Evidence for the Flexible Sensorimotor Strategies Predicted by Optimal Feedback Control

Abstract

Everyday movements pursue diverse and often conflicting mixtures of task goals, requiring sensorimotor strategies customized for the task at hand. Such customization is mostly 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 attributable 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 effect is partly attributable 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 three-dimensional obstacle avoidance and interception tasks in which subjects hit a robotic target with programmable impedance. In additional 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 used previously. The results suggest that the remarkable flexibility of motor behavior arises from sensorimotor control laws optimized for composite cost functions.

Why Don't We Move Slower? The Value of Time in the Neural Control of Action

“…The function l is classical to motor control and may capture various aspects of the trajectory, such as effort, energy, smoothness, or accuracy. It has been the subject of exten- Hoff, 1994;Liu and Todorov, 2007); hyperbolic: G(t) ϭ ␣(1Ϫ1/(1ϩ␤t)) (Shadmehr, 2010;Shadmehr et al, 2010;Shadmehr and Mussa-Ivaldi, 2012); exponential: G͑t͒ ϭ ␣͑1 Ϫ exp͑ Ϫ ␤t͒͒ (Rigoux and Guigon, 2012); quadratic: G͑t͒ ϭ ␣t 2 (Shadmehr et al, 2010). b, The CoT ͵ 0 t l͑x͑s͒, u͑s͒͒ds (assumed to be linear here for simplicity) sums with the trajectory cost ͵ 0 t l͑x͑s͒, u͑s͒͒ds, yielding a total cost ͵ 0 t h͑x͑s͒, u͑s͒, s͒ds that exhibits a "U" shape, the minimum being the optimal MT.…”

“…Typically, the value is chosen ϳ0.04 s in the literature for fast movements (e.g., Liu and Todorov, 2007;Guigon et al, 2007), but we tested values ranging from 0.03 s to 0.08 s to evaluate the effects of varying this parameter on the shape of the CoT. In the reported simulations, we minimized the following effort cost: l͑x, u͒ ϭ 0.005͑u 1 2 ϩ u 2 2 ).…”

“…show that the neural effort cost, yet another plausible candidate trajectory cost known to predict smooth bell-shaped velocity profiles (e.g., Liu and Todorov, 2007;Guigon et al, 2007), also yields a sigmoidal CoT [especially for Ϸ 0.04 s where velocity profiles are close to minimum jerk ones, which are known to well replicate human velocity profiles; Richardson and Flash (2002)]. …”

“…In other words, slow movements may be undesirable because the very passage of time entails a cost per se, thus placing the problem within the normative framework of optimal control (OC) theory (Scott, 2004;Todorov, 2004). The generic concept of a CoT revealed itself sufficient to account for MT in a variety of motor tasks (Hoff, 1994;Liu and Todorov, 2007;Shadmehr et al, 2010;Shadmehr, 2010;Rigoux and Guigon, 2012). The actual shape of the time cost remains, however, rather elusive in neural motor control because it was chosen a priori in most existing investigations.…”

“…The actual shape of the time cost remains, however, rather elusive in neural motor control because it was chosen a priori in most existing investigations. Researchers have assumed linear (Hoff, 1994;Harris and Wolpert, 2006;Liu and Todorov, 2007), concave (hyperbolic, Shadmehr, 2010;Haith et al, 2012;or exponential, Huh et al, 2010;Rigoux and Guigon, 2012) and even convex (quadratic, Shadmehr et al, 2010) shapes for the CoT (Fig. 1a).…”