Review
The coordination of movement: optimal feedback control and beyond

https://doi.org/10.1016/j.tics.2009.11.004Get rights and content

Optimal control theory and its more recent extension, optimal feedback control theory, provide valuable insights into the flexible and task-dependent control of movements. Here, we focus on the problem of coordination, defined as movements that involve multiple effectors (muscles, joints or limbs). Optimal control theory makes quantitative predictions concerning the distribution of work across multiple effectors. Optimal feedback control theory further predicts variation in feedback control with changes in task demands and the correlation structure between different effectors. We highlight two crucial areas of research, hierarchical control and the problem of movement initiation, that need to be developed for an optimal feedback control theory framework to characterise movement coordination more fully and to serve as a basis for studying the neural mechanisms involved in voluntary motor control.

Section snippets

The problem of coordination

The defining feature of coordination is that multiple effectors work together to achieve a goal. Coordination occurs at many levels of the motor control hierarchy: between individual muscles, between joints and between limbs. Movements are made to achieve goals and effectors are coordinated to control task-relevant states of the body and environment (the physical plant). Consider the example of reaching to press an elevator button. The task-relevant state is the position of the index finger and

Optimal (feedback) control theory

OCT assumes that biological systems learn to produce motor commands, which optimise behaviour with respect to biologically relevant task goals. These goals can be formally defined as cost functions. One part of the cost function encodes the external goal of the organism; for example, for eating, grasping a food item and bringing it to the mouth. A second part of the cost function, the regularisation term, penalises some inherent feature of the movement. In earlier formulations of OCT, this term

Distribution of work across multiple effectors

As an example of how the brain solves muscular redundancy, consider movements around the wrist joint. Figure 1 shows the pulling directions (the direction of movement evoked by electrical stimulation of that muscle) of the five main wrist muscles [23]. How would the brain combine these muscles for different movement directions? Because muscles need to work harder to achieve movements that do not lie in their pulling direction, the direction of movement for which each muscle shows the highest

Task-dependent feedback control

Whereas both feedback and non-feedback versions of OCT can account for the sharing of the work across effectors, the power of the approach becomes especially clear when considering optimal feedback control. An example of this is provided by a study on bimanual reaching movements (Figure 2; [32]). In the two-cursor task, participants were instructed to reach for two separate targets, one with each hand. The task-dependent component of the cost function here contains two separate terms, one that

Structure of movement variability

An intriguing characteristic of coordinated movement is that variability is structured; systematic correlations can be found between the actions of different effectors. This structure is often task dependent. In the bimanual one-cursor task described previously, the positions of the two hands are negatively correlated at the end of the movement, deviating in opposite directions from straight ahead (Figure 3a). This correlation minimises variability along the task-relevant dimension (the

Initial gating mechanism

There are situations in which systematic correlations between effectors cannot be attributed to task-dependent feedback control. For example, when the two hands are used to reach simultaneously for two separate goals, OFCT would predict independent control of the two movements. However, strong correlations are observed in both reaction time and initial acceleration 45, 46. This form of coupling is generally considered a hard constraint in coordination [10]: it is not easily modified by task

Coordination through high-level state estimates

In OFCT, coordination is achieved by making the motor commands for one effector dependent on the state of another effector (Figure 2d). Such direct dependence is appropriate when two effectors are biomechanically coupled. Elbow and shoulder muscles need to compensate mutually for the effects of interaction torques 22, 55. In this case, the two joints always need to be controlled as a single entity.

In other situations, the need for coordination arises because two effectors act on the same

Current limitations and outlook

Here, we have outlined how OTC, especially OFCT, provides a powerful tool for understanding coordination. It is important to emphasise that OCT (and OFCT) as a theoretical framework is underspecified and has limitations in terms of generating testable predictions. It is possible to explain any behaviour as ‘optimal’ if the cost function can be chosen without restriction. To avoid circularity, the cost function needs to be specified a priori and tested across different experimental contexts.

We

Acknowledgments

The work was supported by grants from the BBSRC (J.D.: BB/E009174/1), the NSF (R.B.I. and J.D.: BSC 0726685) and the NIH (R.B.I.: HD060306).

Glossary

Control policy
a function that translates a state estimate of the body and task goal into a motor command for the next moment. This function is also referred to as a ‘next-state planner’.
Cost-function
a function that assigns each possible movement a scalar cost. The motor behaviour that minimises this cost function is optimal. Cost functions are unit-less and typically consist of one component that expresses the external task goal and a second component that serves as a regularisation factor,

References (78)

  • A. d’Avella et al.

    Shared and specific muscle synergies in natural motor behaviors

    Proc. Natl. Acad. Sci. U. S. A.

    (2005)
  • A. d’Avella

    Control of fast-reaching movements by muscle synergy combinations

    J. Neurosci.

    (2006)
  • L.H. Ting et al.

    A limited set of muscle synergies for force control during a postural task

    J. Neurophysiol.

    (2005)
  • J.A.S. Kelso

    Dynamic Patterns: The Self-Organization of Brain and Behaviour

    (1995)
  • S.P. Swinnen

    Intermanual coordination: from behavioural principles to neural-network interactions

    Nat. Rev. Neurosci.

    (2002)
  • R.A. Schmidt

    Generalized motor programs and units of action in bimanual coordination

  • R.B. Ivry

    A cognitive neuroscience perspective on bimanual coordination and interference

  • H. Heuer

    Structural constraints on bimanual movements

    Psychol. Res.

    (1993)
  • T. Flash et al.

    The coordination of arm movements: an experimentally confirmed mathematical model

    J. Neurosci.

    (1985)
  • B. Hoff et al.

    Models of trajectory formation and temporal interaction of reach and grasp

    J. Mot. Behav.

    (1993)
  • Y. Uno

    Formation and control of optimal trajectory in human multijoint arm movement. Minimum torque-change model

    Biol. Cybern

    (1989)
  • F.E. Zajac

    Muscle and tendon: properties, models, scaling and application to biomechanics and motor control

    Crit. Rev. Biomed. Eng.

    (1989)
  • C.M. Harris et al.

    Signal-dependent noise determines motor planning

    Nature

    (1998)
  • J. Izawa

    Motor adaptation as a process of reoptimization

    J. Neurosci.

    (2008)
  • A.H. Fagg

    A computational model of muscle recruitment for wrist movements

    J. Neurophysiol.

    (2002)
  • E. Todorov et al.

    Optimal feedback control as a theory of motor coordination

    Nat. Neurosci.

    (2002)
  • E. Todorov

    Stochastic optimal control and estimation methods adapted to the noise characteristics of the sensory motor system

    Neural Comput.

    (2005)
  • D. Liu et al.

    Evidence for the flexible sensorimotor strategies predicted by optimal feedback control

    J. Neurosci.

    (2007)
  • J.A. Pruszynski

    Rapid motor responses are appropriately tuned to the metrics of a visuospatial task

    J. Neurophysiol.

    (2008)
  • D.S. Hoffman et al.

    Step-tracking movements of the wrist

    IV. Muscle activity associated with movements in different directions. J. Neurophysiol.

    (1999)
  • B.M. van Bolhuis et al.

    A comparison of models explaining muscle activation patterns for isometric contractions

    Biol. Cybern.

    (1999)
  • E. Todorov

    Cosine tuning minimizes motor errors

    Neural Comput.

    (2002)
  • D. Nozaki

    Muscle activity determined by cosine tuning with a nontrivial preferred direction during isometric force exertion by lower limb

    J. Neurophysiol.

    (2005)
  • F.A. Mussa Ivaldi

    Kinematic networks. A distributed model for representing and regularizing motor redundancy

    Biol. Cybern

    (1988)
  • A. d’Avella

    Combinations of muscle synergies in the construction of a natural motor behavior

    Nat. Neurosci.

    (2003)
  • S.A. Overduin

    Modulation of muscle synergy recruitment in primate grasping

    J. Neurosci.

    (2008)
  • M. Chhabra et al.

    Properties of synergies arising from a theory of optimal motor behavior

    Neural Comput.

    (2006)
  • J.J. Kutch

    Endpoint force fluctuations reveal flexible rather than synergistic patterns of muscle cooperation

    J. Neurophysiol.

    (2008)
  • J. Diedrichsen

    Independent on-line control of the two hands during bimanual reaching

    Eur. J. Neurosci.

    (2004)
  • Cited by (0)

    View full text