A E Bryson | Search PubMed

PubMed1995

Estimating net joint torques from kinesiological data using optimal linear system theory.

Net joint torques (NJT) are frequently computed to provide insights into the motor control of dynamic biomechanical systems. An inverse dynamics approach is almost always used, whereby the NJT are computed from 1) kinematic measurements (e.g., position of the segments), 2) kinetic measurements (e.g., ground reaction forces) that are, in effect, constraints defining unmeasured kinematic quantities based on a dynamic segmental model, and 3) numerical differentiation of the measured kinematics to estimate velocities and accelerations that are, in effect, additional constraints. Due to errors in the measurements, the segmental model, and the differentiation process, estimated NJT rarely produce the observed movement in a forward simulation when the dynamics of the segmental system are inherently unstable (e.g., human walking). Forward dynamic simulations are, however, essential to studies of muscle coordination. We have developed an alternative approach, using the linear quadratic follower (LQF) algorithm, which computes the NJT such that a stable simulation of the observed movement is produced and the measurements are replicated as well as possible. The LQF algorithm does not employ constraints depending on explicit differentiation of the kinematic data, but rather employs those depending on specification of a cost function, based on quantitative assumptions about data confidence. We illustrate the usefulness of the LQF approach by using it to estimate NJT exerted by standing humans perturbed by support-surface movements. We show that unless the number of kinematic and force variables recorded is sufficiently high, the confidence that can be placed in the estimates of the NJT, obtained by any method (e.g., LQF, or the inverse dynamics approach), may be unsatisfactorily low.

Algorithms↗

PubMed1981

Delay or rate of food delivery as determiners of response rate.

PIGEONS WERE CONFRONTED WITH TWO KEYS: a green food key and a white changeover key. Food became available for a peck to the green key after variable intervals of time (mean = 113 seconds). A single peck on the changeover key changed the color of the food key to red for a fixed period of time during which the timing of the variable-interval schedule in green was suspended and the switching option eliminated and after which the conditions associated with green were reinstated. In Experiment 1 a single food presentation was obtainable during each red-key period after a minimum delay timed from the switch. This delay and the duration of the red-key period were held constant during a condition but varied between conditions (delay = 2.5, 7.5, 15, or 30 seconds; red-period duration = 30, 60, 120, 240, or 480 seconds). In Experiment 2 additional food presentations were scheduled during a 240-second red-key period with the delay to the first food delivery held constant at 30 seconds, and the delays to later food deliveries varied over conditions. Considering the data from both experiments, the rate of switching to red was a decreasing function of the delay to the first food, the delay to the second food, and perhaps the delay to the third food after a switch. There was no clear evidence that the rate of food in the red-key period made an independent contribution. The ordering of response rates among conditions was consistent with the view that each food presentation after a response adds an incremental effect to the rate of the response and that each food presentation's contribution is a decreasing function of its delay timed from the response.

Journal Article↗