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A Movement Pattern Generator Model Using Artificial Neural Networks S . Srinivasan, Robert E. Gander, Senior Member, IEEE, and Hugh C. Wood, Member, IEEE
Abstract-Artificial neural networks (ANN’S) allow a new approach to biological modeling. The main applications of ANN’S have been geared towards the modeling of the association and learning mechanisms of the brain; only a few researchers have explored them for motor control. The fact that A ” ’ s are based on biological systems indicates their potential application for a biological act such as locomotion. Towards this goal, we have developed a “movement pattern generator,” using an ANN for generating periodic movement trajectories. This model is based on the concept of “central pattern generators.” Jordan’s sequential network, which is capable of learning sequences of patterns, was modified and used to generate several bipedal trajectories (or gaits), coded in task space, at different frequencies. The network model successfully learned all of the trajectories presented to it. The model has many attractive properties such as limit cycle behavior, generalization of trajectories and frequencies, phase maintenance, and fault tolerance. The movement pattern generator model is potentially applicable for improved understanding of animal locomotion and for use in legged robots and rehabilitation medicine.
INTRODUCTION
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NHERENT movement is the prime sign of the existence of life. Even though both rhythmic and nonrhythmic movements exist in abundance in animals, the former are more widespread and more often intimately related to the survival of the organism, be it a mollusc or a human. The prime cause of this rhythmic behavior, such as respiration or locomotion, is the nervous system. Studies into the exact nature of the mechanisms involved have revealed that rhythmic motor patterns are centrally generated but modifiable by peripheral sensory feedback [I]. Several modeling approaches have been undertaken which give results in compliance with some of the experimental observations. In this paper, artificial neural networks (ANN’S) are used as a new approach to modeling rhythmic movement control. Specifically, the neuronal mechanisms behind the apparently autonomous rhythmic movements of “spinal” animals will be emulated using an hierarchical ANN structure. This model should help to better understand animal locomotion as well as being potentially applicable in rehabilitation medicine, repetitive control of robot manipulators, and walking machines. Manuscript received October 5 , 1990; revised January 5 , 1992. The authors are with the Division of Biomedical Engineering, University of Saskatchewan, Saskatoon, Saskatchewan S7N OWO, Canada. IEEE Log Number 9200699.
RHYTHMICMOTORCONTROL MODELS Evidence accumulated over a large number of motor control experiments has shown that the central information-processing systems in the animal brain are probably not involved in the control of ongoing repetitive movements, such as locomotion. It has also been shown that feedback from the peripheral sensory receptors is useful but not essential to movement control, and that these movements appear to be structured in advance [l], [2]. The spinal cord itself has a capability of generating slow rhythmic activity as shown in experiments on “spinal” preparations of cats and other animals [3]. As a result of all this evidence, three groups of models of this “lowlevel” motor control have emerged, namely, central pattern generators, motor programs, and the equilibrium point hypotheses. The central pattern generators are a group of neurons which because of their synaptic connections and/or inherent properties result in oscillatory output behavior [4]. Some of the popular models in this group are: the coupled oscillator model and its variations [ 5 ] , the pacemaker models which have inherent oscillatory properties, and ring oscillator models [6]. Using these hypothetical models, the respiratory or locomotor behaviour of a few “simple” animals, such as insects, have been modeled
171, [41. Motor progams are basically a prestructured set of central commands capable of carrying out movements essentially in the open loop mode. They are hypothesized to be centrally organized structures that are capable of handling most of the details of movements, but that are also very sensitive to response-produced sensory information from a variety of sources [8]. One way to view this blending of open- and closed-loop functioning is to consider a hierarchical control scheme in which a higher order openloop control structure has under it a set of closed-loop processes that ensure the movement’s intended goal in the face of various perturbations. If a signal appears in the environment indicating that the higher-order program is no longer relevant, the highest levels in the system become involved in stopping it, or perhaps in initiating a different program. If smaller perturbations occur that do not involve an alteration in the fundamental movement goal, these can be handled by lower levels in the hierarchy, presumably while the original higher level program continues tu operate. There have been proposed
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generalized motor programs as well which are supposed to contain features common to all kinds of movements but have parameters which can be changed to suit a particular movement. In the case of locomotion, for example, these parameters could be the code for the gait itself, the frequency of the strides, and the like. A few other researchers have hypothesized movementcausing mechanisms on a radically different basis [9], [lo]. Their modelling centered around the dynamic behaviour of the musculo-skeletal system. The musculo-tendon units in the limbs can be likened to complicated springs, and hence their behavior can be characterized by their length-tension relationships. This revealed a possible mechanism for movement control known as “massspring” control. The point at which the length-tension curves (or more correctly the torque-joint angle characteristics), for a given set of activations, of the agonist and the antagonist (assuming a simple model of a limb with two opposing muscles to control its hinge-like motion) muscles intersect is called the “equilibrium point. ” This point denotes the joint angle at which the limb is stabilized by the opposing torques of the two muscles. If one of the muscles is stretched and then released, the imbalance of torques will result in an action which will put the system back in the equilibrium position. This view helps to explain how a limb can be stabilized in one position. To explain movement, the muscle activations must vary; this will change the length-tension characteristics and cause a continuously changing equilibrium position resulting in a movement. Evidence for this hypothesis has been found in monkeys with deafferented forelimbs [ 111, and by Kelso et a l . [9] with humans. But the equilibrium point hypothesis supports only simple, unidirectional positioning movements. To what extent this kind of mechanism is involved in rhythmic movements or in movements that involve more than one limb is not very clear. Although this model is capable of explaining how a single joint achieves a given angle, it is not capable of coordinating movements among two or more joints. In this case, the motor program model offers a more plausible explanation [8]. However, Berkinblit et a l . [12] have proposed a very interesting model for sequential actions, based on the wiping reflex (in response to a noxious stimulus) of the spinal frog, in which they argue that the sequential response is really a series of discrete positions; each of these positions is achieved by specifying a sequence of equilibrium positions, each of which is achieved exactly as in the equilibrium-point model. The mechanical characteristics of the muscles themselves are responsible for the details of moving to each position from the former one. Note that such sequences of equilibrium positions have to be produced by some other structure(s), possibly, central pattern generators and/or motor programs. NEURALNETWORKMODEL Advances in the theory and techniques of artificial neural networks seem to offer a good approach to test the
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different hypotheses mentioned above. The work presented here follows a logical step further in integrating the concepts and models from both the fields of motor control and artificial neural networks. Specifically, the study explores and simulates a rhythmic movement control scheme akin to that observed in a “spinal” animal using artificial neural networks. Basically, a hierarchical neural network structure with a pattern generator at the top is proposed. Repetitive open-loop trajectories will be transformed into the appropriate control signals for a rnusculo-skeletal structure modelled along the lines of an equilibrium point hypothesis. To do this, three issues have to be discussed: i) the operating variables, ii) the architecture of the scheme, and, iii) the implementation aspects of the simulation of the proposed scheme. The proposed model is restricted primarily to the kinematics of repetitive motions. Also the motion is assumed to be unconstrained (that is open-loop controlled) and not goal directed. The Operating Variables It is assumed that the movements are basically coded in task space (end point positions) since the task space coordinates involved in a movement form an invariant set of parameters. The task space coordinates also offer minimal degrees of freedom and hence are an easier and more plausible approach to movement generation and monitoring by the higher control structures in the animal nervous systems. Because the pattern generator encodes the movement trajectories, it has been termed as “movement pattern generator.” This is in contrast to the above-mentioned models of ‘‘central pattern generators” which output alternating muscle activations. But whether it is just the positions of the end points which are controlled and not their velocities is an open question. It is more likely that the velocity of movement is an inherent property of the control structure. However, given the end point positions, there must exist a way of transforming them into appropriate control signals for the musculature. Lastly, the way that these control signals effect the appropriate movements also needs to be delineated. Arichitecture The control scheme consists of four modules which are depicted in Fig. 1. The top module is the movement pattern generator emulated by a sequential neural network. The “coordinate transformation” modules can be modelled using associative type, back-propagation networks. Sequential networks are capable of storing pattern sequences. In this work, the sequences or trajectories of equilibrium positions to be stored are oscillatory in nature. Jordan’s network [13] was chosen for this module and is as shown in Fig. 2. This network consists of “plan,” “input,” “hidden,” and “output” units configured to form one or more pattern generators (each pattern generator could be thought of as a set of interconnected oscillators). In this network, none of the input units have self-feedback connections which is a deviation from the network
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neurons. The plan units’ activation vector emulates the supra-spinal commands in the biological central pattern generators in that different plan activation vectors correspond to different sequences or trajectories being stored and recalled. In the “spinal” animals the origin of the trajectories may have come about by learning, by evolution, or by some other process. Therefore, for our model, the trajectories have to be predetermined by either incorporating arbitrary data or that which is observed in animals in a typical gait pattern. These patterns can be obtained from the works of Winter [14], Murray [15] and others. The trajectories, which are the output of this module, after being mapped onto the joint space constitute sets of equilibrium positions. Upon the input of these equilibrium positions, appropriate control parameters will be generated leading to movement of the “model limb(s). ”
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proposed by Jordan. The reason for doing so was that the self-feedback connections introduced a ‘‘remembering’’ factor (in a decaying manner) for all the previous activations of the units which impaired the learning of periodic trajectories. The weighted connections between the units assume both positive and negative values and are similar to the excitatory and inhibitory synaptic connections present in biological networks. The hidden units facilitate nonlinear mappings between the outputs and the inputs. All the units can assume values between 0 and 1 analogous to minimum and maximum firing rates in biological
Implementation of the Movement Pattern Generator The implementation of the first module, namely, the “movement pattern generator” has been investigated and is reported here. The typical structure of the network configuration tested is shown. This network could serve as a movement pattern generator for a pair of simple three link model limbs shown in Fig. 3 . Two pairs of output units are associated with each limb, the reasons for which will be discussed later. A set of tonic outputs from the plan units is combined with those from the input units to a set of hidden units which in turn feed to the output units as shown. Feedback connections exist between the output units and their corresponding input units. Three trajectories depicted in Fig. 4 were chosen. The plan vector is different for each of them. For a rotary motion, the x and y coordinates will change periodically and also have a phase difference of 90” between them. Also for each of the trajectories, an antiphasic trajectory was chosen. Thus, for each limb there are two pairs of output units. This serves two purposes-to be representative of the action of a contralateral limb, and to allow for forward/backward movement with 180” or 0” phase difference between the two limbs. The different configurations of output units for selecting the alternate modes of movement are also shown in Fig. 3 . Several experiments were conducted to test the network, and they are discussed below. These experiments were designed to investigate some of the properties of network operation. Adaptiveness: That is, the capability of the network to learn and faithfully recall different cyclic temporal sequences or trdjectories, and thus act as an “adaptive oscillator network.” This was based on the finding that certain biological networks by their connections alone effect rhythmic outputs [16], [17]. Generalization: That is, the capability of the network pattern generator to generalize from the learned trajectories and output newer ones. Examples of the same set of neurons being involved in a variety of rhythmic behavior, some of which are blendings from
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Frequency Interpolation: That is, the ability of the network to generalize, in terms of the frequency, from the training set of trajectories.
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different rhythms, have also been found in animals [181. Fault Tolerance: That is, the capacity of the network to tolerate erroneous inputs or disturbances in the course of trajectory generation. Phase Maintenance: That is, the ability of the network to maintain the original phase differences between the trajectories generated by the output units despite disturbances which affect the phase relationships.
Adaptiveness and Generalization Fig. 5 shows the original trajectories and those that the network has learned. The learning was accomplished in 10 000 trials (a single presentation of all the trajectories constituting a trial) using the generalized delta rule [19]. Learning was indicated by the value of root mean square error between the learned patterns and the target patterns reaching a value less than 5 % . An increase or a decrease in the number of learning trials resulted in a gradual deterioration in the learning and/or generalization properties of the network. Furthermore, the unmodified Jordan’s network (with self-feedback connections) did not exhibit the same degree of “learning” as the modified one above. Specifically, the root mean square error value settled to a value of fifteen percent and did not vary even when the number of learning trials was increased to 15 000. The network basically operates as an adaptive oscillator set in that it can “oscillate” in different ways and is capable of learning many more (limited only by the number of plan and hidden units). Upon changing the plan inputs, the trajectories generated were found to be totally new, and the more closely related the inputs were to the predetermined ones, the more related the trajectories to the learned ones. This is a clear cut example of generalizing in terms of trajectories. Further explanations are provided below. Fault Tolerance Behavior Regardless of the starting point in a movement, an animal or an insect always can carry on with its original trajectory after a transient period. In dynamical systems theory, this is called “limit cycle behavior” and the original trajectories are called “attractors.” In this case, the different trajectories that are learned have been found to have attractor properties in that perturbations introduced during the course of the trajectory generation are tolerated with minimum disturbance to the original trajectory. Fig. 6 shows such a behavior exhibited by the given network when perturbations in the form of erroneous inputs at the start of the cycle, cut off the feedback to one of the inputs at the 25th step, and erroneous inputs again at the 50th step were introduced. In the state space of the network output, the different trajectories correspond to different attractors and these attractor states are attained by appropriate plan vectors. Upon input of novel plan vectors, the attractor states attained show forms related to the learned trajectories depending on how close they are located in the state space. The ability of the network to tolerate structural deteriorations was also explored. A number of weighted connections, ranging from 10 to 60% of the total number, were randomly removed and the network was tested for its ability to recall the learned trajectories. It was found,
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ferences as shown in Fig. 8(a) and (b). The coupling between the oscillators serves to correct for any deviations in the phase differences. However, the delayed feedback causes the frequency of oscillation to decrease proportionately. This is depicted for one of the trajectories for two different delays (Fig. 9). Apparently the delayed feedback causes the network to slow down its outputs so as to satisfy both the normal and the delayed inputs. The phase locking property is an advantageous one in that the original trajectory is maintained (with certain distortions as the delay increases) even though the frequency may vary.
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however, that the network’s behavior was not predictable, in that the ability to faithfully recall the learned trajectories was not dependent on the number of connections that were removed but was dependent on their location. However, the modified network’s ability to learn new trajectories was dependent only on the remanent set of connections so that the lesser the number of connections available, the lesser the number of trajectories that can be learned and faithfully recalled and also the greater the time required to learn them. Phase Maintenance Fig. 7 reveals that for all the trajectories “learned,” perfect phase relationships were maintained. Further experiments were conducted wherein delays of different magnitudes (in terms of the period) were introduced in the feedback lines of some of the oscillators. This serves to introduce a phase lag in those oscillators. But the outputs of these oscillators were found to be in compliance with those of the normal oscillators with the original phase dif-
Frequency Interpolation Feldman and Orlovsky ’s [20] and Bernstein’s experiments on spinal cats [ 2 ] revealed that the frequency of stepping could be varied by stimulating the mesencephalic regions. In other words, supra-spinal commands are not only involved in selecting the right trajectory but also its frequency [21]. Accordingly, for two of the trajectories, three different frequencies (0.5f,f, and 2f where f is the original frequency) were chosen and the network made to “learn” them. Before doing so, two units of the plan vector were designated for the frequency of the trajectory cycles such that one of the units when fully activated (value 1) would result in the output of the lowest frequency (0.5f)while the full activation of the other would result in an output of the highest frequency (2f) and if neither of the units is activated (value 0) then an output of normal frequency would be generated. After learning, the three trajectories were selected and the frequency specific units were activated as follows. First, both the frequency sensitive units have zero activations and hence normal frequency should be output. Then only the high frequency unit is gradually activated from a value of 0- 1 and subsequently made zero, while the activationof the low frequency unit is increased from a value of 0- 1. During this process, the frequency of any trajectory should exhibit a variation over the two octave range (0.5-2). Fig.
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Fig. 8. An example of the maintenance of phase relationships despite a feedback delay causing a phase difference. Illustrated here are the outputs of two ‘output’ units (Output1 and Output2) found being in-phase despite a constant phase difference of 0.25 ?T between two input units (Input1 and
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Fig. 9. Illustration of the frequency changes that occur upon incorporation of feedback delays into the network. Delays are in terms of the length of the period.
CONCLUSION The implementation of the movement pattern generator based on Jordan’s network reveals many interesting properties similar to those observed in animals. Its capability for learning different movement trajectories and for generating new ones while maintaining phase relationships is promising. Previous models of the central pattern generators, although capable of oscillatory behavior, do not have the capabilities of learning or of generalization which the neural network model offers with a simple architecture. This pattern generator model does not have pacemaking cells or a system clock; instead it functions as a finite state machine since the structural organization of the network takes care of the generation of trajectories. The parallel and distributed nature of the model endows it with good fault tolerance capabilities. Indeed this model differs from the ones presented so far in that it stores and reproduces the movement trajectories while the others incorporate the muscular activations. But the advantage (especially for robotic applications) is that a “central pattern generator” having the invariant aspects (in our case the task space coordinates) of the movement incorporated in it could very well be used with any set of effectors. The incorporation of feedback from the effectors to the movement pattern generator, although not planned for the proposed overall model, would result in a wider variety of behaviour and also may allow voluntary movements. The implemented pattern generator may offer a simpler approach to the repetitive control of robot manipulators as compared to the one proposed by Hara et al. [ 2 2 ] . However, it will require that the robot be included in the feedback loop of the network with the appropriate set of transformations performed to match the control and sensed parameters.
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The experiments of Grillner and others [4]revealed that obstruction of one of the limbs of the spinal animal, while it was “stepping,” did not impair the cyclic motion of the other limbs and also when released it gets in phase with the rest. The idea of separating the movement generator from the dynamical system characterizing the musculo-skeletal system may explain the above finding, because when the limb is held by external means, the activations still occur in the musculature of that limb and when released, the torques generated by the difference between the current position and the equilibrium position as set by the activation levels will effect its return. The control scheme basically offers a compromise between the central pattern generator and motor program models with the equilibrium point models. Experimental evidence has shown that the central pattern generators are located in the spinal cords and their models, so far, output rhythmic muscular activations, whereas in our case, the movement trajectories are generated. Repetitive trajectories are deemed to be produced by motor programs hypothesized as being located in the hippocampal regions of the brain [ 2 3 ] . Again, the task space trajectories, after certain transformations, being considered as sequences of equilibrium positions to be input to the musculo-skeletal model of the limb draws concepts from all the three movement control models. Overall, the hierarchical control scheme with the least degrees of freedom at the top module level is in accordance with “the principle of least interaction” [2]. Although the architecture and functioning of the implemented artificial neural network model are highly simplified, they provide a clue as to the richer possibilities that may exist in the biological sensorimotor systems. REFERENCES [I] T. Delcomyn, “Neural basis of rhythmic behaviour in animals,” Science, vol. 210, pp. 492-498, 1976. [2] N. Bernstein, The Co-ordination and Regulation of Movements. Oxford: Pergamon, 1967, pp. 3-4. [3] G. N. Orlovsky and M. L. Shik, “The standard elements of cyclic movement,” Biophys., vol. 10, pp. 935-944, 1965. [4] S . Grillner, “Locomotion in vertebrates: Central mechanisms and reflex interactions,” Physiological Rev., vol. 55, pp. 247-304, 1975. [5] T. G . Brown, “The intrinsic factors in the act of progression in the mammal,” in Proc. Royal Soc., vol. B 84, 1911, pp. 308-319. [6] A. C. Guyton, Function of the Human Body. Toronto: W. B. Saunders, 1969, pp. 267-271. [7] D. M. Wilson, “Insect walking,” Ann. Rev. Entomol., vol. 11, pp. 102-122, 1966. [8] R. A. Schmidt, “A schema theory of discrete motor skill learning,” Psychological R e v . , vol. 82, pp. 225-260, 1975. [9] J . A. S . Kelso and K . G . Holt, “Exploring a vibratory systems analysis of human movement production,” J . Neurophysiol., vol. 43, pp. 1183-1 196, 1980. [IO] A. G. Fel’dman, “Functional timing of the nervous system with control of movement or maintenance of a steady posture: 11,” Biophys., vol. 11, pp. 565-578, 1966. 1111 A. Polit and E. Bizzi, “Processes controlling arm movements in monkeys,” Science, vol. 201, pp. 1235-1237, 1978. 1121 E. M . Berkinblit et a l . , “Adaptability of innate motor patterns and motor control mechanisms,” The Behavioural and Brain Sci., vol. 9 , pp. 585-638, 1986. [13] M. I. Jordan, “Attractor dynamics and parallelism in a connectionist sequential machine,” in Proc. Cognitive Sci. Soc. Conf., vol. 8, 1986, pp. 531-546.
[I41 D. A. Winter, “Biomechanical motor patterns in normal walking,” J . Motor Behaviour, vol. 15, pp. 302-330, 1983. 1151 M . P. Murray, “Gait as a total pattern of movement,” Amer. J . Phys. Med., vol. 46, pp. 290-333, 1967. 1161 P. A. Getting, “Mechanisms of pattern generation underlying swimming in tritonia. 1-Network formed by monosynaptic connections,” J . Neurophysiol., vol. 46, pp. 65-79, 1981. [I71 J . C . Weeks, “Neuronal basis of leech swimming: Separation of swim initiation, pattern generation and intersegmental coordination by selective lesions,” J . Nrurophjsiol., vol. 45, pp. 698-723, 1981. 1181 P. S . G. Stein er U / . , ”Blends of rostral and caudal scratch reflex motor patterns elicited by simultaneous stimulation of two sites I n the spinal turtle,” J . Neuro.\ci., vol. 6 , pp. 2259-2266, 1986. 1191 D. E. Rumelhart and J . L . McClelland, Eds.. Parallel Distributed Proccssing: Explorarions in the Microstructures of Cognition. Vol. 1. Cambridge, MA: M.I.T., 1986, pp. 322-328. [20] A . G . Fel’dman and G . N . Orlovsky, “Activity of interneurons mediating reciprocal la inhibition during locomotion,” Brain Res. , vol. 84, pp. 181-194, 1975. 1211 S. Miller and P. D. Scott, “A model of the spinal locomotor generator in the cat,” J . Physiol., vol. 269, pp. 20-22, 1977. [22] S . Hara et a l . , “Repetitive control system: A new type servo system for periodic exogenous signals,” IEEE Trans. Automat. Contr., vol. 33, pp. 659-668, 1988. [23] V. B. Brooks, The Neural Basis of Motor Control. New York: Oxford Univ. Press, 1986, pp. 18-37.
S. Srinivasan graduated with a Bachelor‘s degree in electrical engineering from Bangalore University, India. and the Master of Science degree in biomedical engineering from the University of Saskatchewan. He is currently pursuing the Ph.D. degree in biomedical engineering at the University of Saskatchewan, Saskatoon, Saskatchewan, Canada. His research interests are in the areas of artificial neural networks, biological modelling, signal processing and robotics.
Robert E. Gander (S’70-M’72-SM’85) received the B.Sc. degree in electrical engineering in 1972 from the University of Alberta, Edmonton, A h . , Canada, and the M.A.Sc. and Ph.D. degrees from the University of Toronto, Toronto, Ont., Canada, in 1975 and 1980, respectively. He has been a faculty member in the Bioengineering Institute and the Department of Electrical Engineering at the University of New Brunswick. He is currently an Associate Professor in Electrical Engineering and a member of the Division of Biomedical Engineering at the University of Saskatchewan. His research interests are in the application of artificial neural networks, instrumentation and signal processing. Dr. Gander is a member of the Association of Professional Engineers of Saskatchewan, the Canadian Medical and Biological Engineering Society, and RESNA.
Hugh C. Wood (M’82) received the Bachelor’s degree in engineering, and the Master’s and Doctorate degrees in applied physics. He specialized in instrumentation and signal processing for infrared airglow emissions in the atmosphere. Following postdoctoral study in Sweden, he worked in industry for ten years developing instrumentation and analysis techniques for remote sensing data. He then developed a greater interest in electronics and microcomputer signal processing techniques in measurement and control applications, and returned to the University of Saskatchewan Saskatoon, Saskatchewan, Canada, where he became Professor of Electrical Engineering in 1989. His major efforts continue to be in the areas of instrumentation and signal analysis, with a concentration on real time and expert system techniques.
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 39, NO. 7, JULY 1992
A Movement Pattern Generator Model Using Artificial Neural Networks S . Srinivasan, Robert E. Gander, Senior Member, IEEE, and Hugh C. Wood, Member, IEEE
Abstract-Artificial neural networks (ANN’S) allow a new approach to biological modeling. The main applications of ANN’S have been geared towards the modeling of the association and learning mechanisms of the brain; only a few researchers have explored them for motor control. The fact that A ” ’ s are based on biological systems indicates their potential application for a biological act such as locomotion. Towards this goal, we have developed a “movement pattern generator,” using an ANN for generating periodic movement trajectories. This model is based on the concept of “central pattern generators.” Jordan’s sequential network, which is capable of learning sequences of patterns, was modified and used to generate several bipedal trajectories (or gaits), coded in task space, at different frequencies. The network model successfully learned all of the trajectories presented to it. The model has many attractive properties such as limit cycle behavior, generalization of trajectories and frequencies, phase maintenance, and fault tolerance. The movement pattern generator model is potentially applicable for improved understanding of animal locomotion and for use in legged robots and rehabilitation medicine.
INTRODUCTION
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NHERENT movement is the prime sign of the existence of life. Even though both rhythmic and nonrhythmic movements exist in abundance in animals, the former are more widespread and more often intimately related to the survival of the organism, be it a mollusc or a human. The prime cause of this rhythmic behavior, such as respiration or locomotion, is the nervous system. Studies into the exact nature of the mechanisms involved have revealed that rhythmic motor patterns are centrally generated but modifiable by peripheral sensory feedback [I]. Several modeling approaches have been undertaken which give results in compliance with some of the experimental observations. In this paper, artificial neural networks (ANN’S) are used as a new approach to modeling rhythmic movement control. Specifically, the neuronal mechanisms behind the apparently autonomous rhythmic movements of “spinal” animals will be emulated using an hierarchical ANN structure. This model should help to better understand animal locomotion as well as being potentially applicable in rehabilitation medicine, repetitive control of robot manipulators, and walking machines. Manuscript received October 5 , 1990; revised January 5 , 1992. The authors are with the Division of Biomedical Engineering, University of Saskatchewan, Saskatoon, Saskatchewan S7N OWO, Canada. IEEE Log Number 9200699.
RHYTHMICMOTORCONTROL MODELS Evidence accumulated over a large number of motor control experiments has shown that the central information-processing systems in the animal brain are probably not involved in the control of ongoing repetitive movements, such as locomotion. It has also been shown that feedback from the peripheral sensory receptors is useful but not essential to movement control, and that these movements appear to be structured in advance [l], [2]. The spinal cord itself has a capability of generating slow rhythmic activity as shown in experiments on “spinal” preparations of cats and other animals [3]. As a result of all this evidence, three groups of models of this “lowlevel” motor control have emerged, namely, central pattern generators, motor programs, and the equilibrium point hypotheses. The central pattern generators are a group of neurons which because of their synaptic connections and/or inherent properties result in oscillatory output behavior [4]. Some of the popular models in this group are: the coupled oscillator model and its variations [ 5 ] , the pacemaker models which have inherent oscillatory properties, and ring oscillator models [6]. Using these hypothetical models, the respiratory or locomotor behaviour of a few “simple” animals, such as insects, have been modeled
171, [41. Motor progams are basically a prestructured set of central commands capable of carrying out movements essentially in the open loop mode. They are hypothesized to be centrally organized structures that are capable of handling most of the details of movements, but that are also very sensitive to response-produced sensory information from a variety of sources [8]. One way to view this blending of open- and closed-loop functioning is to consider a hierarchical control scheme in which a higher order openloop control structure has under it a set of closed-loop processes that ensure the movement’s intended goal in the face of various perturbations. If a signal appears in the environment indicating that the higher-order program is no longer relevant, the highest levels in the system become involved in stopping it, or perhaps in initiating a different program. If smaller perturbations occur that do not involve an alteration in the fundamental movement goal, these can be handled by lower levels in the hierarchy, presumably while the original higher level program continues tu operate. There have been proposed
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generalized motor programs as well which are supposed to contain features common to all kinds of movements but have parameters which can be changed to suit a particular movement. In the case of locomotion, for example, these parameters could be the code for the gait itself, the frequency of the strides, and the like. A few other researchers have hypothesized movementcausing mechanisms on a radically different basis [9], [lo]. Their modelling centered around the dynamic behaviour of the musculo-skeletal system. The musculo-tendon units in the limbs can be likened to complicated springs, and hence their behavior can be characterized by their length-tension relationships. This revealed a possible mechanism for movement control known as “massspring” control. The point at which the length-tension curves (or more correctly the torque-joint angle characteristics), for a given set of activations, of the agonist and the antagonist (assuming a simple model of a limb with two opposing muscles to control its hinge-like motion) muscles intersect is called the “equilibrium point. ” This point denotes the joint angle at which the limb is stabilized by the opposing torques of the two muscles. If one of the muscles is stretched and then released, the imbalance of torques will result in an action which will put the system back in the equilibrium position. This view helps to explain how a limb can be stabilized in one position. To explain movement, the muscle activations must vary; this will change the length-tension characteristics and cause a continuously changing equilibrium position resulting in a movement. Evidence for this hypothesis has been found in monkeys with deafferented forelimbs [ 111, and by Kelso et a l . [9] with humans. But the equilibrium point hypothesis supports only simple, unidirectional positioning movements. To what extent this kind of mechanism is involved in rhythmic movements or in movements that involve more than one limb is not very clear. Although this model is capable of explaining how a single joint achieves a given angle, it is not capable of coordinating movements among two or more joints. In this case, the motor program model offers a more plausible explanation [8]. However, Berkinblit et a l . [12] have proposed a very interesting model for sequential actions, based on the wiping reflex (in response to a noxious stimulus) of the spinal frog, in which they argue that the sequential response is really a series of discrete positions; each of these positions is achieved by specifying a sequence of equilibrium positions, each of which is achieved exactly as in the equilibrium-point model. The mechanical characteristics of the muscles themselves are responsible for the details of moving to each position from the former one. Note that such sequences of equilibrium positions have to be produced by some other structure(s), possibly, central pattern generators and/or motor programs. NEURALNETWORKMODEL Advances in the theory and techniques of artificial neural networks seem to offer a good approach to test the
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different hypotheses mentioned above. The work presented here follows a logical step further in integrating the concepts and models from both the fields of motor control and artificial neural networks. Specifically, the study explores and simulates a rhythmic movement control scheme akin to that observed in a “spinal” animal using artificial neural networks. Basically, a hierarchical neural network structure with a pattern generator at the top is proposed. Repetitive open-loop trajectories will be transformed into the appropriate control signals for a rnusculo-skeletal structure modelled along the lines of an equilibrium point hypothesis. To do this, three issues have to be discussed: i) the operating variables, ii) the architecture of the scheme, and, iii) the implementation aspects of the simulation of the proposed scheme. The proposed model is restricted primarily to the kinematics of repetitive motions. Also the motion is assumed to be unconstrained (that is open-loop controlled) and not goal directed. The Operating Variables It is assumed that the movements are basically coded in task space (end point positions) since the task space coordinates involved in a movement form an invariant set of parameters. The task space coordinates also offer minimal degrees of freedom and hence are an easier and more plausible approach to movement generation and monitoring by the higher control structures in the animal nervous systems. Because the pattern generator encodes the movement trajectories, it has been termed as “movement pattern generator.” This is in contrast to the above-mentioned models of ‘‘central pattern generators” which output alternating muscle activations. But whether it is just the positions of the end points which are controlled and not their velocities is an open question. It is more likely that the velocity of movement is an inherent property of the control structure. However, given the end point positions, there must exist a way of transforming them into appropriate control signals for the musculature. Lastly, the way that these control signals effect the appropriate movements also needs to be delineated. Arichitecture The control scheme consists of four modules which are depicted in Fig. 1. The top module is the movement pattern generator emulated by a sequential neural network. The “coordinate transformation” modules can be modelled using associative type, back-propagation networks. Sequential networks are capable of storing pattern sequences. In this work, the sequences or trajectories of equilibrium positions to be stored are oscillatory in nature. Jordan’s network [13] was chosen for this module and is as shown in Fig. 2. This network consists of “plan,” “input,” “hidden,” and “output” units configured to form one or more pattern generators (each pattern generator could be thought of as a set of interconnected oscillators). In this network, none of the input units have self-feedback connections which is a deviation from the network
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neurons. The plan units’ activation vector emulates the supra-spinal commands in the biological central pattern generators in that different plan activation vectors correspond to different sequences or trajectories being stored and recalled. In the “spinal” animals the origin of the trajectories may have come about by learning, by evolution, or by some other process. Therefore, for our model, the trajectories have to be predetermined by either incorporating arbitrary data or that which is observed in animals in a typical gait pattern. These patterns can be obtained from the works of Winter [14], Murray [15] and others. The trajectories, which are the output of this module, after being mapped onto the joint space constitute sets of equilibrium positions. Upon the input of these equilibrium positions, appropriate control parameters will be generated leading to movement of the “model limb(s). ”
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proposed by Jordan. The reason for doing so was that the self-feedback connections introduced a ‘‘remembering’’ factor (in a decaying manner) for all the previous activations of the units which impaired the learning of periodic trajectories. The weighted connections between the units assume both positive and negative values and are similar to the excitatory and inhibitory synaptic connections present in biological networks. The hidden units facilitate nonlinear mappings between the outputs and the inputs. All the units can assume values between 0 and 1 analogous to minimum and maximum firing rates in biological
Implementation of the Movement Pattern Generator The implementation of the first module, namely, the “movement pattern generator” has been investigated and is reported here. The typical structure of the network configuration tested is shown. This network could serve as a movement pattern generator for a pair of simple three link model limbs shown in Fig. 3 . Two pairs of output units are associated with each limb, the reasons for which will be discussed later. A set of tonic outputs from the plan units is combined with those from the input units to a set of hidden units which in turn feed to the output units as shown. Feedback connections exist between the output units and their corresponding input units. Three trajectories depicted in Fig. 4 were chosen. The plan vector is different for each of them. For a rotary motion, the x and y coordinates will change periodically and also have a phase difference of 90” between them. Also for each of the trajectories, an antiphasic trajectory was chosen. Thus, for each limb there are two pairs of output units. This serves two purposes-to be representative of the action of a contralateral limb, and to allow for forward/backward movement with 180” or 0” phase difference between the two limbs. The different configurations of output units for selecting the alternate modes of movement are also shown in Fig. 3 . Several experiments were conducted to test the network, and they are discussed below. These experiments were designed to investigate some of the properties of network operation. Adaptiveness: That is, the capability of the network to learn and faithfully recall different cyclic temporal sequences or trdjectories, and thus act as an “adaptive oscillator network.” This was based on the finding that certain biological networks by their connections alone effect rhythmic outputs [16], [17]. Generalization: That is, the capability of the network pattern generator to generalize from the learned trajectories and output newer ones. Examples of the same set of neurons being involved in a variety of rhythmic behavior, some of which are blendings from
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Frequency Interpolation: That is, the ability of the network to generalize, in terms of the frequency, from the training set of trajectories.
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different rhythms, have also been found in animals [181. Fault Tolerance: That is, the capacity of the network to tolerate erroneous inputs or disturbances in the course of trajectory generation. Phase Maintenance: That is, the ability of the network to maintain the original phase differences between the trajectories generated by the output units despite disturbances which affect the phase relationships.
Adaptiveness and Generalization Fig. 5 shows the original trajectories and those that the network has learned. The learning was accomplished in 10 000 trials (a single presentation of all the trajectories constituting a trial) using the generalized delta rule [19]. Learning was indicated by the value of root mean square error between the learned patterns and the target patterns reaching a value less than 5 % . An increase or a decrease in the number of learning trials resulted in a gradual deterioration in the learning and/or generalization properties of the network. Furthermore, the unmodified Jordan’s network (with self-feedback connections) did not exhibit the same degree of “learning” as the modified one above. Specifically, the root mean square error value settled to a value of fifteen percent and did not vary even when the number of learning trials was increased to 15 000. The network basically operates as an adaptive oscillator set in that it can “oscillate” in different ways and is capable of learning many more (limited only by the number of plan and hidden units). Upon changing the plan inputs, the trajectories generated were found to be totally new, and the more closely related the inputs were to the predetermined ones, the more related the trajectories to the learned ones. This is a clear cut example of generalizing in terms of trajectories. Further explanations are provided below. Fault Tolerance Behavior Regardless of the starting point in a movement, an animal or an insect always can carry on with its original trajectory after a transient period. In dynamical systems theory, this is called “limit cycle behavior” and the original trajectories are called “attractors.” In this case, the different trajectories that are learned have been found to have attractor properties in that perturbations introduced during the course of the trajectory generation are tolerated with minimum disturbance to the original trajectory. Fig. 6 shows such a behavior exhibited by the given network when perturbations in the form of erroneous inputs at the start of the cycle, cut off the feedback to one of the inputs at the 25th step, and erroneous inputs again at the 50th step were introduced. In the state space of the network output, the different trajectories correspond to different attractors and these attractor states are attained by appropriate plan vectors. Upon input of novel plan vectors, the attractor states attained show forms related to the learned trajectories depending on how close they are located in the state space. The ability of the network to tolerate structural deteriorations was also explored. A number of weighted connections, ranging from 10 to 60% of the total number, were randomly removed and the network was tested for its ability to recall the learned trajectories. It was found,
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ferences as shown in Fig. 8(a) and (b). The coupling between the oscillators serves to correct for any deviations in the phase differences. However, the delayed feedback causes the frequency of oscillation to decrease proportionately. This is depicted for one of the trajectories for two different delays (Fig. 9). Apparently the delayed feedback causes the network to slow down its outputs so as to satisfy both the normal and the delayed inputs. The phase locking property is an advantageous one in that the original trajectory is maintained (with certain distortions as the delay increases) even though the frequency may vary.
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however, that the network’s behavior was not predictable, in that the ability to faithfully recall the learned trajectories was not dependent on the number of connections that were removed but was dependent on their location. However, the modified network’s ability to learn new trajectories was dependent only on the remanent set of connections so that the lesser the number of connections available, the lesser the number of trajectories that can be learned and faithfully recalled and also the greater the time required to learn them. Phase Maintenance Fig. 7 reveals that for all the trajectories “learned,” perfect phase relationships were maintained. Further experiments were conducted wherein delays of different magnitudes (in terms of the period) were introduced in the feedback lines of some of the oscillators. This serves to introduce a phase lag in those oscillators. But the outputs of these oscillators were found to be in compliance with those of the normal oscillators with the original phase dif-
Frequency Interpolation Feldman and Orlovsky ’s [20] and Bernstein’s experiments on spinal cats [ 2 ] revealed that the frequency of stepping could be varied by stimulating the mesencephalic regions. In other words, supra-spinal commands are not only involved in selecting the right trajectory but also its frequency [21]. Accordingly, for two of the trajectories, three different frequencies (0.5f,f, and 2f where f is the original frequency) were chosen and the network made to “learn” them. Before doing so, two units of the plan vector were designated for the frequency of the trajectory cycles such that one of the units when fully activated (value 1) would result in the output of the lowest frequency (0.5f)while the full activation of the other would result in an output of the highest frequency (2f) and if neither of the units is activated (value 0) then an output of normal frequency would be generated. After learning, the three trajectories were selected and the frequency specific units were activated as follows. First, both the frequency sensitive units have zero activations and hence normal frequency should be output. Then only the high frequency unit is gradually activated from a value of 0- 1 and subsequently made zero, while the activationof the low frequency unit is increased from a value of 0- 1. During this process, the frequency of any trajectory should exhibit a variation over the two octave range (0.5-2). Fig.
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CONCLUSION The implementation of the movement pattern generator based on Jordan’s network reveals many interesting properties similar to those observed in animals. Its capability for learning different movement trajectories and for generating new ones while maintaining phase relationships is promising. Previous models of the central pattern generators, although capable of oscillatory behavior, do not have the capabilities of learning or of generalization which the neural network model offers with a simple architecture. This pattern generator model does not have pacemaking cells or a system clock; instead it functions as a finite state machine since the structural organization of the network takes care of the generation of trajectories. The parallel and distributed nature of the model endows it with good fault tolerance capabilities. Indeed this model differs from the ones presented so far in that it stores and reproduces the movement trajectories while the others incorporate the muscular activations. But the advantage (especially for robotic applications) is that a “central pattern generator” having the invariant aspects (in our case the task space coordinates) of the movement incorporated in it could very well be used with any set of effectors. The incorporation of feedback from the effectors to the movement pattern generator, although not planned for the proposed overall model, would result in a wider variety of behaviour and also may allow voluntary movements. The implemented pattern generator may offer a simpler approach to the repetitive control of robot manipulators as compared to the one proposed by Hara et al. [ 2 2 ] . However, it will require that the robot be included in the feedback loop of the network with the appropriate set of transformations performed to match the control and sensed parameters.
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The experiments of Grillner and others [4]revealed that obstruction of one of the limbs of the spinal animal, while it was “stepping,” did not impair the cyclic motion of the other limbs and also when released it gets in phase with the rest. The idea of separating the movement generator from the dynamical system characterizing the musculo-skeletal system may explain the above finding, because when the limb is held by external means, the activations still occur in the musculature of that limb and when released, the torques generated by the difference between the current position and the equilibrium position as set by the activation levels will effect its return. The control scheme basically offers a compromise between the central pattern generator and motor program models with the equilibrium point models. Experimental evidence has shown that the central pattern generators are located in the spinal cords and their models, so far, output rhythmic muscular activations, whereas in our case, the movement trajectories are generated. Repetitive trajectories are deemed to be produced by motor programs hypothesized as being located in the hippocampal regions of the brain [ 2 3 ] . Again, the task space trajectories, after certain transformations, being considered as sequences of equilibrium positions to be input to the musculo-skeletal model of the limb draws concepts from all the three movement control models. Overall, the hierarchical control scheme with the least degrees of freedom at the top module level is in accordance with “the principle of least interaction” [2]. Although the architecture and functioning of the implemented artificial neural network model are highly simplified, they provide a clue as to the richer possibilities that may exist in the biological sensorimotor systems. REFERENCES [I] T. Delcomyn, “Neural basis of rhythmic behaviour in animals,” Science, vol. 210, pp. 492-498, 1976. [2] N. Bernstein, The Co-ordination and Regulation of Movements. Oxford: Pergamon, 1967, pp. 3-4. [3] G. N. Orlovsky and M. L. Shik, “The standard elements of cyclic movement,” Biophys., vol. 10, pp. 935-944, 1965. [4] S . Grillner, “Locomotion in vertebrates: Central mechanisms and reflex interactions,” Physiological Rev., vol. 55, pp. 247-304, 1975. [5] T. G . Brown, “The intrinsic factors in the act of progression in the mammal,” in Proc. Royal Soc., vol. B 84, 1911, pp. 308-319. [6] A. C. Guyton, Function of the Human Body. Toronto: W. B. Saunders, 1969, pp. 267-271. [7] D. M. Wilson, “Insect walking,” Ann. Rev. Entomol., vol. 11, pp. 102-122, 1966. [8] R. A. Schmidt, “A schema theory of discrete motor skill learning,” Psychological R e v . , vol. 82, pp. 225-260, 1975. [9] J . A. S . Kelso and K . G . Holt, “Exploring a vibratory systems analysis of human movement production,” J . Neurophysiol., vol. 43, pp. 1183-1 196, 1980. [IO] A. G. Fel’dman, “Functional timing of the nervous system with control of movement or maintenance of a steady posture: 11,” Biophys., vol. 11, pp. 565-578, 1966. 1111 A. Polit and E. Bizzi, “Processes controlling arm movements in monkeys,” Science, vol. 201, pp. 1235-1237, 1978. 1121 E. M . Berkinblit et a l . , “Adaptability of innate motor patterns and motor control mechanisms,” The Behavioural and Brain Sci., vol. 9 , pp. 585-638, 1986. [13] M. I. Jordan, “Attractor dynamics and parallelism in a connectionist sequential machine,” in Proc. Cognitive Sci. Soc. Conf., vol. 8, 1986, pp. 531-546.
[I41 D. A. Winter, “Biomechanical motor patterns in normal walking,” J . Motor Behaviour, vol. 15, pp. 302-330, 1983. 1151 M . P. Murray, “Gait as a total pattern of movement,” Amer. J . Phys. Med., vol. 46, pp. 290-333, 1967. 1161 P. A. Getting, “Mechanisms of pattern generation underlying swimming in tritonia. 1-Network formed by monosynaptic connections,” J . Neurophysiol., vol. 46, pp. 65-79, 1981. [I71 J . C . Weeks, “Neuronal basis of leech swimming: Separation of swim initiation, pattern generation and intersegmental coordination by selective lesions,” J . Nrurophjsiol., vol. 45, pp. 698-723, 1981. 1181 P. S . G. Stein er U / . , ”Blends of rostral and caudal scratch reflex motor patterns elicited by simultaneous stimulation of two sites I n the spinal turtle,” J . Neuro.\ci., vol. 6 , pp. 2259-2266, 1986. 1191 D. E. Rumelhart and J . L . McClelland, Eds.. Parallel Distributed Proccssing: Explorarions in the Microstructures of Cognition. Vol. 1. Cambridge, MA: M.I.T., 1986, pp. 322-328. [20] A . G . Fel’dman and G . N . Orlovsky, “Activity of interneurons mediating reciprocal la inhibition during locomotion,” Brain Res. , vol. 84, pp. 181-194, 1975. 1211 S. Miller and P. D. Scott, “A model of the spinal locomotor generator in the cat,” J . Physiol., vol. 269, pp. 20-22, 1977. [22] S . Hara et a l . , “Repetitive control system: A new type servo system for periodic exogenous signals,” IEEE Trans. Automat. Contr., vol. 33, pp. 659-668, 1988. [23] V. B. Brooks, The Neural Basis of Motor Control. New York: Oxford Univ. Press, 1986, pp. 18-37.
S. Srinivasan graduated with a Bachelor‘s degree in electrical engineering from Bangalore University, India. and the Master of Science degree in biomedical engineering from the University of Saskatchewan. He is currently pursuing the Ph.D. degree in biomedical engineering at the University of Saskatchewan, Saskatoon, Saskatchewan, Canada. His research interests are in the areas of artificial neural networks, biological modelling, signal processing and robotics.
Robert E. Gander (S’70-M’72-SM’85) received the B.Sc. degree in electrical engineering in 1972 from the University of Alberta, Edmonton, A h . , Canada, and the M.A.Sc. and Ph.D. degrees from the University of Toronto, Toronto, Ont., Canada, in 1975 and 1980, respectively. He has been a faculty member in the Bioengineering Institute and the Department of Electrical Engineering at the University of New Brunswick. He is currently an Associate Professor in Electrical Engineering and a member of the Division of Biomedical Engineering at the University of Saskatchewan. His research interests are in the application of artificial neural networks, instrumentation and signal processing. Dr. Gander is a member of the Association of Professional Engineers of Saskatchewan, the Canadian Medical and Biological Engineering Society, and RESNA.
Hugh C. Wood (M’82) received the Bachelor’s degree in engineering, and the Master’s and Doctorate degrees in applied physics. He specialized in instrumentation and signal processing for infrared airglow emissions in the atmosphere. Following postdoctoral study in Sweden, he worked in industry for ten years developing instrumentation and analysis techniques for remote sensing data. He then developed a greater interest in electronics and microcomputer signal processing techniques in measurement and control applications, and returned to the University of Saskatchewan Saskatoon, Saskatchewan, Canada, where he became Professor of Electrical Engineering in 1989. His major efforts continue to be in the areas of instrumentation and signal analysis, with a concentration on real time and expert system techniques.
