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Motor control

Motor control refers to the regulation of movement by the nervous system through the coordinated activation of muscles, encompassing both reflexive and voluntary actions to achieve purposeful behaviors in interaction with the environment.^[1] This process integrates sensory feedback, internal predictive models, and hierarchical neural structures to ensure precision, adaptability, and efficiency in tasks ranging from basic locomotion to complex manipulations.^[2] At its core, motor control operates within a hierarchical framework, where lower levels such as spinal circuits and brainstem nuclei handle reflexive and rhythmic patterns like walking via central pattern generators, while higher levels including the motor cortex, basal ganglia, and cerebellum refine goal-directed actions through planning and error correction.^[3] This organization allows for information factorization, segregating sensory inputs (e.g., proprioception at low levels and vision at high levels) to enable modular, partially autonomous control that persists even after disruptions to higher centers, as seen in decorticate animals retaining basic locomotion.^[3] The basal ganglia facilitate action selection, the cerebellum predicts sensory outcomes using forward models, and the primary motor cortex executes fine-tuned commands, all interconnected to manage multi-joint synergies and temporal abstractions for long-term goal pursuit.^[3]^[1] Key theoretical models underpin this system, including the optimal feedback control (OFC) framework, which posits that movements minimize a cost function balancing accuracy, effort, and noise via state estimation, inverse models for command generation, and forward models for prediction.^[4] Complementary theories like the equilibrium-point hypothesis describe control through shifts in muscle length thresholds, explaining both voluntary and spastic movements, while the uncontrolled manifold approach addresses redundancy by stabilizing task-relevant variables amid variability.^[2] These models highlight the brain's use of Bayesian filtering for state estimation and predictive coding to anticipate sensory consequences, with neural implementations in the cerebellum for forward modeling and the neocortex for integration.^[4] Developmentally, motor control matures from reflexive self-movements in infancy to adult precision by adolescence, driven by synaptogenesis and plasticity that strengthens connections through learning.^[1] Disruptions in motor control manifest in various neurological disorders, underscoring its clinical significance; for instance, basal ganglia dysfunction in Parkinson's disease leads to hypokinetic symptoms like bradykinesia and tremor, while cerebellar lesions impair coordination and timing.^[5] Stroke affecting upper motor neurons causes weakness and spasticity, and conditions like amyotrophic lateral sclerosis (ALS) degenerate motor neurons, progressively impairing voluntary movement.^[6]^[7] Rehabilitation leverages neuroplasticity through therapies like brain-machine interfaces to restore function, emphasizing motor control's role in daily mobility and quality of life.^[1]

Neural Foundations

Motor Units and Force Generation

A motor unit consists of a single alpha motor neuron located in the spinal cord and all the skeletal muscle fibers innervated by its axon. This functional unit represents the smallest element capable of producing muscle force, with the motor neuron ensuring synchronous activation of its associated fibers via neuromuscular junctions. The concept of the motor unit was formalized by Liddell and Sherrington in their studies on voluntary muscle tone. Within a motor unit, individual muscle fibers follow the all-or-none principle, contracting fully to maximal tension or not at all in response to a suprathreshold action potential from the motor neuron, without intermediate levels of activation. Force production in a motor unit arises from the mechanical response to neural stimulation, beginning with a single twitch—a transient contraction and relaxation cycle elicited by one action potential, typically lasting 10–100 ms depending on fiber type. Increasing the frequency of action potentials leads to temporal summation, where subsequent twitches overlap before full relaxation of the previous one, resulting in progressively higher peak force. At low frequencies (e.g., 10–20 Hz), this produces unfused tetanus with visible oscillations in force; at higher frequencies (e.g., 30–50 Hz), summation intensifies to yield partially fused tetanus; and beyond 50 Hz, complete fusion occurs, generating a smooth, sustained maximal tetanic force approximately 3–4 times that of a single twitch. This force-frequency relationship reflects the interplay of calcium dynamics and cross-bridge cycling in the muscle fibers, allowing graded force output from repeated neural firing without altering the all-or-none response of individual fibers. Motor units vary in their contractile properties, classified primarily into slow-twitch (Type I) and fast-twitch (Type II) categories based on myosin heavy chain isoforms, contraction speed, and fatigue resistance. Type I units produce lower peak forces but are highly fatigue-resistant, relying on oxidative metabolism for sustained low-intensity activities; in contrast, Type II units generate higher forces rapidly but fatigue quickly due to glycolytic dependence, with Type IIa being more fatigue-resistant than Type IIx (in humans). These differences correlate with motor neuron size, as described by Henneman's size principle, where smaller motor neurons (innervating Type I units) have higher input resistance and lower rheobase, making them more excitable as a prerequisite for orderly activation. Classic experiments using isolated frog sciatic nerve-gastrocnemius muscle preparations demonstrated how graded force emerges from motor unit activity through temporal and spatial summation. Stimulating varying numbers of axons in the sciatic nerve (spatial summation) recruits additional motor units, proportionally increasing total force, while varying stimulation frequency (temporal summation) enhances force via twitch overlap, culminating in tetanus. These preparations, pioneered in early electrophysiological studies, revealed that whole-muscle force is finely tunable despite the all-or-none nature of individual fibers.

Recruitment and Motor Pool Organization

Motor units are recruited in an orderly manner according to Henneman's size principle, which posits that activation begins with the smallest motor neurons and their associated slow-twitch, fatigue-resistant muscle fibers to enable precise, low-force control, progressing to larger fast-twitch units only as greater force is required.^[8] This principle was established through seminal electrophysiological studies on decerebrate cats, where gradual increases in excitatory drive to the soleus muscle—a homogeneous slow muscle—revealed consistent recruitment from small to large motor units based on axon conduction velocity and twitch tension.^[9] Similar experiments on the heterogeneous medial gastrocnemius muscle confirmed the principle across fiber types, demonstrating that recruitment order correlates with motor neuron soma size and input resistance, ensuring efficient force gradation without erratic activation.^[10] Motor pools, defined as clusters of motor neurons innervating synergistic muscles, exhibit a precise spatial organization within the ventral horn of the spinal cord, forming longitudinal columns that span multiple segments.^[11] This arrangement includes rostro-caudal gradients, where motor neurons for proximal muscles are positioned more rostrally and those for distal muscles more caudally, facilitating coordinated activation patterns that support limb synergies during locomotion and posture.^[12] Such topographic organization allows descending inputs from the brainstem and cortex to target pools selectively, optimizing the distribution of motor commands across the cord's length. Recruitment and rate coding together modulate muscle force, with recruitment providing the primary mechanism for increasing output up to about 50% of maximal voluntary contraction by adding motor units in size order, while rate coding—via progressive increases in firing frequency of already active units—contributes further gradation and tetanic fusion.^[13] This dual strategy, governed by the size principle, minimizes fatigue by prioritizing low-threshold, oxidative motor units for sustained efforts, as their earlier derecruitment in reverse order during relaxation preserves efficiency.^[14] In pathological conditions such as amyotrophic lateral sclerosis (ALS), degeneration of motor neurons leads to reduced recruitment of motor units, resulting in fewer active units and contributing to muscle weakness and fatigue.^[15] Electromyographic recordings in ALS patients show reduced recruitment and unstable firing rates, reflecting motoneuron loss and hyperexcitability.^[16]

Control Architectures

Open-Loop Control Mechanisms

Open-loop control mechanisms in motor control involve the execution of movements through pre-planned neural commands without reliance on real-time sensory feedback, allowing for feedforward processing where the motor system issues instructions based solely on internal models of the action. These mechanisms are characterized by their predictive nature, utilizing an efference copy—a duplicate of the motor command sent to sensory areas to anticipate the sensory consequences of the movement, thereby compensating for the absence of ongoing corrections.^[17] This approach is essential for ballistic movements, which are rapid and stereotyped, such as saccadic eye movements that redirect gaze to a target in approximately 20-100 ms, or quick arm swings in pointing tasks, where the trajectory is fully specified at initiation and cannot be altered mid-execution due to the inherent speed.^[18]^[19] At the neural level, open-loop control is supported by central pattern generators (CPGs), networks of spinal interneurons that autonomously generate rhythmic motor outputs for coordinated actions like locomotion, independent of peripheral sensory inputs. Pioneering experiments on decerebrate cats, in which the brainstem was transected to isolate the spinal cord, revealed that these animals could still produce alternating flexor-extensor bursts mimicking stepping patterns when the spinal cord was pharmacologically stimulated, demonstrating the CPGs' capacity for self-sustained rhythmicity.^[20] This spinal circuitry provides a foundational open-loop framework, modulated by descending signals from higher centers but capable of operating without afferent feedback to drive basic locomotor primitives. The primary advantages of open-loop control lie in its speed and computational simplicity, facilitating movements that outpace sensory processing delays—typically exceeding 150 ms for visuomotor loops—thus enabling efficient performance in time-critical scenarios. For instance, speech articulation relies on open-loop commands to produce phonemes in 20-50 ms durations, far too brief for auditory or somatosensory feedback to intervene during a single segment.^[21] Similarly, throwing a ball exemplifies this in voluntary actions, where the arm's acceleration and release are preprogrammed to achieve the desired trajectory without mid-flight adjustments. However, these mechanisms are limited by their lack of adaptability; in unfamiliar environments with perturbations, errors accumulate unchecked, as no error signals are available for correction. Deafferentation experiments, such as those severing dorsal roots in decerebrate cats to eliminate proprioceptive input, showed that rhythmic locomotor patterns persisted, underscoring the preservation of central drive but also highlighting vulnerability to imprecise execution without sensory calibration.^[22]

Closed-Loop Control and Feedback Integration

Closed-loop control in motor systems enables real-time adjustments to ongoing movements by incorporating sensory feedback to minimize errors between intended and actual outcomes. This process relies on sensory afferents, primarily from proprioceptive sources such as muscle spindles and Golgi tendon organs, as well as visual inputs, which provide information about limb position, velocity, and external perturbations. These signals are integrated within neural structures like the cerebellum and basal ganglia, where a comparator mechanism subtracts the predicted sensory state—derived from efference copies of motor commands—from the actual afferent feedback to generate corrective signals.^[23]^[24]^[25] Key feedback modalities include position sensing via Ia afferents from muscle spindles, which detect changes in muscle length, and tension/velocity-related signals from Golgi tendon organs through Ib afferents, which monitor force to prevent overload. These proprioceptive inputs operate with inherent time delays: spinal reflex loops exhibit latencies of 50-100 ms, while transcortical pathways involving higher centers like the motor cortex introduce longer delays exceeding 100 ms, limiting the speed of corrections but allowing for more precise adjustments. Visual feedback, though slower due to processing in visual cortices (often 150-200 ms), contributes to error correction over extended timescales, particularly for goal-directed actions. Open-loop mechanisms complement these by handling rapid, ballistic phases of movement where feedback delays would be prohibitive.^[26] The integration of feedback operates as a servo mechanism, akin to engineering control systems, where gain determines the responsiveness to errors; however, excessively high gain can destabilize the system, leading to oscillations such as clonus observed in spasticity from upper motor neuron lesions. In clonus, delayed reflex feedback amplifies perturbations, resulting in rhythmic muscle contractions at frequencies of 5-8 Hz, as delays and heightened excitability create unstable loops. Stability is maintained in healthy systems through adaptive gain modulation and predictive damping by the cerebellum.^[27]^[27] Empirical evidence for closed-loop feedback integration comes from visuomotor adaptation studies using prism goggles, which displace the visual field and induce initial pointing errors. Participants recalibrate their motor output through repeated trials, achieving adaptation within 30-60 minutes, with aftereffects persisting briefly upon prism removal, demonstrating the system's capacity for error-driven plasticity. These findings underscore the role of feedback in refining sensorimotor maps without altering perceptual representations.^[28]

Sensorimotor Integration

Reflexive Responses to Perturbations

Reflexive responses to perturbations are rapid, involuntary motor actions that help stabilize posture and limb position in response to unexpected sensory inputs, primarily mediated by spinal and supraspinal circuits. These reflexes operate at short latencies to counteract disturbances, such as sudden stretches or impacts, without requiring conscious intervention. They form a foundational layer of motor control, enabling quick adjustments to maintain equilibrium and protect the body from injury.^[29] The stretch reflex, also known as the myotatic reflex, exemplifies a monosynaptic pathway that detects and counters muscle lengthening. When a muscle is suddenly stretched, muscle spindles activate Ia afferent fibers, which directly synapse onto alpha motor neurons in the spinal cord, triggering contraction to resist the perturbation; this response occurs with a latency of 20-50 milliseconds. This mechanism ensures rapid stabilization, as seen in the knee-jerk response elicited by tapping the patellar tendon. Complementing this, the inverse stretch reflex, mediated by Golgi tendon organs, provides autogenic inhibition to limit excessive force: Ib afferents from these organs signal high tension and inhibit the contracting muscle via interneurons, preventing overload with latencies similarly in the short range.^[30]^[31]^[32] Polysynaptic reflexes involve more complex spinal circuitry and interneurons to coordinate multi-muscle responses. The withdrawal reflex, or flexor reflex, is triggered by nociceptive stimuli, causing rapid flexion of the affected limb to remove it from harm; afferent signals from pain receptors converge on spinal interneurons that excite flexor motor neurons while inhibiting extensors, with latencies around 50-100 milliseconds. Accompanying this is the crossed-extensor reflex, which extends the opposite limb for support: interneurons facilitate extensor activation contralaterally, ensuring balance during unilateral withdrawal and mediated entirely within the spinal cord. These reflexes are protective, allowing coordinated escape without supraspinal involvement.^[29]^[33] Long-loop reflexes incorporate transcortical pathways for more adaptive corrections, engaging higher brain regions. Perturbations activate sensory afferents that project to the parietal cortex and motor cortex via ascending pathways, eliciting a response through descending corticospinal tracts with latencies of approximately 50-100 milliseconds. This allows integration of contextual information for refined adjustments, such as in postural recovery, distinguishing them from purely spinal reflexes by their involvement of cortical processing.^[34]^[35] Reflex efficacy is finely tuned through modulation mechanisms. Presynaptic inhibition reduces the impact of afferent inputs at the spinal level, allowing selective suppression of unwanted reflexes based on ongoing motor demands. Additionally, descending control from brainstem structures, such as the vestibulospinal tract, adjusts spinal reflex gain to support balance during whole-body perturbations, integrating vestibular signals to enhance postural stability. These modulatory processes ensure reflexes adapt to environmental and behavioral contexts.^[36]^[37]

Sensory Encoding in Motor Adjustments

Sensory encoding plays a crucial role in motor adjustments by transforming raw inputs from proprioceptive, cutaneous, visual, and vestibular modalities into neural signals that enable precise modifications to ongoing movements. Proprioception, primarily mediated by muscle spindles and Golgi tendon organs, provides continuous feedback on muscle length and tension to facilitate fine-tuning of motor commands during dynamic tasks like posture maintenance or locomotion. Muscle spindles, embedded within skeletal muscles, contain intrafusal fibers that detect changes in muscle length through primary (Ia) afferents, which exhibit both rate sensitivity to the velocity of stretch and dynamic sensitivity to acceleration, while secondary (II) afferents primarily encode static length. Golgi tendon organs, located at the musculotendinous junction, signal muscle tension via Ib afferents, responding proportionally to the force generated by active contraction or passive stretch, thereby preventing overload and contributing to force regulation in motor adjustments.^[38] Cutaneous receptors complement proprioceptive signals by encoding tactile features essential for grip and manipulation adjustments. Slowly adapting type 1 (SA1) afferents, associated with Merkel cells, detect fine spatial details such as surface texture through sustained responses to skin indentation, allowing the motor system to modulate grasp forces accordingly. Rapidly adapting type 1 (FA1) afferents, linked to Meissner corpuscles, sense transient vibrations arising from slip events during object handling, triggering rapid motor corrections to maintain stability. These encodings integrate with proprioceptive feedback to refine hand trajectories and forces in real-time, as evidenced by studies showing tactile signals directly elicit adaptive grip responses.^[39] Visual and vestibular inputs further enrich sensory encoding for whole-body motor adjustments, particularly in navigation and orientation. Optic flow, the visual pattern of environmental motion across the retina during self-movement, encodes heading direction by analyzing radial expansion patterns, enabling predictive corrections to locomotion paths. Semicircular canals in the vestibular system detect angular head acceleration, providing high-fidelity signals of rotational dynamics that are integrated with optic flow in regions like the superior colliculus to stabilize gaze and posture during rapid turns.^[40] This multisensory convergence allows for robust encoding of self-motion, where vestibular cues disambiguate visual ambiguities, such as during curvilinear paths. At the neural level, these sensory modalities are represented through population coding in the somatosensory cortex, where distributed neuronal activity forms dynamic body schemas that update to support motor adjustments. In primary somatosensory cortex (S1), ensembles of neurons encode stimulus features like touch location and intensity via overlapping receptive fields, allowing probabilistic decoding of body state for trajectory corrections. Tool use induces rapid remapping in these populations, extending the body schema to incorporate the tool as a functional extension, as shown by expanded receptive fields in macaque postcentral neurons following rake usage.^[41] Such plasticity ensures that sensory encodings adapt to altered kinematics, maintaining accurate motor control. Sensory encoding drives motor adaptations through error-based learning, exemplified in force-field paradigms where unexpected perturbations during reaching tasks elicit sensory prediction errors that promote cortical plasticity. In these experiments, subjects learn to compensate for viscous force fields applied to the arm, with initial errors in hand position (sensory mismatches) triggering gradual updates in motor commands over trials, leading to aftereffects upon field removal. This process involves cerebellar and cortical circuits, where repeated sensory errors induce long-term potentiation-like changes in primary motor cortex, enhancing generalization to novel conditions. Seminal studies demonstrate that adaptation rates correlate with error magnitude, underscoring how encoded discrepancies fine-tune internal models for precise motor output.

Coordination Strategies

Muscle Synergies and Pattern Formation

Muscle synergies represent a fundamental principle in motor control, where coordinated groups of muscles are activated as modular units to generate complex movement patterns with reduced dimensionality. These synergies simplify the control of the neuromuscular system by organizing muscle activations into a low number of functional modules, typically extracted from electromyographic (EMG) data using non-negative matrix factorization (NMF). For upper limb movements, such as reaching, 4-5 muscle synergies often account for over 90% of the variance in EMG signals, capturing essential patterns like shoulder stabilization, elbow extension, and wrist flexion.^[42]^[43] The neural basis of muscle synergies resides primarily in the spinal cord, where premotor interneurons form the core circuitry for generating these spatiotemporal activation patterns. In primates, spinal interneurons exhibit muscle fields that align with the fixed spatial vectors of synergies, enabling the coordination of hand and arm muscles during precision tasks like grasping. Evidence from primate reaching experiments demonstrates that these synergy vectors remain invariant across different directions and speeds, with variations achieved through modulation of their timing and amplitude rather than altering the muscle composition. Additionally, descending pathways, including the rubrospinal tract originating from the magnocellular red nucleus, contribute to synergy activation by encoding recruitment patterns that facilitate reaching-to-grasp behaviors.^[44]^[45]^[46] Muscle synergies play critical roles in various motor applications, notably in locomotion and grasping. In locomotion, reciprocal flexor-extensor synergies organize hindlimb muscles into alternating patterns that drive stepping cycles in mammals, with spinal circuits ensuring phase-specific activation to maintain gait stability. For grasping, synergies coordinate intrinsic and extrinsic hand muscles to achieve precise force distribution across digits, as observed in primate behaviors where 3-4 modules suffice for diverse grip types. Developmentally, these synergies emerge progressively in human infants; newborns exhibit rudimentary locomotor synergies such as 2 modules in stepping and 4 in kicking, which expand to 4-5 by early walking as cortical and spinal maturation refines modular control.^[47] A key computational framework for understanding synergies was proposed by d'Avella and colleagues, positing that natural behaviors arise from combining a small set of time-varying muscle activation modules. In this model, each synergy consists of a fixed spatial vector of relative muscle weights multiplied by a time profile, with overall patterns constructed by linearly summing scaled and temporally shifted synergies. This approach drastically reduces the control parameters needed—for instance, from hundreds of individual muscle timings to just a few dozen coefficients—while accurately reconstructing EMG patterns in behaviors like cat hindlimb kicking or primate reaching.^[48]^[49]

Handling Redundancy and Degrees of Freedom

The degrees of freedom problem, first articulated by Nikolai Bernstein, highlights the challenge in motor control arising from the abundance of biomechanical elements available to achieve a given task. In the human upper limb, for instance, the arm possesses roughly seven joint degrees of freedom (DOF), including three at the shoulder, one at the elbow, and three at the wrist, while many reaching tasks in three-dimensional space specify only three translational DOF for the hand endpoint. This redundancy results in an infinite number of joint configurations that can accomplish the same task outcome, complicating the neural selection of coordinated movements without overwhelming computational demands.^[50] One prominent neural strategy for resolving this redundancy is the uncontrolled manifold (UCM) hypothesis, which posits that the central nervous system permits greater variability in motor outputs along dimensions that do not affect task performance—the UCM—while suppressing variability in task-relevant dimensions. Under this framework, inter-trial fluctuations in joint angles during repetitive movements are preferentially channeled into the UCM to stabilize important task variables, such as hand position, rather than being randomly distributed across all DOF. Empirical support comes from variance analysis in reaching tasks, where studies have shown that the magnitude of joint variance is significantly larger within the UCM compared to the subspace orthogonal to it, indicating selective control that exploits redundancy for robustness against perturbations.^[51]^[52] Neural mechanisms underlying redundancy resolution often involve optimization criteria that guide trajectory selection among the myriad possibilities. For example, the minimum-jerk model proposes that movements minimize the squared derivative of acceleration (jerk) in endpoint space, yielding smooth, bell-shaped velocity profiles observed in human reaching; this kinematic optimization effectively resolves redundancy by prioritizing efficiency and naturalness in multi-joint coordination. Similarly, criteria like minimum torque change at the joints have been proposed to account for dynamic aspects, reducing energetic costs in redundant systems. The cerebellum plays a key role in implementing these optimizations, using forward internal models to predict and adjust for the consequences of redundant DOF, thereby simplifying adaptive control in nonlinear motor plants.^[53] A practical illustration of redundancy handling occurs in posture maintenance, where co-contraction of antagonist muscles, such as biceps and triceps, modulates joint stiffness without altering the endpoint position. This leverages the null space of the muscle-to-endpoint Jacobian—the set of muscle activations that produce zero net force or torque at the task space—allowing subtle postural adjustments or impedance tuning while preserving task stability, as seen in studies of voluntary co-contraction during static holds. Such strategies underscore how the nervous system exploits redundancy not as a burden but as an opportunity for flexibility and error compensation in everyday motor behaviors.^[54]

Perceptual Guidance

Direct Perception and Affordances

Direct perception, as articulated by psychologist James J. Gibson, asserts that visual perception arises directly from the structured light array in the ambient optic flow, without the need for internal cognitive representations or computational inferences to interpret the environment. Instead, perceivers attune to invariant properties in this optical structure that specify real-world properties, enabling immediate guidance of action. Central to this theory is the concept of affordances, which refer to the action possibilities offered by the environment relative to the perceiver's capabilities, such as the graspability of an object determined by its optic texture gradient indicating size and shape. For instance, the visual array provides information about whether a surface affords support for locomotion based on its texture density and continuity. A key piece of evidence supporting direct perception in motor control comes from tau theory, which describes how time-to-contact with approaching objects is specified directly by the rate of visual expansion (tau) in the optic flow, without requiring explicit distance or velocity computations. In tasks like catching a fly ball, performers scale their hand movements to this tau variable, initiating action when tau reaches a critical value that affords interception, as demonstrated in studies of skilled athletes where timing accuracy correlates with optic expansion rates rather than inferred trajectories. This approach highlights how motor adjustments emerge from prospective control tuned to optical invariants. Applications of direct perception extend to locomotion, where optic flow directly informs gait adjustments over varied terrain. During walking, the global pattern of radial outflow in the visual field specifies self-motion speed and heading, allowing perceivers to scale step length and width proportionally to flow rate without conscious planning; experimental manipulations of simulated optic flow in treadmill walking confirm that participants adapt stride parameters in real-time to maintain stability on virtual slopes or obstacles. Similarly, studies of infant crawling reveal that young children perceive affordances for safe traversal based on optical information about surface rigidity and slope angle, with crawling infants more readily descending shallow slopes than steeper ones, indicating attunement to visual invariants for postural support during the transition to independent mobility. While Gibson's framework has faced criticisms for underemphasizing neural mechanisms underlying perceptual pickup, recent neuroscientific integrations support its viability through evidence of direct visuomotor pathways. In vertebrates, the optic tectum (homologous to the mammalian superior colliculus) facilitates rapid, non-representational mapping from retinal input to motor output, enabling stimulus-specific actions like prey capture or obstacle avoidance based on optical features that specify affordances, such as looming patterns for collision risk. This tectal circuitry provides a biological basis for perception-action coupling without intermediate symbolic processing, bridging ecological theory with anatomical substrates for immediate environmental responsiveness.^[55]

Internal Models for Prediction and Control

Internal models in motor control refer to neural representations that simulate the sensory consequences of motor commands and the commands required to achieve desired sensory outcomes, enabling predictive and adaptive behavior without relying solely on real-time sensory feedback. These models allow the brain to anticipate movement effects, detect errors, and refine actions, particularly in dynamic environments. Seminal computational frameworks, such as those proposed by Wolpert, Ghahramani, and Kawato, posit that forward and inverse models operate in tandem to support precise motor execution.^[56] Forward models predict the sensory state resulting from a given motor command, utilizing an efference copy—a neural signal mirroring the motor output—to forecast outcomes before sensory feedback arrives. Mathematically, this is expressed as \hat{y} = f(e, u), where \hat{y} is the predicted sensory outcome, e represents the current state (e.g., efference copy), and u is the motor command. In the cerebellum, forward models facilitate error detection by comparing predicted outcomes against actual sensory feedback, generating correction signals to minimize discrepancies during ongoing movements.^[56]^[57] Inverse models, conversely, compute the motor commands necessary to produce a desired sensory outcome, formulated as y = g(u), where y is the target state and u the required command, often solved through iterative learning processes. These models are associated with the basal ganglia and cerebral cortex, where they enable goal-directed control by inverting the dynamics of the motor plant. To handle the complexity of multi-joint movements, inverse models employ modular decomposition, breaking down tasks into subcomponents for efficient computation and integration.^[58] The acquisition and refinement of internal models occur through error-driven learning mechanisms, primarily involving long-term depression (LTD) and long-term potentiation (LTP) at synaptic junctions in the cerebellum and related circuits. Sensory prediction errors—discrepancies between expected and actual outcomes—drive synaptic plasticity, updating model parameters to improve future predictions. Evidence from primate studies demonstrates this process: monkeys rapidly adapt to novel dynamics, such as a viscous curl force field that perturbs arm reaches, by forming compensatory internal models within trials, with learning rates reflecting cerebellar plasticity via LTD/LTP. In applications like tool use, internal models dynamically remap the body schema to incorporate external implements, treating a tool as an extension of the limb for predictive control. For instance, wielding a rake updates forward and inverse models to account for altered kinematics and dynamics, enabling seamless integration into the motor repertoire and recalibration upon tool removal. This plasticity underscores the models' role in adaptive behaviors beyond innate anatomy.^[59]

Movement Planning

Motor Program Assembly

Motor program assembly involves the construction of abstract, parameterized representations of action sequences that enable the nervous system to generate repeatable behaviors with flexibility. Central to this process is Schmidt's schema theory, which posits that generalized motor programs (GMPs) serve as stored templates for classes of movements, featuring invariant elements such as relative timing and spatial ordering, while parameters modulate aspects like overall speed, amplitude, and force to adapt to contextual demands.^[60] These schemas allow for the recall and scaling of movements without reprogramming each instance, as demonstrated in experiments where participants adjusted limb trajectories proportionally across varying distances while maintaining timing ratios.^[61] Motor programs exhibit a hierarchical organization, where spinal central pattern generators (CPGs) produce innate primitives for rhythmic actions like stepping or chewing, providing modular building blocks that higher brain regions integrate into novel sequences.^[3] Cortical areas, particularly in the premotor and supplementary motor cortices, assemble these primitives into coherent programs for voluntary, goal-directed tasks, as evidenced by serial reaction time (SRT) studies showing reduced response latencies when sequences form implicit chunks, indicating hierarchical structuring of motor output.^[62] This layered architecture facilitates efficient composition, with CPGs handling low-level coordination and cortical processes enabling adaptive recombination for complex behaviors. The storage and recall of assembled programs rely on the basal ganglia, which reinforce habit-like sequences through dopamine-modulated plasticity, shifting control from effortful, goal-oriented actions to automatic execution over repeated trials.^[63] De novo program formation occurs via trial-and-error learning, where errors drive refinements in sequencing and parameterization through reinforcement signals. In practical examples, such as typing on a keyboard or performing piano scales, novices initially rely on deliberate segmentation, but with practice, integrated GMPs emerge that scale seamlessly with tempo or intensity, preserving invariant relative timings for fluid performance.^[60]

Optimization of Single and Multi-Limb Trajectories

The nervous system optimizes motor trajectories by selecting paths that minimize specific costs, such as smoothness or endpoint variability, during movement planning. One prominent model posits that reaching movements minimize the integral of squared jerk, defined as the third derivative of position with respect to time, formulated as J = \int_0^T \left( \frac{d^3 \mathbf{x}(t)}{dt^3} \right)^2 dt, where \mathbf{x}(t) is the hand position and T is the movement duration. This minimum-jerk criterion, proposed by Flash and Hogan, predicts smooth, straight-line trajectories to targets and has been experimentally validated in human arm movements, yielding bell-shaped velocity profiles consistent with observed kinematics.^[64] Another optimization principle accounts for signal-dependent noise in neural control signals, where variability increases with signal amplitude, leading to trajectories that minimize endpoint variance. Harris and Wolpert's minimum-variance model demonstrates that such noise shapes reaching paths to reduce final position errors, accurately predicting both saccadic eye movements and arm trajectories across varying distances and accuracies.^[65] In single-limb tasks, these principles manifest in speed-accuracy trade-offs described by Fitts' law, where movement time MT = a + b \log_2 \left( \frac{2D}{W} \right), with D as target distance and W as width, reflects the information processing demands on the motor system. Neural recordings in the primary motor cortex (M1) reveal tuning of neuronal activity to these index of difficulty parameters, supporting cortical involvement in trajectory optimization.^[66] For multi-limb movements, optimization incorporates interlimb coupling to coordinate actions while avoiding inefficient asymmetries, such as unintended mirroring between limbs. In bimanual tasks like piano playing, skilled performers exhibit tight temporal synchronization and spatial independence between hands. This coordination minimizes overall effort and error propagation across limbs, as evidenced by reduced variability in inter-hand timing during asymmetric key presses. Computational models in neuroscience frame these optimizations within optimal control theory, where the value function V(\mathbf{x}) satisfies the Hamilton-Jacobi-Bellman equation approximating V(\mathbf{x}) = \min_u \left[ L(\mathbf{x},u) + V(f(\mathbf{x},u)) \right], with L as the instantaneous cost (e.g., energy or jerk), u as control input, and f as system dynamics. Todorov and colleagues have applied this framework to motor coordination, demonstrating how it resolves biomechanical redundancies by selecting controls that minimize cumulative costs over time, aligning with empirical data on both single- and multi-joint movements.

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[PDF] Central Pattern Generators for Locomotion, with Special Reference ...
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The cerebellum as comparator: Increases in cerebellar activity ...
The cerebellum as comparator: Increases in cerebellar activity during motor learning may reflect its role as part of an error detection/correction mechanism.
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The Forward Model: A Unifying Theory for the Role of the ... - Frontiers
Thus, the cerebellum is ideally located to integrate both the motor command (or efference copy), which originates from the motor cortex and the sensory feedback ...
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The contribution of the basal ganglia and cerebellum to motor learning
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Motor Units and Muscle Receptors (Section 3, Chapter 1 ...
The combination of an individual motor neuron and all of the muscle fibers that it innervates is called a motor unit. The number of fibers innervated by a motor ...
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A simulation study of reflex instability in spasticity: origins of clonus
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Prism Adaptation and Aftereffect: Specifying the Properties of a ...
Prism adaptation, a form of procedural learning, is a phenomenon in which the motor system adapts to new visuospatial coordinates imposed by prisms that ...
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Physiology, Withdrawal Response - StatPearls - NCBI Bookshelf - NIH
The withdrawal response (reflex), also known as the nociceptive flexion reflex, is an automatic response of the spinal cord that is critical in protecting ...
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Spinal Circuits Mediate a Stretch Reflex Between the Upper Limbs ...
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Golgi Tendon Organ - an overview | ScienceDirect Topics
Activation of these receptors results in a reflex inhibition of the muscle via the inverse myotatic reflex.7 GTOs are located in the tendons, close to the point ...
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Withdrawal Reflex - an overview | ScienceDirect Topics
When force is excessive, afferent activity on the Ib Golgi tendon organ afferents inhibits further α motor neuron activity. This reflex is called the inverse ...
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Modulation of the long-latency reflex to stretch by the supplementary ...
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The Differential Role of Motor Cortex in Stretch Reflex Modulation ...
The long-latency stretch response was timed to occur within the latter portion of the induced silent period (>100 ms after TMS trigger) to evaluate cortical ...
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Altered Patterns of Reflex Excitability, Balance, and Locomotion ...
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Basic Concepts in Understanding Recovery of Function in Vestibular ...
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Muscle spindle function in healthy and diseased muscle
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Signals in tactile afferents from the fingers eliciting adaptive motor ...
The present report provides direct evidence that signals in tactile afferent units are utilized in this adaptation.<|separator|>
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Visual–Vestibular Integration for Self-Motion Perception - NCBI - NIH
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Population coding in somatosensory cortex - PubMed
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Muscle Synergies Control during Hand-Reaching Tasks in Multiple ...
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Muscle synergy patterns as physiological markers of motor cortical ...
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Modulation of Muscle Synergy Recruitment in Primate Grasping
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Neuronal Correlates of Functional Coupling between Reach
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Spinal control of muscle synergies for adult mammalian locomotion
The control of locomotion is thought to be generated by activating groups of muscles that perform similar actions, which are termed muscle synergies.
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Distinct locomotor precursors in newborn babies - PNAS
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[PDF] Combinations of muscle synergies in the construction of a natural ...
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Control of reaching movements by muscle synergy combinations
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[PDF] The Bernstein Perspective: 1. The Problems of Degrees of Freedom ...
The purpose of this first chapter is to identify the two major problems that shape the analysis of movement in the Bernstein perspective. We begin with a view ...
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[PDF] The uncontrolled manifold concept: identifying control variables for a ...
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A process account of the uncontrolled manifold structure of joint ...
To analyze the structure of variance within the four-dimensional joint space, we used two methods of analysis, the method of the uncontrolled manifold (UCM) and ...
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Recurrent Cerebellar Loops Simplify Adaptive Control of Redundant ...
Recurrent Cerebellar Loops Simplify Adaptive Control of Redundant and Nonlinear Motor ... These are sometimes called redundant degrees of freedom. The cerebellum ...
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Muscle patterns underlying voluntary modulation of co-contraction
Manipulative actions involving unstable interactions with the environment require controlling mechanical impedance through muscle co-contraction.
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[PDF] Internal models in the cerebellum
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Consensus Paper: Roles of the Cerebellum in Motor Control—The ...
These concepts suggest that the cerebellum contributes to timing and sensory acquisition and is involved in the prediction of the sensory consequences of action ...
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[PDF] Multiple paired forward and inverse models for motor control
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(PDF) Internal Models and Body Schema in Tool Use - ResearchGate
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A schema theory of discrete motor skill learning - ResearchGate
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[PDF] Schmidt Generalized Motor Programs - krigolson teaching
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The Serial Reaction Time Task: Implicit Motor Skill Learning? - PMC
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The role of the basal ganglia in habit formation - Nature
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The Coordination of Arm Movements: An Experimentally Confirmed ...
the minimization of mean-squared jerk has been applied successfully to both single-joint (Hogan, 1982, 1984) and multijoint movements. (Flash, 1983). By an ...
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[PDF] Signal-dependent noise determines motor planning
We propose that in the presence of such signal-dependent noise, the shape of a trajectory is selected to minimize the variance of the final eye or arm position.
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Cortical Correlates of Fitts' Law - PMC
To elucidate sensorimotor cortical activity underlying Fitts' law, we implanted two monkeys with multielectrode arrays in the primary motor (M1) and primary ...
[66]
Functional coupling of human cortical sensorimotor areas during ...
Bimanual co-ordination of skilled finger movements is an outstanding capability of the human motor system, and bimanual performance at a high level of skill, ...