Optimal Budget-Constrained Sample Allocation for Selection Decisions with Multiple Uncertain Attributes

A decision-maker, when faced with a limited and fixed budget to collect data in support of a multiple attribute selection decision, must decide how many samples to observe from each alternative and attribute. This allocation decision is of particular importance when the information gained leads to uncertain estimates of the attribute values as with sample data collected from observations such as measurements, experimental evaluations, or simulation runs. For example, when the U.S. Department of Homeland Security must decide upon a radiation detection system to acquire, a number of performance attributes are of interest and must be measured in order to characterize each of the considered systems. We identified and evaluated several approaches to incorporate the uncertainty in the attribute value estimates into a normative model for a multiple attribute selection decision. Assuming an additive multiple attribute value model, we demonstrated the idea of propagating the attribute value uncertainty and describing the decision values for each alternative as probability distributions. These distributions were used to select an alternative. With the goal of maximizing the probability of correct selection we developed and evaluated, under several different sets of assumptions, procedures to allocate the fixed experimental budget across the multiple attributes and alternatives. Through a series of simulation studies, we compared the performance of these allocation procedures to the simple, but common, allocation procedure that distributed the sample budget equally across the alternatives and attributes. We found the allocation procedures that were developed based on the inclusion of decision-maker knowledge, such as knowledge of the decision model, outperformed those that neglected such information. Beginning with general knowledge of the attribute values provided by Bayesian prior distributions, and updating this knowledge with each observed sample, the sequential allocation procedure performed particularly well. These observations demonstrate that managing projects focused on a selection decision so that the decision modeling and the experimental planning are done jointly, rather than in isolation, can improve the overall selection results.

Online Supplement to ‘Myopic Allocation Policy with Asymptotically Optimal Sampling Rate’

This document is the Online Supplement to ‘Myopic Allocation Policy with Asymptotically Optimal Sampling Rate,’ to be published in the IEEE Transactions of Automatic Control in 2017.

Wave impedance selection for passivity-based bilateral teleoperation

When a task must be executed in a remote or dangerous environment, teleoperation systems may be employed to extend the influence of the human operator. In the case of manipulation tasks, haptic feedback of the forces experienced by the remote (slave) system is often highly useful in improving an operator's ability to perform effectively. In many of these cases (especially teleoperation over the internet and ground-to-space teleoperation), substantial communication latency exists in the control loop and has the strong tendency to cause instability of the system. The first viable solution to this problem in the literature was based on a scattering/wave transformation from transmission line theory. This wave transformation requires the designer to select a wave impedance parameter appropriate to the teleoperation system. It is widely recognized that a small value of wave impedance is well suited to free motion and a large value is preferable for contact tasks. Beyond this basic observation, however, very little guidance exists in the literature regarding the selection of an appropriate value. Moreover, prior research on impedance selection generally fails to account for the fact that in any realistic contact task there will simultaneously exist contact considerations (perpendicular to the surface of contact) and quasi-free-motion considerations (parallel to the surface of contact). The primary contribution of the present work is to introduce an approximate linearized optimum for the choice of wave impedance and to apply this quasi-optimal choice to the Cartesian reality of such a contact task, in which it cannot be expected that a given joint will be either perfectly normal to or perfectly parallel to the motion constraint. The proposed scheme selects a wave impedance matrix that is appropriate to the conditions encountered by the manipulator. This choice may be implemented as a static wave impedance value or as a time-varying choice updated according to the instantaneous conditions encountered. A Lyapunov-like analysis is presented demonstrating that time variation in wave impedance will not violate the passivity of the system. Experimental trials, both in simulation and on a haptic feedback device, are presented validating the technique. Consideration is also given to the case of an uncertain environment, in which an a priori impedance choice may not be possible.