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State space analysis of timing: exploiting task redundancy to reduce sensitivity to timing.

Timing is central to many coordinated actions, and the temporal accuracy of central nervous system commands presents an important limit to skilled performance. Using target-oriented throwing in a virtual environment as an example task, this study presents a novel analysis that quantifies contributions of timing accuracy and shaping of hand trajectories to performance. Task analysis reveals that the result of a throw is fully determined by the projectile position and velocity at release; zero error can be achieved by a manifold of position and velocity combinations (solution manifold). Four predictions were tested. 1) Performers learn to release the projectile closer to the optimal moment for a given arm trajectory, achieving timing accuracy levels similar to those reported in other timing tasks (~10 ms). 2) Performers develop a hand trajectory that follows the solution manifold such that zero error can be achieved without perfect timing. 3) Skilled performers exploit both routes to improvement more than unskilled performers. 4) Long-term improvement in skilled performance relies on continued optimization of the arm trajectory as timing limits are reached. Average and skilled subjects practiced for 6 and 15 days, respectively. In 6 days, both timing and trajectory alignment improved for all subjects, and skilled subjects showed an advantage in timing. With extended practice, performance continued to improve due to continued shaping of the trajectory, whereas timing accuracy reached an asymptote at 9 ms. We conclude that skilled subjects first maximize timing accuracy and then optimize trajectory shaping to compensate for intrinsic limitations of timing accuracy.