A Hybrid Observer for a Distributed Linear System with a Changing Neighbor Graph

A hybrid observer is described for estimating the state of an $m>0$ channel, $n$-dimensional, continuous-time, distributed linear system of the form $\dot{x} = Ax,\;y_i = C_ix,\;i\in\{1,2,\ldots, m\}$. The system's state $x$ is simultaneously estimated by $m$ agents assuming each agent $i$ senses $y_i$ and receives appropriately defined data from each of its current neighbors. Neighbor relations are characterized by a time-varying directed graph $\mathbb{N}(t)$ whose vertices correspond to agents and whose arcs depict neighbor relations. Agent $i$ updates its estimate $x_i$ of $x$ at "event times" $t_1,t_2,\ldots$ using a local observer and a local parameter estimator. The local observer is a continuous time linear system whose input is $y_i$ and whose output $w_i$ is an asymptotically correct estimate of $L_ix$ where $L_i$ a matrix with kernel equaling the unobservable space of $(C_i,A)$. The local parameter estimator is a recursive algorithm designed to estimate, prior to each event time $t_j$, a constant parameter $p_j$ which satisfies the linear equations $w_k(t_j-\tau) = L_kp_j+\mu_k(t_j-\tau),\;k\in\{1,2,\ldots,m\}$, where $\tau$ is a small positive constant and $\mu_k$ is the state estimation error of local observer $k$. Agent $i$ accomplishes this by iterating its parameter estimator state $z_i$, $q$ times within the interval $[t_j-\tau, t_j)$, and by making use of the state of each of its neighbors' parameter estimators at each iteration. The updated value of $x_i$ at event time $t_j$ is then $x_i(t_j) = e^{A\tau}z_i(q)$. Subject to the assumptions that (i) the neighbor graph $\mathbb{N}(t)$ is strongly connected for all time, (ii) the system whose state is to be estimated is jointly observable, (iii) $q$ is sufficiently large, it is shown that each estimate $x_i$ converges to $x$ exponentially fast as $t\rightarrow \infty$ at a rate which can be controlled.Comment: 7 pages, the 56th IEEE Conference on Decision and Contro

The Use of Force Feedback Control for Robotic Mating of Umbilical Fuel Lines

NASA has long desired the ability to remotely connect, disconnect, and reconnect the umbilical fuel lines to the Space Shuttle Vehicle (SSV). The Robotic Application and Development Laboratory (RADL) at Kennedy Space Center has been investigating the application of robotics to this problem. A generic remote umbilical system has been identified for a proof-of-concept demonstration, wherein a robot is used to mate an umbilical connector with a moving target representing the SSV. This task is a variation of the classic peg-inthe- hole problem, where the hole is undergoing random motions. For umbilical docking, the ability to minimize and control contact forces between the umbilical lines and the SSV is vital. These forces occur both during the mating of the fuel line with the SSV and also as a result of the relative motion between the robot and the SSV after mating. This paper describes work on the force feedback control problems encountered by the RADL for umbilical mating. An outline of a proposed docking protocol is first presented, indicating the role required offeree feedback. The use of active force feedback control is described, along with the performance requirements and experimental results. Proposed modifications to the existing force feedback controller, including passive compliance requirements are described. Finally description of future work is presented

Ultraluminous X-ray Source Correlations with Star-Forming Regions

Maps of low-inclination nearby galaxies in Sloan Digitized Sky Survey u-g, g-r and r-i colors are used to determine whether Ultraluminous X-ray sources (ULXs) are predominantly associated with star-forming regions of their host galaxies. An empirical selection criterion is derived from colors of HII regions in M81 and M101 that differentiates between the young, blue stellar component and the older disk and bulge population. This criterion is applied to a sample of 58 galaxies of Hubble type S0 and later and verified through an application of Fisher's linear discriminant analysis. It is found that 60% (49%) of ULXs in optically-bright environments are within regions blueward of their host galaxy's HII regions compared to only 27% (0%) of a control sample according to the empirical (Fisher) criterion. This is an excess of 3-sigma above the 32% (27%) expected if the ULXs were randomly distributed within their galactic hosts. This indicates a ULX preference for young, approximately <10 Myr, OB associations. However, none of the ULX environments have the morphology and optical brightness suggestive of a massive young super star cluster though several are in extended or crowded star-forming (blue) environments that may contain clusters unresolved by Sloan imaging. Ten of the 12 ULX candidates with estimated X-ray luminosities in excess of 3e39 erg/s are equally divided among the group of ULX environments redward of HII regions and the group of optically faint regions. This likely indicates that the brightest ULXs turn on at a time somewhat later than typical of HII regions; say 10-20 Myr after star formation has ended. This would be consistent with the onset of an accretion phase as the donor star ascends the giant branch if the donor is a <20 solar-mass star.Comment: 13 pages, accepted to Ap