Imprecise dynamic walking with time-projection control

We present a new walking foot-placement controller based on 3LP, a 3D model of bipedal walking that is composed of three pendulums to simulate falling, swing and torso dynamics. Taking advantage of linear equations and closed-form solutions of the 3LP model, our proposed controller projects intermediate states of the biped back to the beginning of the phase for which a discrete LQR controller is designed. After the projection, a proper control policy is generated by this LQR controller and used at the intermediate time. This control paradigm reacts to disturbances immediately and includes rules to account for swing dynamics and leg-retraction. We apply it to a simulated Atlas robot in position-control, always commanded to perform in-place walking. The stance hip joint in our robot keeps the torso upright to let the robot naturally fall, and the swing hip joint tracks the desired footstep location. Combined with simple Center of Pressure (CoP) damping rules in the low-level controller, our foot-placement enables the robot to recover from strong pushes and produce periodic walking gaits when subject to persistent sources of disturbance, externally or internally. These gaits are imprecise, i.e., emergent from asymmetry sources rather than precisely imposing a desired velocity to the robot. Also in extreme conditions, restricting linearity assumptions of the 3LP model are often violated, but the system remains robust in our simulations. An extensive analysis of closed-loop eigenvalues, viable regions and sensitivity to push timings further demonstrate the strengths of our simple controller

Reducing "Structure From Motion": a General Framework for Dynamic Vision - Part 2: Experimental Evaluation

A number of methods have been proposed in the literature for estimating scene-structure and ego-motion from a sequence of images using dynamical models. Although all methods may be derived from a "natural" dynamical model within a unified framework, from an engineering perspective there are a number of trade-offs that lead to different strategies depending upon the specific applications and the goals one is targeting. Which one is the winning strategy? In this paper we analyze the properties of the dynamical models that originate from each strategy under a variety of experimental conditions. For each model we assess the accuracy of the estimates, their robustness to measurement noise, sensitivity to initial conditions and visual angle, effects of the bas-relief ambiguity and occlusions, dependence upon the number of image measurements and their sampling rate

A pseudospectral matrix method for time-dependent tensor fields on a spherical shell

We construct a pseudospectral method for the solution of time-dependent, non-linear partial differential equations on a three-dimensional spherical shell. The problem we address is the treatment of tensor fields on the sphere. As a test case we consider the evolution of a single black hole in numerical general relativity. A natural strategy would be the expansion in tensor spherical harmonics in spherical coordinates. Instead, we consider the simpler and potentially more efficient possibility of a double Fourier expansion on the sphere for tensors in Cartesian coordinates. As usual for the double Fourier method, we employ a filter to address time-step limitations and certain stability issues. We find that a tensor filter based on spin-weighted spherical harmonics is successful, while two simplified, non-spin-weighted filters do not lead to stable evolutions. The derivatives and the filter are implemented by matrix multiplication for efficiency. A key technical point is the construction of a matrix multiplication method for the spin-weighted spherical harmonic filter. As example for the efficient parallelization of the double Fourier, spin-weighted filter method we discuss an implementation on a GPU, which achieves a speed-up of up to a factor of 20 compared to a single core CPU implementation.Comment: 33 pages, 9 figure

A Novel Convex Relaxation for Non-Binary Discrete Tomography

We present a novel convex relaxation and a corresponding inference algorithm for the non-binary discrete tomography problem, that is, reconstructing discrete-valued images from few linear measurements. In contrast to state of the art approaches that split the problem into a continuous reconstruction problem for the linear measurement constraints and a discrete labeling problem to enforce discrete-valued reconstructions, we propose a joint formulation that addresses both problems simultaneously, resulting in a tighter convex relaxation. For this purpose a constrained graphical model is set up and evaluated using a novel relaxation optimized by dual decomposition. We evaluate our approach experimentally and show superior solutions both mathematically (tighter relaxation) and experimentally in comparison to previously proposed relaxations

Efficient Analysis of Complex Diagrams using Constraint-Based Parsing

This paper describes substantial advances in the analysis (parsing) of diagrams using constraint grammars. The addition of set types to the grammar and spatial indexing of the data make it possible to efficiently parse real diagrams of substantial complexity. The system is probably the first to demonstrate efficient diagram parsing using grammars that easily be retargeted to other domains. The work assumes that the diagrams are available as a flat collection of graphics primitives: lines, polygons, circles, Bezier curves and text. This is appropriate for future electronic documents or for vectorized diagrams converted from scanned images. The classes of diagrams that we have analyzed include x,y data graphs and genetic diagrams drawn from the biological literature, as well as finite state automata diagrams (states and arcs). As an example, parsing a four-part data graph composed of 133 primitives required 35 sec using Macintosh Common Lisp on a Macintosh Quadra 700.Comment: 9 pages, Postscript, no fonts, compressed, uuencoded. Composed in MSWord 5.1a for the Mac. To appear in ICDAR '95. Other versions at ftp://ftp.ccs.neu.edu/pub/people/futrell

Generating and Analyzing Constrained Dark Energy Equations of State and Systematics Functions

Some functions entering cosmological analysis, such as the dark energy equation of state or systematic uncertainties, are unknown functions of redshift. To include them without assuming a particular form we derive an efficient method for generating realizations of all possible functions subject to certain bounds or physical conditions, e.g. w\in[-1,+1] as for quintessence. The method is optimal in the sense that it is both pure and complete in filling the allowed space of principal components. The technique is applied to propagation of systematic uncertainties in supernova population drift and dust corrections and calibration through to cosmology parameter estimation and bias in the magnitude-redshift Hubble diagram. We identify specific ranges of redshift and wavelength bands where the greatest improvements in supernova systematics due to population evolution and dust correction can be achieved.Comment: 12 pages, 11 figures; v2 minor revisions, higher resolution figures, matches PRD versio