Reaction to Disturbances of a Walking Leg During Stance

A system controlling walking movements has to cope with two basic problems. One is to produce the motor output to move the legs in an appropriate spatio-temporally coordinated way. The second problem is to react to different unpredictable disturbances. These disturbances may be classified into two types, obstructions occurring during the swing movement and those occurring during the stance phase. The former are usually handled by different types of avoidance reflexes (e.g. cat, Felis domesticus, Forssberg, 1979; locust, Schistocerca gregaria, Pearson and Franklin, 1984; stick insect, Carausius morosus, Dean, 1985; Dean and Wendler, 1982; Bässler et al., 1991). The latter disturbances are more difficult to handle because the legs are mechanically coupled through the substratum during stance. Such disturbances might, for example, be represented by a sudden movement of the substratum on which the leg is standing or by the leg stepping on unexpectedly soft ground. The present study investigates the reactions that occur during stance. A number of investigations have shown that a suddenly moving substratum elicits a reaction opposing this movement (e.g. humans, Duysens et al., 1992; cat, Felis domesticus, Hiebert et al., 1996; stick insect, Carausius morosus, Cruse, 1981; Cruse and Pflüger, 1981; Schmitz, 1985). In some cases, a so-called assisting reaction has been described. This type of control mechanism implies that the reactions to perturbations should not oppose, but enhance, the externally applied movements (e.g. Bässler, 1976; Skorupski and Sillar, 1986; LeRay and Cattaert, 1997; for a review, see, for example, Pearson, 1995).

Both effects have been particularly well demonstrated in the stick insect. Therefore, this animal is used here to investigate how the leg of a freely walking animal is affected by such disturbances. The geometry of the leg of a stick insect is shown in Fig. 1. The coxa–trochanter and femur–tibia joints, the two distal joints, are simple hinge joints with one degree of freedom corresponding to elevation and to extension of the tarsus, respectively. The subcoxal joint is more complex, but most of its movement is in a rostrocaudal direction around the nearly vertical axis. The additional degree of freedom allowing changes in the alignment of this axis is little used in normal walking (Cruse and Bartling, 1995), so the leg can be considered as a manipulator with three degrees of freedom for movement in three dimensions.

In the standing or passive animal, all joints show resistance reflexes (thoraco-coxal joint, Wendler, 1964; Graham and Wendler, 1981; Schmitz, 1985; Cruse et al., 1992; coxa–trochanter joint, Wendler, 1972; Schmitz, 1985, 1986a,b; Cruse et al., 1992; femur–tibia joint, Bässler, 1967; for a review, see Bässler, 1983). These resistance reflexes show highpass-filter-like adaptation with time constants between 1 s and more than 100 s. A particularly well-investigated system is the femur–tibia joint, which shows time constants of 15 s for a flexion movement and 22 s for an extension movement (Cruse and Storrer, 1977; for a review, see Bässler, 1983). Thus, as a first approximation, these reflexes can be described as a negative feedback system based on the position signal.

For the walking animal, a number of experimental results have been interpreted to show a negative feedback system controlling the movement during stance. In contrast to the standing animal, in the case of the femur–tibia joint, the time constant was estimated to be of the order of approximately 100 ms (Cruse, 1981; Cruse and Pflüger, 1981), suggesting a velocity-based negative feedback system. In these experiments, the animal walked freely over a platform equipped with a force transducer, which was moved by hand when the animal stepped on the platform. Negative feedback mechanisms were also found in other experiments on the ‘standing leg of the walking animal’ (Cruse and Schmitz, 1983). In those studies, animals walked on a treadwheel with five legs while the sixth leg stood on a force transducer. Again, the force transducer was moved manually, and the forces and the activities in the nerves to the extensor and flexor muscles were evaluated. Cruse (1985) modified this experiment so that the force transducer could be moved by hand, both in parallel with the treadwheel motion and at faster or slower rates (or stopped entirely). The results again suggested that a velocity-control system underlies the regulation of leg movements. However, these procedures all had the disadvantage that the perturbations were produced manually and could not easily be controlled. In an alternative approach, Weiland and Koch (1987) investigated the femur–tibia joint in animals that were completely restrained. The passive animal showed the well-known resistance reflex. When the animal was activated by a mechanical stimulus to the abdomen given during an active movement of the leg, the reaction could best be described by a negative feedback system controlling velocity.

In a different series of experiments, Bässler (1976) described a reflex reversal in a stick insect activated by mechanical stimulation. This so-called ‘active reaction’ represents an assistance reflex. Stimulation of the sense organ of the femur–tibia joint, the femoral chordotonal organ, in a way that corresponds to flexion of the joint, activates the flexor muscle. This could be interpreted as positive feedback, but other interpretations are also possible. A study by Schmitz et al. (1995) showed that an assistance reaction can be found for both flexion and extension of the joint, clearly supporting the interpretation of an underlying positive feedback system. This active reaction has been thoroughly investigated at the neuronal level (Bässler, 1976, 1988; for a review, see Bässler, 1993).

Thus, some results support the interpretation of a negative feedback system, others support the interpretation of a positive feedback system. A role for positive feedback was given further support by functional considerations. Cruse et al. (1995) proposed that highpass-filtered positive position feedback (or velocity-based positive feedback) would have many advantages when controlling the movement of a system with a high number of degrees of freedom (up to 18 in the case of a six-legged system). This hypothesis led to the assumption that two joints of each leg, the thoraco-coxal joint and the femur–tibia joint, are under positive velocity control and one joint, the coxa–trochanter joint, is under negative position control. With this assumption, a number of control problems, such as walking with changing body geometry, walking over obstacles, curve walking and so on, could be solved (Cruse et al., 1998).

A direct investigation of this proposal at the neurophysiological level, i.e. using fixed animals mechanically stimulated to perform active movements (J. Schmitz and A. Heuer, in preparation), revealed that the coxa–trochanter joint is always under negative feedback control, in agreement with earlier findings (Schmitz, 1985). For the two other joints, the results only partially supported the predicted pattern. In approximately 30 % of cases, the joints showed positive feedback, in 30 % they showed negative feedback, and in the remaining cases no clear positive or negative reaction was observed. Thus, taken together, both positive and negative feedback seem to occur in the thoraco-coxal joint and the femur–tibia joint, but the mechanisms are labile and the causes of this lability are unknown.

Except for the first studies mentioned, all the experiments cited above were performed using animals either fixed or walking in restrained situations. Because of the apparent lability of the system, these experiments should be carried out with animals walking in as natural a situation as possible. Therefore, in the present study, experiments with freely walking animals are repeated with a significantly improved methodology.

The results support the interpretation that the leg joints of the walking animal are under negative velocity control. Furthermore, a hypothesis is proposed that is concordant with the results suggesting positive and negative velocity feedback. In brief, the hypothesis assumes that a positive feedback channel is used to provide the reference input for a negative feedback velocity controller. This negative feedback velocity channel, however, is only activated when disturbances are detected by another system, which may explain the seemingly labile experimental results.

Experiments were performed on adult female stick insects, Carausius morosus (Brunner von Wattenwyl). The animals walked freely on a horizontal path (33 mm wide, 400 mm long) made from balsa wood. A small piece of the margin of the path (10 mm wide, 12 mm long) was cut away and replaced by a platform mounted on a three-dimensional force transducer.

The force transducer consisted of two perpendicularly mounted steel plates (Fig. 1) each of which bore two semi-conductor strain gauges (BLH Electronics) allowing force to be measured in two horizontal directions. The direction parallel to the long axis of the body (anterior–posterior axis) is the x axis: positive forces point anteriorly. The transverse axis (proximal–distal) is the y axis: positive forces point distally. Both force transducers were connected to Wheatstone bridges and gave linear responses in the range 0–3 mN. As the lower transducer had a larger lever arm, its stiffness was lower by a factor of 2.38.

A special device was developed to measure the vertical force component (z axis). The platform was constructed from a bowl (diameter 10 mm) completely filled with water and covered with a thin latex skin (Fig. 1). The bowl contents were connected to a U-shaped silicone tube (10 cm long, diameter 1 mm, mass with water 556 mg). The end of the tube was sealed, but it contained some air. When the leg stepped onto the latex skin, the resulting pressure caused the water level at the other end of the tube to increase. When the leg was lifted, the compressed air pushed the water back to its original level. The water level was used to measure the vertical force applied by the leg to the force platform; it was measured by two parallel silver wires partly submerged in the water. As the water level increased, the resistance measured between the two wires decreased. The response was linear over the range 0–5 mN. Application of force vectors at different angles revealed a sinusoidal response showing that only the vertical component of the applied force was registered. The sensitivity of the force transducer varied according to the position on the latex surface, decreasing from the centre to the margin. However, as the leg usually touched the platform such that the tarsus grasped the margin, the tip of the tibia (which transmits the force) was consistently approximately 2 mm from the margin, allowing us to calibrate the ventral force measurements appropriately.

The complete three-dimensional force-transducer platform was mounted on a servo-motor (Ling vibrator V204; for further details, see Schmitz, 1986b) by which the platform could be moved by 4 mm in the horizontal plane. Two platform speeds were used in the experiments, slow (7 mm s⁻¹) and fast (20 mm s⁻¹). The movement of the platform was recorded by a position transducer (Philips PR9833) and showed a sigmoidal form with a duration of 200 ms for the fast stimulus and 580 ms for the slow stimulus (compared with an average stance duration of approximately 1000 ms). To apply stimuli in four different directions, the position of the path relative to the force transducer was changed such that the movement of the transducer always occurred parallel to the stiff (upper) force transducer. In a body-fixed coordinate system (Fig. 1), movement directions were parallel to the long axis of the body, either in the anterior or in the posterior direction (x axis) or perpendicular to the long axis, either in the proximal or in the distal direction (y axis). No movements were applied along the vertical axis (z axis).

Forces in the x, y and z directions were recorded on computer with a time resolution of 4.6 ms. The vertical force was used to trigger the stimulus because it showed the most predictable pattern. The force required to trigger the stimulus was 0.15 mN and was reached within 25 ms of leg placement on the platform. Upon this trigger, movement of the platform was started either immediately or after a delay of 300 ms. In the latter case, the stimulus was applied approximately during the middle of the stance phase. Thus, four different types of stimuli were applied, with a delay of 0 or 300 ms and at a fast or slow speed. All measurements were averaged relative to the beginning of the stimulus movement over temporal classes of 25 ms.

To test whether the movement of the platform affected the forces measured, the platform was loaded with 25 % of the body weight of an adult stick insect (i.e. the load provided by a leg during a tetrapod gait). Mean forces were measured in temporal classes of 25 ms (as used in later experiments). Different results were obtained for the slow and the fast movements. For the slow movement, flat curves of force versus time were obtained for all three force transducers, indicating that no movement artefact occurred. For the fast movement, significant artefacts in all three axes were observed. To minimise these artefacts, a fast Fourier transformation was performed for each transducer signal, and the force values measured in the later experiments were corrected accordingly. Fig. 2 shows a comparison between the raw and filtered force signals of the z component (vertical force transducer) during a step as an example of the worst case of such artefacts. Those of the two horizontal force transducers were much smaller, and hence required less filtering. No filtering was necessary for the data obtained for the slow movement of the platform.

In some cases, the walks of the animals were videotaped (50 frames s⁻¹) using a CCD video camera (shutter speed 1/1000 s; model CCD-7240, Fricke GmbH, Germany) and an SVHS recorder (Panasonic RTV-925) equipped with a frame counter. The camera was mounted perpendicularly above the path to obtain views of the body and the legs in the xy plane of movement. Video recordings were evaluated frame-by-frame off-line using a NeXT computer equipped with a NeXT dimension board. Points on the walking surface could be measured with a standard deviation (S.D.) of ±0.21 mm and points on the body with an S.D. of ±0.54 mm.

All values are presented as means ± S.D. Data were analysed using non-parametric tests, e.g. the sign test (after Dixon and Mood, 1946).

To investigate how a walking stick insect reacts to an external movement applied to the tarsus of a stance leg, we first examined whether such a disturbance is compensated for by the leg alone or whether it also influences the position of the body and thereby the movement of the other legs.

We videotaped walking animals, from above, and stimulated the leg when it was placed on the platform. Stimulation was applied in all four directions for both the middle and hind leg. The slow stimulus speed was used and zero delay. We measured changes in the horizontal walking speed, the angle of the long axis of the body relative to the ground (walking direction) and the lateral shift of the body at the coxae of the front and middle legs in response to the stimulus.

During normal straight walking, the body performs regular oscillations (Jander, 1985), and the values obtained during the application of a stimulus were therefore compared with the corresponding values during the step before that stimulus was applied. No significant changes were found in the angle of the body or the lateral shift of the body (four animals, 64 steps), indicating that the slow stimulus did not significantly influence body position during walking. Visual inspection of the body axis during the force measurements with the fast stimulus (see below) also suggested that no compensatory movements of the body axis occurred. Therefore, we can conclude that compensation is performed at the level of the individual leg.

The mean walking speed was 33.8±5.9 mm s⁻¹ (N=4 animals, 64 steps; range 21.5–38.2 mm s⁻¹). In none of the eight stimulus situations did the application of the stimulus affect the walking velocity (P>0.1). A walking velocity of approximately 34 mm s⁻¹ is on the low side of the velocity range of Carausius morosus (15–100 mm s⁻¹; Graham, 1985), suggesting that the animals in our experiments were not performing fast walks corresponding to escape responses.

To allow comparison with previous investigations, forces elicited by passive movements of the legs were measured when the animals were standing still on the platform. Legs were positioned at approximately the middle of their normal range of movement. Results for hind legs are shown in Fig. 3 for forces in the x and y directions only. The results obtained for all legs clearly showed the previously well-described resistance reflexes of the standing animal.

For walking animals, no force measurements were performed on the front legs because the vertical forces produced by these legs were too small to trigger stimulus application (see Materials and methods). In contrast, the middle and hind legs developed larger vertical forces. Two different orientations of the force platform were used to investigate whether stiffness influenced the forces measured. Sequences in which the animal walked straight and at constant speed along the path and in which no legs slipped off the platform were used in this analysis, and no stimuli were applied. The results for the middle and hind legs are given in Fig. 4.

Qualitatively, the results agree with earlier findings reported for stick insects (Cruse, 1976) and for cockroaches (Blaberus discoidalis) (Full et al., 1991; Full and Tu, 1990). In the middle leg, a force is developed in the x direction. This force is directed anteriorly during the first part of the stance and posteriorly during the second part. Along the y axis, after a brief proximally directed force pulse, the force is directed distally (away from the body). The hind leg behaves in a similar way, the main difference being that only a short force pulse in the anterior direction is found in the x direction. The bulk of the force is directed posteriorly. In both legs, the vertical forces are larger, reaching a single ventrally directed maximum of approximately 2–3 mN.

The forces developed against the soft and the stiff force transducers showed clear differences. In the y direction, the forces developed against the stiff force transducer were significantly greater than those developed against the soft transducer (P<0.01). Fig. 5A shows mean forces calculated over a 250 ms period that included the highest forces for both y and z components. With respect to the y component, the force is 3.4 times larger on the stiff than on the soft transducer for the middle leg and 4.0 times larger for the hind leg, whereas the stiffness ratio of the force transducers is 2.38. A qualitatively similar effect is found for the x direction; quantitatively, however, this effect is much smaller (a factor of 1.05 for the middle legs and 1.35 for the hind legs).

Different ground reaction forces on the soft and stiff walking substrata could result in changed trajectories of the tarsus. We therefore compared the excursions of the force platform during middle and hind leg steps. The results (Fig. 5B) confirm that both legs show a significantly greater lateral excursion on the stiff substratum (P<0.01). In the rostro-caudal (x) direction, the change in the trajectories is again much smaller than in the y direction.

Using the above force measurements and the kinematic data on leg movements obtained from the video analysis, we can calculate the torques developed by individual joints. As an approximation, we assume a constant body height during the stance and a straight movement of the tarsus parallel to the long axis of the body. Torque values are shown in Fig. 6 for the hind leg. When the stiff force transducer is oriented in the y direction, the coxa–trochanter joint (angle β) develops a smaller torque than when the soft transducer is oriented in this direction. In the femur–tibia joint (angle γ), the flexor torque is greater on a stiff substratum than on a soft substratum. Qualitatively similar results were found for the β and γ angles of the middle leg (results not shown). The main difference was that the thoraco-coxal joint (angle α) of the middle leg developed a significant torque in the posterior direction on both substrata (corresponding to activation of the retractor muscle).

The forces measured from undisturbed legs could be used as control values for comparison with the results of the disturbance experiments. On a quantitative basis, however, such a comparison is difficult. In the disturbance experiments, the only steps that can be evaluated are those in which the leg remains on the platform during and for some time after the disturbance. Steps in which the leg slips off the platform cannot be evaluated. Therefore, in the disturbance experiments, only ‘safe’ steps are selected for further analysis. A comparable selection cannot be performed for the undisturbed steps. We attempted to make a similar selection by choosing only steps in which a disturbance would have been possible even after a delay of 650 ms (i.e. the stance leg remained on the platform for at least 850 ms).

Because the results for the middle and hind legs were very similar, only the results from hind legs will be discussed below. In these experiments, for each of the four stimulus directions (distal, proximal, anterior, posterior), the slow and the fast stimulus with a delay of zero and of 300 ms was applied, giving 16 stimulus situations. From these, we present eight situations as examples in Fig. 7.

In all situations, the measured forces oppose the experimentally applied movement. In general, the difference between the reactions to the two opposite stimulus directions decreases rapidly after the end of the stimulus. When the slow stimulus was applied to the middle or hind leg at the end of stance, no significant changes in force were observed (results not shown). The effects of the stimulus are mainly in the direction of its application, with only weak effects in the perpendicular direction. The forces in the vertical (z) direction are unchanged by the slow stimulus movement occurring at the beginning of the step. When the slow stimulus is applied with a 300 ms delay, the vertical force decreases slightly for the inward (proximal) movement and the step seems to be shortened to some extent, suggesting that the stimulus here might act to finish the step. A similar result was found for the middle legs. However, no clear tendency to finish the step was found in the other stimulus situations of the middle and hind legs.

During and after the disturbance, the vertical force does not change substantially relative to undisturbed leg values, indicating continuous weight support by the disturbed leg. However, because the length of the lever arm will increase for a distal movement of the tarsus, the torque to be developed by the muscles will increase considerably.

Two qualitative conclusions can be drawn from these experiments. First, the legs always react with a force that opposes the applied disturbance (Fig. 7), indicating a negative feedback system. Second, the legs react differently to substrata of different compliance (Fig. 4). In the y direction, a softer substratum elicits smaller forces than does a stiffer substratum. Below, we discuss the possible control mechanisms underlying the responses to perturbations and then examine whether these mechanisms could account for the effects of substratum compliance. For a multi-legged system such as an insect, a simple way of dealing with a disturbance such as those used here is simply to lift the leg, or at least to unload it, because the remaining legs can guarantee stability. However, a substantial decrease in the vertical (z) force component during a disturbance relative to undisturbed walking was never observed, suggesting that this solution was not used.

A number of different control architectures have been described for the control of a biological or a technical manipulator. The classical ones involve negative feedback of position, velocity or force. A special application derived for the antagonistic architecture of biological systems is impedance control (Hogan, 1982; Polit and Bizzi, 1978), which considers only the passive properties of the muscles, but behaves qualitatively like a negative position feedback system. More recently, positive velocity feedback or positive force feedback have been investigated as control mechanisms. For all these systems, an additional problem is how to obtain a suitable reference signal for the controller.

Of the control architectures we investigated in this way, only negative velocity feedback and positive force feedback showed qualitative agreement with the biological results of the present study. In all other cases, either the sign of the response (positive velocity feedback) or its form differed from the biological results. For both negative position feedback and impedance control, the effects of disturbances remained after the disturbance had ended. For negative force feedback, the force signals varied little during the disturbance due to the activity of the force controller and therefore cannot explain the biological results. For positive force feedback, the absolute force values provided by the controller were extremely small even when the gain was increased to a value of 3, leading to instability in the system. Therefore, as in previous studies (e.g. Weiland and Koch, 1987; Cruse, 1985), only a negative velocity feedback system appears to be able to explain the results sufficiently well.

What is the reference input for this velocity controller? There is usually assumed to be an internal, time-dependent memory providing, for each joint, the desired angles during stance. This method of applying a precalculated look-up table or a calculated angle trajectory would provide a solution, because a negative feedback system could detect any deviation from these values. However, this method is not very flexible, in particular with respect to changes in the geometry of the system (either caused by injury or simply due to changes in body orientation relative to gravity) and it requires considerable computing power (for a detailed discussion, see Cruse et al., 1998).

An alternative solution would be to use a highpass-filtered position signal (i.e. a velocity signal) with a positive feedback controller. This solution has several technical advantages, as discussed by Cruse et al. (1998), and is supported by certain experimental results (Bässler, 1976; Schmitz et al., 1995). The signal necessary to initiate the positive velocity feedback controller at the beginning of stance could be provided either by the movement of the other walking legs or by a centrally generated impulse-like signal to the stance leg at the beginning of stance which triggers a movement of the leg in approximately the appropriate direction (pushing the thoraco-coxal joints backwards is sufficient; Cruse et al., 1995, 1998).

Posteriorly directed forces have been observed in all legs of starting stick insects (Cruse and Saxler, 1980).

However, a positive feedback system cannot explain the reactions to the disturbances applied here. One possible solution would be to use the velocity signal as a positive feedback providing the reference input for a negative feedback system controlling the velocity. How could positive and negative feedback exist at the same time? Because the negative feedback system is only required for reactions during the disturbance, a solution might be to use a signal that registers the disturbance to switch on the negative feedback circuit. The latter, if strong enough, can then override the positive feedback circuit.

Angular acceleration could provide the means of distinguishing between a normal, undisturbed step and a disturbance as used in our experiments. Fig. 8 shows the acceleration of the three joint angles during a normal step and during a step disturbed by a fast (20 mm s⁻¹) movement of the platform. Fig. 9 shows a circuit that could function in this way. We assume that the velocity signal is negatively fed back only if the acceleration exceeds a given threshold value. This threshold is chosen such that acceleration values occurring during normal steps are below the threshold. Other circuits could achieve the same result; that shown in Fig. 9 assumes that the acceleration signal inhibits the positive feedback channel. Inhibitory influences from acceleration-sensitive afferents on velocity-sensitive afferents in the stick insect have been described by Stein and Sauer (1999).

This circuit can qualitatively explain the results found here for normal steps on the stiff substratum and for disturbances of both velocities and in all four directions, for both the middle and hind legs. During a disturbance, the negative feedback overrides the effect of the positive feedback signal, thus avoiding positive feedback support of the effect of the disturbance and, instead, returning the angular velocity of the leg to its pre-disturbance value. After the disturbance has been corrected, the positive velocity feedback can again take over the control. The resistive forces involved are not strong enough to affect the movement of the central body significantly. In this way, flexion of the femur–tibia joint, e.g. by a proximal disturbance, will elicit activation of the extensor muscle. However, we also found that an increase in extensor torque is combined with decreased depressor torque and vice versa (Fig. 6), suggesting the existence of an interjoint reflex in the walking animal that excites the depressor when the femur–tibia joint is extended. In experiments in which legs were moved passively, however, no such effect has been found (Hess and Büschges, 1999). Instead, excitation of the extensor tibiae was found to be correlated with levator excitation. Using force measurements in the passive stick insect, Cruse et al. (1992) found that the levator muscle produces more force when the femur–tibia joint is extended simultaneously with a depression of the coxa–trochanter joint compared with when the latter joint is depressed alone. In contrast, Delcomyn (1971) found that an increase in femur extension (i.e. increased depressor trochanteris activity) in the cockroach (Periplaneta americana) was accompanied by a reflexively driven excitation of the tibia extensor. Interestingly, this result was obtained after the connectives between the supra- and suboesophageal ganglia had been cut, an operation considered to bring about an active state in the animal (Graham, 1979).

Therefore, for the active animal, but apparently not for the passive animal, the model should be expanded by an additional interjoint reflex not shown in Fig. 9. Lesion of trochanteral campaniform sensilla has shown that, although they underlie several reflexes during walking (Schmitz, 1993; Schmitz and Stein, 2000) and influence the forces developed during a normal step (C. Bartling and J. Schmitz, in preparation), they do not appear to influence reactions to the slow and fast disturbances used here.

A second important result of the present study is that, for an undisturbed step on the soft platform, the force in the y direction was smaller than for a step on the stiffer substratum by a factor of approximately 2. When loaded by a given force, the soft platform will move further than the stiff platform. However, when stepping on the soft platform, the animals actually produce such a small force that the movement of the platform in the y direction was smaller than on the stiff platform (Fig. 5). Therefore, a kinematic signal such as a velocity or acceleration threshold, as used in the circuit of Fig. 9, is unable to explain the results for the soft platform. Therefore, another mechanism must be responsible for the different reaction on the soft platform.

How can the compliance of the substratum be identified? At present, we do not know. A precalculated reference value could be used here, but with the same drawbacks as discussed above. It is possible that this detection occurs immediately after the first ground contact following the swing movement. The leg usually develops a small anteriorly and proximally directed force peak at this point (see Fig. 4). Depending on the compliance of the substratum, this force peak will lead to a smaller or larger anterio-proximal movement of the leg after ground contact. The amplitude and direction of this movement could provide the necessary information and might lead the leg controller to develop a more vertically oriented force vector, i.e. activate the depressor and the flexor muscles (Fig. 5). In this way, the leg will avoid a situation in which the platform is too far from the body. Alternatively, or in addition, the small resistive force at the beginning of touch-down could be measured by the campaniform sensilla. Both these solutions require some kind of memory because this mode should be switched on during the whole stance. A simpler reactive mechanism, i.e. one not requiring a memory, could take the form of continuous measurements of the stiffness of the ground, which would then be used to activate the flexor muscle and, via the circuit discussed above, also the depressor muscle. However, no biological mechanism for making such measurements is yet known.

No notable reaction to soft ground was found in the x direction. Functionally, this makes sense because the leg must be moved in a posterior direction whether the ground is soft or stiff. A technical reason for the small response to anterior–posterior stimulation measured in the present study could be that, during anterior–posterior disturbances, the femur–tibia joint is moved only slightly; it is at this joint, however, that acceleration is particularly well measured by the sensory cells of the femoral chordotonal organ (Hofmann and Koch, 1985).

In conclusion, the present study has shown that the leg movements of walking stick insects are controlled in a subtle way. Normal, undisturbed stance could be generated by an underlying positive velocity feedback, as proposed by Cruse et al. (1995), while negative velocity feedback may come into play when adapting the ongoing stance to unexpected disturbances. This control scheme is advantageous and could be a common feature of other walking systems.

We thank Holk Cruse for his steady support of this work and his helpful discussions. We are grateful to Annelie Exter for her help with the figures. This study was supported by ‘Deutsche Forschungsgemeinschaft’ (Cr58/9-3).