A Local Convergence Proof for the Minvar Algorithm for Computing Continuous Piecewise Linear Approximations

The class of continuous piecewise linear (PL) functions represents a useful family of approximants because invertibility can be readily imposed, and if a PL function is invertible, then it can be inverted in closed form. Many applications, arising, for example, in control systems and robotics, involve the simultaneous construction of a forward and inverse system model from data. Most approximation techniques require that separate forward and inverse models be trained, whereas an invertible continuous PL affords, simultaneously, the forward and inverse system model in a single representation. The minvar algorithm computes a continuous PL approximation to data. Local convergence of minvar is proven for the case when the data generating function is itself a PL function and available directly rather than through data

A Framework for the Coordination of Legged Robot Gaits

This paper introduces a framework for representing, generating, and then tuning gaits of legged robots. We introduce a convenient parametrization of gait generators as dynamical systems possessing designer specified stable limit cycles over an appropriate torus. This parametrization affords a continuous selection of operation within a coordination design plane, inspired by biology, spanned by axes that determine the mix of feedforward/feedback and centralized/decentralized control. Tuning the gait generator parameters through repeated physical experiments with our robot hexapod, RHex, determines the appropriate operating point - the mix of feedback and degree of control decentralization - to achieve significantly increased performance relative to the centralized feedforward operating point that has governed its previous behavior. The present preliminary experiments with these new gaits suggest that they may permit for the first time locomotion over extremely rough terrain that is almost as reliable, rapid, and energy efficient as the very fastest or most efficient outcomes centralized feedforward gaits can achieve on level ground

Invertible Piecewise Linear Approximations for Color Reproduction

We consider the use of linear splines with variable knots for the approximation of unknown functions from data, motivated by control and estimation problems arising in color systems management. Unlike most popular nonlinear-in-parameters representations, piecewise linear (PL) functions can be simply inverted in a closed form. For the one-dimensional case, we present a study comparing PL and neural network (NN) approximations for several function families. Preliminary results suggest that PL, in addition to their analytical benefits, are at least competitive with NN in terms of sum square error, computational effort and training time

Piecewise Linear Homeomorphisms: The Scalar Case

The class of piecewise linear homeomorphisms (PLH) provides a convenient functional representation for many applications wherein an approximation to data is required that is invertible in closed form. In this paper we introduce the graph intersection (GI) algorithm for learning piecewise linear scalar functions in two settings: approximation, where an oracle outputs accurate functional values in response to input queries; and estimation, where only a fixed discrete data base of input-output pairs is available. We provide a local convergence result for the approximation version of the GI algorithm as well as a study of its numerical performance in the estimation setting. We conclude that PLH offers accuracy closed to that of a neural net while requiring, via our GI algorithm, far shorter training time and preserving desired invariant properties unlike any other presently popular basis family

Representation of Color Space Transformations for Effective Calibration and Control

We propose the minvar algorithm for computing continuous, continuously invertible, piecewise linear (PL) approximations of color space transformations that can serve as functional replacements wherever look-up tables are presently used. After motivating the importance of invertible approximants in color space management applications, we review the parameterization and computational implementation of PL functions as representing one useful instance of this notion. Finally, we describe the present version of the minvar algorithm and compare the approximations it yields with standard industrial practice — interpolation of look-up table data

Gait Generation and Optimization for Legged Robots

This paper presents a general framework for representing and generating gaitsfor legged robots. We introduce a convenient parametrization of gait generators as dynamical systems possessing specified stable limit cycles over an appropriate torus. Inspired by biology, this parametrization affords a continuous selection of operation within a coordination design plane spanned by axes that determine the mix of ”feedforward/feedback” and centralized/decentralized” control. Applying optimization to the parameterized gait generation system allowed RHex, our robotic hexapod, to learn new gaits demonstrating significant performance increases. For example, RHex can now run at 2.4m/s (up from 0.8m/s), run with a specific resistance of 0.6 (down from 2.0), climb 45◦ inclines (up from 25◦), and traverse 35◦ inclines (up from 15◦)

Modeling and Control of Color Xerographic Processes

The University of Michigan and Xerox\u27s Wilson Research Center have been collaborating on problems in color management systems since 1996, supported in part by an NSF GOALI grant. The paper is divided into three sections. The first discusses the basics of xerography and areas where systems methodology can have a potential impact. The second section describes the authors\u27 approach to the approximation of color space transformations using piecewise linear approximants and the graph intersection algorithm, with a brief review of some of the analytical and numerical results. The last section expounds on some of the benefits and difficulties of industry-university-government collaboration

Boundary of oxidative and overflow metabolism (boom) controller for CHO cell feed control

There is limited literature for CHO cell cultures with low batch glucose concentrations (Gowtham et al. 2017; Lu et al. 2005; Wong et al. 2005). Work like Xu et al. (2016) and Berry et al. (2016) have shown positive results for controlled fed-batch cultures at low glucose concentrations following standard high glucose (5-6 g/L) batch cultures. However, the Xu et al. (2016) and Berry et al. (2016) approaches still accumulate lactate. Controlling glucose earlier could potentially avoid lactate accumulation and lead to even greater improvements in culture outcomes. The objective of this project was to develop an advanced feed controller for CHO cell cultures that maximizes cell growth by maintaining the culture in a state of maximal oxidative metabolism while minimizing overflow metabolism. The Boundary of Oxidative and Overflow Metabolism (BOOM) controller periodically manipulates the feed rate while monitoring online signals to gauge the remaining oxidative “space”, in order to decide whether feed can be increased while remaining in oxidative metabolism. The Oxygen Uptake Rate (OUR) is the primary signal of interest, since it plateaus when a culture shifts from oxidative to overflow metabolism, encoding vital information about metabolic state. This project’s approach is different from past work in that the batch glucose concentrations is much lower (on the order of 1 g/L), the glucose and/or glutamine feeding begins very early in the process, and glucose feed is triggered/controlled by the off-gas sensing of the metabolic state instead of a targeted glucose concentration. During early runs several chemistry effects were observed directly due to the bolus feed additions interfering with the media-dissolved gas equilibrium. For example, a bolus feed that only contained 5 mM bicarbonate, resulted in an observed short sharp decrease in CO2 off-gas as the feed absorbed CO2 from the 5% CO2 sparge gas. Continuous feeding was introduced in subsequent runs as a means to mitigate disrupting the media-dissolved gas-equilibrium and disturbing the off-gas sensing. In order to have effective continuous feeding, the feed pump used a pulse width modulation (PWM) with a 10-minute period to allow extremely low effective feed rates required for the 1-L vessel. Two runs were used to demonstrate that the PWM feed pump could provide these very low pump feed rates for the 1-L vessel containing as little as 500 mL media. Initial glucose concentrations between 0.6 to 2.0 g/L were used (compared to 8 g/L glucose in the standard media formulation). Feedings have started between 6- and 20-hour post-inoculation. Distinct qualitative and quantitative differences have been observed in the corresponding oxygen uptake rate (OTR) responses due to the feeding spikes, suggesting that metabolic state can be detected. The development of the state estimator to control glucose feeding will be presented

Automated Gait Adaptation for Legged Robots

Gait parameter adaptation on a physical robot is an error-prone, tedious and time-consuming process. In this paper we present a system for gait adaptation in our RHex series of hexapedal robots that renders this arduous process nearly autonomous. The robot adapts its gait parameters by recourse to a modified version of Nelder-Mead descent while managing its self-experiments and measuring the outcome by visual servoing within a partially engineered environment. The resulting performance gains extend considerably beyond what we have managed with hand tuning. For example, the hest hand tuned alternating tripod gaits never exceeded 0.8 m/s nor achieved specific resistance helow 2.0. In contrast, Nelder-Mead based tuning has yielded alternating tripod gaits at 2.7 m/s (well over 5 body lengths per second) and reduced specific resistance to 0.6 while requiring little human intervention at low and moderate speeds. Comparable gains have been achieved on the much larger ruggedized version of this machine

The Ursinus Weekly, March 21, 1938

Peace to be topic of all-Ursinus conference • Dr. Graves stresses value of education for leadership • War is inevitable, peace group fears • Sophisticated Swing for junior prom • Name-forgetting theme of junior play • Local thespians offer double bill Friday • Former Ursinus athlete to address Ys Wednesday • May Day finery for rent; see committee members • Women hear Sweden lecture this afternoon • Men and women debaters argue at six colleges during week • Science blind spot topic of lecturer tomorrow • Chamber music, speaker featured at vespers • Comprehensive grade three-tenths of senior\u27s final mark • Commencement in the gymnasium? • Letters to the editor: Student avers majority do not want speakers; A six point program for introduction to science; A reader criticizes the Weekly\u27s news evaluation • Co-ed undergraduates vote to start junior women\u27s club • Chemical Society to send delegates to I. S. C. meet • Faculty club hears Miller at March 9 meeting • Fraternity row • Michael sends list of expectant teachers to schools • Recordings, solos heard at meeting of Music Club Monday • Roberts\u27 Northwest Passage reviewed for English Club • Students\u27 attitudes toward peace strike movement to be IRC topic • Barnard encourages organization of pre-law society at Y tea • Notices • Alumni note • Questionnaire reveals alumni most help in informing prospective students • Wrestlers choose Meklos 1939 captain • Coed basketeers end lucrative year with 35-20 win from Temple • Astheimer high scorer during mat season • 35 infielders, outfielders report for practice • Winter sports summaries • Women pick class captains for basketball tourney • Day is dorm champion by defeating Brodbeck • Frosh courtmen win single game in hapless season • Ys combat ho-hum Saturdays with informal bingo party • Sheeder names committee for open house day • Apes take plaque • Wreath placed on Bomberger grave by son • Ys old fashioned dance attracts 150 personshttps://digitalcommons.ursinus.edu/weekly/3113/thumbnail.jp