Motor control is the regulation of movement in organisms that possess a nervous

system. Motor control includes reflexes[1] as well as directed movement.

To control movement, the nervous system must integrate multimodal sensory

information (both from the external world as well as proprioception) and elicit the
necessary signals to recruit muscles to carry out a goal. This pathway spans many
disciplines, including multisensory integration, signal processing, coordination,
biomechanics, and cognition,[2][3] and the computational challenges are often
discussed under the term sensorimotor control.[4] Successful motor control is
crucial to interacting with the world to carry out goals as well as for posture,
balance, and stability.

Some researchers (mostly neuroscientists studying movement, such as Daniel Wolpert

and Randy Flanagan) argue that motor control is the reason brains exist at all.[5]

Neural control of muscle force

All movements, e.g. touching your nose, require motor neurons to fire action
potentials that results in contraction of muscles. In humans, ~150,000 motor
neurons control the contraction of ~600 muscles. To produce movements, a subset of
600 muscles must contract in a temporally precise pattern to produce the right
force at the right time.[6]

Motor units and force production

A single motor neuron and the muscle fibers it innervates are called a motor unit.
For example, the rectus femoris contains approximately 1 million muscle fibers,
which are controlled by around 1000 motor neurons. Activity in the motor neuron
causes contraction in all of the innervated muscle fibers so that they function as
a unit. Increasing action potential frequency (spike rate) in the motor neuron
increases the muscle fiber contraction force, up to the maximal force.[6][7] The
maximal force depends on the contractile properties of the muscle fibers. Within a
motor unit, all the muscle fibers are of the same type (e.g. type I (slow twitch)
or Type II fibers (fast twitch)), and motor units of multiple types make up a given
muscle. Motor units of a given muscle are collectively referred to as a motor pool.

The force produced in a given muscle thus depends on: 1) How many motor neurons are
active, and their spike rates; 2) the contractile properties and number of muscle
fibers innervated by the active neurons. To generate more force, increase the spike
rates of active motor neurons and/or recruiting more and stronger motor units. In
turn, how the muscle force produces limb movement depends on the limb biomechanics,
e.g. where the tendon and muscle originate (which bone, and precise location) and
where the muscle inserts on the bone that it moves.

Recruitment order
Motor units within a motor pool are recruited in a stereotypical order, from motor
units that produce small amounts of force per spike, to those producing the largest
force per spike. The gradient of motor unit force is correlated with a gradient in
motor neuron soma size and motor neuron electrical excitability. This relationship
was described by Elwood Henneman and is known as Henneman's size principle, a
fundamental discovery of neuroscience and an organizing principle of motor control.
[8]

For tasks requiring small forces, such as continual adjustment of posture, motor
units with fewer muscle fibers that are slowly-contracting, but less fatigueable,
are used. As more force is required, motor units with fast twitch, fast-fatigeable
muscle fibers are recruited.

High|
| _________________
Force required | /
 | |
| |
| _____________|_________________
| __________|_______________________________
Low|__________|__________________________________________
↑ ↑ ↑ Time
Type I Recruit first Type II A Type IIB
Computational issues of motor control
The nervous system produces movement by selecting which motor neurons are
activated, and when. The finding that a recruitment order exists within a motor
pool is thought to reflect a simplification of the problem: if a particular muscle
should produce a particular force, then activate the motor pool along its
recruitment hierarchy until that force is produced.

But then how to choose what force to produce in each muscle? The nervous system
faces the following issues in solving this problem.[4]

Redundancy. Infinite trajectories of movements can accomplish a goal (e.g. touch my

nose). How is a trajectory chosen? Which trajectory is best?
Noise. Noise is defined as small fluctuations that are unrelated to a signal, which
can occur in neurons and synaptic connections at any point from sensation to muscle
contraction.
Delays. Motor neuron activity precedes muscle contraction, which precedes the
movement. Sensory signals also reflect events that have already occurred. Such
delays affect the choice of motor program.
Uncertainty. Uncertainty arises because of neural noise, but also because
inferences about the state of the world may not be correct (e.g. speed of on coming
ball).
Nonstationarity. Even as a movement is being executed, the state of the world
changes, even through such simple effects as reactive forces on the rest of the
body, causing translation of a joint while it is actuated.
Nonlinearity. The effects of neural activity and muscle contraction are highly non-
linear, which the nervous system must account for when predicting the consequences
of a pattern of motor neuron activity.
Much ongoing research is dedicated to investigating how the nervous system deals
with these issues, both at the behavioral level, as well as how neural circuits in
the brain and spinal cord represent and deal with these factors to produce the
fluid movements we witness in animals.

"Optimal feedback control" is an influential theoretical framing of these

computation issues.[9]

Model systems for motor control

All organisms face the computational challenges above, so neural circuits for motor
control have been studied in humans, monkeys,[10] horses, cats,[11] mice,[12]
fish[13] lamprey,[14] flies, locusts,[15] and nematodes,[16] among many others.
Mammalian model systems like mice and monkeys offer the most straightforward
comparative models for human health and disease. They are widely used to study the
role of higher brain regions common to vertebrates, including the cerebral cortex,
thalamus, basal ganglia and deep brain medullary and reticular circuits for motor
control.[17] The genetics and neurophysiology of motor circuits in the spine have
also been studied in mammalian model organisms, but protective vertebrae make it
difficult to study the functional role of spinal circuits in behaving animals.
Here, larval and adult fish have been useful in discovering the functional logic of
the local spinal circuits that coordinate motor neuron activity. Invertebrate model
organisms do not have the same brain regions as vertebrates, but their brains must
solve similar computational issues and thus are thought to have brain regions
homologous to those involved in motor control in the vertebrate nervous system,[18]
The organization of arthropod nervous systems into ganglia that control each leg as
allowed researchers to record from neurons dedicated to moving a specific leg
during behavior.

Model systems have also demonstrated the role of central pattern generators in
driving rhythmic movements.[14] A central pattern generator is a neural network
that can generate rhythmic activity in the absence of an external control signal,
such as a signal descending from the brain or feedback signals from sensors in the
limbs (e.g. proprioceptors). Evidence suggests that real CPGs exist in several key
motor control regions, such as the stomachs of arthropods or the pre-Boetzinger
complex that control breathing in humans. Furthermore, as a theoretical concept,
CPGs have been useful to frame the possible role of sensory feedback in motor
control.

Sensorimotor feedback
Response to stimuli
The process of becoming aware of a sensory stimulus and using that information to
influence an action occurs in stages. Reaction time of simple tasks can be used to
reveal information about these stages. Reaction time refers to the period of time
between when the stimulus is presented, and the end of the response. Movement time
is the time it takes to complete the movement. Some of the first reaction time
experiments were carried out by Franciscus Donders, who used the difference in
response times to a choice task to determine the length of time needed to process
the stimuli and choose the correct response.[19] While this approach is ultimately
flawed, it gave rise to the idea that reaction time was made up of a stimulus
identification, followed by a response selection, and ultimately culminates in
carrying out the correct movement. Further research has provided evidence that
these stages do exist, but that the response selection period of any reaction time
increases as the number of available choices grows, a relationship known as Hick's
law.[20]

Closed loop control

The classical definition of a closed loop system for human movement comes from Jack
A. Adams (1971).[21][22] A reference of the desired output is compared to the
actual output via error detection mechanisms; using feedback, the error is
corrected for. Most movements that are carried out during day-to-day activity are
formed using a continual process of accessing sensory information and using it to
more accurately continue the motion. This type of motor control is called feedback
control, as it relies on sensory feedback to control movements. Feedback control is
a situated form of motor control, relying on sensory information about performance
and specific sensory input from the environment in which the movement is carried
out. This sensory input, while processed, does not necessarily cause conscious
awareness of the action. Closed loop control[23]: 
186  is a feedback based mechanism
of motor control, where any act on the environment creates some sort of change that
affects future performance through feedback. Closed loop motor control is best
suited to continuously controlled actions, but does not work quickly enough for
ballistic actions. Ballistic actions are actions that continue to the end without
thinking about it, even when they no longer are appropriate.[citation needed]
Because feedback control relies on sensory information, it is as slow as sensory
processing. These movements are subject to a speed-accuracy trade-off, because
sensory processing is being used to control the movement, the faster the movement
is carried out, the less accurate it becomes.

Open loop control

The classical definition from Jack A. Adams is:[21][22] “An open loop system has no
feedback or mechanisms for error regulation. The input events for a system exert
their influence, the system effects its transformation on the input and the system
has an output...... A traffic light with fixed timing snarls traffic when the load
is heavy and impedes the flow when the traffic is light. The system has no
compensatory capability.”
Some movements, however, occur too quickly to integrate sensory information, and
instead must rely on feed forward control. Open loop control is a feed forward form
of motor control, and is used to control rapid, ballistic movements that end before
any sensory information can be processed. To best study this type of control, most
research focuses on deafferentation studies, often involving cats or monkeys whose
sensory nerves have been disconnected from their spinal cords. Monkeys who lost all
sensory information from their arms resumed normal behavior after recovering from
the deafferentation procedure. Most skills were relearned, but fine motor control
became very difficult.[24] It has been shown that the open loop control can be
adapted to different disease conditions and can therefore be used to extract
signatures of different motor disorders by varying the cost functional governing
the system.[25]

Coordination
A core motor control issue is coordinating the various components of the motor
system to act in unison to produce movement.

Peripheral neurons receive input from the central nervous system and innervate the
muscles. In turn, muscles generate forces which actuate joints. Getting the pieces
to work together is a challenging problem for the motor system and how this problem
is resolved is an active area of study in motor control research.

Reflexes
In some cases the coordination of motor components is hard-wired, consisting of
fixed neuromuscular pathways that are called reflexes. Reflexes are typically
characterized as automatic and fixed motor responses, and they occur on a much
faster time scale than what is possible for reactions that depend on perceptual
processing.[26] Reflexes play a fundamental role in stabilizing the motor system,
providing almost immediate compensation for small perturbations and maintaining
fixed execution patterns. Some reflex loops are routed solely through the spinal
cord without receiving input from the brain, and thus do not require attention or
conscious control. Others involve lower brain areas and can be influenced by prior
instructions or intentions, but they remain independent of perceptual processing
and online control.

The simplest reflex is the monosynaptic reflex or short-loop reflex, such as the
monosynaptic stretch response. In this example, Ia afferent neurons are activated
by muscle spindles when they deform due to the stretching of the muscle. In the
spinal cord, these afferent neurons synapse directly onto alpha motor neurons that
regulate the contraction of the same muscle.[27] Thus, any stretching of a muscle
automatically signals a reflexive contraction of that muscle, without any central
control. As the name and the description implies, monosynaptic reflexes depend on a
single synaptic connection between an afferent sensory neuron and efferent motor
neuron. In general the actions of monosynaptic reflexes are fixed and cannot be
controlled or influenced by intention or instruction. However, there is some
evidence to suggest that the gain or magnitude of these reflexes can be adjusted by
context and experience.[28]

Polysynaptic reflexes or long-loop reflexes are reflex arcs which involve more than
a single synaptic connection in the spinal cord. These loops may include cortical
regions of the brain as well, and are thus slower than their monosynaptic
counterparts due to the greater travel time. However, actions controlled by
polysynaptic reflex loops are still faster than actions which require perceptual
processing.[29]: 
171, 578  While the actions of short-loop reflexes are fixed,
polysynaptic reflexes can often be regulated by instruction or prior experience.
[30] A common example of a long loop reflex is the asymmetrical tonic neck reflex
observed in infants.
Synergies
A motor synergy is a neural organization of a multi-element system that (1)
organizes sharing of a task among a set of elemental variables; and (2) ensures co-
variation among elemental variables with the purpose to stabilize performance
variables.[31][32] The components of a synergy need not be physically connected,
but instead are connected by their response to perceptual information about the
particular motor task being executed. Synergies are learned, rather than being
hardwired like reflexes, and are organized in a task-dependent manner; a synergy is
structured for a particular action and not determined generally for the components
themselves. Nikolai Bernstein famously demonstrated synergies at work in the
hammering actions of professional blacksmiths. The muscles of the arm controlling
the movement of the hammer are informationally linked in such a way that errors and
variability in one muscle are automatically compensated for by the actions of the
other muscles. These compensatory actions are reflex-like in that they occur faster
than perceptual processing would seem to allow, yet they are only present in expert
performance, not in novices. In the case of blacksmiths, the synergy in question is
organized specifically for hammering actions and is not a general purpose
organization of the muscles of the arm. Synergies have two defining characteristics
in addition to being task dependent; sharing and flexibility/stability.[33]

"Sharing" requires that the execution of a particular motor task depends on the
combined actions of all the components that make up the synergy. Often, there are
more components involved than are strictly needed for the particular task (see
"Redundancy" below), but the control of that motor task is distributed across all
components nonetheless. A simple demonstration comes from a two-finger force
production task, where participants are required to generate a fixed amount of
force by pushing down on two force plates with two different fingers.[34] In this
task, participants generated a particular force output by combining the
contributions of independent fingers. While the force produced by any single finger
can vary, this variation is constrained by the action of the other such that the
desired force is always generated.

Co-variation also provides "flexibility and stability" to motor tasks. Considering

again the force production task, if one finger did not produce enough force, it
could be compensated for by the other.[34] The components of a motor synergy are
expected to change their action to compensate for the errors and variability in
other components that could affect the outcome of the motor task. This provides
flexibility because it allows for multiple motor solutions to particular tasks, and
it provides motor stability by preventing errors in individual motor components
from affecting the task itself.

Synergies simplify the computational difficulty of motor control. Coordinating the

numerous degrees of freedom in the body is a challenging problem, both because of
the tremendous complexity of the motor system, as well as the different levels at
which this organization can occur (neural, muscular, kinematic, spatial, etc.).
Because the components of a synergy are functionally coupled for a specific task,
execution of motor tasks can be accomplished by activating the relevant synergy
with a single neural signal.[35] The need to control all of the relevant components
independently is removed because organization emerges automatically as a
consequence of the systematic covariation of components. Similar to how reflexes
are physically connected and thus do not require control of individual components
by the central nervous system, actions can be executed through synergies with
minimal executive control because they are functionally connected. Beside motor
synergies, the term of sensory synergies has recently been introduced.[36] Sensory
synergy are believed to play an important role in integrating the mixture of
environmental inputs to provide low-dimensional information to the CNS thus guiding
the recruitment of motor synergies.

Synergies are fundamental for controlling complex movements, such as the ones of
the hand during grasping. Their importance has been demonstrated for both muscle
control and in the kinematic domain in several studies, lately on studies including
large cohorts of subjects.[37][38][39] The relevance of synergies for hand grasps
is also enforced by studies on hand grasp taxonomies, showing muscular and
kinematic similarities among specific groups of grasps, leading to specific
clusters of movements.[40]

Motor Programs
While synergies represent coordination derived from peripheral interactions of
motor components, motor programs are specific, pre-structured motor activation
patterns that are generated and executed by a central controller (in the case of a
biological organism, the brain).[29]: 
227  They represent at top-down approach to
motor coordination, rather than the bottom-up approach offered by synergies. Motor
programs are executed in an open-loop manner, although sensory information is most
likely used to sense the current state of the organism and determine the
appropriate goals. However, once the program has been executed, it cannot be
altered online by additional sensory information.

Evidence for the existence of motor programs comes from studies of rapid movement
execution and the difficulty associated with changing those movements once they
have been initiated. For example, people who are asked to make fast arm swings have
extreme difficulty in halting that movement when provided with a "STOP" signal
after the movement has been initiated.[41] This reversal difficulty persists even
if the stop signal is presented after the initial "GO" signal but before the
movement actually begins. This research suggests that once selection and execution
of a motor program begins, it must run to completion before another action can be
taken. This effect has been found even when the movement that is being executed by
a particular motor program is prevented from occurring at all. People who attempt
to execute particular movements (such as pushing with the arm), but unknowingly
have the action of their body arrested before any movement can actually take place,
show the same muscle activation patterns (including stabilizing and support
activation that does not actually generate the movement) as when they are allowed
to complete their intended action.[42]

Although the evidence for motor programs seems persuasive, there have been several
important criticisms of the theory. The first is the problem of storage. If each
movement an organism could generate requires its own motor program, it would seem
necessary for that organism to possess an unlimited repository of such programs and
where these would be kept is not clear. Aside from the enormous memory requirements
such a facility would take, no motor program storage area in the brain has yet been
identified. The second problem is concerned with novelty in movement. If a specific
motor program is required for any particular movement, it is not clear how one
would ever produce a novel movement. At best, an individual would have to practice
any new movement before executing it with any success, and at worst, would be
incapable of new movements because no motor program would exist for new movements.
These difficulties have led to a more nuanced notion of motor programs known as
generalized motor programs.[29]: 
240–257  A generalized motor program is a program
for a particular class of action, rather than a specific movement. This program is
parameterized by the context of the environment and the current state of the
organism.

Redundancy
An important issue for coordinating the motor system is the problem of the
redundancy of motor degrees of freedom. As detailed in the "Synergies" section,
many actions and movements can be executed in multiple ways because functional
synergies controlling those actions are able to co-vary without changing the
outcome of the action. This is possible because there are more motor components
involved in the production of actions than are generally required by the physical
constraints on that action. For example, the human arm has seven joints which
determine the position of the hand in the world. However, only three spatial
dimensions are needed to specify any location the hand could be placed in. This
excess of kinematic degrees of freedom means that there are multiple arm
configurations that correspond to any particular location of the hand.

Some of the earliest and most influential work on the study of motor redundancy
came from the Russian physiologist Nikolai Bernstein. Bernstein's research was
primarily concerned with understanding how coordination was developed for skilled
actions. He observed that the redundancy of the motor system made it possible to
execute actions and movements in a multitude of different ways while achieving
equivalent outcomes.[35] This equivalency in motor action means that there is no
one-to-one correspondence between the desired movements and the coordination of the
motor system needed to execute those movements. Any desired movement or action does
not have a particular coordination of neurons, muscles, and kinematics that make it
possible. This motor equivalency problem became known as the degrees of freedom
problem because it is a product of having redundant degrees of freedom available in
the motor system.

Perception in motor control

Related, yet distinct from the issue of how the processing of sensory information
affects the control of movements and actions is the question of how the perception
of the world structures action. Perception is extremely important in motor control
because it carries the relevant information about objects, environments and bodies
which is used in organizing and executing actions and movements. What is perceived
and how the subsequent information is used to organize the motor system is an
ongoing area of research.

Model based control strategies

Most model based strategies of motor control rely on perceptual information, but
assume that this information is not always useful, veridical or constant. Optical
information is interrupted by eye blinks, motion is obstructed by objects in the
environment, distortions can change the appearance of object shape. Model based and
representational control strategies are those that rely on accurate internal models
of the environment, constructed from a combination of perceptual information and
prior knowledge, as the primary source information for planning and executing
actions, even in the absence of perceptual information.[43]

Inference and indirect perception

Many models of the perceptual system assume indirect perception, or the notion that
the world that gets perceived is not identical to the actual environment.
Environmental information must go through several stages before being perceived,
and the transitions between these stages introduce ambiguity. What actually gets
perceived is the mind's best guess about what is occurring in the environment based
on previous experience. Support for this idea comes from the Ames room illusion,
where a distorted room causes the viewer to see objects known to be a constant size
as growing or shrinking as they move around the room. The room itself is seen as
being square, or at least consisting of right angles, as all previous rooms the
perceiver has encountered have had those properties. Another example of this
ambiguity comes from the doctrine of specific nerve energies. The doctrine presents
the finding that there are distinct nerve types for different types of sensory
input, and these nerves respond in a characteristic way regardless of the method of
stimulation. That is to say, the color red causes optical nerves to fire in a
specific pattern that is processed by the brain as experiencing the color red.
However, if that same nerve is electrically stimulated in an identical pattern, the
brain could perceive the color red when no corresponding stimuli is present.

Forward models
Forward models are a predictive internal model of motor control that takes the
available perceptual information, combined with a particular motor program, and
tries to predict the outcome of the planned motor movement. Forward models
structure action by determining how the forces, velocities, and positions of motor
components affect changes in the environment and in the individual. It is proposed
that forward models help with the Neural control of limb stiffness when individuals
interact with their environment. Forward models are thought to use motor programs
as input to predict the outcome of an action. An error signal is generated when the
predictions made by a forward model do not match the actual outcome of the
movement, prompting an update of an existing model and providing a mechanism for
learning. These models explain why it is impossible to tickle yourself. A sensation
is experienced as ticklish when it is unpredictable. However, forward models
predict the outcome of your motor movements, meaning the motion is predictable, and
therefore not ticklish.[44]

Evidence for forward models comes from studies of motor adaptation. When a person's
goal-directed reaching movements are perturbed by a force field, they gradually,
but steadily, adapt the movement of their arm to allow them to again reach their
goal. However, they do so in such a way that preserves some high level movement
characteristics; bell-shaped velocity profiles, straight line translation of the
hand, and smooth, continuous movements.[45] These movement features are recovered,
despite the fact that they require startlingly different arm dynamics (i.e. torques
and forces). This recovery provides evidence that what is motivating movement is a
particular motor plan, and the individual is using a forward model to predict how
arm dynamics change the movement of the arm to achieve particular task level
characteristics. Differences between the expected arm movement and the observed arm
movement produces an error signal which is used as the basis for learning.
Additional evidence for forward models comes from experiments which require
subjects to determine the location of an effector following an unvisualized
movement[46]

Inverse models
Inverse models predict the necessary movements of motor components to achieve a
desired perceptual outcome. They can also take the outcome of a motion and attempt
to determine the sequence of motor commands that resulted in that state. These
types of models are particularly useful for open loop control, and allow for
specific types of movements, such as fixating on a stationary object while the head
is moving. Complementary to forward models, inverse models attempt to estimate how
to achieve a particular perceptual outcome in order to generate the appropriate
motor plan. Because inverse models and forward model are so closely associated,
studies of internal models are often used as evidence for the roles of both model
types in action.

Motor adaptation studies, therefore, also make a case for inverse models. Motor
movements seem to follow predefined "plans" that preserve certain invariant
features of the movement. In the reaching task mentioned above, the persistence of
bell-shaped velocity profiles and smooth, straight hand trajectories provides
evidence for the existence of such plans.[45] Movements that achieve these desired
task-level outcomes are estimated by an inverse model. Adaptation therefore
proceeds as a process of estimating the necessary movements with an inverse model,
simulating with a forward model the outcome of those movement plans, observing the
difference between the desired outcome and the actual outcome, and updating the
models for a future attempt.

Information based control

An alternative to model based control is information based control. Informational
control strategies organize movements and actions based on perceptual information
about the environment, rather than on cognitive models or representations of the
world. The actions of the motor system are organized by information about the
environment and information about the current state of the agent.[47] Information
based control strategies often treat the environment and the organism as a single
system, with action proceeding as a natural consequence of the interactions of this
system. A core assumption of information based control strategies is that
perceptions of the environment are rich in information and veridical for the
purposes of producing actions. This runs counter to the assumptions of indirect
perception made by model based control strategies.

Direct perception
Direct perception in the cognitive sense is related to the philosophical notion of
naïve or direct realism in that it is predicated on the assumption that what we
perceive is what is actually in the world. James J. Gibson is credited with
recasting direct perception as ecological perception.[48] While the problem of
indirect perception proposes that physical information about object in our
environment is not available due to the ambiguity of sensory information,
proponents of direct perception (like Gibson) suggest that the relevant information
encoded in sensory signals is not the physical properties of objects, but rather
the action opportunities the environment affords. These affordances are directly
perceivable without ambiguity, and thus preclude the need for internal models or
representations of the world. Affordances exist only as a byproduct of the
interactions between an agent and its environment, and thus perception is an
"ecological" endeavor, depending on the whole agent/environment system rather than
on the agent in isolation.

Because affordances are action possibilities, perception is directly connected to

the production of actions and movements. The role of perception is to provide
information that specifies how actions should be organized and controlled,[49] and
the motor system is "tuned" to respond to specific type of information in
particular ways. Through this relationship, control of the motor system and the
execution of actions is dictated by the information of the environment. As an
example, a doorway "affords" passing through, but a wall does not. How one might
pass through a doorway is specified by the visual information received from the
environment, as well as the information perceived about one's own body. Together,
this information determines the pass-ability of a doorway, but not a wall. In
addition, the act of moving towards and passing through the doorway generates more
information and this in turn specifies further action. The conclusion of direct
perception is that actions and perceptions are critically linked and one cannot be
fully understood without the other.

Behavioral dynamics
Building on the assumptions of direct perception behavioral dynamics is a
behavioral control theory that treats perceptual organisms as dynamic systems that
respond to informational variables with actions, in a functional manner.[47] Under
this understanding of behavior, actions unfold as the natural consequence of the
interaction between the organisms and the available information about the
environment, which specified in body-relevant variables. Much of the research in
behavioral dynamics has focused on locomotion, where visually specified information
(such as optic flow, time-to-contact, optical expansion, etc.) is used to determine
how to navigate the environment[50][51] Interaction forces between the human and
the environment also affect behavioral dynamics as seen in by the Neural control of
limb stiffness.

Planning in motor control

Individual movement optimization
There are several mathematical models that describe how the central nervous system
(CNS) derives reaching movements of limbs and eyes. The minimum jerk model states
that the CNS minimizes jerk of a limb endpoint trajectory over the time of
reaching, which results in a smooth trajectory.[52] However, this model is based
solely on the kinematics of movement and does not consider the underlying dynamics
of the musculoskeletal system. Hence, the minimum torque-change model was
introduced as an alternative, where the CNS minimizes the joint torque change over
the time of reaching.[53]

Later it was argued that there is no clear explanation about how could the CNS
actually estimate complex quantities such as jerk or torque change and then
integrate them over the duration of a trajectory. In response, model based on
signal-dependent noise was proposed instead, which states that the CNS selects a
trajectory by minimizing the variance of the final position of the limb endpoint.
Since there is a motor noise in the neural system that is proportional to the
activation of the muscles, the faster movements induce more motor noise and are
thus less precise.[54] This is also in line with the Fitts' Law and speed-accuracy
trade-off.[55] Optimal control theory was used to further extend the model based on
signal-dependent noise, where the CNS optimizes an objective function that consists
of a term related to accuracy and additionally a term related to metabolic cost of
movement.[56]

Another type of models is based on cost-benefit trade-off, where the objective

function includes metabolic cost of movement and a subjective reward related to
reaching the target accurately. In this case the reward for a successful reach
within the desired target is discounted by the duration of reaching, since the
gained reward is perceived less valuable when spending more time on it.[57][58]
However, these models were deterministic and did not account for motor noise, which
is an essential property of stochastic motor control that results in speed-accuracy
trade-off. To address that, a new model was later proposed to incorporate the motor
noise and to unify cost-benefit and speed-accuracy trade-offs.[59]

Multi-component movements
Some studies observed that the CNS can split a complex movement into sub-movements.
The initial sub-movement tends to be fast and imprecise in order to bring the limb
endpoint into vicinity of the target as soon as possible. Then, the final sub-
movement tends to be slow and precise in order to correct for accumulated error by
the first initial sub-movement and to successfully reach the target.[60][61] A
later study further explored how the CNS selects a temporary target of the initial
sub-movement in different conditions. For example, when the actual target size
decreases and thus complexity increases, the temporary target of the initial sub-
movement moves away from the actual target in order to give more space for the
final corrective action. Longer reaching distances have a similar effect, since
more error is accumulated in the initial sub-movement and thus requiring more
complex final correction. In less complex conditions, when the final actual target
is large and the movement is short, the CNS tends to use a single movement, without
splitting it into multiple competents.[62]

See also
Motor learning
Motor skill
Motor coordination
Motor cortex
Multisensory integration
Proprioception
Sensory processing
Sensory-motor coupling
Two-alternative forced choice
Psychomotor learning