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STATE ESTIMATION FOR ROBOTICS

STATE ESTIMATION FOR. ROBOTICS . Timothy D. Barfoot c 2019. Copyright Cambridge University Press is the Official Publisher This Unofficial Version Compiled on October 1, 2019. Send errata to Revision History 13 May 2017 Version best matching published first edition 12 Aug 2017 Equation ( ): x changed to xx 12 Aug 2017 Page 111, bullet 4: y changed to yy 12 Aug 2017 Page 117, bullet (ii): changed 4(a) to 3. 12 Aug 2017 Equation ( ): P changed to P k 12 Aug 2017 Equation ( ): P k changed to P k 12 Aug 2017 Equation ( ): xop,k,0 changed to xop,k,i 12 Aug 2017 Equation ( ): removed negative sign 22 Nov 2017 Fixed typo in Jacobi identity (page 218). 10 Dec 2017 Equation ( ): 1yy yx changed to xy yy 1. vk i 10 Dec 2017 Inline above ( ): rvi i changed to ri T. 10 Dec 2017 Equation ( ): 0 changed to 0. 10 Dec 2017 Inline below ( ): e(xop ) = Lu(xop ) changed to e(xop ) = L 1 u(xop ). 10 Dec 2017 Angular acceleration: 21 changed to .. 21.. 10 Dec 2017 Equation ( ): corrected a double comma 10 Dec 2017 Equation ( ): nk,j changed to y k,j 5 Jan 2018 Page 227, definition of Ad(SE(3)): removed extra comma before final bracket 5 Jan 2018 Equation ( ): changed j?

viii Contents 7 Matrix Lie Groups 215 7.1 Geometry 215 7.1.1 Special Orthogonal and Special Euclidean Groups 215 7.1.2 Lie Algebras 217 7.1.3 Exponential Map 219 7.1.4 Adjoints 226 7.1.5 Baker-Campbell-Hausdor 230 7.1.6 Distance, Volume, Integration 237 7.1.7 Interpolation 240 7.1.8 Homogeneous Points 246 7.1.9 Calculus and Optimization 246 7.1.10 Identities 254 7.2 …

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