A vision system planner for increasing the autonomy of the Extravehicular Activity Helper/Retriever

The Extravehicular Activity Retriever (EVAR) is a robotic device currently being developed by the Automation and Robotics Division at the NASA Johnson Space Center to support activities in the neighborhood of the Space Shuttle or Space Station Freedom. As the name implies, the Retriever's primary function will be to provide the capability to retrieve tools and equipment or other objects which have become detached from the spacecraft, but it will also be able to rescue a crew member who may have become inadvertently de-tethered. Later goals will include cooperative operations between a crew member and the Retriever such as fetching a tool that is required for servicing or maintenance operations. This paper documents a preliminary design for a Vision System Planner (VSP) for the EVAR that is capable of achieving visual objectives provided to it by a high level task planner. Typical commands which the task planner might issue to the VSP relate to object recognition, object location determination, and obstacle detection. Upon receiving a command from the task planner, the VSP then plans a sequence of actions to achieve the specified objective using a model-based reasoning approach. This sequence may involve choosing an appropriate sensor, selecting an algorithm to process the data, reorienting the sensor, adjusting the effective resolution of the image using lens zooming capability, and/or requesting the task planner to reposition the EVAR to obtain a different view of the object. An initial version of the Vision System Planner which realizes the above capabilities using simulated images has been implemented and tested. The remaining sections describe the architecture and capabilities of the VSP and its relationship to the high level task planner. In addition, typical plans that are generated to achieve visual goals for various scenarios are discussed. Specific topics to be addressed will include object search strategies, repositioning of the EVAR to improve the quality of information obtained from the sensors, and complementary usage of the sensors and redundant capabilities

Surface Words are Determined by Word Measures on Groups

Every word $w$ in a free group naturally induces a probability measure on every compact group $G$. For example, if $w=\left[x,y\right]$ is the commutator word, a random element sampled by the $w$-measure is given by the commutator $\left[g,h\right]$ of two independent, Haar-random elements of $G$. Back in 1896, Frobenius showed that if $G$ is a finite group and $\psi$ an irreducible character, then the expected value of $\psi\left(\left[g,h\right]\right)$ is $\frac{1}{\psi\left(e\right)}$. This is true for any compact group, and completely determines the $\left[x,y\right]$-measure on these groups. An analogous result holds with the commutator word replaced by any surface word. We prove a converse to this theorem: if $w$ induces the same measure as $\left[x,y\right]$ on every compact group, then, up to an automorphism of the free group, $w$ is equal to $\left[x,y\right]$. The same holds when $\left[x,y\right]$ is replaced by any surface word. The proof relies on the analysis of word measures on unitary groups and on orthogonal groups, which appears in separate papers, and on new analysis of word measures on generalized symmetric groups that we develop here.Comment: 16 pages, fixed the proof of Theorem 3.6, updated reference

Allocating Awards Across Noncomparable Categories

Suppose an agency awards a …xed number of prizes to applicants in different categories such that the applicant-to-winner ratio is constant by category. It is demonstrated in a simple theoretical model that the number of awards in a category will typically be positively related to the degree of applicant uncertainty. The theoretical …ndings are related to awards data from the Social Sciences and Humanities Research Council of Canada doctoral fellowship competition.