leans and sways just by changes in the orientation of the visual field on the retina. The brain can maintain equilibrium by relying on vision alone, but vision seems less important than the vestibular senses. That vision plays a significant role is obvious when we are blindfolded or in the dark. Without the aid of vision, we are more likely to stagger. Yet the blind do without it quite well. In comparison, when the vestibular senses go awry, it can take a long time to learn to use vision alone.
The various reflexes that contribute to balance inevitably interact, and balance is the result of their interplay. This interplay takes place at the level of the motor neuron, often called the "final common path;' which commands the individual muscles to contract. Various commands, including those for voluntary movements, reach the motor neuron along various paths. Some commands are strong. Some are weak. Some are excitatory. Some are inhibitory. The motor neuron sums them all and orders the muscle to contract only when the sum is above a certain level. Gradations in the strength of a muscle's contraction arise because each muscle is commanded by a pool of many motor neurons. Since each neuron receives its own mix of commands, not all members of the pool order contractions at the same time, except in the case of the strongest contractions.
The balance achieved by interacting reflexes is smooth and flexible. It is equal to the demands of walking, running, dancing, and carrying wine glasses full of nitroglycerin, even on rough ground. It does not distract the brain from other tasks.
The living biped's ability to balance is the envy of the roboticist. Yetit should be possible to build a legged machine that can move quickly,smoothly, and gracefully,and does not need all its brain to control its movements. The trick may be to imitate the methods of life. Have the central computer issue only a rough locomotor guide, a sequence of limb activations, or even a single activating command to a subsidiary control center. Give each limb its own control circuitry, analogous to the neuronal circuitry of the living biped's spinal cord. Design this local circuitry to respond in set, corrective ways to the signals from sensors for limb configuration, gravity, acceleration, and "skin" pressure, and allow the signals to interact in determining the proper responses of the machine's servos. The result will be a machine that uses reflexes. It will correct imbalances quickly and smoothly, and its computer will be free to handle other tasks.
