Feedback Synthesis for Controllable Underactuated Systems using Sequential Second Order Actions

This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actions---the needle variations of optimal control---as the basis for choosing each control response to the current state. A second result of the paper is that the method provably exploits the nonlinear controllability of a system by virtue of an explicit dependence of the second-order needle variation on the Lie bracket between vector fields. As a result, each control decision necessarily decreases the objective when the system is nonlinearly controllable using first-order Lie brackets. Simulation results using a differential drive cart, an underactuated kinematic vehicle in three dimensions, and an underactuated dynamic model of an underwater vehicle demonstrate that the method finds control solutions when the first-order analysis is singular. Moreover, the simulated examples demonstrate superior convergence when compared to synthesis based on first-order needle variations. Lastly, the underactuated dynamic underwater vehicle model demonstrates the convergence even in the presence of a velocity field.Comment: 9 page

Omnidirectional Sensory and Motor Volumes in Electric Fish

Active sensing organisms, such as bats, dolphins, and weakly electric fish, generate a 3-D space for active sensation by emitting self-generated energy into the environment. For a weakly electric fish, we demonstrate that the electrosensory space for prey detection has an unusual, omnidirectional shape. We compare this sensory volume with the animal's motor volume—the volume swept out by the body over selected time intervals and over the time it takes to come to a stop from typical hunting velocities. We find that the motor volume has a similar omnidirectional shape, which can be attributed to the fish's backward-swimming capabilities and body dynamics. We assessed the electrosensory space for prey detection by analyzing simulated changes in spiking activity of primary electrosensory afferents during empirically measured and synthetic prey capture trials. The animal's motor volume was reconstructed from video recordings of body motion during prey capture behavior. Our results suggest that in weakly electric fish, there is a close connection between the shape of the sensory and motor volumes. We consider three general spatial relationships between 3-D sensory and motor volumes in active and passive-sensing animals, and we examine hypotheses about these relationships in the context of the volumes we quantify for weakly electric fish. We propose that the ratio of the sensory volume to the motor volume provides insight into behavioral control strategies across all animals

Separability of drag and thrust in undulatory animals and machines

For nearly a century, researchers have tried to understand the swimming of aquatic animals in terms of a balance between the forward thrust from swimming movements and drag on the body. Prior approaches have failed to provide a separation of these two forces for undulatory swimmers such as lamprey and eels, where most parts of the body are simultaneously generating drag and thrust. We nonetheless show that this separation is possible, and delineate its fundamental basis in undulatory swimmers. Our approach unifies a vast diversity of undulatory aquatic animals (anguilliform, sub-carangiform, gymnotiform, bal- istiform, rajiform) and provides design principles for highly agile bioinspired underwater vehicles. This approach has practical utility within biology as well as engineering. It is a predictive tool for use in understanding the role of the mechanics of movement in the evolutionary emergence of morphological features relating to locomotion. For example, we demonstrate that the drag-thrust separation framework helps to predict the observed height of the ribbon fin of electric knifefish, a diverse group of neotropical fishes which are an important model system in sensory neurobiology. We also show how drag-thrust separation leads to models that can predict the swimming velocity of an organism or a robotic vehicle.Comment: 41 pages, 13 figures, 4 table

Validity of interpretation: A user validity perspective beyond the test score

This paper introduces the concept of user validity and provides a new perspective on the validity of interpretations from tests. Test interpretation is based on outputs such as test scores, profiles, reports, spreadsheets of multiple candidates' scores, etc. The user validity perspective focuses on the interpretations a test user makes given the purpose of the test and the information provided in the test output. This innovative perspective focuses on how user validity can be extended to content, criterion, and to some extent construct-related validity. It provides a basis for researching the validity of interpretations and an improved understanding of the appropriateness of different approaches to score interpretation, as well as how to design test outputs and assessments that are pragmatic and optimal

Reading Quintus Reading Homer Intertextual Engagement in Quintus Smyrnaeus’ Posthomerica

This thesis is a study of Quintus Smyrnaeus’ Posthomerica, a Greek epic of the third century C.E. written in Greek hexameters in Homeric diction and in a Homeric style and about the post-Iliadic events of the Trojan War. My thesis deals with intertextuality, that is, the relationship between the Posthomerica and the Homeric texts. The Posthomerica has been called a hyper-Homeric text, which has been viewed as a negative trait of the poem. I analyse this Homeric-emulative tendency and discuss the interaction between the cultural and literary influences contemporary to the Posthomerica, and the poem’s overwhelmingly Homeric intertextuality. I assess how Quintus, as a Late Antique reader, reads Homer, and I focus in on the originality and Late Antique interpretative bias of Quintus in his readings and emulation of Homer. Intertextuality points to resemblances and differences, and indicates how a poem that can be called “Homeric” is in fact neo-Homeric in its updating of Homeric ethics, ideologies and poetics. I also discuss throughout the thesis how the Posthomerica is Alexandrian in its indebtedness to Homer. The Posthomerica is a learned text where application of intertextuality by the reader activates and vivifies a poem that has otherwise been dismissed as second-rate. There are four sections in my thesis, all dealing specifically with three separate aspects of poetics. The first section is a study of similes in the Posthomerica. I present a complete statistical analysis of similes in the poem, and compare practice in earlier epics. I then focus on specific examples of similes in the poem, and show how Homeric intertextuality vivifies meaning and characterisation of these similes. Very often the context of the Homeric passage implicated in the Posthomeric simile adds a varying sense and meaning. I also highlight the concern for pattern and structure in the placement of similes in the Posthomerica in a way that derives more from the style of Apollonius Rhodius than Homer. Thus Quintus reads Homer through later Greek epic lenses. My second and third sections are related. I discuss gnomai in the Posthomerica, and present detailed statistics for this understudied area of the poem. I argue that the widespread use of gnomai, particularly in the voice of the primary narrator, provides an ethical thread in the poem, and that the content of these gnomai is non- Homeric, and influenced by Stoicism. Thus within a Homeric-emulative poem we read a recurrent non-Homeric philosophy and ethics carried by gnomai. The third section then focuses on one simile (in Book 14), which, in a very original way, contains a gnome. The simile derives its content from Odyssey 8 and the story of Aphrodite and Ares caught in the act of adultery. I read Quintus updating Homer in this simile and re-presenting the Homeric story with a definite moral, and therefore un-Homeric, emphasis. The fourth section concentrates on ecphrasis and the Shield of Achilles in Posthomerica 5. I show how Quintus presents radically non-Homeric devices within this ecphrasis first narrated in Iliad 18. I argue that this originality within a very Homeric template is reflective of the overall status of the Posthomerica in relation to Homer. I focus in particular on the figure of the Mountain of Arete on the Shield of Achilles, and illustrate how this figure, which is Stoic in its inheritance, behaves as a mise-en-abîme for the key ethical content of the poem found in gnomai. I then discuss the implications of Quintus revising the Homeric Shield of Achilles into a symbol of the Stoic ethics that the Posthomerica, this most “Homeric” of poems, contains. That is the overall focus of this thesis: the interaction of Homeric indebtedness and non-Homeric influences in the Posthomerica

Validity of interpretation: a user validity perspective beyond the test score

YesThis paper introduces the concept of user validity and provides a new perspective on the validity of interpretations from tests. Test interpretation is based on outputs such as test scores, profiles, reports, spread-sheets of multiple candidates’ scores, etc. The user validity perspective focuses on the interpretations a test user makes given the purpose of the test and the information provided in the test output. This innovative perspective focuses on how user validity can be extended to content, criterion and to some extent construct-related validity. It provides a basis for researching the validity of interpretations and an improved understanding of the appropriateness of different approaches to score interpretation, as well as how to design test outputs and assessments which are pragmatic and optimal

Modeling active electrolocation in weakly electric fish

In this paper, we provide a mathematical model for the electrolocation in weakly electric fishes. We first investigate the forward complex conductivity problem and derive the approximate boundary conditions on the skin of the fish. Then we provide a dipole approximation for small targets away from the fish. Based on this approximation, we obtain a non-iterative location search algorithm using multi-frequency measurements. We present numerical experiments to illustrate the performance and the stability of the proposed multi-frequency location search algorithm. Finally, in the case of disk- and ellipse-shaped targets, we provide a method to reconstruct separately the conductivity, the permittivity, and the size of the targets from multi-frequency measurements.Comment: 37 pages, 11 figure