Central Pattern Generators And Sensory Feedback

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6.7.1 Cyclical Motor Patterns Generated without Sensory Input

Literally hundreds of studies in which sensory input has been reduced or abolished by deafferentation have since demonstrated beyond doubt that isolated neuronal networks in the CNS can generate the basic rhythmical motor patterns involved not only in walking but also in the activities of breathing, chewing, swimming, flying, scratching, paw-shaking, and autonomic functions such as micturition and sexual "reflexes" (Grillner 1975; Prochazka 1996b; Kiehn et al. 1998; Orlovsky et al. 1999).

There has been much discussion about the ability of CPGs, in the absence of sensory input, to generate complex coordinated patterns of muscle activity such as those required for overground locomotion. After deafferentation in the cat, many subtle features of normal activation sequences can still be seen (e.g., the small burst of activity in knee flexor muscles at the end of the swing phase in cat locomotion [Grillner and Zangger 1975]). However, the locomotor rhythm is generally more labile (Grillner and Zangger 1975; Wetzel et al. 1976; Goldberger and Murray 1980; Grillner and Zangger 1984; Giuliani and Smith 1987; Koshland and Smith 1989) and above all, there is an inability to compensate for the changes in loading or terrain (Allum et al. 1998).

This latter defect is more serious than it may sound. If information on joint angles, body posture, loading, and displacement of the extremities are all unavailable to the central controller, the amplitude and timing of the cyclical motor output can only be set to some default level and cannot be matched to the varying requirements. To quote Brown (1911):

A purely central mechanism of progression ungraded by proprioceptive stimuli would clearly be inefficient in determining the passage of an animal through an uneven environment. Across a plain of perfect evenness the central mechanism of itself might drive an animal with precision. Or it might be efficient for instance in the case of an elephant charging over ground of moderate unevenness. But it alone would make impossible the fine stalking of a cat over rough ground. In such a case each step may be somewhat different to all others, and each must be graded to its conditions if the whole progression of the animal is to be efficient. The hind limb which at one time is somewhat more extended in its posture as it is in contact with the ground, in another step may be more flexed. But the forward thrust it gives as its contribution to the passage of the animal must be of a comparatively uniform degree in each consecutive step. It may only be so if it is graded by the posture of the limb when in contact with the ground, and by the duration of its contact with the ground. This grading can only be brought about by peripheral stimuli. Of these we must regard the proprioceptive stimuli from the muscles themselves as the most important, and the part which they play is essentially the regulative — not the causative.

The loss of proprioceptive input in humans is more devastating than in quadrupeds: without vision and/or external supports, people with large-fiber sensory loss find it difficult to take more than a step or two without stumbling and falling, even on a flat floor (Lajoie et al. 1996). Though evidence has been adduced for the existence of a locomotor CPG in the human lumbosacral spinal cord in people with spinal cord injury, the types of rhythmical movement observed were weak and inadequate for weight-bearing locomotion (Calancie et al. 1994; Dimitrijevic et al. 1998) and because the legs were suspended and sensory input was intact, it is possible that they could have resulted from reciprocating stretch reflexes. In a recent study in normal subjects, steady vibration of the legs resulted in cyclical air stepping (Gurfinkel et al. 1998). It was suggested that the steady sensory input activated "the central structures responsible for stepping generation." However, vibration of pha-sically contracting muscles is known to produce phasic firing of muscle spindles (Matthews and Watson 1981; Prochazka and Trend 1988), so the development of pendular reflexive motion in the suspended legs cannot be ruled out here either.

In certain cases, it has been claimed that accurate, goal-directed movements in a normal animal can only be attributed to central programming, because the moment-to-moment participation of sensory input can be ruled out. For example, in cockroaches, it has been shown that sensory feedback in fast walking is too delayed to have a reflex effect within a given cycle, the duration of which is 40 ms or less (Zill 1985; Delcomyn 1991a; Delcomyn 1991b). In the most rapid ballistic movements in humans, sensory feedback is also too slow to modify the movements once they are underway (Desmedt and Godaux 1979).

Does this mean that in very rapid movements sensory input is unimportant? If a very rapid movement is considered in isolation it is true that the sensory input related to that movement may come too late to contribute to its control. But that movement, like all others, was preceded by sensory input that provided the CNS with information on the overall biomechanical state of the limbs and the rest of the body in the immediately preceding period. In locusts, it has been shown that sensory input influences the wing-beat cycle following the one in which it was elicited (Wolf and Pearson 1988). Similarly, it has been suggested that in the example of cockroach locomotion given above, the sensory input from one step cycle provides postural information for the control of ensuing step cycles (Prochazka 1985). This could either be viewed as delayed feedback or as prediction, depending on the way the signals are handled. We would argue that in the generation of ballistic movements that accurately reach their target, the CNS has taken into account the biomechanical initial conditions and the relative position of the target, which is only possible with prior sensory input. The only movements that might be controlled entirely open-loop (without any significant involvement of sensory input) would be escape behaviors in which the animal propels itself forward as rapidly as possible without regard for stability or the likelihood of a fall.

6.7.2 Interaction between CPGs and Sensory Feedback

In the mid-1960s, it was found that cats, decerebrated rostral to the superior colli-culus, were more likely to walk than those with a mid-collicular decerebration, particularly with steady electrical stimulation of a region that has since become known as the midbrain locomotor region (MLR) (Shik et al. 1966; Shik et al. 1969). This allowed the spinal mechanisms of locomotion to be studied with microelec-trodes, pharmacological interventions, and lesioning experiments. Some of the early observations of Sherrington, Brown, and their predecessors on the effect of limb position on locomotor-like reactions were soon confirmed and extended to stable treadmill locomotion. In one such experiment, both hindlimbs were de-efferented, leaving sensory input to the spinal cord intact (Orlovsky and Feldman 1972). MLR-evoked locomotor rhythms recorded electrically in S1 ventral root filaments were then found to be entrained by cyclical imposed movements of one of the limbs. The rhythm could be halted by moving the limb into extreme flexion or extension. After partial deafferentation, the rhythm could also be halted by arresting locomotor movements of one of the limbs in mid-cycle, just as Sherrington had described. In a more sophisticated version of this experiment a few years later, it was found that the hindlimbs of chronic spinal kittens walking on a split-belt treadmill could adapt their cadence to each belt separately, i.e., the sensory input to each limb was entraining that limb individually (Forssberg et al. 1980).

Entrainment and override of the locomotor rhythm by sensory input from a limb has been confirmed and studied in detail in dozens of experiments since the early 1970s in the high decerebrate MLR cat, chronic spinal cats, and acute spinal cats treated with clonidine (rev: Rossignol 1996). By the mid-1980s, two separate sensory variables had been identified as being capable of entraining or overriding the locomotor rhythm: hip position (Andersson and Grillner 1983; Kriellaars et al. 1994) and extensor force (Duysens and Pearson 1980). In a recent review of these findings, it was realized that the same two variables had been implicated in triggering the switch from stance to swing in species as widely separated as cats, crayfish, and locusts (Prochazka 1996b). In simple terms, the sensory rule that seemed to prevail in all these animals could be stated as follows: IF the leg has become very extended and extensor force has become very low, THEN initiate swing. This same rule had been quite independently "discovered" in the technological control of above-knee prostheses as well as in the control of functional electrical stimulation in human gait.

It is clear from all of the above that the basic locomotor pattern can be generated by the CNS without sensory input, but sensory input can promote, delay, or even block the switching between stance and swing phases and thereby completely determine step cycle frequency. The question of the relative importance that should be placed on central vs. sensory control has been quite bothersome to neurophysiolo-gists over the years, some taking the view that sensory input is only important when the CPG-generated pattern fails to produce the required movements (the centralist view), while others suggest that the CPG rhythm is a default pattern that is only manifested when sensory input is withdrawn (the peripheralist view).

The paradox can be partly understood by considering the family of electronic circuits called multivibrators (also known as flip-flops). These consist of a pair of switchable elements such as transistors, interconnected such that when one is active, it suppresses the other by applying an "off" signal to its gate. In a free-running ("astable") flip-flop, the "off" signal discharges through a capacitor from the moment it is applied. Consequently, halfway through the cycle, the suppressed partner is "released," turns "on," and becomes the "oppressor" for the next half-cycle. The frequency can be modulated by controlling the rate of discharge or decay of the "off" signals by varying passive circuit components or by applying external inputs to the gates. These can override the oscillation completely and hold the circuit in one or the other half-cycle indefinitely. Thus, although the core circuit can generate a default rhythm, the additional circuit components promote, delay, or block phase switching and are therefore integral parts of the system as a whole. The flip-flop analogy was recognized in the late 1970s (Miller and Scott 1977) and forms the basis of some CPG models to this day (Orlovsky et al. 1999).

The usual compromise position between centralists and peripheralists is that the CPG generates the basic locomotor pattern, but this is "sculpted" or "fine-tuned" by sensory input. However, given the fact that sensory input can entrain and halt the rhythm, and given the extreme disability in human bipedal gait caused by even partial deafferentation (Lajoie et al. 1996), "sculpting" and "fine-tuning" seem to understate the case.

6.7.3 Human Locomotion

A puzzle remains about the role of local reflexes mediated by muscle receptors in human locomotion. As already mentioned, large-fiber deafferentation (which can eliminate input from muscle spindle primary and tendon organ afferents from the legs and trunk) can have a devastating effect on human locomotion (Lajoie et al. 1996). Yet, when these receptors are excited by test mechanical stimuli applied to muscles during gait, the effects are disappointingly small. For example, bursts of powerful vibration of the lower leg muscles, which most likely entrain the firing of many spindle group Ia spindle afferents and probably numerous group Ib afferents too, have virtually no effect on the trajectory of locomotor movements (Ivanenko et al. 2000a; Ivanenko et al. 2000b). Interestingly, tonic vibration of the upper leg muscles or the subject's neck did have a generalized effect on body tilt and speed of locomotion.

Short-latency EMG responses can certainly be elicited during gait by electrical stimulation of the large afferents (Garrett et al. 1984; Capaday and Stein 1986), by tapping on tendons (Llewellyn et al. 1987) or by applying rapid joint rotations via pneumatic orthoses (Sinkjaer et al. 1996). But the muscle stretches have to be faster than those occurring in unimpeded locomotion for the EMG responses to be significantly larger than the prevailing levels. Ischaemic block of large afferents had very little effect on short-latency soleus EMG unloading responses elicited by the pneumatic orthosis, though longer-latency responses persisted (Sinkjaer et al. 2000). This led to the suggestion that presynaptic inhibition effectively eliminates any significant contribution of Ia signals to homonymous muscle activation during normal locomotion, and it is only in very rapid perturbations that Ia-mediated activation of MNs "breaks through." A significant contribution to EMG activation (up to 50%) was claimed for the longer-latency pathways, though these reactions were delayed enough and of long enough duration to involve more complex central processing rather than simple segmental reflexes.

6.7.4 Robots

Recently there have been two interesting developments in technology that may provide insight into these issues. The first is the design of walking robots. Some of the most advanced work in this area is of a corporate nature (e.g., the humanoid robots developed by the Honda company), and the information available on the control strategies used tends to be sketchy. Nonetheless, it is quite clear that the most versatile robots, including the extraordinary Honda Asimo P4, rely heavily on sensory input to generate locomotion over uneven terrain. The robot designers carefully reviewed the essential aspects of biological locomotor control in insects, quadruped mammals, and humans and then implemented the most promising aspects in their machines. The instructive thing here is to consider which control strategies turned out to be effective. Two hexapod robots, a "stick insect" and a "cockroach," developed in Cleveland, provide useful information in this regard (Espenschied et al. 1996; Nelson and Quinn 1999). In both cases, the robots have six two- or three-segment limbs. Each joint has a passive spring for compliance, an actuator, and a position sensor. The actuator is under proportional position feedback control of variable gain, providing a controllable stiffness that adds to the passive "inherent" spring stiffness. The stiffness properties of each joint therefore mimic the intrinsic properties of biological muscles under stretch reflex control. Locomotion is achieved by a mixture of processes local to joints and legs, and two governing ("global") algorithms. The local processes include the active stiffness control just mentioned, as well as If-Then control rules based on end-point position for stance-swing and swing-stance transitions, and special rules for adaptive responses to tripping (stumble reaction) and "foot-in-hole" (Gorassini et al. 1994). Figure 6.6 shows the reactions of a leg of the hexapod robot in three situations, perturbed stance, placing reaction, and "foot-in-hole." For comparison, we have included a panel showing the searching movements of a locust in which the leading limb enters a hole (at 2), searches, and is eventually placed (at 3) (from a movie kindly provided by K. G. Pearson).

Regarding the two "global" algorithms, one adjusts leg trajectories to distribute force equally among weight-bearing legs, and to match leg "lengths" according to the terrain (i.e., to keep the body horizontal in the face of slopes and other unevenness of ground support). Interestingly, leg length (the distance from the end of the paw

FIGURE 6.6 Kinematics of leg movement in a hexapod robot (A, B, and C) and a locust (D). A. perturbed stance: imposed movement of the foot from 1 to 2 evokes a corrective reaction with placement at 3. B. tripping reaction: foot contacts obstacle at 2, is lifted and placed beyond the obstacle at 3. C. "foot-in-hole:" foot enters hole, which triggers searching movements at 2 and eventually a placing reaction at 3. D. locust "foot-in-hole." Stick figures traced from frames of a movie. Leading limb enters a hole at 2, searches, and is eventually placed at 3. A, B, and C reproduced with permission from Espenschied et al., Robotics and Autonomous Systems, 18, 59, 1996.

FIGURE 6.6 Kinematics of leg movement in a hexapod robot (A, B, and C) and a locust (D). A. perturbed stance: imposed movement of the foot from 1 to 2 evokes a corrective reaction with placement at 3. B. tripping reaction: foot contacts obstacle at 2, is lifted and placed beyond the obstacle at 3. C. "foot-in-hole:" foot enters hole, which triggers searching movements at 2 and eventually a placing reaction at 3. D. locust "foot-in-hole." Stick figures traced from frames of a movie. Leading limb enters a hole at 2, searches, and is eventually placed at 3. A, B, and C reproduced with permission from Espenschied et al., Robotics and Autonomous Systems, 18, 59, 1996.

to the hip joint) has recently been identified as an emergent variable that accounts best for the firing behavior of dorsal spinocerebellar tract neurons in the cat, even when individual joints are constrained (Bosco and Poppele 2001). These authors suggest that the spinocerebellar system may be viewed as the end-point of processing of proprioceptive sensory information in the spinal cord. The other global algorithm quoted "encourages stance legs to lift into their swing phases in a coordinated manner, swing forward, and transition to stance" (Quinn and Ritzmann 1998).

Like the hexapod robots, the Honda robot also utilizes local active and passive joint compliances, IF-THEN phase transitions, special adaptive reactions similar to the ones just described and a novel global strategy of setting a moving target of ground reaction force as the command for forward or backward locomotion. The actual ground reaction force is continually computed from the sensor signals. The difference between this vector and the target vector is referred to as the "falling moment." This falling moment is minimized by "reflexes" to the joint actuators, which are presumably synergistically coupled.

Notice that in neither of the above robots is it easy to extract the notion of an autonomous CPG from the various global algorithms. Rather, the central controllers respond to external requirements by issuing general commands to move in particular directions (e.g., by proposing a virtual trajectory for the ground reaction force), selecting sensory rule bases appropriate to the task and context, and evaluating performance for predictive adjustments. Hazard rules are also computed (e.g., the Honda robot resists lateral imposed forces by stiffness control, but when sway exceeds the imbalance point, it yields and takes a step in the direction of the imposed force).

6.7.5 Virtual Animals

The other useful advance in technology is the development of powerful biomechan-ical modelling tools suitable for personal computers. These programs allow one to design quite complex models of "virtual animals" with limbs, joints, and muscles whose intrinsic properties can be approximated to those of real animals. Muscle activation profiles based on EMG patterns recorded during locomotion can be used to activate the muscles. The ensuing locomotor performance, which is displayed as a slow-motion movie as the computations proceed, provides similar types of insight to the mechanical robots above, but because changes can be made easily and tested quickly, many different sensorimotor rules and parametric variations can be explored.

Figure 6.7 shows a biomechanical locomotor model we have been working on for some time. The model is based on the cat hindquarters but it is intentionally not an accurate replica. Many muscles are absent. The origins and insertions of the muscles that are represented do not correspond exactly to those in real cats. The model uses a Hill-based force-velocity relationship and monotonic passive and active force-length curves (Figure 6.7B), as our recent results indicated that the static isometric force-length curve with its descending limb is invalid in continuous movements (Gillard et al. 2000). Short-range stiffness properties are neglected. The purpose of the model is to test some general hypotheses, not to provide a definitive analysis of gait in any given species.

Once we had "fine-tuned" the EMG activation patterns of its various actuators (Figure 6.7C), which were based on EMG profiles of cat locomotion (Prochazka et al. 1989), the model produced stable locomotion on a flat surface indefinitely, in spite of being "deafferented" (Figure 6.8A). Each step was slightly different from the last, which showed that the intrinsic stiffnesses of the muscles provided enough flexibility to make continuous adjustments to compensate for small variations in body speed, height, and the relative positions of the limb segments. The deafferented virtual cat could also adapt to modest uphill slopes (Figure 6.8A). As mentioned above, intrinsic muscle stiffness is equivalent to a length feedback system which resists deviations from some set equilibrium length. Thus, locomotion in a deaffer-ented animal is not entirely open-loop.

The stability of the deafferented model was unexpected, because we were aware of the difficulty Gerritsen at al. (Gerritsen et al. 1998) had experienced in generating more than three or four steps in a similar model of bipedal human locomotion, though other groups have been able to overcome this by optimizing the EMG patterns with inverse dynamics or neural network learning techniques (Taga et al. 1991; Taga 1995a; Taga 1995b; Yamazaki et al. 1996; Taga 1998; Neptune et al. 2001; Ogihara and Yamazaki 2001). Of course, the cart that supports the front of our virtual cat greatly simplifies the problem of maintaining a stable upright posture. It is also a simplification of quadrupedal gait, which requires forelimb-hindlimb coupling for stability. It is very interesting that Gerritsen and Nagano (1999) recently obtained a far more stable performance when they incorporated some sensory feedback into their bipedal model.

The deafferented virtual cat immediately gets into trouble when the read-out rate of its EMG patterns is increased or decreased, producing a higher or lower gait

FIGURE 6.7 Biomechanical locomotor model based loosely on the cat hindlimb. A. Muscle groups are represented by actuators HF (hip flexors), HE (hip extensors), KF (knee flexors), KE (knee extensors), AF (ankle flexors), and AE (ankle extensors). B. Hill-based force-velocity relationship and passive and active force-length curves used in each actuator. C. Step-cycle activation profiles of the actuators.

FIGURE 6.7 Biomechanical locomotor model based loosely on the cat hindlimb. A. Muscle groups are represented by actuators HF (hip flexors), HE (hip extensors), KF (knee flexors), KE (knee extensors), AF (ankle flexors), and AE (ankle extensors). B. Hill-based force-velocity relationship and passive and active force-length curves used in each actuator. C. Step-cycle activation profiles of the actuators.

velocity (Figure 6.8B). It does not help just to add stretch reflexes, because these merely augment the muscle intrinsic stiffnesses without affecting step cycle phase-switching. On the other hand, If-Then rules are useful in coping with variations of this type. In Figure 6.8B, the If-Then rules governing the transitions from stance to swing and back (see below) allowed the model to adapt to the increased EMG readout rate and hence increased velocity, though it did not fare so well with the lowered read-out rate.

FIGURE 6.8 Kinematic analysis of behavior of the model of Figure 6.7 in different situations. A. locomotion of the model without feedback rules. The intrinsic stiffnesses of the muscles sufficed to compensate for kinematic and kinetic variations in locomotion over flat surface and up a small slope. B. Gait velocity increased (top) or decreased (bottom) by ~20%. Locomotion failed in the "deafferented" case, but improved with If-Then rules (triggering of stance-swing transitions marked with upward triangles; note that the contralateral leg was phase-locked to ipsilateral leg, so it did not "fire" its rules except in one case of a swing-to-stance transition marked by downward triangle). C. Obstacle impeded forward swing of one leg. The deafferented model (left) failed to compensate and dragged its foot over obstacle, causing a subsequent fall. Inclusion of a "tripping rule" (triggered at *) resulted in good reactive compensation with ensuing stable steps.

FIGURE 6.8 Kinematic analysis of behavior of the model of Figure 6.7 in different situations. A. locomotion of the model without feedback rules. The intrinsic stiffnesses of the muscles sufficed to compensate for kinematic and kinetic variations in locomotion over flat surface and up a small slope. B. Gait velocity increased (top) or decreased (bottom) by ~20%. Locomotion failed in the "deafferented" case, but improved with If-Then rules (triggering of stance-swing transitions marked with upward triangles; note that the contralateral leg was phase-locked to ipsilateral leg, so it did not "fire" its rules except in one case of a swing-to-stance transition marked by downward triangle). C. Obstacle impeded forward swing of one leg. The deafferented model (left) failed to compensate and dragged its foot over obstacle, causing a subsequent fall. Inclusion of a "tripping rule" (triggered at *) resulted in good reactive compensation with ensuing stable steps.

For the challenging situation of an obstacle impeding the forward swing of one leg, these simple rules were not enough to prevent a fall either. In this case, a separate "hazard" rule was needed, which was invoked when the front of the foot contacted the obstacle (see "tripping reaction" rule below). This initiated an EMG sequence similar to that previously recorded in the tripping reaction of normal cats (Wand et al. 1980). The result was a response that looked very true to life (Figure 6.8C).

6.7.6 If-Then Rules Governing Phase Switching and the Selection of "Hazard" Responses

The control of forces in muscles within the flexion or extension phases of locomotion is a smoothly graded process involving continuous proportional feedback, whereas the switching between these phases is usually discontinuous and abrupt. Control systems that switch between well-defined states are known as finite-state systems and switching is triggered when certain sensory conditions are met (e.g., IF swing AND hip angle small (flexed) AND extensor force low THEN terminate flexion, initiate extension) (Tomovic and McGhee 1966; Tomovic et al. 1990). Note that "small" and "low" are imprecise terms. This is intentional: the nervous system most likely uses sensory inputs in a probabilistic way rather than setting precise threshold values and requiring each threshold to be met before firing the rule.

A control systems analogy for probabilistic finite-state control is "fuzzy logic," in which sensory variables are accorded weighting ("membership") functions, the sum of the weighted sensory signals determining the motor outcomes. If-Then rules are crafted to suit specific behavioral states. More than one rule may be "active" in a behavior or a part of a behavior (e.g., in the stance phase of gait, the stance-swing rule and the "foot-in-hole" rule are both active: see below). The system constantly monitors the "firing strength" of the rules and retires behaviors and/or recruits new behaviors according to predetermined thresholds of the firing strengths. A higher level "arbitration mechanism" may decide which behaviors are appropriate for the current global state (Prochazka 1996a).

In such systems, each input effectively "votes" for a range of possible motor outcomes according to the currently active If-Then rules, the sum of the votes determining what actually happens (Chen et al. 1997; Jacobs 1997; Davoodi and Andrews 1999; Jonic et al. 1999). Bässler has suggested a similar process in the control of locomotion in stick insects and used the term the "Parliamentary Principle" as a metaphor for the voting mechanism (Bässler 1993). Fuzzy logic has also been discussed in relation to the changes that occur in forward, sideways, and backward treadmill walking in infants (Pang and Yang 2000).

On the understanding that If-Then rules may be used in this probabilistic way, let us now consider some of the rules that might underlie phase switching in biological locomotor control.

Stance phase (forward step)

Rule 1 (stance-swing transition): IF stance AND extensor force low AND hip angle large (extended) AND contralateral limb supported, THEN switch to swing.

Rule 2 ("foot-in-hole" reaction): IF mid-stance (hip angle medium) AND no ground contact AND contralateral limb supported, THEN switch to placing reaction.

Swing phase (forward step)

Rule 1 (swing-stance transition): IF swing AND hip angle small AND knee angle large (knee extended) THEN switch to stance.

Rule 2 ("tripping" reaction): IF swing AND skin stimulus to front of foot THEN switch to placing reaction; IF stance AND skin stimulus to front of foot THEN prolong stance.

Stance phase (backward step)

Rule 1 (stance-swing transition): IF backward gait AND extensor force low AND hip flexed AND contralateral limb supported THEN initiate backward swing.

Swing phase (backward step)

Rule 2 (swing-stance transition): IF backward gait AND hip angle large THEN initiate stance.

The following rule describes the way the Honda robot invokes the "hopping reaction" of Magnus (Magnus 1924) when it is pushed in the face:

Static Postural Rule 1 (hopping reaction): IF falling moment is small AND gravity vector is within support surface, activate extensors; IF falling moment is large AND gravity vector is outside support surface, take a step back.

Notes to the rules:

a. The above list of rules describes sensorimotor interactions that occur in locomotion in many animals and that are explicitly programmed in robots, prostheses, and bio-mimetic models. Identifying the neural control systems responsible is no trivial matter, just as it remains no trivial matter to identify Brown's "intrinsic factor" (the locomotor CPG) after 100 years of research.

b. Not only is the list far from complete, but the variables chosen are not necessarily the only ones that would "work," nor the ones that might be used in biological systems. For example, a possible alternative to "hip is extended" is "leg length is long" (Bosco and Poppele 2000; Bosco et al. 2000; Bosco and Poppele 2001). Likewise, the variables in the postural rule must clearly be derived from several sets of sensors in different parts of the body.

c. As gait speed increases, it is important to phase-advance the switching back and forth between stance and swing to compensate for the delays due to inertia and muscle properties. Rather than invoke more rules using angular velocities, if we assume that muscle-spindle signals are used in place of joint angles, their velocity dependence would automatically provide this phase advance.

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