Optimal Control theory postulates that movements are the result of minimizing a composite movement ‘cost’ function, which typically has terms to penalize distance from intended target, energy used in the movement, time taken by the movement, etc… Each term has a weighting factor which expresses how important minimizing that term is in finding the optimal movement. Optimal Feedback Control takes this process one step further by finding a feedback controller that will not only, on average, produce the optimal movement, but will also respond optimally to any perturbations during the movement.
The mathematical machinery exists for finding a feedback controller that does the best at minimizing a cost function, but the empirical question remains as to whether real movements appear to be controlled in this way. Tomorrow, at Sensorimotor Journal Club, I will present a paper that reports on a series of experiments that attempt to address this question:
Liu, D., & Todorov, E. (2007). Evidence for the flexible sensorimotor strategies predicted by optimal feedback control. Journal of Neuroscience, 27(35), 9354-9368. (link to pdf of article)
Everyday movements pursue diverse and often conflicting mixtures of task goals, requiring sensorimotor strategies customized for the task at hand. Such customization is largely ignored by traditional theories emphasizing movement geometry and servo control. In contrast, the relationship between the task and the strategy most suitable for accomplishing it lies at the core of our optimal feedback control theory of coordination. Here we show that the predicted sensitivity to task goals affords natural explanations to a number of novel psychophysical findings. Our point of departure is the little-known fact that corrections for target perturbations introduced late in a reaching movement are incomplete. We show that this is not simply due to lack of time -- in contradiction with alternative models, and, somewhat paradoxically, in agreement with our model. Analysis of optimal feedback gains reveals that the e¤ect is partly due to a previously unknown trade-off between stability and accuracy. This yields a testable prediction: if stability requirements are decreased then accuracy should increase. We confirm the prediction experimentally in 3D ob- stacle avoidance and interception tasks where subjects hit a robotic target with programmable impedance. In further agreement with the theory, we find that subjects do not rely on rigid control strategies but instead exploit every opportunity for increased performance. The modeling methodology needed to capture this extra flexibility is more general than the linear-quadratic methods we have used previously. The results suggest that the remarkable flexibility of motor behavior arises from sensorimotor control laws optimized for composite cost functions.