Second-Order Theory of Error Propagation on Motion Groups.

In this paper we show how errors propagated by convolution on the Euclidean motion group, SE(3), can be approximated to second order using the theory of Lie algebras and Lie groups. ... Error propagation on the Euclidean motion group arises in a number of areas such as in dead reckoning errors in mobile robot navigation and joint errors that accumulate from the base to the distal end ... Wooram Park for useful discussions on stochastic simulations of needles. ...

doi:10.1177/0278364908097583 pmid:20333324 pmcid:PMC2843106 fatcat:ztwkgxxzvbesfm2cou4vdksr4y

In this paper we show how errors propagated by convolution on the Euclidean motion group, SE(3), can be approximated to second order using the theory of Lie algebras and Lie groups. ... Error propagation on the Euclidean motion group arises in a number of areas such as and in dead reckoning errors in mobile robot navigation and joint errors that accumulate from the base to the distal ... In the second-order theory of error propagation on Lie groups (and SE(3) in particular), we now make the approximation log(k −1 • q) = X − Y + 1 2 [X, Y ], or equivalently [log(k −1 • q)] ∨ = x − y + 1 ...

doi:10.1007/978-3-540-68405-3_10 fatcat:dpv3dtkoffdkxfd5wuijvt4px4

Errors in run-up distance and overtopping volume are then assessed by repeating the test cases using second-order accurate wave generation signals. ... Focused wave groups generated using first-order wave-maker theory are found to be substantially contaminated by a preceding long error wave, resulting in erroneously enhanced run-up distances and overtopping ... Acknowledgments The research was conducted at the Department of Engineering Science, University of Oxford while Jana Orszaghova was a DPhil student under the supervision of Prof. Paul H. ...

doi:10.1016/j.coastaleng.2014.08.007 fatcat:bjwszzazs5c7rluomywgya3hdm

Error propagation on the Euclidean motion group arises in a number of areas such as errors that accumulate from the base to the distal end of manipulators. ... In this paper, we show that errors propagate by convolution on the Euclidean motion group, (3). When local errors are small, they can be described well as distributions on the Lie algebra (3). ... ACKNOWLEDGMENT The authors would like to thank the reviewers of this paper for the many useful comments that they contributed. ...

doi:10.1109/tro.2006.878978 fatcat:orqfrmkwzvec3dslscffkew25e

Higher order resummations allow derivation of an effective one-dimensional potential which accurately represents quantum dynamics for even strongly coupled low-frequency modes. ... The accuracy of the method for even highly nonadiabatic applications, and the ease of implementation suggests that this approach will be useful in the calculation of the quantum dynamics of many dimensional ... Recombination of the system plus coupling propagator and the first order resummation propagator would yield errors of the same order of magnitude as the second order resummation propagator. ...

doi:10.1063/1.466734 fatcat:4zxf2fvunjfw3iqs37vqdbs5ae

Evaluation is based on a corvette model, and the stability parameter of wave has been evaluated by using MATLAB software. ... In this paper, a BP (back propagation) neural network is presented that keeps sea keeping indexes under the categories of input and output of the network. ... One parameter or one variable cannot be used in order to evaluate and define seakeeping ability; rather a group of variables and parameters is required for evaluation. ...

doi:10.12691/ajme-2-1-4 fatcat:pclso76aefhodigsevjj7h7hjy

A~tract--The theory of group velocity is generalized to waves on curved surfaces, and applied to calculating the effect of the earth's rotation on the trajectory and wave vector of a wave packet whose ... ; they are of the order of t2/o~ for deep water waves; and they are largest for waves with kh ~ 1"878973. 1. ... Rotation would produce an error in the observed direction, but smaller by one or two orders of magnitude, depending on the periods of the waves. - f~ u + fx v + ~w -_ _ ~_p_~. 5t 5z *Institute of Geophysics ...

doi:10.1016/0011-7471(62)90168-7 fatcat:boaycnq43bc5dlfjwvrvfi462e

We have computed the light and strange quark masses and the renormalization constants of the quark bilinear operators, by studying the large-p^2 behaviour of the lattice quark propagator and 3-point functions ... The method used to compute the quark masses has never been applied so far, and it does not require an explicit determination of the quark mass renormalization constant. ... The second remark concerns the sizeable discrepancy between the nonperturbative determination of Z P (but see also Z S ) and the prediction of one-loop perturbation theory. ...

doi:10.1016/s0920-5632(00)91828-0 fatcat:dksymzk73rabxn3wywsijywbpi

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One tool that we develop in this paper to increase efficiency of the POP algorithm is a second order closed-form uncertainty propagation formula. ... Many robotics applications involve motion planning with uncertainty. In this paper, we focus on path planning for planar systems by optimizing the probability of successfully arriving at a goal. ... The formulas are different than those of the Kalman methods because we use the theory of Lie algebras and Lie groups and propagate the error to second order. ...

doi:10.1007/978-3-642-36279-8_28 fatcat:v27g3x4nyvahjplczppfol72ne

Prager dealt with ispects ol the theory of p! isticitv, and M. Reiner discussed second-order effects in elasticity and hydrodynamics. ... The theory of turbu] also received considerable attention. In papers on applicat; work on airfoil theory and experiment was most popular, The section III address was by A. ...

We have computed the light and strange quark masses and the renormalization constants of the quark bilinear operators, by studying the large-p 2 behaviour of the lattice quark propagator and 3-point functions ... The method used to compute the quark masses has never been applied so far, and it does not require an explicit determination of the quark mass renormalization constant. ... The second remark concerns the sizeable discrepancy between the nonperturbative determination of Z P (but see also Z S ) and the prediction of one-loop perturbation theory. ...

doi:10.1016/s0920-5632(00)00466-7 fatcat:gfvv3qywkzh6hclhimnwotc5t4

This implies, Neumann force condition at a boundary should read as a spatial gradient of order one. ... Both kinetically local and nonlocal formulations of BBPD are considered. It is argued that only one wave mode may propagate in a BBPD rod. ... The second and other relations express a higher order moments in a rod. Rod is a structure with one degree of freedom having only a longitudinal motion of material particles. ...

doi:10.1007/s42102-020-00033-y fatcat:nelm45vshjb47ils42n6bc6jym

Transverse (off-plane) dust grain oscillatory motion is considered, in the form of a backward propagating wavepacket whose linear and nonlinear characteristics are investigated. ... The propagation of nonlinear dust-lattice waves in a two-dimensional hexagonal crystal is investigated. ... This is expected to incur a relative error of the order of 2 2 / g ω ν , which is reportedly small in experiments. ...

doi:10.1063/1.3121221 fatcat:kojlu5u4u5hj5ntdg5kluqwrke

Using the Frenet-Serret frame, that is, an element of the special orthogonal group SO(3) we cast the tracking problem into a filtering on Lie groups framework. ... The dynamical model used is based on assumptions of nearly constant tangential velocity, curvature, and torsion, of the target trajectory. ... Linearization of the error system and gain computation To tune the gains, we need to compute how the error (13) evolves during the propagation, and to write the update step, up to first order terms in ...

doi:10.1109/cdc.2017.8263937 dblp:conf/cdc/PilteBB17 fatcat:saprcu7n2vafzkylasgbpsirkm

A hybrid orbit propagator based on the analytical integration of the Kepler problem is designed to determine the future position and velocity of any orbiter, usually an artificial satellite or space debris ... fragment, in two steps: an initial approximation generated by means of an integration method, followed by a forecast of its error, determined by a prediction technique that models and reproduces the missing ... The propagation of perturbed orbits is a well-known problem which implies hav- ing to tackle a set of three second-order or six first-order differential ...

doi:10.1007/978-3-319-59650-1_55 fatcat:h7a3ykadtfgkhiv3yuqrekho3e

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Nonparametric Second-order Theory of Error Propagation on Motion Groups

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