A Real-Time Solver For Time-Optimal Control Of Omnidirectional Robots with Bounded Acceleration

We are interested in the problem of time-optimal control of omnidirectional robots with bounded acceleration (TOC-ORBA). While there exist approximate solutions for such robots, and exact solutions with unbounded acceleration, exact solvers to the TOC-ORBA problem have remained elusive until now. In this paper, we present a real-time solver for true time-optimal control of omnidirectional robots with bounded acceleration. We first derive the general parameterized form of the solution to the TOC-ORBA problem by application of Pontryagin's maximum principle. We then frame the boundary value problem of TOC-ORBA as an optimization problem over the parametrized control space. To overcome local minima and poor initial guesses to the optimization problem, we introduce a two-stage optimal control solver (TSOCS): The first stage computes an upper bound to the total time for the TOC-ORBA problem and holds the time constant while optimizing the parameters of the trajectory to approach the boundary value conditions. The second stage uses the parameters found by the first stage, and relaxes the constraint on the total time to solve for the parameters of the complete TOC-ORBA problem. We further implement TSOCS as a closed loop controller to overcome actuation errors on real robots in real-time. We empirically demonstrate the effectiveness of TSOCS in simulation and on real robots, showing that 1) it runs in real time, generating solutions in less than 0.5ms on average; 2) it generates faster trajectories compared to an approximate solver; and 3) it is able to solve TOC-ORBA problems with non-zero final velocities that were previously unsolvable in real-time

Hardness results for decoding the surface code with Pauli noise

Real quantum computers will be subject to complicated, qubit-dependent noise, instead of simple noise such as depolarizing noise with the same strength for all qubits. We can do quantum error correction more effectively if our decoding algorithms take into account this prior information about the specific noise present. This motivates us to consider the complexity of surface code decoding where the input to the decoding problem is not only the syndrome-measurement results, but also a noise model in the form of probabilities of single-qubit Pauli errors for every qubit. In this setting, we show that Maximum Probability Error (MPE) decoding and Maximum Likelihood (ML) decoding for the surface code are NP-hard and #P-hard, respectively. We reduce directly from SAT for MPE decoding, and from #SAT for ML decoding, by showing how to transform a boolean formula into a qubit-dependent Pauli noise model and set of syndromes that encode the satisfiability properties of the formula. We also give hardness of approximation results for MPE and ML decoding. These are worst-case hardness results that do not contradict the empirical fact that many efficient surface code decoders are correct in the average case (i.e., for most sets of syndromes and for most reasonable noise models). These hardness results are nicely analogous with the known hardness results for MPE and ML decoding of arbitrary stabilizer codes with independent $X$ and $Z$ noise.Comment: 37 pages, 18 figures. 26 pages, 12 figures in main tex

Die Schweizer Gewerkschaften und die Europäisierung helvetischer Politik

'Dieser Beitrag untersucht mit einem einfachen spieltheoretischen Instrumentarium, wie sich die Europäisierung auf die strategischen Handlungsmöglichkeiten der Gewerkschaften in der Schweiz auswirkt. Dazu wird als Beispiel für die Europäisierung über einen Staatsvertrag das Personenverkehrs-Abkommen mit dem Entscheidungsprozess über die Entbündelung der letzten Meile verglichen, der als Beispiel für den 'autonomen Nachvollzug' untersucht wird. Bei der vertraglichen Europäisierung steht den Gewerkschaften in jedem Fall eine Referendumsmöglichkeit zur Verfügung. Sofern die Gewerkschaften sich als Vetospielerin präsentieren können, sind sie in der Lage, entweder die Ratifizierung zu verhindern oder Side-Payments zum Vertrag einzufordern. Insofern ist ihre Stellung im Vergleich zu einem rein nationalen Gesetzgebungsprozess nicht geschwächt - je nach Akteurs-Konstellation kann sie sogar gestärkt werden. Beim autonomen Nachvollzug steht diese Blockadedrohung hingegen nur dann zur Verfügung, wenn das EU-Recht über eine Gesetzesrevision implementiert werden soll. Weil die ausführenden Behörden in europäisierten Politikbereichen vielfach weit reichende Kompetenzen erhalten haben, kann jedoch der Vetopunkt des Referendums oft umgangen werden. Damit verlieren die Gewerkschaften ihre Rolle als Vetospielerin.' (Autorenreferat)'By using some simple tools of game theory, this contribution examines the impact of Europeanisation on the strategic bargaining capacities of the unions in Switzerland. To this end, the bilateral agreement on the free movement of persons - as an example of Europeanisation by international treaty - is compared to the process of the unbundling of the local loop, an example where Switzerland takes over European law without contractual commitment. In the case of Europeanisation by treaty, the unions always have the possibility of resorting to the referendum. Thus, provided that the unions can credibly present themselves as an important veto player in the process, they can either block the ratification or receive side-payments in exchange for their support. In this perspective, Europeanisation does not weaken their position compared to a purely national law-making process - depending on the actor constellation, their position may even be strengthened. With regard to 'autonomous adaptation', however, the threat of blocking the procedure is only available if the ordinary law-making procedure is chosen. Yet, given that Europeanisation leads to delegation of important competencies to executive authorities, possibilities to circumvent these veto points often exist. In this case, the unions lose their veto player position.' (author's abstract

Low significance of evidence for black hole echoes in gravitational wave data

Recent detections of merging black holes allow observational tests of the nature of these objects. In some proposed models, non-trivial structure at or near the black hole horizon could lead to echo signals in gravitational wave data. Recently, Abedi et al. claimed tentative evidence for repeating damped echo signals following the gravitational-wave signals of the binary black hole merger events recorded in the first observational period of the Advanced LIGO interferometers. We reanalyse the same data, addressing some of the shortcomings of their method using more background data and a modified procedure. We find a reduced statistical significance for the claims of evidence for echoes, calculating increased p-values for the null hypothesis of echo-free noise. The reduced significance is entirely consistent with noise, and so we conclude that the analysis of Abedi et al. does not provide any observational evidence for the existence of Planck-scale structure at black hole horizons.Comment: As accepted by Physical Review