Degrees of freedom problem

The study of motor control historically breaks down into two broad areas: "Western" neurophysiological studies, and "Bernsteinian" functional analysis of movement. The latter has become predominant in motor control, as Bernstein's theories have held up well and are considered founding principles of the field as it exists today. Pre-Bernstein In the latter 19th and early 20th centuries, many scientists believed that all motor control came from the spinal cord, as experiments with stimulation in frogs displayed patterned movement ("motor primitives"), and spinalized cats were shown to be able to walk. This tradition was closely tied with the strict nervous system localizationism advocated during that period; since stimulation of the frog spinal cord in different places produced different movements, it was thought that all motor impulses were localized in the spinal cord. However, fixed structure and localizationism were slowly broken down as the central dogma of neuroscience. It is now known that the primary motor cortex and premotor cortex at the highest level are responsible for most voluntary movements. Animal models, though, remain relevant in motor control and spinal cord reflexes and central pattern generators are still a topic of study. Bernstein Although Lashley (1933) first formulated the motor equivalence problem, it was Bernstein who articulated the DOF problem in its current form. In Bernstein's formulation, the problem results from infinite redundancy, yet flexibility between movements; thus, the nervous system apparently must choose a particular motor solution every time it acts. In Bernstein's formulation, a single muscle never acts in isolation. Rather, large numbers of "nervous centres" cooperate in order to make a whole movement possible. Nervous impulses from different parts of the CNS may converge on the periphery in combination to produce a movement; however, there is great difficulty for scientists in understanding and coordinating the facts linking impulses to a movement. Bernstein's rational understanding of movement and prediction of motor learning via what we now call "plasticity" was revolutionary for his time. In Bernstein's view, movements must always reflect what is contained in the "central impulse", in one way or another. However, he recognized that effectors (feed-forward) were not the only important component to movement; feedback was also necessary. Thus, Bernstein was one of the first to understand movement as a closed circle of interaction between the nervous system and the sensory environment, rather than a simple arc toward a goal. He defined motor coordination as a means for overcoming indeterminacy due to redundant peripheral DOFs. With increasing DOFs, it is increasingly necessary for the nervous system to have a more complex, delicate organizational control. Because humans are adapted to survive, the "most important" movements tend to be reflexes -- pain or defensive reflexes needed to be carried out in very short time scales in order for ancient humans to survive their harsh environment. Most of our movements, though, are voluntary; voluntary control had historically been under-emphasized or even disregarded altogether. Bernstein saw voluntary movements as structured around a "motor problem" where the nervous system needed two factors to act: a full and complete perception of reality, as accomplished by multisensory integration, and objectivity of perception through constant and correct recognition of signals by the nervous system. Only with both may the nervous system choose an appropriate motor solution. ==Difficulties==

The DOF problem is still a topic of study because of the complexity of the neuromuscular system of the human body. Not only is the problem itself exceedingly difficult to tackle, but the vastness of the field of study makes synthesis of theories a challenge. Counting degrees of freedom One of the largest difficulties in motor control is quantifying the exact number of DOFs in the complex neuromuscular system of the human body. In addition to having redundant muscles and joints, muscles may span multiple joints, further complicating the system. Properties of muscle change as the muscle length itself changes, making mechanical models difficult to create and understand. Individual muscles are innervated by multiple nerve fibers (motor units), and the manner in which these units are recruited is similarly complex. While each joint is commonly understood as having an agonist-antagonist pair, not all joint movement is controlled locally. Finally, movement kinematics are not identical even when performing the same motion repeatedly; natural variation in position, velocity, and acceleration of the limb occur even during seemingly identical movements. ==Hypotheses and proposed solutions==

There have been many attempts to offer solutions or conceptual models that explain the DOF problem. One of the first hypotheses was Fitts' Law, which states that a trade-off must occur between movement speed and movement accuracy in a reaching task. Since then, many other theories have been offered. Optimal control hypothesis A general paradigm for understanding motor control, optimal control has been defined as "optimizing motor control for a given aspect of task performance," or as a way to minimize a certain "cost" associated with a movement. Furthermore, the cost function may be quite complex (for instance, it may be a functional instead of function) and be also related to the representations in the internal space. For example, the speech produced by biomechanical tongue models, controlled by the internal model which minimizes the length of the path traveled in the internal space under the constraints related to the executed task (e.g., quality of speech, stiffness of tongue), was found to be quite realistic. Two key components of all optimal control systems are: a "state estimator" which tells the nervous system about what it is doing, including afferent sensory feedback and an efferent copy of the motor command; and adjustable feedback gains based on task goals. A component of these adjustable gains might be a "minimum intervention principle" where the nervous system only performs selective error correction rather than heavily modulating the entirety of a movement. Open-loop models are simpler but have severe limitations—they model a movement as prerecorded in the nervous system, ignoring sensory feedback, and also fail to model variability between movements with the same task-goal. In both models, the primary difficulty is identifying the cost associated with a movement. A mix of cost variables such as minimum energy expenditure and a "smoothness" function is the most likely choice for a common performance criterion. Limits of optimal control Optimal control is a way of understanding motor control and the motor equivalence problem, but as with most mathematical theories about the nervous system, it has limitations. The theory must have certain information provided before it can make a behavioral prediction: what the costs and rewards of a movement are, what the constraints on the task are, and how state estimation takes place. In essence, the difficulty with optimal control lies in understanding how the nervous system precisely executes a control strategy. Multiple muscles are contained within each synergy at fixed ratios of co-activation, and multiple synergies can contain the same muscle. It has been proposed that muscle synergies emerge from an interaction between constraints and properties of the nervous and musculoskeletal systems. This organization may require less computational effort for the nervous system than individual muscle control because fewer synergies are needed to explain a behavior than individual muscles. Furthermore, it has been proposed that synergies themselves may change as behaviors are learned and/or optimized. However, synergies may also be innate to some degree, as suggested by postural responses of humans at very young ages. Evidence for this structure comes from electromyographical (EMG) data in frogs, cats, and humans, where various mathematical methods such as principal components analysis and non-negative matrix factorization are used to "extract" synergies from muscle activation patterns. Similarities have been observed in synergy structure even across different tasks such as kicking, jumping, swimming and walking in frogs. The equilibrium-point hypothesis is also reported to be well suited for the design of biomechanical robots controlled by appropriated internal models. Force control and internal models The force control hypothesis states that the nervous system uses calculation and direct specification of forces to determine movement trajectories and reduce DOFs. In this theory, the nervous system must form internal models—a representation of the body's dynamics in terms of the surrounding environment. Uncontrolled manifold (UCM) hypothesis It has been noted that the nervous system controls particular variables relevant to performance of a task, while leaving other variables free to vary; this is called the uncontrolled manifold hypothesis (UCM). The uncontrolled manifold is defined as the set of variables not affecting task performance; variables perpendicular to this set in Jacobian space are considered controlled variables (CM). For example, during a sit-to-stand task, head and center-of-mass position in the horizontal plane are more tightly controlled than other variables such as hand motion. Another study indicates that the quality of tongue's movements produced by bio-robots, which are controlled by a specially designed internal model, is practically uncorrelated with the stiffness of the tongue; in other words, during the speech production the relevant parameter is the quality of speech, while the stiffness is rather irrelevant. At the same time, the strict prescription of the stiffness' level to the tongue's body affects the speech production and creates some variability, which is however, not significant for the quality of speech (at least, in the reasonable range of stiffness' levels). UCM theory makes sense in terms of Bernstein's original theory because it constrains the nervous system to only controlling variables relevant to task performance, rather than controlling individual muscles or joints. ==Unifying theories==

Not all theories about the selection of movement are mutually exclusive. Necessarily, they all involve reduction or elimination of redundant DOFs. Optimal feedback control is related to UCM theory in the sense that the optimal control law may not act along certain dimensions (the UCM) of lesser importance to the nervous system. Furthermore, this lack of control in certain directions implies that controlled variables will be more tightly correlated; this correlation is seen in the low-dimensionality of muscle synergies. Furthermore, most of these theories incorporate some sort of feedback and feed-forward models that the nervous system must utilize. Most of these theories also incorporate some sort of hierarchical neural control scheme, usually with cortical areas at the top and peripheral outputs at the lowest level. However, none of the theories is perfect; the DOF problem will continue to be relevant as long as the nervous system is imperfectly understood. ==See also==