1211
The Journal of Experimental Biology 203, 1211–1233 (2000)
Printed in Great Britain © The Company of Biologists Limited 2000
JEB2521
REACTION TO DISTURBANCES OF A WALKING LEG DURING STANCE
CHRISTIAN BARTLING AND JOSEF SCHMITZ*
Department of Biological Cybernetics, Faculty of Biology, University of Bielefeld, PO Box 100131, D-33501
Bielefeld, Germany
*Author for correspondence (e-mail: [email protected])
Accepted 20 January; published on WWW 9 March 2000
Summary
The ground reaction forces exerted by the legs of freely
Perturbations were applied either immediately after leg
walking stick insects, Carausius morosus, were recorded
contact or after a delay of 300 ms. The reactions to these
during normal and perturbed locomotion. The animals
disturbances were compatible with the hypothesis that the
walked along a path into which a three-dimensional force
velocity of leg movement is under negative feedback
control. This interpretation is also supported by
transducer was integrated. The transducer registered all
comparison with simulations based upon other control
three components of the forces produced by a single leg
when, by chance, it walked on the force platform. The
schemes. We propose a model circuit that provides a
stiffness of the walking surface was found to be a critical
combination of negative and positive feedback control
mechanisms to resolve the apparent discrepancies between
variable affecting the forces and the trajectories of leg
our results and those of previous studies.
movements during undisturbed walking. The forces
produced by a leg were considerably smaller and the
trajectories were closer to the body during walking on soft
Key words: locomotion, disturbance reaction, ground reaction force,
versus stiff surfaces. Perturbations during stance were
movement control, substratum compliance, positive feedback
generated by moving the platform in various directions
system, modelling, stick insect, Carausius morosus.
within the horizontal plane and at two different rates.
Introduction
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
1212 C. BARTLING AND J. SCHMITZ
Femur z
ψ
α
Caudal
Thorax
γ
Tibia
−y
β
x
ϕ
Tarsus
Coxa
Rostral
Leg plane
Foothold and force transducer
for vertical force
Upper transducer for
horizontal force
Lower transducer for
horizontal force
Axis of stimulus
motor
Fig. 1. Schematic drawing of a left leg of a stick insect. The
arrangement of the joints, and their axes of rotation (red: α, β, γ, ϕ,
ψ), are shown together with the definition of the body-centred x, y, z
coordinate system (blue). The leg is shown standing on the threedimensional force transducer (not to scale). The uppermost, vertical
force transducer also provides a foothold. One of the two horizontal
force transducers is mounted on top of the other with a 90 ° angle
between them. The whole force transducer system is mounted on the
axis of a stimulus motor. Leg displacements could be applied by
moving the force transducer system within the horizontal plane (x, y)
as indicated.
show highpass-filter-like adaptation with time constants
between 1 s and more than 100 s. A particularly wellinvestigated 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
Disturbance reactions of walking legs 1213
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.
Materials and methods
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.
Force measurements
The force transducer consisted of two perpendicularly
mounted steel plates (Fig. 1) each of which bore two semiconductor 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.
Stimulation
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.
1214 C. BARTLING AND J. SCHMITZ
2
Force (mN)
0
-2
-4
-6
Touch-down
Lift-off
Raw data
Filtered data
-8
0
0.5
1.0
1.5
2.0
2.5
Time (ms)
3.0
3.5
4.0
Fig. 2. Comparison of the raw and filtered force signals in the z
direction (vertical force) obtained from a single, undisturbed step of
a middle leg; see Materials and methods for further details.
Data evaluation
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.
Video recordings
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-byframe 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).
Results
Video analysis
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.
Force measurements of undisturbed legs
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
Disturbance reactions of walking legs 1215
Hind leg, resistance reflexes
x component
y component
A
Anterior
Force (mN)
8
x
4
4
0
0
-4
-4
-8
0
B
500
1000
Force (mN)
0
-4
-4
1000
Force (mN)
0
0
-4
-4
-8
0
500
1000
2000
Anterior
8
Force (mN)
1500
0
0
-4
-4
0
500
1000
Time (ms)
1500
500
1000
2000
2000
1500
2000
Distal
-8
Posterior
1500
Proximal
8
4
-8
1000
Distal
0
4
y
500
-8
Posterior
2000
Proximal
8
4
1500
Distal
0
4
y
x
2000
Anterior
8
D
1500
1000
-8
Posterior
500
500
8
0
0
Proximal
0
4
-8
x
2000
4
y
C
1500
Anterior
8
x
-8
Posterior
y
Distal
8
Proximal
0
500
1000
1500
2000
Time (ms)
Fig. 3. Mean force profiles of resistance reflexes in the right hind leg of a standing animal. Only the x and y force components are shown. The
stimulus directions are indicated by arrows in the respective sketches of the animal. The stimulus (amplitude 4 mm, velocity 20 mm s−1,
duration 200 ms) was applied at time zero. Data were obtained from 18 trials for each stimulus direction. The force data were averaged for each
25 ms time interval, and the median and first and third quartiles are shown. Thus, the bars represent interquartile ranges. The directions of
elicited force responses are indicated.
1216 C. BARTLING AND J. SCHMITZ
Middle leg, force profiles of control steps
A
x component
2 Stiff
Anterior
y component
2 Soft
Distal
1
z component
Force (mN)
0
1
1
0
0
-1
-1
-2
-2
-1
-2
-3
-750 -500 -250
B
0
Posterior
250 500
Anterior
2 Soft
-750 -500 -250
0
Proximal
250 500
Distal
2 Stiff
-4
-750 -500 -250
0
Ventral
250 500
-750 -500 -250
0
Ventral
250 500
0
250 500
1
Force (mN)
0
1
1
0
0
-1
-1
-1
-2
-3
-2
-750 -500 -250
0
Posterior
250 500
-2
-750 -500 -250
0
Proximal
250 500
-4
Hind leg, force profiles of control steps
C
y component
x component
Anterior
2 Stiff
Distal
2 Soft
1
z component
Force (mN)
0
1
1
0
0
-1
-1
-1
-2
-3
-2
Posterior
-750 -500 -250
D
0
2 Soft
-2
250 500
Anterior
Proximal
-750 -500 -250
0
250 500
Distal
2 Stiff
-4
Ventral
-750 -500 -250
1
Force (mN)
0
1
1
0
0
-1
-1
-1
-2
-3
-2
-750 -500 -250 0
Time (ms)
Posterior
250 500
-2
-750 -500 -250 0
Time (ms)
Proximal
250 500
-4
-750 -500 -250 0
Time (ms)
Ventral
250 500
Fig. 4. Mean force profiles of free-walking, undisturbed animals. Results for the three different force components (x, y, z) are arranged in
columns. (A) Middle legs (29 steps, 13 animals); (B) middle legs (26 steps, eight animals); (C) hind legs (18 steps, 13 animals); (D) hind legs
(39 steps, eight animals). In A and C, the stiff force transducer was aligned with the x axis of the animal; it was aligned with the y axis in B and
D (see Fig. 1). The median (symbols) and first and third quartiles (bars) are shown for 25 ms time classes. The time axis is offset by 650 ms
from stance onset, i.e. the time at which a disturbance would have been possible (see text for further details). The onset of stance is indicated by
an upward-pointing arrow. Directions of forces are as in Fig. 3.
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
Disturbance reactions of walking legs 1217
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
A
0
Soft
Middle leg
Mean z force (mN)
-0.5
Stiff
-1.0
Soft
Hind leg
Stiff
-1.5
-2.0
-2.5
-3.0
Distal
-3.5
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Mean y force (mN)
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
y position (mm)
Anterior
600
0.8
Hind leg
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
0
200 400 600
Time (ms)
800
1000
Anterior
y position (mm)
x position (mm)
x position (mm)
B
0.8
Middle leg
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
0
200 400
800
1000
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
Distal
Soft
Stiff
0
200
400
600
800
1000
Distal
Soft
Stiff
0
200
400 600
Time (ms)
800
1000
Fig. 5. (A) Comparison of the different
forces elicited over a 250 ms period during
stance in response to a change in ground
stiffness (stiff versus soft force transducer).
The resulting force vector in the yz plane of
both the middle and hind legs is shifted
distally when the ground stiffness is
increased. (B) Comparison of the different
excursions of the force platform in the x and
y directions produced by the middle (upper
row) and hind (lower row) legs during a
stance. Data were derived from the force
profiles shown in Fig. 4. Positional data
obtained from animals walking over the soft
transducer are indicated by open symbols,
data obtained from the stiff transducer are
indicated by filled symbols. Mean values for
25 ms time classes are shown. The onset of
stance is indicated by an upward-pointing
arrow.
1218 C. BARTLING AND J. SCHMITZ
Hind leg torques during stance
Torque (µN m)
40
30
20
10
0
-10
-20
-30
-40
60
50
40
30
20
10
0
-10
-20
40
30
20
10
0
-10
-20
-30
-40
Angle α
A
Soft
Stiff
0
250
500
250
500
750
1000
Angle γ
C
0
1000
Angle β
B
0
750
250
500
750
Time (s)
1000
Fig. 6. (A–C) Comparison of the torques generated during stance by
the three leg joints (angle α, thoraco-coxal joint; angle β,
coxa–trochanter joint; angle γ, femur–tibia joint) in response to a
change in ground stiffness. Data were obtained from hind legs (soft,
13 animals, 18 steps; stiff, eight animals, 39 steps). Positive values
correspond to net torques pointing in the direction of protraction
(angle α), depression (angle β) and flexion (angle γ), respectively.
Mean values for 25 ms time classes are shown.
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).
Force measurements of disturbed steps
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.
Discussion
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.
To compare the properties of all these control architectures
with those found in experiments, we simulated the behaviour
of these control structures using appropriate time courses for
Disturbance reactions of walking legs 1219
Hind leg, disturbance reactions during stance
x component
A
3
Force (mN)
2 Stiff
x
1
Soft
Anterior
Distal
2
0
1
-1
0
-2
0
-1
Posterior
-500 -250
0
250
500
750
-1
Proximal
-2
-500 -250
0
250
500
750
Force (mN)
2 Soft
x
Anterior
Stiff
Distal
2
Posterior
0
250
-1
0
-2
500
750
-1
Proximal
-2
-500 -250
Anterior
0
250
500
750
Force (mN)
Ventral
-4
-500 -250
0
250
500
750
1
Distal
Soft
2
0
1
-1
0
-2
-1
Posterior
-1
Proximal
0
250
500
750 1000
0
250
500
0
250
500
750 1000
1
Stiff
Anterior
Ventral
750 1000
3
2 Soft
-3
-4
-2
Force (mN)
-3
0
y
Distal
2
0
1
-1
0
-2
1
0
-1
Posterior
-2
y
750
1
-2
x
500
0
1
3
D
250
-1
2 Stiff
x
0
0
-500 -250
C
Ventral
-4
-500 -250
1
-2
y
-3
1
3
B
z component
1
-2
y
y component
-1
Proximal
-2
0
250 500 750 1000
Time (ms)
-3
Ventral
-4
0
250 500 750 1000
Time (ms)
0
250 500 750 1000
Time (ms)
Fig. 7. Comparison of the mean force profiles of hind legs of free-walking animals disturbed during the stance phase. The results for the three
different force components (x, y, z) are arranged in columns. The stimulus (application indicated by the black bar; amplitude 4 mm, velocity
20 mm s−1) in A and B was applied with a delay of 300 ms after the start of stance. The stimulus directions are indicated by open [rostrad (A) and
distad (B)] and filled [caudad (A) and proximad (B)] symbols as indicated on the sketches of the animal. In C and D, the arrangement of the panels
is analogous; however, the stimulus velocity is 7 mm s−1 and the stimuli were applied immediately after the start of stance (zero delay). The force
directions are indicated in the figure. Symbols represent mean values within 25 ms time classes; data were obtained from at least five animals and at
least 23 steps. The corresponding mean force profiles of undisturbed, free-walking hind legs (see also Fig. 4) are shown by the continuous line in
each panel. The orientation of the stiff force transducer was always in the direction of the stimulus, as indicated in each panel.
the reference inputs (position feedback was investigated using
both a step and a ramp reference input). In all cases, we used
a proportional controller with lowpass filter properties.
Simulations of the mechanical system were performed using
the Roboop1.06 library (Gourdeau, 1997) for a single joint, but
included dynamic properties. The simulation of the mechanical
system is given by:
T = D(q̇,q̈) + G(q) + F(q̇) + Textern .
(1)
The torque T results from the sum of the inertial properties of
1220 C. BARTLING AND J. SCHMITZ
the leg mechanics D(q̇,q̈), gravity G(q), frictional forces F(q̇)
and external torques Textern. The first three terms are dependent
on position (q) and/or the first and second derivatives of
position (q̇,q̈). The last term is determined by:
Textern = Tdisturb + Tanimal + Tcontroller + Tgroundstiffness ,
(2)
i.e. the sum of torques applied by the external disturbance
moving the platform Tdisturb, the torque developed by the other
walking legs via the body Tanimal, the torque provided by the
neuronal controller Tcontroller and the passive elastic properties
of the substratum Tgroundstiffness. Coriolis forces are neglected
because we consider only a single joint.
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
A
Start +
+
α
β
γ
50
Controller
Om
−
+
.
α
..
αlow
B
Start +
100
Joint acceleration (degrees s-2)
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 thoracocoxal joints backwards is sufficient; Cruse et al., 1995, 1998).
+
+
Controller
Om
−
.
α
0
..
αhigh
-50
-100
0
250
500
750
Time (ms)
Fig. 8. Comparison of the angular acceleration of the three leg angles
(α, β, γ) during an undisturbed (eight animals, 26 steps; continuous
lines) and a disturbed stance (13 animals, 52 steps; dashed lines with
symbols). Data are from middle legs moved distally by 4 mm at a
velocity of 20 mm s−1. Note that during the undisturbed stance only
negligibly small accelerations occur. Symbols represent mean
values of 25 ms time classes. α, thoraco-coxal joint angle; β,
coxa–trochanter joint angle; γ, femur–tibia joint angle.
Fig. 9. Model circuit of a controller that can switch from positive
velocity feedback, as used during an undisturbed stance (A), to
negative velocity feedback for use in reactions to disturbances (B).
The active nodes and pathways are indicated by the grey shading.
Only one channel for the control of a single joint angle (α) is shown.
(A) During normal walking (low acceleration α̈low, open arrows), the
velocity (α̇) of the joint during the ongoing stance is fed back
directly onto the controller (the start signal is only used to trigger
walking). (B) During a disturbance (high acceleration α̈high, open
arrows), this pathway is gated out by the action of the characteristic
on the left hand side (the result of the multiplication is zero) and
the negative feedback pathway is gated in by the action of the
characteristic on the right hand side. Thus, the motor output (Om)
will reflect either positive or negative feedback control.
Disturbance reactions of walking legs 1221
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
1222 C. BARTLING AND J. SCHMITZ
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).
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