Reflexes and preflexes: on the role of sensory feedback on rhythmic patterns in insect locomotion

Neuromuscular systems are stabilized and controlled by both feedforward and feedback signals. Feedforward pathways driven by central pattern generators (CPGs), in conjunction with preflexive mechanical reaction forces and nonlinear muscle properties, can produce stable stereotypical gaits. Feedback is nonetheless present in both slow and rapid running, and preflexive mechanisms can join with neural reflexes originating in proprioceptive sensors to yield robust behavior in uncertain environments. Here, we develop a single degree-of-freedom neuromechanical model representing a joint actuated by an agonist/antagonist muscle pair driven by motoneurons and a CPG in a periodic rhythm characteristic of locomotion. We consider two characteristic feedback modes: phasic and tonic. The former encodes states such as position in the timing of individual spikes, while the latter can transmit graded measures of force and other continuous variables as spike rates. We use results from phase reduction and averaging theory to predict phase relationships between CPG and motoneurons in the presence of feedback and compare them with simulations of the neuromechanical model, showing that both phasic and tonic feedback can shift motoneuronal timing and thereby affect joint motions. We find that phase changes in neural activation can cooperate with preflexive displacement and velocity effects on muscle force to compensate for externally applied forces, and that these effects qualitatively match experimental observations in the cockroach.     

Evaluating functional roles of phase resetting in generation of adaptive human bipedal walking with a physiologically based model of the spinal pattern generator

The central pattern generators (CPGs) in the spinal cord strongly contribute to locomotor behavior. To achieve adaptive locomotion, locomotor rhythm generated by the CPGs is suggested to be functionally modulated by phase resetting based on sensory afferent or perturbations. Although phase resetting has been investigated during fictive locomotion in cats, its functional roles in actual locomotion have not been clarified. Recently, simulation studies have been conducted to examine the roles of phase resetting during human bipedal walking, assuming that locomotion is generated based on prescribed kinematics and feedback control. However, such kinematically based modeling cannot be used to fully elucidate the mechanisms of adaptation. In this article we proposed a more physiologically based mathematical model of the neural system for locomotion and investigated the functional roles of phase resetting. We constructed a locomotor CPG model based on a two-layered hierarchical network model of the rhythm generator (RG) and pattern formation (PF) networks. The RG model produces rhythm information using phase oscillators and regulates it by phase resetting based on foot-contact information. The PF model creates feedforward command signals based on rhythm information, which consists of the combination of five rectangular pulses based on previous analyses of muscle synergy. Simulation results showed that our model establishes adaptive walking against perturbing forces and variations in the environment, with phase resetting playing important roles in increasing the robustness of responses, suggesting that this mechanism of regulation may contribute to the generation of adaptive human bipedal locomotion.     

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.     

An Approach for Adaptive Limbless Locomotion Using a CPG-Based Reflex Mechanism

Animals＇ free movement in natural environments has attracted many researchers to explore control methods for bio-inspired robots. This paper presents a novel reflex mechanism based on a Central Pattern Generator （CPG） for adaptive locomotion of limbless robots. First, inspired by the concept of reflex arc, the reflex mechanism is designed on a connectionist CPG model. Since the CPG model inspired by the spinal cord of lampreys is developed at the neuron level, it provides a possible natural solution for sensory reflex integration. Therefore, sensory neurons that bridge the external stimuli and the CPG model, together with the concept of reflex arc, are utilized for designing the sensory reflex mechanism. Then, a border reflex and a body reflex are further developed and applied on the ends and the middle part of a limbless robot, respectively. Finally, a ball hitting scenario and a corridor passing scenario are designed to verify the proposed method. Results of simulations and on-site experiments show the feasibility and effectiveness of the reflex mechanism in realizing fast response and adaptive limbless locomotion.     

Multi-layered multi-pattern CPG for adaptive locomotion of humanoid robots

In this paper, we present an extended mathematical model of the central pattern generator (CPG) in the spinal cord. The proposed CPG model is used as the underlying low-level controller of a humanoid robot to generate various walking patterns. Such biological mechanisms have been demonstrated to be robust in locomotion of animal. Our model is supported by two neurophysiological studies. The first study identified a neural circuitry consisting of a two-layered CPG, in which pattern formation and rhythm generation are produced at different levels. The second study focused on a specific neural model that can generate different patterns, including oscillation. This neural model was employed in the pattern generation layer of our CPG, which enables it to produce different motion patterns—rhythmic as well as non-rhythmic motions. Due to the pattern-formation layer, the CPG is able to produce behaviors related to the dominating rhythm (extension/flexion) and rhythm deletion without rhythm resetting. The proposed multi-layered multi-pattern CPG model (MLMP-CPG) has been deployed in a 3D humanoid robot (NAO) while it performs locomotion tasks. The effectiveness of our model is demonstrated in simulations and through experimental results.     

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.     

Modular neuromuscular control of human locomotion by central pattern generator

The central pattern generators (CPG) in the spinal cord are thought to be responsible for producing the rhythmic motor patterns during rhythmic activities. For locomotor tasks, this involves much complexity, due to a redundant system of muscle actuators with a large number of highly nonlinear muscles. This study proposes a reduced neural control strategy for the CPG, based on modular organization of the co-active muscles, i.e., muscle synergies. Four synergies were extracted from the EMG data of the major leg muscles of two subjects, during two gait trials each, using non-negative matrix factorization algorithm. A Matsuoka׳s four-neuron CPG model with mutual inhibition, was utilized to generate the rhythmic activation patterns of the muscle synergies, using the hip flexion angle and foot contact force information from the sensory afferents as inputs. The model parameters were tuned using the experimental data of one gait trial, which resulted in a good fitting accuracy (RMSEs between 0.0491 and 0.1399) between the simulation and experimental synergy activations. The model׳s performance was then assessed by comparing its predictions for the activation patterns of the individual leg muscles during locomotion with the relevant EMG data. Results indicated that the characteristic features of the complex activation patterns of the muscles were well reproduced by the model for different gait trials and subjects. In general, the CPG- and muscle synergy-based model was promising in view of its simple architecture, yet extensive potentials for neuromuscular control, e.g., resolving redundancies, distributed and fast control, and modulation of locomotion by simple control signals.     

Analysis of the gait generation principle by a simulated quadruped model with a CPG incorporating vestibular modulation

This study aims to understand the principles of gait generation in a quadrupedal model. It is difficult to determine the essence of gait generation simply by observation of the movement of complicated animals composed of brains, nerves, muscles, etc. Therefore, we build a planar quadruped model with simplified nervous system and mechanisms, in order to observe its gaits under simulation. The model is equipped with a mathematical central pattern generator (CPG), consisting of four coupled neural oscillators, basically producing a trot pattern. The model also contains sensory feedback to the CPG, measuring the body tilt (vestibular modulation). This spontaneously gives rise to an unprogrammed lateral walk at low speeds, a transverse gallop while running, in addition to trotting at a medium speed. This is because the body oscillation exhibits a double peak per leg frequency at low speeds, no peak (little oscillation) at medium speeds, and a single peak while running. The body oscillation autonomously adjusts the phase differences between the neural oscillators via the feedback. We assume that the oscillations of the four legs produced by the CPG and the body oscillation varying according to the current speed are synchronized along with the varied phase differences to keep balance during locomotion through postural adaptation via the vestibular modulation, resulting in each gait. We succeeded in determining a single simple principle that accounts for gait transition from walking to trotting to galloping, even without brain control, complicated leg mechanisms, or a flexible trunk.     

Sensory Feedback Mechanism Underlying Entrainment of Central Pattern Generator to Mechanical Resonance

Rhythmic body motions observed in animal locomotion are known to be controlled by neuronal circuits called central pattern generators (CPGs). It appears that CPGs are energy efficient controllers that cooperate with biomechanical and environmental constraints through sensory feedback. In particular, the CPGs tend to induce rhythmic motion of the body at a natural frequency, i.e., the CPGs are entrained to a mechanical resonance by sensory feedback. The objective of this paper is to uncover the mechanism of entrainment resulting from the dynamic interaction of the CPG and mechanical system. We first develop multiple CPG models for the reciprocal inhibition oscillator (RIO) and examine through numerical experiments whether they can be entrained to a simple pendulum. This comparative study identifies the neuronal properties essential for the entrainment. We then analyze the simplest model that captures the essential dynamics via the method of harmonic balance. It is shown that robust entrainment results from a strong, positive-feedback coupling of a lightly damped mechanical system and the RIO consisting of neurons with the complete adaptation property     

Central pattern generators: some principles learned from invertebrate model systems.

1. Central pattern generators (CPGs) underlie a wide variety of rhythmic behaviours such as locomotion and respiration in most multi-cellular organisms. 2. The CPG's are capable of generating a patterned output without phasic sensory input. 3. The organization of the CPG is due to both intrinsic properties of the individual neurons and their network interactions. 4. To gain an understanding of the mechanisms which underlie rhythmicity a CPG has been reconstructed in culture. This will allow investigators to test directly the mechanisms underlying the generation of rhythmic output and will allow the direct testing of the mechanisms by which various modulators affect the CPG.     

Retuning of segmental responses to peripheral stimulation in cats during fictitious locomotion

Segmental responses of the lumbosacral region of the spinal cord to peripheral afferent stimulation were studied in decorticated, immobilized cats before and during fictitious locomotion. The appearance of fictitious locomotion was accompanied by a tonic increase in the N₁-component of the dorsal cord potential and dorsal root potential. Against the background of this tonic increase, modulation of these responses depending on the phase of fictitious locomotion was observed. When the N₁-component and dorsal root potential were evoked at the end of the "extension" phase and at the beginning of the "flexion" phase their amplitude was greater, but when they were evoked at the end of the "flexion" phase and the beginning of the "extension" phase it was smaller. Polysynaptic and monosynaptic reflex response of motoneurons exhibited the same phase dependence during fictitious locomotion. The mechanisms and physiological importance of this retuning of segmental responses are discussed.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 13, No. 3, pp. 283–291, May–June, 1981.     

Experiments and models of sensorimotor interactions during locomotion

During locomotion sensory information from cutaneous and muscle receptors is continuously integrated with the locomotor central pattern generator (CPG) to generate an appropriate motor output to meet the demands of the environment. Sensory signals from peripheral receptors can strongly impact the timing and amplitude of locomotor activity. This sensory information is gated centrally depending on the state of the system (i.e., rest vs. locomotion) but is also modulated according to the phase of a given task. Consequently, if one is to devise biologically relevant walking models it is imperative that these sensorimotor interactions at the spinal level be incorporated into the control system.     

Hopping and swimming in the leopard frog,Rana pipiens: I. Step cycles and kinematics

This study presents a model for the step cycle patterns used during both hopping and swimming by the leopard frog, Rana pipiens. The two behaviors are essentially similar in movement pattern and in the ways they are modified from quadrupedal gaits. In hopping, there is marked hind limb extension throughout stance. The swing begins with a suspension equivalent to the leap that occurs in a galloping or bounding quadruped. Following suspension, as the frog descends from the apex of its leap, the hind limbs remain posterior and in line with the spine while they flex. Near the end of flexion, there is a rapid downward rotation of the hindquarters to bring the hind feet underneath the body. This movement utilizes the planted forelimb as a pivot. A similar pattern of movement occurs in swimming; the stance (propulsion) phase involves extension at all hind limb joints. The swing (recovery) phase begins with the hind feet fully extended and includes a protracted gliding phase, equivalent to the suspension in the hop. The hind limb then recovers to its initial position during a flexion phase. Since there is no landing and the hind limbs remain lateral rather than ventral to the pelvis, less flexion occurs in the spine or the limb joints. In both behaviors, the extensor muscles of hip (M. semimembranosus), knee (M. cruralis), and ankle (M. plantaris longus) achieve their longest lengths, when they likely can produce near maximal force, at the beginning of extension. All three muscles shorten during extension, but, because they are multiple-joint muscles, the amount of shortening is relatively small (≈ 15%). Hopping and swimming in frogs are comparable asymmetrical gaits with the same relative contact intervals (25% of stride). The step cycles in both gaits are modified from quadrupedal locomotion in the same ways: by 1) loss of knee and ankle extension toward the ground prior to landing (or end of flexion in swimming), 2) loss of a yield phase on landing (or end of flexion in swimming), and 3) inclusion of extended suspensions in both gaits. © 1996 Wiley-Liss, Inc.     

Quantitative assessment of the accuracy for three interpolation techniques in kinematic analysis of human movement

Marker obstruction during human movement analyses requires interpolation to reconstruct missing kinematic data. This investigation quantifies errors associated with three interpolation techniques and varying interpolated durations. Right ulnar styloid kinematics from 13 participants performing manual wheelchair ramp ascent were reconstructed using linear, cubic spline and local coordinate system (LCS) interpolation from 11-90% of one propulsive cycle. Elbow angles (flexion/extension and pronation/supination) were calculated using real and reconstructed kinematics. Reconstructed kinematics produced maximum elbow flexion/extension errors of 37.1 (linear), 23.4 (spline) and 9.3 (LCS) degrees. Reconstruction errors are unavoidable [minimum errors of 6.7?mm (LCS); 0.29?mm (spline); 0.42?mm (linear)], emphasising careful motion capture system setup must be performed to minimise data interpolation. For the observed movement, LCS-based interpolation (average error of 14.3?mm; correlation of 0.976 for elbow flexion/extension) was most suitable for reconstructing durations longer than 200?ms. Spline interpolation was superior for shorter durations.     

A comparison of resonance tuning with positive versus negative sensory feedback

We used a computational model of rhythmic movement to analyze how the connectivity of sensory feedback affects the tuning of a closed-loop neuromechanical system to the mechanical resonant frequency (ω_r). Our model includes a Matsuoka half-center oscillator for a central pattern generator (CPG) and a linear, one-degree-of-freedom system for a mechanical component. Using both an open-loop frequency response analysis and closed-loop simulations, we compared resonance tuning with four different feedback configurations as the mechanical resonant frequency, feedback gain, and mechanical damping varied. The feedback configurations consisted of two negative and two positive feedback connectivity schemes. We found that with negative feedback, resonance tuning predominantly occurred when ω_r was higher than the CPG’s endogenous frequency (ω_CPG). In contrast, with the two positive feedback configurations, resonance tuning only occurred if ω_r was lower than ω_CPG. Moreover, the differences in resonance tuning between the two positive (negative) feedback configurations increased with increasing feedback gain and with decreasing mechanical damping. Our results indicate that resonance tuning can be achieved with positive feedback. Furthermore, we have shown that the feedback configuration affects the parameter space over which the endogenous frequency of the CPG or resonant frequency the mechanical dynamics dominates the frequency of a rhythmic movement.     

Sensory feedback in CNN-based central pattern generators

Central Pattern Generators (CPGs) are a suitable paradigm to solve the problem of locomotion control in walking robots. CPGs are able to generate feed-forward signals to achieve a proper coordination among the robot legs. In literature they are often modelled as networks of coupled nonlinear systems. However the topic of feedback in these systems is rarely addressed. On the other hand feedback is essential for locomotion. In this paper the CPG for a hexapod robot is implemented through Cellular Neural Networks (CNNs). Feedback is included in the CPG controller by exploiting the dynamic properties of the CPG motor-neurons, such as synchronization issue and local bifurcations. These universal paradigms provide the essential issues to include sensory feedback in CPG architectures based on coupled nonlinear systems. Experiments on a dynamic model of a hexapod robot are presented to validate the approach introduced.     

Corollary discharge enables proprioception from lateral line sensory feedback

Animals modulate sensory processing in concert with motor actions. Parallel copies of motor signals, called corollary discharge (CD), prepare the nervous system to process the mixture of externally and self-generated (reafferent) feedback that arises during locomotion. Commonly, CD in the peripheral nervous system cancels reafference to protect sensors and the central nervous system from being fatigued and overwhelmed by self-generated feedback. However, cancellation also limits the feedback that contributes to an animal’s awareness of its body position and motion within the environment, the sense of proprioception. We propose that, rather than cancellation, CD to the fish lateral line organ restructures reafference to maximize proprioceptive information content. Fishes’ undulatory body motions induce reafferent feedback that can encode the body’s instantaneous configuration with respect to fluid flows. We combined experimental and computational analyses of swimming biomechanics and hair cell physiology to develop a neuromechanical model of how fish can track peak body curvature, a key signature of axial undulatory locomotion. Without CD, this computation would be challenged by sensory adaptation, typified by decaying sensitivity and phase distortions with respect to an input stimulus. We find that CD interacts synergistically with sensor polarization to sharpen sensitivity along sensors’ preferred axes. The sharpening of sensitivity regulates spiking to a narrow interval coinciding with peak reafferent stimulation, which prevents adaptation and homogenizes the otherwise variable sensor output. Our integrative model reveals a vital role of CD for ensuring precise proprioceptive feedback during undulatory locomotion, which we term external proprioception.

Animals modulate sensory processing in concert with motor actions. A study of the corollary discharge in zebrafish reveals that it modulates the sensitivity of the lateral line during swimming to prevent sensor adaptation and maintain the high-quality feedback necessary for kinematic control.     

Contribution of stretch reflexes to locomotor control: a modeling study

It is known that the springlike properties of muscles provide automatic load compensation during weight bearing. How crucial is sensory control of the motor output given these basic properties of the locomotor system? To address this question, a neuromuscular model was used to test two hypotheses. (1) Stretch reflexes are too weak and too delayed to contribute significantly to weight-bearing. (2) The important contributions of sensory input involve state-dependent processing. We constructed a two-legged planar locomotor model with 9 segments, driven by 12 musculotendon actuators with Hill-type force-velocity and monotonic force-length properties. Electromyographic (EMG) profiles of the simulated muscle groups during slow level walking served as actuator activation functions. Spindle Ia and tendon organ Ib sensory inputs were represented by transfer functions with a latency of 35 ms, contributing 30% to the net EMG profile and gated to be active only when the receptor-bearing muscles were contracting. Locomotor stability was assessed by parametric variations of actuator maximum forces during locomotion in open-loop ("deafferented") trials and in trials with feedback control based on either sensory-evoked stretch reflexes or finite-state rules. We arrived at the following conclusions. (1) In the absence of sensory control, the intrinsic stiffness of limb muscles driven by a stereotyped rhythmical pattern can produce surprisingly stable gait. (2) When the level of central activity is low, the contribution of stretch reflexes to load compensation can be crucial. However, when central activity provides adequate load compensation, the contribution of stretch reflexes is less significant. (3) Finite-state control can greatly extend the adaptive capability of the locomotor system.     

Quantitative assessment of the accuracy for three interpolation techniques in kinematic analysis of human movement

Marker obstruction during human movement analyses requires interpolation to reconstruct missing kinematic data. This investigation quantifies errors associated with three interpolation techniques and varying interpolated durations. Right ulnar styloid kinematics from 13 participants performing manual wheelchair ramp ascent were reconstructed using linear, cubic spline and local coordinate system (LCS) interpolation from 11–90% of one propulsive cycle. Elbow angles (flexion/extension and pronation/supination) were calculated using real and reconstructed kinematics. Reconstructed kinematics produced maximum elbow flexion/extension errors of 37.1 (linear), 23.4 (spline) and 9.3 (LCS) degrees. Reconstruction errors are unavoidable [minimum errors of 6.7 mm (LCS); 0.29 mm (spline); 0.42 mm (linear)], emphasising careful motion capture system setup must be performed to minimise data interpolation. For the observed movement, LCS-based interpolation (average error of 14.3 mm; correlation of 0.976 for elbow flexion/extension) was most suitable for reconstructing durations longer than 200 ms. Spline interpolation was superior for shorter durations.