Trajectory Optimization Through Contacts and Automatic Gait Discovery for Quadrupeds

In this work we present a trajectory Optimization framework for whole-body motion planning through contacts. We demonstrate how the proposed approach can be applied to automatically discover different gaits and dynamic motions on a quadruped robot. In contrast to most previous methods, we do not pre-specify contact switches, timings, points or gait patterns, but they are a direct outcome of the optimization. Furthermore, we optimize over the entire dynamics of the robot, which enables the optimizer to fully leverage the capabilities of the robot. To illustrate the spectrum of achievable motions, here we show eight different tasks, which would require very different control structures when solved with state-of-the-art methods. Using our trajectory Optimization approach, we are solving each task with a simple, high level cost function and without any changes in the control structure. Furthermore, we fully integrated our approach with the robot's control and estimation framework such that optimization can be run online. By demonstrating a rough manipulation task with multiple dynamic contact switches, we exemplarily show how optimized trajectories and control inputs can be directly applied to hardware.Comment: Video: https://youtu.be/sILuqJBsyK

A Family of Iterative Gauss-Newton Shooting Methods for Nonlinear Optimal Control

This paper introduces a family of iterative algorithms for unconstrained nonlinear optimal control. We generalize the well-known iLQR algorithm to different multiple-shooting variants, combining advantages like straight-forward initialization and a closed-loop forward integration. All algorithms have similar computational complexity, i.e. linear complexity in the time horizon, and can be derived in the same computational framework. We compare the full-step variants of our algorithms and present several simulation examples, including a high-dimensional underactuated robot subject to contact switches. Simulation results show that our multiple-shooting algorithms can achieve faster convergence, better local contraction rates and much shorter runtimes than classical iLQR, which makes them a superior choice for nonlinear model predictive control applications.Comment: 8 page

Portfolioallokation: Einbezug verschiedener Assetklassen

Die Stabilität der Europäischen Währungsunion ist durch die derzeit angespannte Haushaltslage und den hohen Verschuldungsgrad einiger Mitgliedstaaten in Frage gestellt. Diese Arbeit untersucht die Auswirkungen verschiedener (Krisen-)Szenarien auf das Portfolio eines durchschnittlichen deutschen Privatanlegers. Zum Zweck der Anlageoptimierung wird die Entwicklung des varianzminimalen Portfoliooptimierungsansatzes nach Markowitz und einer Gleichgewichtungsmethode (1/n-Heuristik) mit fünf ausgewählten Anlageklassen analysiert. Anschließend werden die Entwicklungen der Portfolios über verschiedene Zeiträume für drei vergangenheitsorientierte Szenarien betrachtet. Im Ergebnis kann festgestellt werden, dass das heuristische Portfolio und das Minimum-Varianz-Portfolio (MVP) die durchschnittlichen Privatanlegerportfolios im Bad-Case-Szenario sowohl in Bezug auf die Rendite als auch auf die Volatilität dominieren. Da die untersuchten Privatanlegerportfolios exklusiv aus Aktien- und Rentenwerten bestehen, weisen sie im Good-Case- und Mid-Case-Szenario höhere Renditen als die Benchmark-Portfolios, aber gleichzeitig auch eine höhere Volatilität auf. Insgesamt kann abgeleitet werden, dass eine Anlage in Gold und insbesondere in Währungen die Portfolios stabilisiert. Die Darstellung eines Portfolios mit geringer Volatilität könnte daher vereinfachend und transparent mittels des heuristischen Portfolios umgesetzt werden.High levels of public debt have recently unsettled the European Monetary Union. This paper examines the effect of different downside scenarios on the portfolio of an average German investor. To identify the right asset allocation, this paper analyzes the minimal variance portfolio optimization according to Markowitz as well as a heuristic method (whereby each asset class is weighted equally) with five different asset classes. Subsequently, the analysis examines the development of these portfolios for three historic scenarios over different periods of time. In summary, this paper concludes that investments in the heuristic portfolio and in the minimum variance portfolio provide both a higher return and lower volatility in the bad case scenario, compared to the average portfolio of a private investor. Since the portfolios of private investors exclusively comprise shares and bonds, these portfolios display a higher return, yet also higher volatility, in the good case and mid case scenarios. Overall, analysis reveals that allocations into gold and especially into currencies stabilize the portfolios of an average German investor. As a result, the 1/n-heuristic method offers a simplified and transparent way to design a low volatility portfolio

Physician decision making in selection of second-line treatments in immune thrombocytopenia in children.

Immune thrombocytopenia (ITP) is an acquired autoimmune bleeding disorder which presents with isolated thrombocytopenia and risk of hemorrhage. While most children with ITP promptly recover with or without drug therapy, ITP is persistent or chronic in others. When needed, how to select second-line therapies is not clear. ICON1, conducted within the Pediatric ITP Consortium of North America (ICON), is a prospective, observational, longitudinal cohort study of 120 children from 21 centers starting second-line treatments for ITP which examined treatment decisions. Treating physicians reported reasons for selecting therapies, ranking the top three. In a propensity weighted model, the most important factors were patient/parental preference (53%) and treatment-related factors: side effect profile (58%), long-term toxicity (54%), ease of administration (46%), possibility of remission (45%), and perceived efficacy (30%). Physician, health system, and clinical factors rarely influenced decision-making. Patient/parent preferences were selected as reasons more often in chronic ITP (85.7%) than in newly diagnosed (0%) or persistent ITP (14.3%, P = .003). Splenectomy and rituximab were chosen for the possibility of inducing long-term remission (P < .001). Oral agents, such as eltrombopag and immunosuppressants, were chosen for ease of administration and expected adherence (P < .001). Physicians chose rituximab in patients with lower expected adherence (P = .017). Treatment choice showed some physician and treatment center bias. This study illustrates the complexity and many factors involved in decision-making in selecting second-line ITP treatments, given the absence of comparative trials. It highlights shared decision-making and the need for well-conducted, comparative effectiveness studies to allow for informed discussion between patients and clinicians