![Comparison of gait between the model and human. (a) Series of frames of the model and human at the same points in the gait cycle. (b) Model's hip, knee, and ankle angles compared with human's in the sagittal plane [28].](https://www.researchgate.net/profile/Nicholas-Szczecinski/publication/305214453/figure/fig3/AS:388081514500096@1469537251247/Comparison-of-gait-between-the-model-and-human-a-Series-of-frames-of-the-model-and_Q320.jpg)
Content uploaded by Nicholas S. Szczecinski
Author content
All content in this area was uploaded by Nicholas S. Szczecinski on May 17, 2019
Content may be subject to copyright.
A Neural Network with Central Pattern Generators
Entrained by Sensory Feedback Controls
Walking of a Bipedal Model
Wei Li
(✉)
, Nicholas S. Szczecinski, Alexander J. Hunt, and Roger D. Quinn
Department of Mechanical and Aerospace Engineering, Case Western Reserve University,
Cleveland, OH 44106-7222, USA
wxl155@case.edu
Abstract. A neuromechanical simulation of a planar, bipedal walking robot has
been developed. It is constructed as a simplified musculoskeletal system to mimic
the biomechanics of the human lower body. The controller consists of a dynamic
neural network with central pattern generators (CPGs) entrained by force and
movement sensory feedback to generate appropriate muscle forces for walking.
The CPG model is a two-level architecture, which consists of separate rhythm
generator (RG) and pattern formation (PF) networks. The presented planar biped
model walks stably in the sagittal plane without inertial sensors or a centralized
posture controller or a “baby walker” to help overcome gravity. Its gait is similar
to humans’ with a walking speed of 1.2 m/s. The model walks over small obstacles
(5 % of the leg length) and up and down 5° slopes without any additional higher
level control actions.
Keywords: Biologically inspired · Central pattern generator · Sensory
feedback · Bipedal walking
1 Introduction
It is generally accepted that basic rhythmic motor signals driving walking and other
forms of locomotion in various animals are generated centrally by the neural networks
in the spinal cord (reviewed by [1–3]). These neural networks, capable of producing
coordinated and rhythmic locomotor activity without any input from sensory afferents
or from higher control centers are referred to as central pattern generators (CPGs). Cats
with transection of spinal cord and removal of major afferents can still produce rhythmic
locomotor patterns [4, 5]. Despite lacking clear evidence of CPGs in humans, observa‐
tions in patients with spinal cord injury provide some support [6]. Sensory input also
plays an important role in locomotion. Locomotion is the result of dynamic interactions
between the central nervous system, body biomechanics, and the external environment
[7]. As a closely coupled neural control system, sensory feedback provides the infor‐
mation about the status of the biomechanics and the relationship between the body and
the external environment to make locomotion adaptive to the real environment. Sensory
input could reinforce CPG activities, provide signals to ensure correct motor output for
all body parts, and entrain the rhythmic pattern to facilitate phase transition when a
© Springer International Publishing Switzerland 2016
N.F. Lepora et al. (Eds.): Living Machines 2016, LNAI 9793, pp. 144–154, 2016.
DOI: 10.1007/978-3-319-42417-0_14
proper body posture is achieved [8, 9]. There is strong evidence [10, 11] to suggest that
sensory feedback affects motoneuron activity through common networks, rather than
directly through reflex pathways acting on specific motoneurons. It implies sensory
feedback and CPGs are highly integrated networks in the spinal cord.
Several 2D bipedal walking models have been previously developed with controllers
containing CPGs and reflexes. Some simulation models [12, 13] had over-simplified
multi-link structures driven by motors at joints, which lack the viscoelasticity of muscu‐
loskeletal structures. This lack provides poor mechanical properties that may reduce
stability. Some models [14, 15] adopt more realistic musculoskeletal structures, but their
CPG activities are not affected by sensory feedback. Instead, sensory afferents are
connected directly with motoneurons. This is contradictory to findings that sensory
feedback could strongly affect CPG activities [11, 12]. Geyer et al. [16] produced real‐
istic human walking and muscle activities in a 2D model. They claim that their model
only relies on muscle reflexes without CPGs or any other neural networks. It is realized
by two sets (swing phase and stance phase) of coupled equations for every muscle to
produce human walking and muscle activities. However, these equations could be
viewed as abstract mathematical expressions of neural networks controlling muscle
activities and the transition between two phases works like a finite-state machine. More
recently, CPGs were added to a similar muscle-reflex model to control muscles actuating
the hip joint [17]. Both of these works rely on precisely tracking muscle and other
biomechanical parameters and provide limited insight into how the central nervous
system is structured in humans. CPGs have also been applied to physical bipedal robots
[18, 19], but usually these CPGs are abstract mathematical oscillators tuned to generate
desirable trajectories of joints angles or torques, and the phases of the oscillators could
simply be reset by reflexes. Klein and Lewis [20] claimed that their robot is the first that
fully models human walking in a biologically accurate manner. But it has to rely on a
baby walker-like frame to prevent it from falling down in the sagittal plane. Its knees
remain bent distinctly before the foot touches the ground and its heels are always off the
ground. It looks like it is pushing a heavy box, fundamentally different from a human’s
normal gait.
In this paper we present a biologically rooted neuromechanical simulation model of
a planar, bipedal walker. It has a musculoskeletal structure and is controlled by a two-
level CPG neural network incorporating biological reflexes via sensory afferents. The
model is developed in Animatlab, which can model biomechanical structures and
biologically realistic neural networks, and simulate their coupled dynamics [21]. We
demonstrate that natural-looking, stable walking can be achieved by this relatively
simple but biologically plausible controller combined with a human like morphological
structure.
2 Structure of the Model
We based the biomechanical structure of our model on the human lower body, which
has been shaped and selected by millions of years’ evolution, and is energetically close
to optimal [22]. The planar skeleton is made up of rigid bodies, and is actuated by
A Neural Network with CPGs Entrained by Sensory Feedback Controls 145
antagonistic pairs of linear Hill muscles. The morphology structure employed signifi‐
cantly reduces the control effort with its inherent self-stability and provides a basis for
comparison to the real human gait. The simulated biped (Fig. 1) is modeled as a pelvis
supported by two legs. Each leg has 3 segments (thigh, shank and foot), which are
connected by 3 hinge joints (hip, knee and ankle) and actuated by 6 muscles. The foot
is composed of two parts connected by one hinge joint, spanned by a passive spring with
damping (spring constant = 16 kN/m, damping coefficient = 20 N·m/s). This makes the
foot flexible, which is the basis of the toe-off motion. The foot has a compliance of
10 μm/N to mimic the soft tissue of a human foot. The mass and length ratio of different
segments (except the foot length) are based on human data [23]. The total mass of the
model is 50 kg and its height is approximately 1 m (leg length is 0.84 m). The mass of
the pelvis, thigh, shank and foot are 25 kg, 8 kg, 4 kg and 0.5 kg. The lengths of the
thigh, shank and foot are 0.42 m, 0.42 m and 0.24 m.
Fig. 1. Left: biomechancal model in Animatlab. Right: the muscle and skeleton system of the
simulated biped.
3 Neural Control System
3.1 Neural Model
The neurons are leaky “integrate-and-fire” models. Each neuron is modeled as a “leaky
integrator” of currents it receives, including synaptic current and injected current:
(1)
where is the membrane potential, is the membrane capacitance, is negative
current due to the passive leak of the membrane, is the current from total synaptic
146 W. Li et al.
input to the neuron, is the current externally injected into the neuron. The leak
current is:
(2)
where is the leak conductance, is the resting potential. When the membrane
potential reaches the threshold value the neuron is said to fire a spike, and is reset to
.
Transmitter-activated ion channels are modeled with a time-dependent postsynaptic
conductance . The current that passes channels depends on the reversal
potential of the synapse and the postsynaptic neuron membrane potential :
(3)
If , the synapse is inhibitory and it induces negative inhibitory postsy‐
naptic current. If , the synapse is excitatory and it induces positive excitatory
postsynaptic current. The postsynaptic conductance increases to a value with a
time delay to the arrival of the presynaptic spike and then decays exponentially to zero:
(4)
where is the initial amplitude of the postsynaptic conductance increase, denotes
the arrival time of a presynaptic spike, is the time delay between the presynaptic
spike and the postsynaptic response, and is the time constant of the decay rate.
3.2 Half-Center Oscillator
A basic neural pattern generator is a half-center neural oscillator composed of two
reciprocally inhibited neurons. When one neuron spikes, it inhibits the other. Due to the
facilitation of the synapse [24] the repeated spiking of the presynaptic neuron gradually
hampers the synaptic transmission and reduces the postsynaptic conductance so the
amplitude of the postsynaptic current gradually declines. The postsynaptic neuron would
spike again as soon as the total current input recovers to the threshold value. When it
starts to spike it would inhibit the other neuron in the same way.
3.3 CPG
Rybak et al. [25] proposed a two-level CPG architecture composed of a central rhythm
generator (RG) network controlling several coupled unit pattern formation (UPF)
modules in the pattern formation (PF) level. Sensory afferents could access and affect
RG and PF networks separately. In this model the CPG network adopts a similar archi‐
tecture as shown in Fig. 2. The RG is a half-center oscillator that generates the basic
periodic stance signal for both legs. The PF network contains half-center oscillators as
A Neural Network with CPGs Entrained by Sensory Feedback Controls 147
UPF modules and each joint of each leg (hip, knee, and ankle) has one. Each half-center
in the UPF module is connected to the corresponding extensor and flexor motoneurons
to drive the extensor and flexor muscles for each joint. All half-center oscillators consist
of two reciprocally inhibited “integrate-and-fire” neurons as described previously.
Fig. 2. The architecture of the CPG network. Black lines are synaptic connections between CPG
neurons. Blue lines are synaptic connections from sensory neurons. (Color figure online)
Each neuron in the RG has an excitatory connection with a hip extension neuron and
the other leg’s hip flexion neuron. It encourages the legs to step in antiphase. At the PF
level the hip flexion neuron has an excitatory connection with the ankle dorsiflexion
neuron and an inhibitory connection with knee extension neuron. The hip extension
neuron has an excitatory connection with the knee extension neuron. This controller
uses a layer of interneurons to combine and filter afferent inputs from different receptors.
These interneurons have inhibitory connections to the interneurons in the RG and PF
networks.
3.4 Sensory Afferents
It is generally agreed that sensory input affects CPG timing directly since stimulation
of corresponding afferents entrains or resets the locomotor rhythm [26]. In legged
animals, there are three main categories of afferents that satisfy this requirement; group
I muscle afferents in extensor muscles, cutaneous afferents in feet, and muscle afferents
around the hip joint signaling its position. The first two largely depend on leg loading
information, and the last is based on movement.
148 W. Li et al.
1. Ground Contact Afferents
Studies show that increasing the load on an infants’ feet while they walk with support
significantly increases the duration of the stance phase. It suggests that load receptor
reflex activity can strongly modify and regulate gait timing and resides within the spinal
circuits [27]. In our model, separate force sensors located on the plantar surface of the
heels and toes separately detect and measure the ground contact force. As shown in
Fig. 2, heel ground contact sensors excite afferent neurons which make inhibitory
connections to the hip flexion, knee flexion, and ankle plantarflexion neurons at the PF
level. They also apply inhibition to the other leg’s stance neuron in the RG. Toe ground
contact sensors inhibit the knee flexion and ankle dorsiflexion neurons at the PF level.
2. Hip Middle Position Afferents
During normal walking the knee extends in swing before the foot touches the ground.
The knee reaches its peak flexion between 25 % and 40 % of the swing phase before
extending. As shown in Fig. 2 in our model the hip middle position afferent is connected
to the knee flexion neuron at the PF level and inhibits it when hip movement passes the
predetermined hip angle during hip flexion.
4 Experiment and Results
In software simulation experiments, we confined the movement of the body to the
sagittal plane, but it has no gravitational or pitching support, so it can fall forward or
backward.
4.1 Normal Walking
The model walks at a moderate speed (1.2 m/s) on a rigid surface. Figure 3(a) shows a
frame by frame comparison to that of a human. It is interesting to observe that they
appear similar at corresponding phases of the cycle. Figure 3(b) compares hip, knee,
and ankle angles between the model and human data during one gait cycle. The model’s
motion matches a human’s in several aspects. The range of motion and general shapes
of hip, knee and ankle angle curves are similar to a human’s, although the model’s knee
motion lacks initial flexion at early stance phase, and the ankle dorsiflexion is insuffi‐
cient. The knee reaches maximum flexion at about 75 % of the cycle and begins to extend
before the hip reaches the anterior extreme position to prepare for ground contact. The
transition from stance to swing is at about 60 % of the cycle, when the hip and knee
begins to flex, and ankle reaches maximum plantarflexion. Figure 3(a) also compares
the motion of the model’s foot with a human’s foot at early, middle and late stance
phases.
A Neural Network with CPGs Entrained by Sensory Feedback Controls 149
4.2 Interaction Between Sensory Feedback and CPGs
When the right leg enters stance (frame A in Fig. 3(a)) the right heel load sensor causes
the heel ground contact sensor neuron to spike. This triggers the right leg stance RG
neuron, causing right leg hip and knee UPF extension neurons to spike and initiate stance
(time A in Fig. 4(c)). At time B in Fig. 3(a) the right heel just leaves ground and right
heel ground contact sensor neuron stops spiking (time B in Fig. 4(a)). The right ankle
UPF plantarflexion neuron is released from inhibition and begins to spike, causing right
ankle plantarflexion (time B in Fig. 4(c)). The double support phase can be seen just
following time C in Fig. 3(a). At this point, both the right toe and the left heel are in
Fig. 3. Comparison of gait between the model and human. (a) Series of frames of the model and
human at the same points in the gait cycle. (b) Model’s hip, knee, and ankle angles compared with
human’s in the sagittal plane [28].
150 W. Li et al.
contact with the ground. The left heel ground contact sensor neuron begins to spike (time
C in Fig. 4(b)) and inhibit the right leg stance RG neuron (time C in Fig. 4(c)). The left
leg enters stance and begins to take load from the right leg. Loading of the left leg triggers
right leg swing and further encourages stance in the left leg. At time D in Fig. 3(a) the
right foot toe part leaves the ground. Right toe sensor neuron stops spiking (time D in
Fig. 4(a)), releasing right knee UPF flexion neuron and right ankle UPF dorsiflexion
neuron from inhibition (time D in Fig. 4(c)). Right knee further flexes and right ankle
goes into dorsiflexion. Toward the end of the right leg’s swing phase (time E in Fig. 3(a))
the right hip middle position sensor neuron spikes (time E in Fig. 4(a)), inhibiting the
right knee UPF flexion neuron from spiking (time E in Fig. 4(c)). This causes the knee
to extend and prepare for ground contact.
Fig. 4. Neuron membrane potentials in the gait cycle. (a) Right leg sensor neuron membrane
potentials. GC: ground contact, Mid: middle position. (b) Left leg sensor neuron membrane
potentials. (c) Right leg RG and PF neuron membrane potentials. EXT: extension, FLX: flexion,
PF: plantarflexion, DF: dorsiflexion.
4.3 Walking on Irregular Terrain
The model can walk on some irregular terrains with the CPG network alone. No higher
control actions are needed. It can walk over a 45 mm high obstacle, approximately 5 %
of the leg length (Fig. 5(a)). It can also walk up a 5° incline (Fig. 5(b)) and walk down
a 5° decline (Fig. 5(c)).
A Neural Network with CPGs Entrained by Sensory Feedback Controls 151
Fig. 5. Walking on irregular terrain (a) Walking over a 45 mm high obstacle. (b) Walking up a
5° incline. (c) Walking down a 5° decline.
5Conclusions
In this paper we present a bipedal simulation model that can walk naturally and stably in
the sagittal plane controlled by a biologically inspired neural network. It notably does
not have inertial sensors or a central posture controller, nor does it use a “baby walker”
to oppose gravity. Its structure and actuators are modeled after a human’s lower body.
Our model uses Hill’s muscle model as actuators instead of motors at joints, which
models the force profile of muscles and stores and dissipates energy during walking
similar to humans. A two-component foot structure not only enhances the leg’s ground
contact late in the stance phase but also makes it possible to provide accurate dynamic
sensory information of the relation between the foot and ground during stance by using
individual sensors on toe and heel.
Using a neural network as a controller provides a more tangible and consistent
imitation of the human central nervous system related to walking than switching between
two sets of abstract equations to coordinate muscle reflexes. Compared to other bipedal
models or robots adopting CPGs, our neural network has several more biologically
plausible features. The rhythmic patterns are generated by oscillators composed of
biological neuron models, not by mathematical oscillators tuned to reproduce the trajec‐
tory of joint movement. In our model sensory inputs are all biologically realistic and
they access the CPG network and entrain its output instead of directly modifying activ‐
ities of motoneurons. In the two-level architecture the movement of hip joints are
152 W. Li et al.
coordinated under a higher level rhythm generator instead of directly coupling hip
pattern generators of two legs.
Our developed controller and simulation not only demonstrates that stable bipedal
walking in the sagittal plane can be achieved through a biologically based neural
controller, but can also be used as a platform to help researchers test hypotheses related
to the neural control of human locomotion.
References
1. Guertin, P.A.: Central pattern generator for locomotion: anatomical, physiological, and
pathophysiological considerations. Front. Neurol. 3, 4–15 (2013)
2. Mackay-Lyons, M.: Central pattern generation of locomotion: a review of the evidence. Phys.
Ther. 82, 69–83 (2002)
3. Ijspeert, A.J.: Central pattern generators for locomotion control in animals and robots: a
review. Neural Netw. 21, 642–653 (2008)
4. Grillner, S., Zangger, P.: On the central generation of locomotion in the low spinal cat. Exp.
Brain Res. 34, 241–261 (1979)
5. Pearson, K.G., Rossignol, S.: Fictive motor patterns in chronic spinal cats. J. Neurophysiol.
66, 1874–1887 (1991)
6. Dimitrijevic, M.R., Gerasimenko, Y., Pinter, M.M.: Evidence for a spinal central pattern
generator in humans. Ann. N. Y. Acad. Sci. 860, 360–376 (1998)
7. Dickinson, M.H., et al.: How animals mo ve: an integrative view. Science 288, 100–106 (2000)
8. Pearson, K.G.: Common principles of motor control in vertebrates and invertebrates. Ann.
Rev. Neurosci. 16, 265–297 (1993)
9. Rossignol, S., Dubuc, R., Gossard, J.P.: Dynamic sensorimotor interactions in locomotion.
Physiol. Rev. 86, 89–154 (2006)
10. McCrea, D.A.: Spinal circuitry of sensorimotor control of locomotion. J. Physiol. 533,
41–50 (2001)
11. Pearson, K.G.: Generating the walking gait: role of sensory feedback. Prog. Brain Res. 143,
123–129 (2004)
12. Taga, G., Yamaguchi, Y., Shimizu, H.: Self-organized control of bipedal locomotion by
neural oscillators in unpredictable environment. Biol. Cybern. 65, 147–159 (1991)
13. Aoi, S., Tsuchiya, K.: Locomotion control of a biped robot using nonlinear oscillators. Auton.
Robots 19, 219–232 (2005)
14. Ogihara, N., Yamazaki, N.: Generation of human bipedal locomotion by a bio-mimetic neuro-
musculo-skeletal model. Biol. Cybern. 84, 1–11 (2001)
15. Paul, C., Bellotti, M., Jezernik, S., Curt, A.: Development of a human neuro-musculo-skeletal
model for investigation of spinal cord injury. Biol. Cybern. 93, 153–170 (2005)
16. Geyer, H., Herr, H.: A muscle-reflex model that encodes principles of legged mechanics
produces human walking dynamics and muscle activities. IEEE Trans. Neural Syst. Rehabil.
Eng. 18(3), 263–273 (2010)
17. Van der Noot, N., Ijspeert, A.J., Ronsse, R.: Biped gait controller for large speed variations,
combining reflexes and a central pattern generator in a neuromuscular model. In: IEEE
International Conference on ICRA 2015, pp. 6267–6274 (2015)
18. Morimoto, J., Endo, G., Nakanishi, J., Cheng, G.: A biologically inspired bipded locomotion
strategy for humanoid robots: modulation of sinusoidal patterns by a coupled oscillator model.
IEEE Trans. Robot. 24(1), 185–191 (2008)
A Neural Network with CPGs Entrained by Sensory Feedback Controls 153
19. Righetti, L., Ijspeert, A.J.: Programmable central pattern generators: an application to biped
locomotion control. In: Proceedings of 2006 IEEE International Conference on ICRA 2006,
pp. 1585–1590 (2006)
20. Klein, T.J., Lewis, M.A.: A physical model of sensorimotor interactions during locomotion.
J. Neural Eng. 9(4), 1–14 (2012)
21. Cofer, D.W., Cymbalyuk, G., Reid, J., Zhu, Y., Heitler, W.J., Edwards, D.H.: AnimatLab: a
3D graphics environment for neuromechanical simulation. J. Neurosci. Methods 187(2),
280–288 (2010)
22. Fischer, M., Witte, H.: Legs evolved only at the end. Philos. Trans. R. Soc. A 365, 185–198
(2006)
23. Plagenhoef, S., Evans, F.G., Abdelnour, T.: Anatomical data for analyzing human motion.
Res. Q. Exerc. Sport 54, 169–178 (1983)
24. Zucker, R.S., Regehr, W.G.: Short-term synaptic plasticity. Annu. Rev. Physiol. 64(1),
355–405 (2002)
25. Rybak, I.A., Stecina, K., Shevtsova, N.A., Lafreniere-Roula, M., McCrea, D.A.: Modeling
spinal circuitry involved in locomotor pattern generation: insights from deletions during
fictive locomotion. J. Physiol. 577, 617–639 (2006)
26. Dietz, V., Duysens, J.: Significance of load receptor input during locomotion: a review. Gait
and Posture 11, 102–110 (2000)
27. Pang, M.Y.C., Yang, J.F.: The initiation of the swing phase in human infant stepping:
importance of hip position and leg load. J. Physiol. 528(2), 389–404 (2010)
28. Kadaba, M.P., Ramakrishnan, H.K., Wootten, M.E.: Measurement of lower extremity
kinematics during level walking. J. Orthop. Res. 8, 383–392 (1990)
154 W. Li et al.
