Neural Control of Interlimb Coordination and Gait Timing in Bipeds and Quadrupeds

1) A large body of behavioral data conceming animal and human gaits and gait transitions is simulated as emergent properties of a central pattern generator (CPG) model. The CPG model incorporates neurons obeying Hodgkin-Huxley type dynamics that interact via an on-center off-surround anatomy whose excitatory signals operate on a faster time scale than their inhibitory signals. A descending cornmand or arousal signal called a GO signal activates the gaits and controL their transitions. The GO signal and the CPG model are compared with neural data from globus pallidus and spinal cord, among other brain structures. 2) Data from human bimanual finger coordination tasks are simulated in which anti-phase oscillations at low frequencies spontaneously switch to in-phase oscillations at high frequencies, in-phase oscillations can be performed both at low and high frequencies, phase fluctuations occur at the anti-phase in-phase transition, and a "seagull effect" of larger errors occurs at intermediate phases. When driven by environmental patterns with intermediate phase relationships, the model's output exhibits a tendency to slip toward purely in-phase and anti-phase relationships as observed in humans subjects. 3) Quadruped vertebrate gaits, including the amble, the walk, all three pairwise gaits (trot, pace, and gallop) and the pronk are simulated. Rapid gait transitions are simulated in the order--walk, trot, pace, and gallop--that occurs in the cat, along with the observed increase in oscillation frequency. 4) Precise control of quadruped gait switching is achieved in the model by using GO-dependent modulation of the model's inhibitory interactions. This generates a different functional connectivity in a single CPG at different arousal levels. Such task-specific modulation of functional connectivity in neural pattern generators has been experimentally reported in invertebrates. Phase-dependent modulation of reflex gain has been observed in cats. A role for state-dependent modulation is herein predicted to occur in vertebrates for precise control of phase transitions from one gait to another. 5) The primary human gaits (the walk and the run) and elephant gaits (the amble and the walk) are sirnulated. Although these two gaits are qualitatively different, they both have the same limb order and may exhibit oscillation frequencies that overlap. The CPG model simulates the walk and the run by generating oscillations which exhibit the same phase relationships. but qualitatively different waveform shapes, at different GO signal levels. The fraction of each cycle that activity is above threshold quantitatively distinguishes the two gaits, much as the duty cycles of the feet are longer in the walk than in the run. 6) A key model properly concerns the ability of a single model CPG, that obeys a fixed set of opponent processing equations to generate both in-phase and anti-phase oscillations at different arousal levels. Phase transitions from either in-phase to anti-phase oscillations, or from anti-phase to in-phase oscillations, can occur in different parameter ranges, as the GO signal increases.

A Model of Cerebellar Adaptation of Grip Forces During Lifting

We investigated adaptive neural control of precision grip forces during object lifting. A model is presented that adjusts reactive and anticipatory grip forces to a level just above that needed to stabilize lifted objects in the hand. The model obeys priciples of cerebellar structure and function by using slip sensations as error signals to adapt phasic motor commands to tonic force generators associated with output synergies controlling grip aperture. The learned phasic commands are weight and texture-dependent. Simulations of the new curcuit model reproduce key aspects of experimental observations of force application. Over learning trials, the onset of grip force buildup comes to lead the load force buildup, and the rate-of-rise of grip force, but not load force, scales inversely with the friction of the gripped object.

From Parallel Sequence Representations to Calligraphic Control: A Conspiracy of Neural Circuits

Calligraphic writing presents a rich set of challenges to the human movement control system. These challenges include: initial learning, and recall from memory, of prescribed stroke sequences; critical timing of stroke onsets and durations; fine control of grip and contact forces; and letter-form invariance under voluntary size scaling, which entails fine control of stroke direction and amplitude during recruitment and derecruitment of musculoskeletal degrees of freedom. Experimental and computational studies in behavioral neuroscience have made rapid progress toward explaining the learning, planning and contTOl exercised in tasks that share features with calligraphic writing and drawing. This article summarizes computational neuroscience models and related neurobiological data that reveal critical operations spanning from parallel sequence representations to fine force control. Part one addresses stroke sequencing. It treats competitive queuing (CQ) models of sequence representation, performance, learning, and recall. Part two addresses letter size scaling and motor equivalence. It treats cursive handwriting models together with models in which sensory-motor tmnsformations are performed by circuits that learn inverse differential kinematic mappings. Part three addresses fine-grained control of timing and transient forces, by treating circuit models that learn to solve inverse dynamics problems.

Neural Representations for Sensory-Motor Control, III: Learning a Body-Centered Representation of 3-D Target Position

A neural model is described of how the brain may autonomously learn a body-centered representation of 3-D target position by combining information about retinal target position, eye position, and head position in real time. Such a body-centered spatial representation enables accurate movement commands to the limbs to be generated despite changes in the spatial relationships between the eyes, head, body, and limbs through time. The model learns a vector representation--otherwise known as a parcellated distributed representation--of target vergence with respect to the two eyes, and of the horizontal and vertical spherical angles of the target with respect to a cyclopean egocenter. Such a vergence-spherical representation has been reported in the caudal midbrain and medulla of the frog, as well as in psychophysical movement studies in humans. A head-centered vergence-spherical representation of foveated target position can be generated by two stages of opponent processing that combine corollary discharges of outflow movement signals to the two eyes. Sums and differences of opponent signals define angular and vergence coordinates, respectively. The head-centered representation interacts with a binocular visual representation of non-foveated target position to learn a visuomotor representation of both foveated and non-foveated target position that is capable of commanding yoked eye movementes. This head-centered vector representation also interacts with representations of neck movement commands to learn a body-centered estimate of target position that is capable of commanding coordinated arm movements. Learning occurs during head movements made while gaze remains fixed on a foveated target. An initial estimate is stored and a VOR-mediated gating signal prevents the stored estimate from being reset during a gaze-maintaining head movement. As the head moves, new estimates arc compared with the stored estimate to compute difference vectors which act as error signals that drive the learning process, as well as control the on-line merging of multimodal information.

Unsupervised Neural Network for the Control of a Mobile Robot

This article introduces an unsupervised neural architecture for the control of a mobile robot. The system allows incremental learning of the plant during robot operation, with robust performance despite unexpected changes of robot parameters such as wheel radius and inter-wheel distance. The model combines Vector associative Map (VAM) learning and associate learning, enabling the robot to reach targets at arbitrary distances without knowledge of the robot kinematics and without trajectory recording, but relating wheel velocities with robot movements.

Adaptive Neural Networks for Control of Movement Trajectories Invariant under Speed and Force Rescaling

This article describes two neural network modules that form part of an emerging theory of how adaptive control of goal-directed sensory-motor skills is achieved by humans and other animals. The Vector-Integration-To-Endpoint (VITE) model suggests how synchronous multi-joint trajectories are generated and performed at variable speeds. The Factorization-of-LEngth-and-TEnsion (FLETE) model suggests how outflow movement commands from a VITE model may be performed at variable force levels without a loss of positional accuracy. The invariance of positional control under speed and force rescaling sheds new light upon a familiar strategy of motor skill development: Skill learning begins with performance at low speed and low limb compliance and proceeds to higher speeds and compliances. The VITE model helps to explain many neural and behavioral data about trajectory formation, including data about neural coding within the posterior parietal cortex, motor cortex, and globus pallidus, and behavioral properties such as Woodworth's Law, Fitts Law, peak acceleration as a function of movement amplitude and duration, isotonic arm movement properties before and after arm-deafferentation, central error correction properties of isometric contractions, motor priming without overt action, velocity amplification during target switching, velocity profile invariance across different movement distances, changes in velocity profile asymmetry across different movement durations, staggered onset times for controlling linear trajectories with synchronous offset times, changes in the ratio of maximum to average velocity during discrete versus serial movements, and shared properties of arm and speech articulator movements. The FLETE model provides new insights into how spina-muscular circuits process variable forces without a loss of positional control. These results explicate the size principle of motor neuron recruitment, descending co-contractive compliance signals, Renshaw cells, Ia interneurons, fast automatic reactive control by ascending feedback from muscle spindles, slow adaptive predictive control via cerebellar learning using muscle spindle error signals to train adaptive movement gains, fractured somatotopy in the opponent organization of cerebellar learning, adaptive compensation for variable moment-arms, and force feedback from Golgi tendon organs. More generally, the models provide a computational rationale for the use of nonspecific control signals in volitional control, or "acts of will", and of efference copies and opponent processing in both reactive and adaptive motor control tasks.

Dynamic Programming for Optimal Control of Set-Up Scheduling with Neural Network Modifications

This paper demonstrates an optimal control solution to change of machine set-up scheduling based on dynamic programming average cost per stage value iteration as set forth by Cararnanis et. al. [2] for the 2D case. The difficulty with the optimal approach lies in the explosive computational growth of the resulting solution. A method of reducing the computational complexity is developed using ideas from biology and neural networks. A real time controller is described that uses a linear-log representation of state space with neural networks employed to fit cost surfaces.

A Self-Organizing Neural Network Model for Redundant Sensory-Motor Control, Motor Equivalence, and Tool Use

A neural network is introduced which provides a solution of the classical motor equivalence problem, whereby many different joint configurations of a redundant manipulator can all be used to realize a desired trajectory in 3-D space. To do this, the network self-organizes a mapping from motion directions in 3-D space to velocity commands in joint space. Computer simulations demonstrate that, without any additional learning, the network can generate accurate movement commands that compensate for variable tool lengths, clamping of joints, distortions of visual input by a prism, and unexpected limb perturbations. Blind reaches have also been simulated.

Equilibria and Dynamics of a Neural Network Model for Opponent Muscle Control

One of the advantages of biological skeleto-motor systems is the opponent muscle design, which in principle makes it possible to achieve facile independent control of joint angle and joint stiffness. Prior analysis of equilibrium states of a biologically-based neural network for opponent muscle control, the FLETE model, revealed that such independent control requires specialized interneuronal circuitry to efficiently coordinate the opponent force generators. In this chapter, we refine the FLETE circuit variables specification and update the equilibrium analysis. We also incorporate additional neuronal circuitry that ensures efficient opponent force generation and velocity regulation during movement.

Neural Representations for Sensory-Motor Control I: Head-Centered 3-D Target Positions from Opponent Eye Commands

This article describes how corollary discharges from outflow eye movement commands can be transformed by two stages of opponent neural processing into a head-centered representation of 3-D target position. This representation implicitly defines a cyclopean coordinate system whose variables approximate the binocular vergence and spherical horizontal and vertical angles with respect to the observer's head. Various psychophysical data concerning binocular distance perception and reaching behavior are clarified by this representation. The representation provides a foundation for learning head-centered and body-centered invariant representations of both foveated and non-foveated 3-D target positions. It also enables a solution to be developed of the classical motor equivalence problem, whereby many different joint configurations of a redundant manipulator can all be used to realize a desired trajectory in 3-D space.

A Neural Model of Surface Perception: Lightness, Anchoring, and Filling-in

This article develops a neural model of how the visual system processes natural images under variable illumination conditions to generate surface lightness percepts. Previous models have clarified how the brain can compute the relative contrast of images from variably illuminate scenes. How the brain determines an absolute lightness scale that "anchors" percepts of surface lightness to us the full dynamic range of neurons remains an unsolved problem. Lightness anchoring properties include articulation, insulation, configuration, and are effects. The model quantatively simulates these and other lightness data such as discounting the illuminant, the double brilliant illusion, lightness constancy and contrast, Mondrian contrast constancy, and the Craik-O'Brien-Cornsweet illusion. The model also clarifies the functional significance for lightness perception of anatomical and neurophysiological data, including gain control at retinal photoreceptors, and spatioal contrast adaptation at the negative feedback circuit between the inner segment of photoreceptors and interacting horizontal cells. The model retina can hereby adjust its sensitivity to input intensities ranging from dim moonlight to dazzling sunlight. A later model cortical processing stages, boundary representations gate the filling-in of surface lightness via long-range horizontal connections. Variants of this filling-in mechanism run 100-1000 times faster than diffusion mechanisms of previous biological filling-in models, and shows how filling-in can occur at realistic speeds. A new anchoring mechanism called the Blurred-Highest-Luminance-As-White (BHLAW) rule helps simulate how surface lightness becomes sensitive to the spatial scale of objects in a scene. The model is also able to process natural images under variable lighting conditions.

Adaptive Neural Models of Queuing and Timing in Fluent Action

Temporal structure in skilled, fluent action exists at several nested levels. At the largest scale considered here, short sequences of actions that are planned collectively in prefrontal cortex appear to be queued for performance by a cyclic competitive process that operates in concert with a parallel analog representation that implicitly specifies the relative priority of elements of the sequence. At an intermediate scale, single acts, like reaching to grasp, depend on coordinated scaling of the rates at which many muscles shorten or lengthen in parallel. To ensure success of acts such as catching an approaching ball, such parallel rate scaling, which appears to be one function of the basal ganglia, must be coupled to perceptual variables, such as time-to-contact. At a fine scale, within each act, desired rate scaling can be realized only if precisely timed muscle activations first accelerate and then decelerate the limbs, to ensure that muscle length changes do not under- or over-shoot the amounts needed for the precise acts. Each context of action may require a much different timed muscle activation pattern than similar contexts. Because context differences that require different treatment cannot be known in advance, a formidable adaptive engine-the cerebellum-is needed to amplify differences within, and continuosly search, a vast parallel signal flow, in order to discover contextual "leading indicators" of when to generate distinctive parallel patterns of analog signals. From some parts of the cerebellum, such signals controls muscles. But a recent model shows how the lateral cerebellum, such signals control muscles. But a recent model shows how the lateral cerebellum may serve the competitive queuing system (in frontal cortex) as a repository of quickly accessed long-term sequence memories. Thus different parts of the cerebellum may use the same adaptive engine system design to serve the lowest and the highest of the three levels of temporal structure treated. If so, no one-to-one mapping exists between levels of temporal structure and major parts of the brain. Finally, recent data cast doubt on network-delay models of cerebellar adaptive timing.

Neural Modeling and Imaging of the Cortical Interactions Underlying Syllable Production

This paper describes a neural model of speech acquisition and production that accounts for a wide range of acoustic, kinematic, and neuroimaging data concerning the control of speech movements. The model is a neural network whose components correspond to regions of the cerebral cortex and cerebellum, including premotor, motor, auditory, and somatosensory cortical areas. Computer simulations of the model verify its ability to account for compensation to lip and jaw perturbations during speech. Specific anatomical locations of the model's components are estimated, and these estimates are used to simulate fMRI experiments of simple syllable production with and without jaw perturbations.

SOVEREIGN: An Autonomous Neural System for Incrementally Learning Planned Action Sequence to Navigate Towards a Rewarded Goal

How do reactive and planned behaviors interact in real time? How are sequences of such behaviors released at appropriate times during autonomous navigation to realize valued goals? Controllers for both animals and mobile robots, or animats, need reactive mechanisms for exploration, and learned plans to reach goal objects once an environment becomes familiar. The SOVEREIGN (Self-Organizing, Vision, Expectation, Recognition, Emotion, Intelligent, Goaloriented Navigation) animat model embodies these capabilities, and is tested in a 3D virtual reality environment. SOVEREIGN includes several interacting subsystems which model complementary properties of cortical What and Where processing streams and which clarify similarities between mechanisms for navigation and arm movement control. As the animat explores an environment, visual inputs are processed by networks that are sensitive to visual form and motion in the What and Where streams, respectively. Position-invariant and sizeinvariant recognition categories are learned by real-time incremental learning in the What stream. Estimates of target position relative to the animat are computed in the Where stream, and can activate approach movements toward the target. Motion cues from animat locomotion can elicit head-orienting movements to bring a new target into view. Approach and orienting movements are alternately performed during animat navigation. Cumulative estimates of each movement are derived from interacting proprioceptive and visual cues. Movement sequences are stored within a motor working memory. Sequences of visual categories are stored in a sensory working memory. These working memories trigger learning of sensory and motor sequence categories, or plans, which together control planned movements. Predictively effective chunk combinations are selectively enhanced via reinforcement learning when the animat is rewarded. Selected planning chunks effect a gradual transition from variable reactive exploratory movements to efficient goal-oriented planned movement sequences. Volitional signals gate interactions between model subsystems and the release of overt behaviors. The model can control different motor sequences under different motivational states and learns more efficient sequences to rewarded goals as exploration proceeds.

Quadruped Gait Transitions from a Neural Pattern Generator with Arousal Modulated Interactions

A four-channel neural pattern generator is described in which both the frequency and the relative phase of oscillations are controlled by a scalar arousal or GO signal. The generator is used to simulate quadruped gaits; in particular, rapid transitions are simulated in the order - walk, trot, pace, and gallop - that occurs in the cat. Precise switching control is achieved by using an arousal dependent modulation of the model's inhibitory interactions. This modulation generates a different functional connectivity in a single network at different arousal levels.