A Neuromorphic VLSI System for Modeling 
the Neural Control of Axial Locomotion 
Girish N. Patel 
giri sh @ ece. gatech.edu 
Edgar A. Brown 
ebrown @ ece. gatech.edu 
Stephen P. DeWeerth 
steved@ece.gatech.edu 
School of Electrical and Computer Engineering 
Georgia Institute of Technology 
Atlanta, Ga. 30332-0250 
Abstract 
We have developed and tested an analog/digital VLSI system that mod- 
els the coordination of biological segmental oscillators underlying axial 
locomotion in animals such as leeches and lampreys. In its current form 
the system consists of a chain of twelve pattern generating circuits that 
are capable of arbitrary contralateral inhibitory synaptic coupling. Each 
pattern generating circuit is implemented with two independent silicon 
Morris-Lecar neurons with a total of 32 programmable (floating-gate 
based) inhibitory synapses, and an asynchronous address-event inter- 
connection element that provides synaptic connectivity and implements 
axonal delay. We describe and analyze the data from a set of experi- 
ments exploring the system behavior in terms of synaptic coupling. 
1 Introduction 
In recent years, neuroscientists and modelers have made great strides towards illuminat- 
ing structure and computational properties in biological motor systems. For example, 
much progress has been made toward understanding the neural networks that elicit rhyth- 
mic motor behaviors, including leech heartbeat, crustacean stomatogastric mill and lam- 
prey swimming (a good review on these is in [1] and [2]). It is thought that these same 
mechanisms form the basis for more complex motor behaviors. The neural substrate for 
these control mechanisms are called central pattern generators (CPG). In the case of loco- 
motion these circuits are distributed along the body (in the spinal cord of vertebrates or in 
the ganglia of invertebrates) and are richly interactive with sensory input and descending 
connections from the brain, giving rise to a highly distributed system as shown in 
Figure 1. In cases in which axial locomotion is involved, such as leech and lamprey 
swimming, synaptic interconnection patterns among autonomous segmental oscillators 
along the animal's axis produce coordinated motor patterns. These intersegmental coordi- 
nation architectures have been well studied through both physiological experimentation 
and mathematical modeling. In addition, undulatory gaits in snakes have also been stud- 
ied from a robotics perspective [3]. However, a thorough understanding of the computa- 
tional principles in these systems is still lacking. 
A Neuromorphic System for Modeling Axial Locomotion 725 
Muscle 
Muscle 
T 
I 
I 
I 
__ 
Figure 1: Neuroanatomy of segmented animals. 
In order to better understand the computational paradigms that mediate intersegmental 
coordination and the resulting neural control of axial locomotion (and other motor pat- 
terns), we are using neuromorphic very large-scale integrated (VLSI) circuits to develop 
models of these biological systems. The goals in our research are (i) to study how the 
properties of individual neurons in a network affect the overall system behavior; (ii) to 
facilitate the validation of the principles underlying intersegmental coordination; and (iii) 
to develop a real-time, low power, motion control system. We want to exploit these prin- 
ciples and architectures both to improve our understanding of the biology and to design 
artificial systems that perform autonomously in various environments. 
Parameter Input 
GUI ] 
Address-Event Communication Network 
Event x / 
Output 12 $eg*ment$ 
Figure 2: Block-level diagram of the implemented system. The intersegmental 
communications network facilitates communication among the intrasegmental units with 
pipelined stages. 
In this paper, we present a VLSI model of intersegmental coordination as shown in 
Figure 2. Each segment in our system is implemented with a custom IC containing a CPG 
consisting of two silicon model neurons, each one with 16 inhibitory synapses whose val- 
ues are stored on chip and are continuously variable; an asynchronous address event com- 
munications IC that implements the queuing and delaying of events providing synaptic 
connectivity and thus simulating axonal properties; and a microcontroller (with internal 
A/D converter and timer) that facilitates the modification of individual parameters 
through a serial bus. The entire system consists of twelve such segments linked to a com- 
puter on which a graphical user interface (GUI) is implemented. By using the GUI, we 
are able to control all of the synaptic connections in the system and to measure the result- 
726 G. N. Patel, E. A. Brown and $. P DeWeerth 
ing neural outputs. We present the system model, and we investigate the role of synaptic 
coupling in the establishment of phase lags along this chain of neural oscillators. 
2 Pattern generating circuits 
The smallest neural system capable of generating the basic alternating activity that char- 
acterizes the swimming CPGs is the half-center oscillator, essentially two bursting neu- 
rons with reciprocally inhibitory connections [1] as shown in Figure 3a. In biological 
systems, the associated neurons have both slow and fast time constants to facilitate the 
fast spiking (action potentials) and the slower bursting oscillations that control the elic- 
ited movements as shown in Figure 3b. To simplify the parameter space of our system, 
we use reduced two-state silicon neurons [4]. The output of each silicon neuron is an 
oscillation that represents the envelope of the bursting activity (i.e. the spiking activity 
and corresponding fast time constants are eliminated) as shown in Figure 3c. Each neu- 
ron also has 16 analog synapses that receive off-chip input. The synaptic parameters are 
stored in an array of floating-gate transistors [5] that provide nonvolatile analog memory. 
CPG 
B 
c 
1 
Figure 3: Half-center oscillator and the generation of events in spiking and nonspiking 
silicon neurons. Events are generated by detecting rapid rises in the membrane potential of 
spiking neurons or by detecting rapid rises and falls in nonspiking neurons. 
3 Intersegmental communication 
Our segmented system consists of an array of CPG circuits interconnected via an commu- 
nication network that implements an asynchronous, address-event protocol [6][7]. Each 
CPG is connected to one node of this address-event intersegmental communication sys- 
tem as illustrated in Figure 2. This application-specific architecture uses a pipelined 
broadcast scheme that is based upon its biological counterpart. The principal advantage of 
using this custom scheme is that requisite addresses and delays are generated implicitly 
based upon the system architecture. In particular the system implements distance-depen- 
dent delays and relative addressing. The delays, which are thought to be integral to the 
network computation, replicate the axonal delays that result as action potentials propa- 
gate down an animal's body [2]. The relative addressing greatly simplifies the implemen- 
tation of synaptic spread [8], the hypothesized translational invariance in the 
intersegmental connectivity in biological axial locomotion systems. Thus, we can set the 
synaptic parameters identically at every segment, greatly reducing system complexity. 
In this architecture (which is described in more depth in [4]), each event is passed from 
segment to neighboring segment bidirectionally down the length of the one-dimensional 
A Neuromorphic System for Modeling Axial Locomotion 72 7 
communications network. By delaying each event at every segment, the pipeline architec- 
ture facilitates the creation of distance-dependent delays. The other primary advantage of 
this architecture is that it can easily generate a relative addressing scheme. Figure 4 illus- 
trates the event-passing architecture with respect to the relative addressing and distance- 
dependent delays. Each event, generated at a particular node (the center node, in this 
example), is transmitted bidirectionally down the length of the network. It is delayed by 
time AT at each segment, not including the initiating segment. 
t = t0+2AT t = t0+AT t = t0+AT t = t0+2AT 
Figure 4: Relative addressing and distance-dependent delays. 
The events are generated by the neurons in each segment. Because these are not spiking 
neurons, we could not use the typical scheme of generating one event per action poten- 
tial. Instead, we generate one event at the beginning and end of each burst (as illustrated 
in Figure 3) and designate the individual events as rising or falling. In each segment the 
events are stored in a queue (Figure 5), which implements delay based upon uniform con- 
duction velocities. As an event arrives at each new segment, it is time stamped, its rela- 
tive address is incremented (or decremented), and then it is stored in the queue for the 
A T interval. As the event exits the queue, its data is decoded by the intrasegmental units, 
and synaptic inputs are applied to the appropriate intrasegmental neurons. 
ovonts from ovonts from 
rostral segment intrasegmental unit 
(closer to head) [ l tlror  
(event storage stral and 
-- and processing) caudal segments 
events from and intrasegmental 
caudal segment 
(closer to tail) unit 
Figure 5: Block-level diagram of a communications node illustrating how events enter 
and exit each stage of the pipeline. 
4 Experiments and Discussion 
We have implemented the complete system shown in Figure 2, and have performed a 
number of experiments on the system. In Figure 6, we show the behaviors the system 
exhibits when it is configured with asymmetrical nearest-neighbor connections. The sys- 
tem displays traveling waves whose directions depend on the direction of the dominant 
coupling. Note that the intersegmental phase lags vary for different swim frequencies. 
One important set of experiments focussed on the role of long-distance connections on 
the system behaviors. In these experiments, we configured the system with strong 
descending (towards the tail) connections such that robust rearward traveling waves (for- 
ward swimming) are observed. The long-distance connections are weak enough to avoid 
any bifurcations in behavior (different type of behavior). Thus, the traveling wave solu- 
tion resulting from the nearest-neighbor connections persists as we progressively add 
long-distance connections. In Figure 7 we show the dependency of the swim frequency 
and the total phase lag (summation of the normalized intersegmental phase lags, where 
1 = 360  ) on the extent of the connections. The results show a clear difference in behav- 
728 G. N. Patel, E. A. Brown and S. P. DeWeerth 
stronger ascending coupling 
05 -   ra 
0-' / \'" ' , '2' 
-0.2 -0.1 0 0.1 0.2 
time (see) 
stronger descending coupling 
-0.2 -0.1 0 0.1 0.2 
time (see) 
, .'. 
-0.05 0 0.05 -0.05 0 0.05 
time (see) time (see) 
Figure 6: Traveling waves in the system with asymmetrical, nearest-neighbor 
connections. Plots are cross-correlations between rising edge events generated by a neuron 
in segment six and events generated by homolog neurons in each segment. Stronger 
ascending connections (A & B) produce forward traveling waves (backward swimming) 
and stronger descending connections (C & D) produce rearward traveling waves (forward 
swimming). An externally applied current (Iext) controls the swim frequency. At small 
values of Iex t (6.7 nA) the periods of the swim cycles are approximately 0.180 ms and 
0.150 ms for A & C, respectively; for large values of Iex t (32.8 nA), the periods of the 
swim cycles are approximately 36 ms and 33 ms for B & D, respectively. 
iors between the lowest tonic drive (Icx t = 21.9 nA) and the two higher tonic drives. (By 
tonic drive, we mean a constant dc current is applied to all neurons.) In the former, the 
sensitivity of long-distance connections on frequency and intersegmental phase lags is 
considerably greater than in the latter. The demarcation in behavior may be attributed to 
different behaviors at different tonic drives. For lower tonic drive, the long-distance con- 
nections tend to synchronize the system (decrease the intersegmental phase lags). At the 
higher tonic drives, long-distance connections do not affect the system considerably. For 
Iex t = 32.8 nA, connections that span up to four segments aid in producing uniformity in 
the intersegmental phase lags. Although this does not hold for Icx t = 48.1 nA, long-dis- 
tance connections play a more significant role in preserving the total phase difference. At 
Iex t - 32.8 nA and Iex t = 48.1 nA, the system with short-distance connections produces a 
total phase difference of 1.19 and 1.33, respectively. In contrast, for Icx t = 32.8 nA and 
Iex t = 48.1 nA, the system with long-distance connections that span up to seven segments 
produces a total phase difference of 1.20 and 1.25, respectively. 
In the above experiments, we have demonstrated that, in a specific parameter regime, 
weak long-distance connections can affect the intersegmental phase lags. However, these 
weight profiles should not be construed as a possible explanation on what the weight pro- 
files in a biological system might be. The parameter regime in which we observed this 
behavior is small; at moderate strengths of coupling, the traveling wave solutions disap- 
pear and move towards synchronous behavior. Recent experiments done on spinalized 
lampreys reveal that long-distance connections are moderately strong [10]. Thus, our cur- 
rent model is unable to replicate this aspect of intersegmental coordination. There are 
several explanations that may account for this discrepancy. 
A Neuromorphic System for Modeling Axial Locomotion 729 
A 40 B 1.5 
30 
-, 20 
10 
0 2 4 6 8 0 2 4 6 8 
extent extent 
Figure 7: Effects of weak long-distance connections on swimming frequency (A), on the 
total phase difference (summation of the normalized intersegmental phase lags) (B), and 
on the standard deviation of the intersegmental phase lags (C). 5 < = denote Iex t = 48.1 nA, 
32.8 nA, and 21 nA, respectively. 
In the segmental CPG network of the animal, there are many classes of neurons that send 
projections to many other classes of neurons. The phase a connection imposes is deter- 
mined by which neuron class connects with which other neuron class. In our system, the 
segmental CPG network has only a single class of neurons upon which the long-distance 
connections can impose their phase. Depending on where in parameter space we operate 
our system, the long-distance connections have too little or too great an effect on the 
behavior of the system. At high tonic drives, the sensitivity of the weak long-distance 
connections on the intersegmental phase lags is small, whereas for small tonic drives, the 
long-distance connections have a great effect on the intersegmental phase lags. 
It has been shown that if the waveform of the oscillators is sinusoidal (i.e., the time scales 
of the two state variables are not too different), traveling wave solutions exist and have a 
large basin of attraction [11]. However, as the disparity between the two time scales is 
made larger (i.e., the neurons are stiff and the waveform of the oscillations appears 
square-wave like), the system will move towards synchrony. In our implementation, to 
facilitate accurate communication of events, we bias the neurons with relatively large dif- 
ferences in the time scales. Thus, this restriction reduces the parameter regime in which 
we can observe stable traveling waves. 
Another factor that determines the range of parameters in which stable traveling waves 
are observed is the slope of our synaptic coupling function. When the slope of the cou- 
pling function is steep, the total synaptic current over a cycle can increase significantly, 
causing weak connections to appear strong. This has an overall effect of synchronizing 
the network [ 11]. For coupling functions whose slopes are shallow, the total synaptic cur- 
rent over a cycle is reduced; therefore, the connections appear weak and larger interseg- 
mental phase lags are possible. Thus, the sharp synaptic coupling function in our 
implementation, which is necessary for communication, is another factor that diminishes 
the parameter regime in which we can observe stable traveling waves. 
The above factors limit the parameter range in which we observe traveling waves. How- 
ever, all of these issues can be addressed by improving our CPG network. The first issue 
can be addressed by increasing the number of neuron classes or adding more segments. 
The second and third issues can be addressed by adding spiking neurons in our CPG net- 
work so that the form of the oscillations can be coded in the spike train and the synaptic 
coupling functions can be implemented on the receiving side of the CPG chip. The fourth 
730 G. N. Patel, E. A. Brown and S. P. DeWeerth 
issue can be addressed by designing self-adapting neurons that tune their internal parame- 
ters so that their waveforms and intrinsic frequencies are matched. Although weak cou- 
pling may not be biologically plausible, producing traveling waves based on phase 
oscillators would be an interesting research direction. 
5 Conclusions and Future Work 
In this paper, we described a functional, neuromorphic VLSI system that implements an 
array of neural oscillators interconnected by an address-event communication network. 
This system represents our most ambitious neuromorphic VLSI effort to date, combining 
24 custom ICs, a special-purpose asynchronous communication architecture designed 
analogously to its biological counterpart, large-scale synaptic interconnectivity with 
parameters stored using floating-gate devices, and a computer interface for setting the 
parameters and for measuring the neural activity. The working system represents the cul- 
mination of a four-year effort, and now provides a testbed for exploring a variety of bio- 
logical hypotheses and theoretical predictions. 
Our future directions in the development of this system are threefold. First, we will con- 
tinue to explore, in depth, the operation of the present system, comparing it to theoretical 
predictions and biological hypotheses. Second, we are implementing a segmented 
mechanical system that will provide a moving output and will facilitate the implementa- 
tion of sensory feedback. Third, we are developing new CPG model centered around sen- 
sory feedback and motor learning. The modular design of the system, which puts all of 
the neural and synaptic specificity on the CPG IC, allows us to design a completely new 
CPG and to replace it in the system without changing the communication architecture. 
References 
[1] 
[21 
[3] 
[4] 
[5] 
[61 
[7] 
[8] 
[9] 
[lO] 
[11] 
[12] 
E. Marder & R.L. Calabrese. Principles of rhythmic motor pattern generation. Physiological 
Reviews 76 (3): 687-717, 1996. 
A.H. Cohen, G.B. Ermentrout, T Kiemel, N. Kopell, K.A. Sigvardt, & T.L. Williams. Modeling 
of intersegmental coordination in the lamprey central pattern generator for locomotion. TINS 
15:434-438, 1992. 
S. Hirose. Biologically Inspired Robots: Snake-like Locomotors and Manipulators. Oxford 
University Press, 1993. 
S. DeWeerth, G. Patel, D. Schimmel, M. Simoni, & R.L. Calabrese. A VLSI Architecture for 
Modeling Intersegmental Coordination. In Proceedings of the Seventeenth Conference on 
Advanced Research in VLSI, R.B. Brown and A.T. Ishii (eds), Los Alamitos, CA: IEEE 
Computer Society, 182-200, 1997. 
P. Hasler, B.A. Minch, and C. Diorio. Adaptive circuits using pFet floating-gate devices. In Scott 
Wills and Stephen DeWeerth editors, 20th Conference of Advanced Research in VLSI, pages 
215-230, Los Alamitos, California, CA: IEEE Computer Society, 1999. 
M.A. Mahowald. VLSI Analogs of Neuronal Visual Processing: A Synthesis of Form and 
Function. Ph.D. Thesis, California Institute of Technology, Pasadena, CA, 1992. 
K.A. Boahen. Communicating Neuronal Ensembles between Neuromorphic Chips. Analog 
Integrated Circuits and Signal Processing, 1997. 
T Willams. Phase Coupling and Synaptic Spread in Chains of Coupled Neuronal Oscillators. 
Science, vol. 258, 1992. 
G. Patel. A Neuromorphic Architecture for Modeling Intersegmental Coordination. Ph.D. 
Thesis, Georgia Institute of Technology, Atlanta, GA, 1999. 
A. H. Cohen. Personal communication. 
D. Somers & N. Kopell. Waves and synchrony in networks of oscillators of relaxation and non- 
relaxation type. Phyica D, 89:169-183, 1995. 
N. Kopell & G.B. Ermentrout. Coupled oscillators and the design of central pattern generators. 
Mathematical Biosciences, 90:87-109, 1988. 
