Throwing by a powered manipulator is an effective way for wide range transportation of an object and carrying an object in unmanned environments. The main problems of throwing are (i) how far the manipulator can throw the object and (ii) the accuracy of the landing position. Focusing on (ii), this paper proposes sensitivity analysis of the landing position with respect to the error covariance of dynamic parameters. Focusing on a planar 3-DOF manipulator, (1) the minimum set of dynamic parameters is introduced and identified based on a frequency weighted method for a nonlinear system, and its error covariance is also identified. (2) The calculation algorithm for sensitivity of landing position with respect to the minimum set of dynamic parameters is proposed. (3) By considering the error covariance of identification, an optimal throwing is designed and evaluated by simulations and/or experiments. Moreover, (4) the principal of sensitivity analysis is discussed from error ellipsoid point of view, and zero error throwing is designed.
The validity of the thru-only de-embedding method that uses mathematically bisected halves of a left-right symmetric THRU pattern is assessed in this paper. The popularly used Πequivalent representation of a THRU and the bisection thereof is neither unique nor its validity firmly established. It is shown that an equally simple T-equivalent-based bisection gives better results than the Π-equivalent-based bisection by comparing the two bisecting methods with a result obtained from an independent method. The thru-only de-embedding method is also compared with the conventional open-short and short-open methods, and the interrelationship among them expected from the assumed equivalent circuit representations of the relevant dummy patterns is confirmed. This is made possible by using the odd-mode responses of symmetric 4-port devices as the 2-ports under study. This way, nonidealities associated with ordinary 2-port dummy patterns is avoided.
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