A Quasar Microlensing Light Curve Generator for LSST

We present a tool to generate mock quasar microlensing light curves and sample them according to any observing strategy. An updated treatment of the fixed and random velocity components of observer, lens, and source is used, together with a proper alignment with the external shear defining the magnification map caustic orientation. Our tool produces quantitative results on high magnification events and caustic crossings, which we use to study three lensed quasars known to display microlensing, viz. RX J1131-1231, HE 0230-2130, and Q 2237+0305, as they would be monitored by The Rubin Observatory Legacy Survey of Space and Time (LSST). We conclude that depending on the location on the sky, the lens and source redshift, and the caustic network density, the microlensing variability may deviate significantly than the expected $\sim$20-year average time scale (Mosquera & Kochanek 2011, arXiv:1104.2356). We estimate that $\sim300$ high magnification events with $\Delta$mag$>1$ mag could potentially be observed by LSST each year. The duration of the majority of high magnification events is between 10 and 100 days, requiring a very high cadence to capture and resolve them. Uniform LSST observing strategies perform the best in recovering microlensing high magnification events. Our web tool can be extended to any instrument and observing strategy, and is freely available as a service at http://gerlumph.swin.edu.au/tools/lsst_generator/, along with all the related code.Comment: 10 pages, 6 figures, 2 tables. Published in MNRAS. Updated Table

Footstep and Motion Planning in Semi-unstructured Environments Using Randomized Possibility Graphs

Traversing environments with arbitrary obstacles poses significant challenges for bipedal robots. In some cases, whole body motions may be necessary to maneuver around an obstacle, but most existing footstep planners can only select from a discrete set of predetermined footstep actions; they are unable to utilize the continuum of whole body motion that is truly available to the robot platform. Existing motion planners that can utilize whole body motion tend to struggle with the complexity of large-scale problems. We introduce a planning method, called the "Randomized Possibility Graph", which uses high-level approximations of constraint manifolds to rapidly explore the "possibility" of actions, thereby allowing lower-level motion planners to be utilized more efficiently. We demonstrate simulations of the method working in a variety of semi-unstructured environments. In this context, "semi-unstructured" means the walkable terrain is flat and even, but there are arbitrary 3D obstacles throughout the environment which may need to be stepped over or maneuvered around using whole body motions.Comment: Accepted by IEEE International Conference on Robotics and Automation 201

Reactive Planar Manipulation with Convex Hybrid MPC

This paper presents a reactive controller for planar manipulation tasks that leverages machine learning to achieve real-time performance. The approach is based on a Model Predictive Control (MPC) formulation, where the goal is to find an optimal sequence of robot motions to achieve a desired object motion. Due to the multiple contact modes associated with frictional interactions, the resulting optimization program suffers from combinatorial complexity when tasked with determining the optimal sequence of modes. To overcome this difficulty, we formulate the search for the optimal mode sequences offline, separately from the search for optimal control inputs online. Using tools from machine learning, this leads to a convex hybrid MPC program that can be solved in real-time. We validate our algorithm on a planar manipulation experimental setup where results show that the convex hybrid MPC formulation with learned modes achieves good closed-loop performance on a trajectory tracking problem

Adaptive Protection and Control in Power System for Wide-Area Blackout Prevention

This paper presents a new approach in adaptive outof-step (OOS) protection settings in power system in real-time. The proposed method uses extended equal area criterion (EEAC) to determine the critical clearing time (CCT) and critical clearing angle (CCA) of the system, which are vital information for OOS protection setting calculation. The dynamic model parameters and the coherency groups of the system for EEAC analysis are determined in real time to ensure that the newly calculated settings suit with the prevalent system operating condition. The effectiveness of the method is demonstrated in a simulated data from 16-machine 68-bus system model

Comparative evaluation of approaches in T.4.1-4.3 and working definition of adaptive module

The goal of this deliverable is two-fold: (1) to present and compare different approaches towards learning and encoding movements us- ing dynamical systems that have been developed by the AMARSi partners (in the past during the first 6 months of the project), and (2) to analyze their suitability to be used as adaptive modules, i.e. as building blocks for the complete architecture that will be devel- oped in the project. The document presents a total of eight approaches, in two groups: modules for discrete movements (i.e. with a clear goal where the movement stops) and for rhythmic movements (i.e. which exhibit periodicity). The basic formulation of each approach is presented together with some illustrative simulation results. Key character- istics such as the type of dynamical behavior, learning algorithm, generalization properties, stability analysis are then discussed for each approach. We then make a comparative analysis of the different approaches by comparing these characteristics and discussing their suitability for the AMARSi project

Real-Time Motion Planning of Legged Robots: A Model Predictive Control Approach

We introduce a real-time, constrained, nonlinear Model Predictive Control for the motion planning of legged robots. The proposed approach uses a constrained optimal control algorithm known as SLQ. We improve the efficiency of this algorithm by introducing a multi-processing scheme for estimating value function in its backward pass. This pass has been often calculated as a single process. This parallel SLQ algorithm can optimize longer time horizons without proportional increase in its computation time. Thus, our MPC algorithm can generate optimized trajectories for the next few phases of the motion within only a few milliseconds. This outperforms the state of the art by at least one order of magnitude. The performance of the approach is validated on a quadruped robot for generating dynamic gaits such as trotting.Comment: 8 page