{"title": "A Neuromorphic VLSI System for Modeling the Neural Control of Axial Locomotion", "book": "Advances in Neural Information Processing Systems", "page_first": 724, "page_last": 730, "abstract": null, "full_text": "A Neuromorphic VLSI System for Modeling \n\nthe Neural Control of Axial Locomotion \n\nGirish N. Patel \n\ngirish@ece.gatech.edu \n\nEdgar A. Brown \n\nebrown@ece.gatech.edu \n\nStephen P. De Weerth \nsteved@ece.gatech.edu \n\nSchool of Electrical and Computer Engineering \n\nGeorgia Institute of Technology \n\nAtlanta, Ga. 30332-0250 \n\nAbstract \n\nWe have developed and tested an analog/digital VLSI system that mod(cid:173)\nels the coordination of biological segmental oscillators underlying axial \nlocomotion in animals such as leeches and lampreys. In its current form \nthe system consists of a chain of twelve pattern generating circuits that \nare capable of arbitrary contralateral inhibitory synaptic coupling. Each \npattern generating circuit is implemented with two independent silicon \nMorris-Lecar neurons with a total of 32 programmable (floating-gate \nbased) inhibitory synapses, and an asynchronous address-event inter(cid:173)\nconnection element that provides synaptic connectivity and implements \naxonal delay. We describe and analyze the data from a set of experi(cid:173)\nments exploring the system behavior in terms of synaptic coupling. \n\n1 Introduction \n\nIn recent years, neuroscientists and modelers have made great strides towards illuminat(cid:173)\ning structure and computational properties in biological motor systems. For example, \nmuch progress has been made toward understanding the neural networks that elicit rhyth(cid:173)\nmic motor behaviors, including leech heartbeat, crustacean stomatogastric mill and lam(cid:173)\nprey swimming (a good review on these is in [1] and [2]). It is thought that these same \nmechanisms form the basis for more complex motor behaviors. The neural substrate for \nthese control mechanisms are called central pattern generators (CPG). In the case of loco(cid:173)\nmotion these circuits are distributed along the body (in the spinal cord of vertebrates or in \nthe ganglia of invertebrates) and are richly interactive with sensory input and descending \nconnections from the brain, giving rise to a highly distributed system as shown in \nFigure 1. In cases in which axial locomotion is involved, such as leech and lamprey \nswimming, synaptic interconnection patterns among autonomous segmental oscillators \nalong the animal's axis produce coordinated motor patterns. These intersegmental coordi(cid:173)\nnation architectures have been well studied through both physiological experimentation \nand mathematical modeling. In addition, undulatory gaits in snakes have also been stud(cid:173)\nied from a robotics perspective [3]. However, a thorough understanding of the computa(cid:173)\ntional principles in these systems is still lacking. \n\n\fA Neuromorphic System for Modeling Axial Locomotion \n\n725 \n\nFigure 1: Neuroanatomy of segmented animals. \nIn order to better understand the computational paradigms that mediate intersegmental \ncoordination and the resulting neural control of axial locomotion (and other motor pat(cid:173)\nterns), we are using neuromorphic very large-scale integrated (VLSI) circuits to develop \nmodels of these biological systems. The goals in our research are (i) to study how the \nproperties of individual neurons in a network affect the overall system behavior; (ii) to \nfacilitate the validation of the principles underlying intersegmental coordination; and (iii) \nto develop a real-time, low power, motion control system. We want to exploit these prin(cid:173)\nciples and architectures both to improve our understanding of the biology and to design \nartificial systems that perform autonomously in various environments. \n\nParameter Input \n\nEmbedded \nController \n\nEvent \nOutput \n\n\" \n\nAddress-Event Communication Network \n\n/ \n\n12 segments \n\nFigure 2: Block-level diagram of the implemented system. The intersegmental \ncommunications network facilitates communication among the intrasegmental units with \npipelined stages. \n\nIn this paper, we present a VLSI model of intersegmental coordination as shown in \nFigure 2. Each segment in our system is implemented with a custom Ie containing a CPG \nconsisting of two silicon model neurons, each one with 16 inhibitory synapses whose val(cid:173)\nues are stored on chip and are continuously variable; an asynchronous address event com(cid:173)\nmunications IC that implements the queuing and delaying of events providing synaptic \nconnectivity and thus simulating axonal properties; and a microcontroller (with internal \nAID converter and timer) that facilitates the modification of individual parameters \nthrough a serial bus. The entire system consists of twelve such segments linked to a com(cid:173)\nputer on which a graphical user interface (GUI) is implemented. By using the GUI, we \nare able to control all of the synaptic connections in the system and to measure the result-\n\n\f726 \n\nG. N Patel, E. A. Brown and S. P. DeWeerth \n\ning neural outputs. We present the system model, and we investigate the role of synaptic \ncoupling in the establishment of phase lags along this chain of neural oscillators. \n\n2 Pattern generating circuits \n\nThe smallest neural system capable of generating the basic alternating activity that char(cid:173)\nacterizes the swimming ePGs is the half-center oscillator, essentially two bursting neu(cid:173)\nrons with reciprocally inhibitory connections [1] as shown in Figure 3a. In biological \nsystems, the associated neurons have both slow and fast time constants to facilitate the \nfast spiking (action potentials) and the slower bursting oscillations that control the elic(cid:173)\nited movements as shown in Figure 3b. To simplify the parameter space of our system, \nwe use reduced two-state silicon neurons [4]. The output of each silicon neuron is an \noscillation that represents the envelope of the bursting activity (i.e. the spiking activity \nand corresponding fast time constants are eliminated) as shown in Figure 3c. Each neu(cid:173)\nron also has 16 analog synapses that receive off-chip input. The synaptic parameters are \nstored in an array of floating-gate transistors [5] that provide nonvolatile analog memory. \n\nB \n\nC \n\nCPG \n\nA \n\n1 JW~WID~,J,U~l.v \n\n111\n\n11111 1111111 11111 11111111111 11 111 \n\n111111 1111 1111 \n\nIII \n\n2 \n\n1 \n\n2 \n\nFigure 3: Half-center oscillator and the generation of events in spiking and nonspiking \nsilicon neurons. Events are generated by detecting rapid rises in the membrane potential of \nspiking neurons or by detecting rapid rises and falls in nonspiking neurons. \n\n3 Intersegmental communication \n\nOur segmented system consists of an array of ePG circuits interconnected via an commu(cid:173)\nnication network that implements an asynchronous, address-event protocol [6][7]. Each \nePG is connected to one node of this address-event intersegmental communication sys(cid:173)\ntem as illustrated in Figure 2. This application-specific architecture uses a pipelined \nbroadcast scheme that is based upon its biological counterpart. The principal advantage of \nusing this custom scheme is that requisite addresses and delays are generated implicitly \nbased upon the system architecture. In particular the system implements distance-depen(cid:173)\ndent delays and relative addressing. The delays, which are thought to be integral to the \nnetwork computation, replicate the axonal delays that result as action potentials propa(cid:173)\ngate down an animal's body [2]. The relative addressing greatly simplifies the implemen(cid:173)\ntation of synaptic spread [8], \nthe \nintersegmental connectivity in biological axial locomotion systems. Thus, we can set the \nsynaptic parameters identically at every segment, greatly reducing system complexity. \n\nthe hypothesized \n\ntranslational \n\ninvariance \n\nin \n\nIn this architecture (which is described in more depth in [4]), each event is passed from \nsegment to neighboring segment bidirectionally down the length of the one-dimensional \n\n\fA Neuromorphic System for Modeling Axial Locomotion \n\n727 \n\ncommunications network. By delaying each event at every segment, the pipeline architec(cid:173)\nture facilitates the creation of distance-dependent delays. The other primary advantage of \nthis architecture is that it can easily generate a relative addressing scheme. Figure 4 illus(cid:173)\ntrates the event-passing architecture with respect to the relative addressing and distance(cid:173)\ndependent delays. Each event, generated at a particular node (the center node, in this \nexample), is transmitted bidirectionally down the length of the network. It is delayed by \ntime /). T at each segment, not including the initiating segment. \n\nt=to+2/).T \n\nt=to+/).T \n\nt=to+/).T t=to+2/).T \n\n'8\"'O\"'8~8~c;( \n\nA = 1 V \n\nA = -2 \n\nA = -1 \n\nA = 0 \n\nFigure 4: Relative addressing and distance-dependent delays. \n\nThe events are generated by the neurons in each segment. Because these are not spiking \nneurons, we could not use the typical scheme of generating one event per action poten(cid:173)\ntial. Instead, we generate one event at the beginning and end of each burst (as illustrated \nin Figure 3) and designate the individual events as rising or falling . In each segment the \nevents are stored in a queue (Figure 5), which implements delay based upon uniform con(cid:173)\nduction velocities. As an event arrives at each new segment, it is time stamped, its rela(cid:173)\ntive address is incremented (or decremented), and then it is stored in the queue for the \n/). T interval. As the event exits the queue, its data is decoded by the intrasegmental units, \nand synaptic inputs are applied to the appropriate intrasegmental neurons. \n\nevents from \nintrasegmental unit \n\nevents from \nrostral segment \n(clo ser to head) \n\n.. ... 9: \n.. -\n\nev ents from \ncaudal segment \n(closer to tail) \n\n.. - (event storage \n\nand processing) \n\nQUEUE \n\nl. 9: \n.. ... \n\n.. ... \n\nto ro stral and \ncau dal segments \nand \nunit \n\nintrasegmental \n\nFigure 5: Block-level diagram of a communications node illustrating how events enter \nand exit each stage of the pipeline. \n\n4 Experiments and Discussion \n\nWe have implemented the complete system shown in Figure 2, and have performed a \nnumber of experiments on the system. In Figure 6, we show the behaviors the system \nexhibits when it is configured with asymmetrical nearest-neighbor connections. The sys(cid:173)\ntem displays traveling waves whose directions depend on the direction of the dominant \ncoupling. Note that the intersegmental phase lags vary for different swim frequencies. \n\nOne important set of experiments focussed on the role of long-distance connections on \nthe system behaviors. In these experiments, we configured the system with strong \ndescending (towards the tail) connections such that robust rearward traveling waves (for(cid:173)\nward swimming) are observed. The long-distance connections are weak enough to avoid \nany bifurcations in behavior (different type of behavior). Thus, the traveling wave solu(cid:173)\ntion resulting from the nearest-neighbor connections persists as we progressively add \nlong-distance connections. In Figure 7 we show the dependency of the swim frequency \nand the total phase lag (summation of the normalized intersegmental phase lags, where \n1 == 360 0 ) on the extent of the connections. The results show a clear difference in behav-\n\n\f728 \n\nG. N. Patel, E. A. Brown and S. P. DeWeerth \n\nstronger ascending coupling \n......... . .. , \n\nstronger descending coupling \n\n1 \n0.5 \no \n-0.2 \n\nB \n\n-0.1 \n\no 0.1 \ntime (sec) \n\n0.2 \n\no \n\ntime (sec) \n\n0.05 \n\nc :: . \n\n..... \n1O&-\" \n8 ~ \n6 (l) \n4 CI) \n2 \n\n1 \no.~ ~t=~~~~~ \n\n-0.2 -0.1 \n\no 0.1 \ntime (sec) \n\n0.2 \n\n1 \n0.5 \no .L.fI==::1.L:;:::1l:::=:,:..:-.J \n-0.05 \n\n0.05 \n\no \n\ntime (sec) \n\nFigure 6: Traveling waves in the system with asymmetrical, nearest-neighbor \nconnections. Plots are cross-correlations between rising edge events generated by a neuron \nin segment six and events generated by homolog neurons in each segment. Stronger \nascending connections (A & B) produce forward traveling waves (backward swimming) \nand stronger descending connections (C & D) produce rearward traveling waves (forward \nswimming) . An externally applied current (lext) controls the swim frequency. At small \nvalues of lext (6.7 nA) the periods of the swim cycles are approximately 0.180 ms and \n0.150 ms for A & C, respectively; for large values of lext (32.8 nA), the periods of the \nswim cycles are approximately 36 ms and 33 ms for B & D, respectively. \niors between the lowest tonic drive (lext = 21.9 nA) and the two higher tonic drives. (By \ntonic drive, we mean a constant dc current is applied to all neurons.) In the former, the \nsensitivity of long-distance connections on frequency and intersegmental phase lags is \nconsiderably greater than in the latter. The demarcation in behavior may be attributed to \ndifferent behaviors at different tonic drives. For lower tonic drive, the long-distance con(cid:173)\nnections tend to synchronize the system (decrease the intersegmental phase lags). At the \nhigher tonic drives, long-distance connections do not affect the system considerably. For \nlext = 32.8 nA, connections that span up to four segments aid in producing uniformity in \nthe intersegmental phase lags. Although this does not hold for lext = 48.1 nA, long-dis(cid:173)\ntance connections playa more significant role in preserving the total phase difference. At \nlext = 32.8 nA and lext = 48.1 nA, the system with short-distance connections produces a \ntotal phase difference of 1.19 and 1.33, respectively. In contrast, for lext = 32.8 nA and \nlext = 48.1 nA, the system with long-distance connections that span up to seven segments \nproduces a total phase difference of 1.20 and 1.25, respectively. \n\nIn the above experiments, we have demonstrated that, in a specific parameter regime, \nweak long-distance connections can affect the intersegmental phase lags. However, these \nweight profiles should not be construed as a possible explanation on what the weight pro(cid:173)\nfiles in a biological system might be. The parameter regime in which we observed this \nbehavior is small; at moderate strengths of coupling, the traveling wave solutions disap(cid:173)\npear and move towards synchronous behavior. Recent experiments done on spinalized \nlampreys reveal that long-distance connections are moderately strong [10]. Thus, our CUT(cid:173)\nrent model is unable to replicate this aspect of intersegmental coordination. There are \nseveral explanations that may account for this discrepancy. \n\n\fA Neuromorphic System for Modeling Axial Locomotion \n\n729 \n\nA 40 r---~-~-~----' \n\nB 1.5 .---~-~-~--, \n\n30 \n\ni)' \nc \n~ 20 \nc(cid:173)\nO> \n\n.... - 10 \n\nm 1 \n~ .c \nc. \n~ \n\n:\u00a7 0.5 \n\no~--~----~--~--~ \n8 \n\no \n\n6 \n\n2 \n\n4 \n\nextent \n\no'----~----~--~----' \n8 \n\n6 \n\no \n\n4 \n\n2 \n\nextent \n\nFigure 7: Effects of weak long-distance connections on swimming frequency (A), on the \ntotal phase difference (summation of the normalized intersegmental phase lags) (B), and \non the standard deviation of the intersegmental phase lags (C). 5 < = denote Iext = 48.1 nA, \n32.8 nA, and 21 nA, respectively. \nIn the segmental CPG network of the animal, there are many classes of neurons that send \nprojections to many other classes of neurons. The phase a connection imposes is deter(cid:173)\nmined by which neuron class connects with which other neuron class. In our system, the \nsegmental CPG network has only a single class of neurons upon which the long-distance \nconnections can impose their phase. Depending on where in parameter space we operate \nour system, the long-distance connections have too little or too great an effect on the \nbehavior of the system. At high tonic drives, the sensitivity of the weak long-distance \nconnections on the intersegmental phase lags is small, whereas for small tonic drives, the \nlong-distance connections have a great effect on the intersegmental phase lags. \n\nIt has been shown that if the waveform of the oscillators is sinusoidal (i.e., the time scales \nof the two state variables are not too different), traveling wave solutions exist and have a \nlarge basin of attraction [11]. However, as the disparity between the two time scales is \nmade larger (i.e., the neurons are stiff and the waveform of the oscillations appears \nsquare-wave like), the system will move towards synchrony. In our implementation, to \nfacilitate accurate communication of events, we bias the neurons with relatively large dif(cid:173)\nferences in the time scales. Thus, this restriction reduces the parameter regime in which \nwe can observe stable traveling waves. \n\nAnother factor that determines the range of parameters in which stable traveling waves \nare observed is the slope of our synaptic coupling function. When the slope of the cou(cid:173)\npling function is steep, the total synaptic current over a cycle can increase significantly, \ncausing weak connections to appear strong. This has an overall effect of synchronizing \nthe network [11]. For coupling functions whose slopes are shallow, the total synaptic cur(cid:173)\nrent over a cycle is reduced; therefore, the connections appear weak and larger interseg(cid:173)\nmental phase lags are possible. Thus, the sharp synaptic coupling function in our \nimplementation, which is necessary for communication, is another factor that diminishes \nthe parameter regime in which we can observe stable traveling waves. \n\nThe above factors limit the parameter range in which we observe traveling waves. How(cid:173)\never, all of these issues can be addressed by improving our CPG network. The first issue \ncan be addressed by increasing the number of neuron classes or adding more segments. \nThe second and third issues can be addressed by adding spiking neurons in our CPG net(cid:173)\nwork so that the form of the oscillations can be coded in the spike train and the synaptic \ncoupling functions can be implemented on the receiving side of the CPG chip. The fourth \n\n\f730 \n\nG. N. Patel, E. A. Brown and S. P. DeWeerth \n\nissue can be addressed by designing self-adapting neurons that tune their internal parame(cid:173)\nters so that their waveforms and intrinsic frequencies are matched. Although weak cou(cid:173)\npling may not be biologically plausible, producing traveling waves based on phase \noscillators would be an interesting research direction. \n\n5 Conclusions and Future Work \n\nIn this paper, we described a functional, neuromorphic VLSI system that implements an \narray of neural oscillators interconnected by an address-event communication network. \nThis system represents our most ambitious neuromorphic VLSI effort to date, combining \n24 custom ICs, a special-purpose asynchronous communication architecture designed \nanalogously to its biological counterpart, large-scale synaptic interconnectivity with \nparameters stored using floating-gate devices, and a computer interface for setting the \nparameters and for measuring the neural activity. The working system represents the cul(cid:173)\nmination of a four-year effort, and now provides a testbed for exploring a variety of bio(cid:173)\nlogical hypotheses and theoretical predictions. \n\nOur future directions in the development of this system are threefold. First, we will con(cid:173)\ntinue to explore, in depth, the operation of the present system, comparing it to theoretical \npredictions and biological hypotheses. Second, we are implementing a segmented \nmechanical system that will provide a moving output and will facilitate the implementa(cid:173)\ntion of sensory feedback. Third, we are developing new CPG model centered around sen(cid:173)\nsory feedback and motor learning. The modular design of the system, which puts all of \nthe neural and synaptic specificity on the CPG IC, allows us to design a completely new \nCPG and to replace it in the system without changing the communication architecture. \n\nReferences \n\n[1] E. Marder & R.L. Calabrese. 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Ermentrout. Coupled oscillators and the design of central pattern generators. \n\nMathematical Biosciences, 90:87-109, 1988. \n\n\f", "award": [], "sourceid": 1720, "authors": [{"given_name": "Girish", "family_name": "Patel", "institution": null}, {"given_name": "Edgar", "family_name": "Brown", "institution": null}, {"given_name": "Stephen", "family_name": "DeWeerth", "institution": null}]}