Trends in Cognitive Sciences
ReviewThe coordination of movement: optimal feedback control and beyond
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,
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