A model of the neuro-musculo-skeletal system for human locomotion

The generation of human locomotion was examined by linking computational neuroscience with biomechanics from the perspective of nonlinear dynamical theory. We constructed a model of human locomotion, which includes a musculo-skeletal system with 8 segments and 20 muscles, a neural rhythm generator composed of 7 pairs of neural oscillators, and mechanisms for processing and transporting sensory and motor signals. Using a computer simulation, we found that locomotion emerged as a stable limit cycle that was generated by the global entrainment between the musculo-skeletal system, the neural system, and the environment. Moreover, the walking movements of the model could be compared quantitatively with those of experimental studies in humans.Part of this paper was presented to IVth International Symposium on Computer Simulation in Biomechanics, Paris, France, July 1, 1993     

Decoding the mechanisms of gait generation in salamanders by combining neurobiology, modeling and robotics

Vertebrate animals exhibit impressive locomotor skills. These locomotor skills are due to the complex interactions between the environment, the musculo-skeletal system and the central nervous system, in particular the spinal locomotor circuits. We are interested in decoding these interactions in the salamander, a key animal from an evolutionary point of view. It exhibits both swimming and stepping gaits and is faced with the problem of producing efficient propulsive forces using the same musculo-skeletal system in two environments with significant physical differences in density, viscosity and gravitational load. Yet its nervous system remains comparatively simple. Our approach is based on a combination of neurophysiological experiments, numerical modeling at different levels of abstraction, and robotic validation using an amphibious salamander-like robot. This article reviews the current state of our knowledge on salamander locomotion control, and presents how our approach has allowed us to obtain a first conceptual model of the salamander spinal locomotor networks. The model suggests that the salamander locomotor circuit can be seen as a lamprey-like circuit controlling axial movements of the trunk and tail, extended by specialized oscillatory centers controlling limb movements. The interplay between the two types of circuits determines the mode of locomotion under the influence of sensory feedback and descending drive, with stepping gaits at low drive, and swimming at high drive.     

A model of the neuro-musculo-skeletal system for anticipatory adjustment of human locomotion during obstacle avoidance

Theoretical studies on human locomotion have shown that a stable and flexible gait emerges from the dynamic interaction between the rhythmic activity of a neural system composed of a neural rhythm generator (RG) and the rhythmic movement of the musculo-skeletal system. This study further explores the mechanism of the anticipatory control of locomotion based on the emergent properties of a neural system that generates the basic pattern of gait. A model of the neuro-musculo-skeletal system to execute the task of stepping over a visible obstacle with both limbs during walking is described. The RG in the neural system was combined with a system referred to as a discrete movement generator (DM), which receives both the output of the RG and visual information regarding the obstacle and generates discrete signals for modification of the basic gait pattern. A series of computer simulations demonstrated that an obstacle placed at an arbitrary position can be cleared by sequential modifications of gait: (1) modulating the step length when approaching the obstacle and (2) modifying the trajectory of the swing limbs while stepping over it. This result suggests that anticipatory adjustments are produced not by the unidirectional flow of the information from visual signals to motor commands but by the bi-directional circulation of information between the DM and the RG. The validity of this model is discussed in relation to motor cortical activity during anticipatory modifications in cats and the ecological psychology of visuo-motor control in humans. Received: 19 September 1996 / Accepted in revised form: 21 March 1997     

Generation of human bipedal locomotion by a bio-mimetic neuro-musculo-skeletal model

To emulate the actual neuro-control mechanism of human bipedal locomotion, an anatomically and physiologically based neuro-musculo-skeletal model is developed. The human musculo-skeletal system is constructed as seven rigid links in a sagittal plane, with a total of nine principal muscles. The nervous system consists of an alpha motoneuron and proprioceptors such as a muscle spindle and a Golgi tendon organ for each muscle. At the motoneurons, feedback signals from the proprioceptors are integrated with the signal induced by foot–ground contact and input from the rhythm pattern generator; a muscle activation signal is produced accordingly. Weights of connection in the neural network are optimized using a genetic algorithm, thus maximizing walking distance and minimizing energy consumption. The generated walking pattern is in remarkably good agreement with that of actual human walking, indicating that the locomotory pattern could be generated automatically, according to the musculo-skeletal structures and the connections of the peripheral nervous system, particularly due to the reciprocal innervation in the muscle spindles. Using the proposed model, the flow of sensory-motor information during locomotion is estimated and a possible neuro-control mechanism is discussed. Received: 03 December 1998 / Accepted in revised form: 09 June 2000     

The discontinuous nature of motor execution II. Merging discrete and rhythmic movements in a single-joint system -- the phase entrainment effect

 Initiation of rapid discrete flexion movements is significantly altered when a secondary rhythmic movement is performed simultaneously with the same limb; the onset of a stimulus-evoked discrete movement tends to occur time-locked to the oscillation: i.e., the rhythmic movement entrains the discrete response. This nonlinear interaction may reflect a specific principle of coordination of motor tasks which are simultaneously executed with the same effector. This part II of a tripartite research report on such single-muscle multiple-task coordination investigates the contribution of the dynamic properties of the muscle and its reflex circuitry to phase entrainment. Assuming a simple threshold-linear relationship between the control signals generated by the central nervous system and the observable kinematic and electromyographic signals, a secondary rhythmic movement will cause an additional phase-dependent delay between the central “go” command and the first observable change in actual kinematics of the compound movement. Several indicators for such threshold-linear interaction are derived and tested on real data obtained in psychophysical experiments. Four healthy subjects performed rapid lateral abductions of the index finger in response to a visual “go” signal. During a portion of the experiments, subjects produced additional low-amplitude oscillatory movements before stimulus presentation with either the same finger (one-handed task), or with the index finger of the other hand (two-handed task). Results showed phase entrainment and modulation of reaction times when the cyclic and the discrete movements were simultaneously executed by the same finger. But there was no entrainment in the bimanual execution of the tasks. The model was capable of reproducing the observed effects. It is concluded that coordination of voluntary movements which are concurrently performed by the same effector involves specific discontinuous operations, which represents an essential part of the mechanism of motor coordination. Phase entrainment reflects this characteristic discontinuous behavior of the lower stages of motor execution and does not necessarily require nonlinear interaction of motor commands at higher levels of motor processing. Received: 5 September 2001 / Accepted in revised form: 19 December 2001     

The Effects of Rhythmicity and Amplitude on Transfer of Motor Learning

We perform rhythmic and discrete arm movements on a daily basis, yet the motor control literature is not conclusive regarding the mechanisms controlling these movements; does a single mechanism generate both movement types, or are they controlled by separate mechanisms? A recent study reported partial asymmetric transfer of learning from discrete movements to rhythmic movements. Other studies have shown transfer of learning between large-amplitude to small-amplitude movements. The goal of this study is to explore which aspect is important for learning to be transferred from one type of movement to another: rhythmicity, amplitude or both. We propose two hypotheses: (1) Rhythmic and discrete movements are generated by different mechanisms; therefore we expect to see a partial or no transfer of learning between the two types of movements; (2) Within each movement type (rhythmic/discrete), there will be asymmetric transition of learning from larger movements to smaller ones. We used a learning-transfer paradigm, in which 70 participants performed flexion/extension movements with their forearm, and switched between types of movement, which differed in amplitude and/or rhythmicity. We found partial transfer of learning between discrete and rhythmic movements, and an asymmetric transfer of learning from larger movements to smaller movements (within the same type of movement). Our findings suggest that there are two different mechanisms underlying the generation of rhythmic and discrete arm movements, and that practicing on larger movements helps perform smaller movements; the latter finding might have implications for rehabilitation.     

Resonance tuning in a neuro-musculo-skeletal model of the forearm

In rhythmic movements, humans activate their muscles in a robust and energy efficient way. These activation patterns are oscillatory and seem to originate from neural networks in the spinal cord, called central pattern generators (CPGs). Evidence for the existence of CPGs was found for instance in lampreys, cats and rats. There are indications that CPGs exist in humans as well, but this is not proven yet. Energy efficiency is achieved by resonance tuning: the central nervous system is able to tune into the resonance frequency of the limb, which is determined by the local reflex gains. The goal of this study is to investigate if the existence of a CPG in the human spine can explain the resonance tuning behavior, observed in human rhythmic limb movement. A neuro-musculo-skeletal model of the forearm is proposed, in which a CPG is organized in parallel to the local reflexloop. The afferent and efferent connections to the CPG are based on clues about the organization of the CPG, found in literature. The model is kept as simple as possible (i.e., lumped muscle models, groups of neurons are lumped into half-centers, simple reflex model), but incorporates enough of the essential dynamics to explain behavior—such as resonance tuning—in a qualitative way. Resonance tuning is achieved above, at and below the endogenous frequency of the CPG in a highly non-linear neuro- musculo-skeletal model. Afferent feedback of muscle lengthening to the CPG is necessary to accomplish resonance tuning above the endogenous frequency of the CPG, while feedback of muscle velocity is necessary to compensate for the phase lag, caused by the time delay in the loop coupling the limb to the CPG. This afferent feedback of muscle lengthening and velocity represents the Ia and II fibers, which—according to literature—is the input to the CPG. An internal process of the CPG, which integrates the delayed muscle lengthening and feeds it to the half-center model, provides resonance tuning below the endogenous frequency. Increased co-contraction makes higher movement frequencies possible. This agrees with studies of rhythmic forearm movements, which have shown that co-contraction increases with movement frequency. Robustness against force perturbations originates mainly from the CPG and the local reflex loop. The CPG delivers an increasing part of the necessary muscle activation for increasing perturbation size. As far as we know, the proposed neuro-musculo-skeletal model is the first that explains the observed resonance tuning in human rhythmic limb movement.     

Coordinated network functioning in the spinal cord: An evolutionary perspective

The successful achievement of harmonious locomotor movement results from the integrated operation of all body segments. Here, we will review current knowledge on the functional organization of spinal networks involved in mammalian locomotion. Attention will not simply be restricted to hindlimb muscle control, but by also considering the necessarily coordinated activation of trunk and forelimb muscles, we will try to demonstrate that while there has been a progressive increase in locomotor system complexity during evolution, many basic organizational features have been preserved across the spectrum from lower vertebrates through to humans. Concerning the organization of axial neuronal networks that control trunk muscles, it has been found across the vertebrate range that during locomotor movement a motor wave travels longitudinally in the spinal cord via the coupling of rhythmic segmental networks. For hindlimb activation it has been found in all species studied that the rostral lumbar segments contain the key elements for pattern generation. We also showed that rhythmic arm movements are under the control of cervical forelimb generators in quadrupeds as well as in human. Finally, it is highlighted that the coordination of quadrupedal movements during locomotion derives principally from an asymmetrical coordinating influence occurring in the caudo-rostral direction from the lumbar hindlimb networks.     

A mathematical modeling study of inter-segmental coordination during stick insect walking

The biomechanical conditions for walking in the stick insect require a modeling approach that is based on the control of pairs of antagonistic motoneuron (MN) pools for each leg joint by independent central pattern generators (CPGs). Each CPG controls a pair of antagonistic MN pools. Furthermore, specific sensory feedback signals play an important role in the control of single leg movement and in the generation of inter-leg coordination or the interplay between both tasks. Currently, however, no mathematical model exists that provides a theoretical approach to understanding the generation of coordinated locomotion in such a multi-legged locomotor system. In the present study, I created such a theoretical model for the stick insect walking system, which describes the MN activity of a single forward stepping middle leg and helps to explain the neuronal mechanisms underlying coordinating information transfer between ipsilateral legs. In this model, CPGs that belong to the same leg, as well as those belonging to different legs, are connected by specific sensory feedback pathways that convey information about movements and forces generated during locomotion. The model emphasizes the importance of sensory feedback, which is used by the central nervous system to enhance weak excitatory and inhibitory synaptic connections from front to rear between the three thorax-coxa-joint CPGs. Thereby the sensory feedback activates caudal pattern generation networks and helps to coordinate leg movements by generating in-phase and out-of-phase thoracic MN activity.     

A model of neuro-musculo-skeletal system for human locomotion under position constraint condition

The human locomotion was studied on the basis of the interaction of the musculo-skeletal system, the neural system and the environment. A mathematical model of human locomotion under position constraint condition was established. Besides the neural rhythm generator, the posture controller and the sensory system, the environment feedback controller and the stability controller were taken into account in the model. The environment feedback controller was proposed for two purposes, obstacle avoidance and target position control of the swing foot. The stability controller was proposed to imitate the self-balancing ability of a human body and improve the stability of the model. In the stability controller, the ankle torque was used to control the velocity of the body gravity center. A prediction control algorithm was applied to calculate the torque magnitude of the stability controller. As an example, human stairs climbing movement was simulated and the results were given. The simulation result proved that the mathematical modeling of the task was successful.     

Are interlimb interactions disturbed in patients with Parkinson’s disease? A study under unloading conditions

During natural human locomotion, neural connections are activated that are typical of regulation of the quadrupedal walking. The interaction between the neural networks generating rhythmic movements of the upper and lower limbs depends on tonic state of each of these networks regulated by motor signals from the brain. Distortion of these signals in patients with Parkinson’s disease (PD) may lead to disruption of the interlimb interactions. We examined the effect of movements of the limbs of one girdle on the parameters of the motor activity of another limb girdle at their joint cyclic movements under the conditions of arm and leg unloading in 17 patients with PD and 16 healthy subjects. We have shown that, in patients, the effect of voluntary and passive movements of arms, as well as the active movement of the distal parts of arms, on the voluntary movement of legs is weak, while in healthy subjects, the effect of arm movements on the parameters of voluntary stepping is significant. The effect of arm movements on the activation of the involuntary stepping by vibrational stimulation of-legs in patients was absent, while in healthy subjects, the motor activity of arms increased the possibility of involuntary rhythmic movements activation. Differences in the effect of leg movements on the rhythmic movements of arms were found in both patients and healthy subjects. The interlimb interaction appeared after drug administration. However, the effect of the drug was not sufficient for the recovery of normal state of the neural networks in patients. In PD patients, neural networks generating stepping rhythm have an increased tonic activity, which prevents the activation and appearance of involuntary rhythmic movements facilitating the effects of arms on legs.     

A mathematical model of adaptive behavior in quadruped locomotion

Locomotion involves repetitive movements and is often executed unconsciously and automatically. In order to achieve smooth locomotion, the coordination of the rhythms of all physical parts is important. Neurophysiological studies have revealed that basic rhythms are produced in the spinal network called, the central pattern generator (CPG), where some neural oscillators interact to self-organize coordinated rhythms. We present a model of the adaptation of locomotion patterns to a variable environment, and attempt to elucidate how the dynamics of locomotion pattern generation are adjusted by the environmental changes. Recent experimental results indicate that decerebrate cats have the ability to learn new gait patterns in a changed environment. In those experiments, a decerebrate cat was set on a treadmill consisting of three moving belts. This treadmill provides a periodic perturbation to each limb through variation of the speed of each belt. When the belt for the left forelimb is quickened, the decerebrate cat initially loses interlimb coordination and stability, but gradually recovers them and finally walks with a new gait. Based on the above biological facts, we propose a CPG model whose rhythmic pattern adapts to periodic perturbation from the variable environment. First, we design the oscillator interactions to generate a desired rhythmic pattern. In our model, oscillator interactions are regarded as the forces that generate the desired motion pattern. If the desired pattern has already been realized, then the interactions are equal to zero. However, this rhythmic pattern is not reproducible when there is an environmental change. Also, if we do not adjust the rhythmic dynamics, the oscillator interactions will not be zero. Therefore, in our adaptation rule, we adjust the memorized rhythmic pattern so as to minimize the oscillator interactions. This rule can describe the adaptive behavior of decerebrate cats well. Finally, we propose a mathematical framework of an adaptation in rhythmic motion. Our framework consists of three types of dynamics: environmental, rhythmic motion, and adaptation dynamics. We conclude that the time scale of adaptation dynamics should be much larger than that of rhythmic motion dynamics, and the repetition of rhythmic motions in a stable environment is important for the convergence of adaptation. Received: 10 July 1997 / Accepted in revised form: 13 March 1998     

Analytic analysis of the force sharing among synergistic muscles in one- and two-degree-of-freedom models

Mathematical optimization of specific cost functions has been used in theoretical models to calculate individual muscle forces. Measurements of individual muscle forces and force sharing among individual muscles show an intensity-dependent, non-linear behavior. It has been demonstrated that the force sharing between the cat Gastrocnemius, Plantaris and Soleus shows distinct loops that change orientation systematically depending on the intensity of the movement. The purpose of this study was to prove whether or not static, non-linear optimization could inherently predict force sharing loops between agonistic muscles. Using joint moment data from a step cycle of cat locomotion, the forces in three cat ankle plantar flexors (Gastrocnemius, Plantaris and Soleus) were calculated using two popular optimization algorithms and two musculo-skeletal models. The two musculo-skeletal models included a one-degree-of-freedom model that considered the ankle joint exclusively and a two-degree-of-freedom model that included the ankle and the knee joint. The main conclusion of this study was that solutions of the one-degree-of-freedom model do not guarantee force-sharing loops, but the two-degree-of-freedom model predicts force-sharing loops independent of the specific values of the input parameters for the muscles and the musculo-skeletal geometry. The predicted force-sharing loops were found to be a direct result of the loops formed by the knee and ankle moments in a moment-moment graph.     

Weight-Bearing Locomotion in the Developing Opossum,Monodelphis domestica following Spinal Transection: Remodeling of Neuronal Circuits Caudal to Lesion

Complete spinal transection in the mature nervous system is typically followed by minimal axonal repair, extensive motor paralysis and loss of sensory functions caudal to the injury. In contrast, the immature nervous system has greater capacity for repair, a phenomenon sometimes called the infant lesion effect. This study investigates spinal injuries early in development using the marsupial opossum Monodelphis domestica whose young are born very immature, allowing access to developmental stages only accessible in utero in eutherian mammals. Spinal cords of Monodelphis pups were completely transected in the lower thoracic region, T10, on postnatal-day (P)7 or P28 and the animals grew to adulthood. In P7-injured animals regrown supraspinal and propriospinal axons through the injury site were demonstrated using retrograde axonal labelling. These animals recovered near-normal coordinated overground locomotion, but with altered gait characteristics including foot placement phase lags. In P28-injured animals no axonal regrowth through the injury site could be demonstrated yet they were able to perform weight-supporting hindlimb stepping overground and on the treadmill. When placed in an environment of reduced sensory feedback (swimming) P7-injured animals swam using their hindlimbs, suggesting that the axons that grew across the lesion made functional connections; P28-injured animals swam using their forelimbs only, suggesting that their overground hindlimb movements were reflex-dependent and thus likely to be generated locally in the lumbar spinal cord. Modifications to propriospinal circuitry in P7- and P28-injured opossums were demonstrated by changes in the number of fluorescently labelled neurons detected in the lumbar cord following tracer studies and changes in the balance of excitatory, inhibitory and neuromodulatory neurotransmitter receptors’ gene expression shown by qRT-PCR. These results are discussed in the context of studies indicating that although following injury the isolated segment of the spinal cord retains some capability of rhythmic movement the mechanisms involved in weight-bearing locomotion are distinct.     

A proprioceptive neuromechanical theory of crawling

The locomotion of many soft-bodied animals is driven by the propagation of rhythmic waves of contraction and extension along the body. These waves are classically attributed to globally synchronized periodic patterns in the nervous system embodied in a central pattern generator (CPG). However, in many primitive organisms such as earthworms and insect larvae, the evidence for a CPG is weak, or even non-existent. We propose a neuromechanical model for rhythmically coordinated crawling that obviates the need for a CPG, by locally coupling the local neuro-muscular dynamics in the body to the mechanics of the body as it interacts frictionally with the substrate. We analyse our model using a combination of analytical and numerical methods to determine the parameter regimes where coordinated crawling is possible and compare our results with experimental data. Our theory naturally suggests mechanisms for how these movements might arise in developing organisms and how they are maintained in adults, and also suggests a robust design principle for engineered motility in soft systems.     

Enhanced locomotion caused by loss of the Drosophila DEG/ENaC protein Pickpocket1

Coordination of rhythmic locomotion depends upon a precisely balanced interplay between central and peripheral control mechanisms. Although poorly understood, peripheral proprioceptive mechanosensory input is thought to provide information about body position for moment-to-moment modifications of central mechanisms mediating rhythmic motor output. Pickpocket1 (PPK1) is a Drosophila subunit of the epithelial sodium channel (ENaC) family displaying limited expression in multiple dendritic (md) sensory neurons tiling the larval body wall and a small number of bipolar neurons in the upper brain. ppk1 null mutant larvae had normal external touch sensation and md neuron morphology but displayed striking alterations in crawling behavior. Loss of PPK1 function caused an increase in crawling speed and an unusual straight path with decreased stops and turns relative to wild-type. This enhanced locomotion resulted from sustained peristaltic contraction wave cycling at higher frequency with a significant decrease in pause period between contraction cycles. The mutant phenotype was rescued by a wild-type PPK1 transgene and duplicated by expressing a ppk1RNAi transgene or a dominant-negative PPK1 isoform. These results demonstrate that the PPK1 channel plays an essential role in controlling rhythmic locomotion and provide a powerful genetic model system for further analysis of central and peripheral control mechanisms and their role in movement disorders.     

Rhythmic dynamics and synchronization via dimensionality reduction: application to human gait

Reliable characterization of locomotor dynamics of human walking is vital to understanding the neuromuscular control of human locomotion and disease diagnosis. However, the inherent oscillation and ubiquity of noise in such non-strictly periodic signals pose great challenges to current methodologies. To this end, we exploit the state-of-the-art technology in pattern recognition and, specifically, dimensionality reduction techniques, and propose to reconstruct and characterize the dynamics accurately on the cycle scale of the signal. This is achieved by deriving a low-dimensional representation of the cycles through global optimization, which effectively preserves the topology of the cycles that are embedded in a high-dimensional Euclidian space. Our approach demonstrates a clear advantage in capturing the intrinsic dynamics and probing the subtle synchronization patterns from uni/bivariate oscillatory signals over traditional methods. Application to human gait data for healthy subjects and diabetics reveals a significant difference in the dynamics of ankle movements and ankle-knee coordination, but not in knee movements. These results indicate that the impaired sensory feedback from the feet due to diabetes does not influence the knee movement in general, and that normal human walking is not critically dependent on the feedback from the peripheral nervous system.     

A model of handwriting

The research reported here is concerned with hand trajectory planning for the class of movements involved in handwriting. Previous studies show that the kinematics of human two-joint arm movements in the horizontal plane can be described by a model which is based on dynamic minimization of the square of the third derivative of hand position (jerk), integrated over the entire movement. We extend this approach to both the analysis and the synthesis of the trajectories occurring in the generation of handwritten characters. Several basic strokes are identified and possible stroke concatenation rules are suggested. Given a concise symbolic representation of a stroke shape, a simple algorithm computes the complete kinematic specification of the corresponding trajectory. A handwriting generation model based on a kinematics from shape principle and on dynamic optimization is formulated and tested. Good qualitative and quantitative agreement was found between subject recordings and trajectories generated by the model. The simple symbolic representation of hand motion suggested here may permit the central nervous system to learn, store and modify motor action plans for writing in an efficient manner.     

Kinematics of the Coordination of Pointing during Locomotion

In natural motor behaviour arm movements, such as pointing or reaching, often need to be coordinated with locomotion. The underlying coordination patterns are largely unexplored, and require the integration of both rhythmic and discrete movement primitives. For the systematic and controlled study of such coordination patterns we have developed a paradigm that combines locomotion on a treadmill with time-controlled pointing to targets in the three-dimensional space, exploiting a virtual reality setup. Participants had to walk at a constant velocity on a treadmill. Synchronized with specific foot events, visual target stimuli were presented that appeared at different spatial locations in front of them. Participants were asked to reach these stimuli within a short time interval after a “go” signal. We analysed the variability patterns of the most relevant joint angles, as well as the time coupling between the time of pointing and different critical timing events in the foot movements. In addition, we applied a new technique for the extraction of movement primitives from kinematic data based on anechoic demixing. We found a modification of the walking pattern as consequence of the arm movement, as well as a modulation of the duration of the reaching movement in dependence of specific foot events. The extraction of kinematic movement primitives from the joint angle trajectories exploiting the new algorithm revealed the existence of two distinct main components accounting, respectively, for the rhythmic and discrete components of the coordinated movement pattern. Summarizing, our study shows a reciprocal pattern of influences between the coordination patterns of reaching and walking. This pattern might be explained by the dynamic interactions between central pattern generators that initiate rhythmic and discrete movements of the lower and upper limbs, and biomechanical factors such as the dynamic gait stability.     

Modeling discrete and rhythmic movements through motor primitives: a review

Rhythmic and discrete movements are frequently considered separately in motor control, probably because different techniques are commonly used to study and model them. Yet the increasing interest in finding a comprehensive model for movement generation requires bridging the different perspectives arising from the study of those two types of movements. In this article, we consider discrete and rhythmic movements within the framework of motor primitives, i.e., of modular generation of movements. In this way we hope to gain an insight into the functional relationships between discrete and rhythmic movements and thus into a suitable representation for both of them. Within this framework we can define four possible categories of modeling for discrete and rhythmic movements depending on the required command signals and on the spinal processes involved in the generation of the movements. These categories are first discussed in terms of biological concepts such as force fields and central pattern generators and then illustrated by several mathematical models based on dynamical system theory. A discussion on the plausibility of theses models concludes the work.