The time-optimal control of a system of rigid bodies connected in series by single-degree-of-freedom joints is studied. The dynamical equations of the system are highly nonlinear and a closed-form representation of the minimum-time feedback control is not possible. However, a suboptimal feedback control which provides a close approximation to the optimal control is developed. The suboptimal control is expressed in terms of switching curves for each of the system controls. These curves are obtained from the linearized equations of motion for the system. Approximations are made for the effects of gravity loads and angular velocity terms in the nonlinear equations of motion. Digital simulation is used to obtain a comparison of response of the optimal and suboptimal controls. The speed of response of the suboptimal control is found to compare quite favorably with the response speed of the optimal control. The analysis is applied to the control of three joints of a mechanical manipulator. Modifications of the suboptimal control for use in a sampled-data system are shown to result in good performance of a hydraulic manipulator under computer control. (Author).

These results are intended to provide quantitative flight-test information which may be useful to designers in attempting to provide for adequate low-speed control and which may be correlated with analytical analyses as presented in the third and finai report in this series (Technical Note 3677).

This report summarizes the activities and progress of Department of Agriculture entomologists working in 13 countries during the period 1951-1957. It describes the nature of the cooperative effort between the Department of Agriculture and the International Cooperation Administration, and the coordination of project activities within the host countries. Tables are presented containing data to emphasize the important material and financial participation in this program by friendly cooperative countries, and the fact that their contributions far surpass those of the United States.