English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

This paper derives a complete analytical solution for the probabilitydistribution of the configuration of a non-holonomic vehicle that moves in twospatial dimensions by satisfying the unicycle kinematic constraints and inpresence of Brownian noises. In contrast to previous solutions, the one herederived holds even in the case of arbitrary linear and angular speed. Thissolution is obtained by deriving the analytical expression of any-order momentof the probability distribution. To the best of our knowledge, an analyticalexpression for any-order moment that holds even in the case of arbitrary linearand angular speed, has never been derived before. To compute these moments, adirect integration of the Langevin equation is carried out and each moment isexpressed as a multiple integral of the deterministic motion (i.e., the knownmotion that would result in absence of noise). For the special case when theratio between the linear and angular speed is constant, the multiple integralscan be easily solved and expressed as the real or the imaginary part ofsuitable analytic functions. As an application of the derived analyticalresults, the paper investigates the diffusivity of the considered Brownianmotion for constant and for arbitrary time-dependent linear and angular speed.

Complete analytic solution to Brownian unicycle dynamics