6,791 research outputs found
Trajectory generation for the N-trailer problem using Goursat normal form
Develops the machinery of exterior differential forms, more particularly the Goursat normal form for a Pfaffian system, for solving nonholonomic motion planning problems, i.e., motion planning for systems with nonintegrable velocity constraints. The authors use this technique to solve the problem of steering a mobile robot with n trailers. The authors present an algorithm for finding a family of transformations which will convert the system of rolling constraints on the wheels of the robot with n trailers into the Goursat canonical form. Two of these transformations are studied in detail. The Goursat normal form for exterior differential systems is dual to the so-called chained-form for vector fields that has been studied previously. Consequently, the authors are able to give the state feedback law and change of coordinates to convert the N-trailer system into chained-form. Three methods for planning trajectories for chained-form systems using sinusoids, piecewise constants, and polynomials as inputs are presented. The motion planning strategy is therefore to first convert the N-trailer system into Goursat form, use this to find the chained-form coordinates, plan a path for the corresponding chained-form system, and then transform the resulting trajectory back into the original coordinates. Simulations and frames of movie animations of the N-trailer system for parallel parking and backing into a loading dock using this strategy are included
Nonholonomic motion planning: steering using sinusoids
Methods for steering systems with nonholonomic constraints between arbitrary configurations are investigated. Suboptimal trajectories are derived for systems that are not in canonical form. Systems in which it takes more than one level of bracketing to achieve controllability are considered. The trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. A class of systems that can be steered using sinusoids (claimed systems) is defined. Conditions under which a class of two-input systems can be converted into this form are given
Estimation of automobile-driver describing function from highway tests using the double steering wheel
The automobile-driver describing function for lateral position control was estimated for three subjects from frequency response analysis of straight road test results. The measurement procedure employed an instrumented full size sedan with known steering response characteristics, and equipped with a lateral lane position measuring device based on video detection of white stripe lane markings. Forcing functions were inserted through a servo driven double steering wheel coupling the driver to the steering system proper. Random appearing, Gaussian, and transient time functions were used. The quasi-linear models fitted to the random appearing input frequency response characterized the driver as compensating for lateral position error in a proportional, derivative, and integral manner. Similar parameters were fitted to the Gabor transformed frequency response of the driver to transient functions. A fourth term corresponding to response to lateral acceleration was determined by matching the time response histories of the model to the experimental results. The time histories show evidence of pulse-like nonlinear behavior during extended response to step transients which appear as high frequency remnant power
Control and Synchronization of Neuron Ensembles
Synchronization of oscillations is a phenomenon prevalent in natural, social,
and engineering systems. Controlling synchronization of oscillating systems is
motivated by a wide range of applications from neurological treatment of
Parkinson's disease to the design of neurocomputers. In this article, we study
the control of an ensemble of uncoupled neuron oscillators described by phase
models. We examine controllability of such a neuron ensemble for various phase
models and, furthermore, study the related optimal control problems. In
particular, by employing Pontryagin's maximum principle, we analytically derive
optimal controls for spiking single- and two-neuron systems, and analyze the
applicability of the latter to an ensemble system. Finally, we present a robust
computational method for optimal control of spiking neurons based on
pseudospectral approximations. The methodology developed here is universal to
the control of general nonlinear phase oscillators.Comment: 29 pages, 6 figure
Summation of visual and mechanosensory feedback in Drosophila flight control
The fruit fly Drosophila melanogaster relies on feedback from multiple sensory modalities to control flight maneuvers. Two sensory organs, the compound eyes and mechanosensory hindwings called halteres, are capable of encoding angular velocity of the body during flight. Although motor reflexes driven by the two modalities have been studied individually, little is known about how the two sensory feedback channels are integrated during flight. Using a specialized flight simulator we presented tethered flies with simultaneous visual and mechanosensory oscillations while measuring compensatory changes in stroke kinematics. By varying the relative amplitude, phase and axis of rotation of the visual and mechanical stimuli, we were able to determine the contribution of each sensory modality to the compensatory motor reflex. Our results show that over a wide range of experimental conditions sensory inputs from halteres and the visual system are combined in a weighted sum. Furthermore, the weighting structure places greater influence on feedback from the halteres than from the visual system
Dimensionality and dynamics in the behavior of C. elegans
A major challenge in analyzing animal behavior is to discover some underlying
simplicity in complex motor actions. Here we show that the space of shapes
adopted by the nematode C. elegans is surprisingly low dimensional, with just
four dimensions accounting for 95% of the shape variance, and we partially
reconstruct "equations of motion" for the dynamics in this space. These
dynamics have multiple attractors, and we find that the worm visits these in a
rapid and almost completely deterministic response to weak thermal stimuli.
Stimulus-dependent correlations among the different modes suggest that one can
generate more reliable behaviors by synchronizing stimuli to the state of the
worm in shape space. We confirm this prediction, effectively "steering" the
worm in real time.Comment: 9 pages, 6 figures, minor correction
Overcomplete steerable pyramid filters and rotation invariance
A given (overcomplete) discrete oriented pyramid may be converted into a steerable pyramid by interpolation. We present a technique for deriving the optimal interpolation functions (otherwise called 'steering coefficients'). The proposed scheme is demonstrated on a computationally efficient oriented pyramid, which is a variation on the Burt and Adelson (1983) pyramid. We apply the generated steerable pyramid to orientation-invariant texture analysis in order to demonstrate its excellent rotational isotropy. High classification rates and precise rotation identification are demonstrated
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