# Probabilistic Robotic: Errata (First and Second Printing)

All corrected pages can be found in this directory.

Errata for the third printing are also available.

 Location Erratum Corrected text Found by Page 65, Eq. 3.66 In the third case, the index should be (i-n) instead of i Page 65 Authors Page 67, last paragraph The reference to lines 7 and 8 should point to lines 6 and 7. Page 67 Patrick Beeson Page 77, Eqs 3.104-107 Sign correction. The term H_t\bar{\mu}_t should be added, not subtracted. The same error occurs in Line 7 of Table 3.6 (page 76) Page 77 Gabe Sibley Page 89, Eq 4.5 The term |x_{k,t}| should be a multiplicative term, as in Eq. 4.10. Page 89 Patrick Beeson Page 96, Eq. 4.21 Sign error (or: enumerator and denominator should be swapped in the log term). Page 96 Rahul Biswas Page 103, Eq. 4.33 Replace p(x_{0:t-1} | z_{0:t-1}, u_{0:t-1}) by p(x_{0:t-1} | z_{1:t-1}, u_{1:t-1}), that is, change 0 to 1 in the two rightmost variables, to make the definition of the function bel() consistent with Eq. 4.31 Page 103 Cedric Tessier Page 103, text following Eq. 4.31 Replace the reference to Table 4.4 by Table 4.3. Page 103 Maxim Kolesnikov Page 126, Fig. 5.5 Replace 90-theta by theta-90. Page 126 Oscar Martinez Mozos Page 128, Eq. 5.12 As printed, this isn't really a density; it is just a definition of the distribution. The correct density is on page 124, table 5.4, line 4. Page 128 Ernest Ngaruiya Page 131 "The angle of the final rotation $\hat{\gamma}$ can be determined according to (5.14) as:" should be replaced by "The rotational velocity $\hat{\gamma}$ needed to achieve the final heading $\theta'$ of the robot in (x' y') within $\Delta t$ can be determined according to~(\ref{eqVelMotion6}) as:" Page 131 Authors Page 139, Eq. 5.40 One theta too many in the bottom row Page 139 Ben Pitzer Page 141, line 3 in text Change x_{t-1} to x_t Page 141 Nikos Vlassis Page 197, Table 7.1, line 3 The integration should be with respect to x_{t-1}, not just x Page 197 Patrick Beeson Pages 122-221 Throughout chapters 5 and 7, the book uses standard deviations as parameters of the function prob() and the error variables \varspeilon. The problem with those expressions is that standard deviations are not additive. The correct notation (which will be in the second printing) involves variances, which are additive. In chapter 5: page 122, first paragraph page 123, table 5.1, line 10 and table caption page 123, table 5.1, lines 1 and 3 and table caption page 124, table 5.3, lines 2-4 and table caption page 124, table 5.4, lines 1 and 3 and table caption page 127, eq. 5.10 and the sentence that follows page 128, figure 5.6, figure caption page 128, eqs. 5.11 and 5.12 and adjacent text page 129, eq 5.15 page 131, eq 5.29-5.32 and adjacent text page 134, table 5.5, lines 8-10 page 135, 4th paragraph page 136, table 5.6, lines 5-7 page 139, eqs 5.37-5.39 and 5.44-5.46 and adjacent text page 147, exercise 8 In chapter 7: page 204, table 7.2, line 5 page 205, eq. 7.5 page 206, eq. 7.10 page 217, table 7.3, line 5 page 221, table 7.4, line 2. Pages 122-139, 147 204-206, 217 221 Steffen Gutmann Page 204 line 4, page 206 Eq 7.11 sign error in the first term of the matrix V_t Pages 204-206 Jack Collier Page 238, Table 8.1, Line 4 Should be multiplied by \bar{p}_{k,t}, to make it consistent with page 87, table 4.1, line 4. Page 238 Rodney Bates Page 264-265, Table 8.4. In line 3, initialize M_\chi to zero. In line 19 add "or M < M_chi_min", where M_chi_min is the user-specified minimum number of particles. This change avoids an infinite loop in case all particles fall in the same bin. Pages 264-265 Patrick Beeson Page 271, Table 8.5, Line 4. In line 4, replace p_{hit} by p_{short}, and z_{hit} by z_{short}. Page 271 Change-bae Moon Page 262, Eq 8.7 misplaced bracket Page 262 David Stavens Page 288, table 9.2. In line 8, replace |r-z_{max}| by |r-z_t^{k}| Page 288 Ernest Ngaruiya Page 293, Eq 9.9 There is a typo: p(m_i)^k should be p(m_i^k) Page 293 Patrick Beeson Page 318 The derivation of Eq. 10.14 should refer back to Eq. 7.7, not 7.11. Page 318 Authors Page 318, Eq. 10.16; Page 314, Table 10.1, line 4; Page 321, Table 10.2, line 5; Page 347 Table 11.2, line 6 There is a sign error with all four non-zero terms. The correct expression can be found in Table 7.2, line 3 on page 204. Page 318, 314, 321, 347 Gabe Hoffman Page 319, Eq 10.20; and Page 322, Table 10.2, line 15 This expression contains multiple errors. It will be corrected in the second printing of this book. Page 319, 322 Gabe Hoffman Page 348, Table 11.2, lines 7 and 8; page 356, Eq 11.19; page 357, Eqs. 11.22 and 11.23 There is a transpose missing for G_t^T, whenever G_t occurs in a column vector. Page 348 Gabe Hoffman Page 348, Table 11.2, lines 17 and 19 Added a missing dimension for the matrix H (landmark vectors are three-dimensional in the book; but the printed version omitted the third dimension) Page 348 Keith Sevcik Page 354, Eqs. 11.7 and 11.8 y_{1:t-1} should be y_{0:t-1} Page 354 Patrick Beeson Page 356, Eq. 11.19; Page 357 Eqs. 11.23 and 11.25; Page 348, Table 11.2, Line 8 line 19 A dual sign errors in Eq. 11.19: the term with G_t has to be subtracted, and the last term with H_t^i has to be added. Page 356, 357, 348 Gabe Hoffman Page 356, Eq 11.19; Page 357 Eqs. 11.22-23; Page 348, Table 11.2, Lines 7 and 8 Terms of the type (1 -G_t) and (1 -G_t^T)^T need to be re-ordered to match the definition of vectors x_{t-1:t} in Eq. 11.4. They should be of the form (-G_t 1) and (-G_t^T 1)^T. With the correct ordering, x_{t-1} will be multiplied by -G_t^T. Page 356, 357, 348 Steffen Gutmann Page 359, Table 11.7 Error in the conditional of a Gaussian: The information vector should be \xi_x - \Omega_{xy} y (replace '+' by '-'). There is also an obsolete plus sign in the derivation. (The lemma is applied correctly in the remaining text). Page 359 Hugh Durrant-Whyte Pages 446-464 The transpose of the matrix H (formerly G) should be swapped in certain equations (replace H by H^T and H^T by H.). page 446, eq. 13.16, 13.18; page 450, table 13.1, lines 14, 15, and 17 page 456, eq 13.53 (left term) page 459, eq 13.62 page 461, table 13.2, lines 8, 18, 21, and 23 pages 463-464, table 13.3, lines 24, 29, 31, and 33 Pages 446-464 Zach Dodds Page 447, Eq. 13.19 The posterior is of the form p(x_{1:t}|...), not just p(x_t|...) Page 447 Steffen Gutmann Page 448, Eq. 13.21-23 While this is correct, the last expression in Eq. 13.21 can be simplified by dropping more conditioning variables, to p(z_t | x_t^{[k]},c_t). As a result, Eqs. 13.22-23 become shorter. Page 448 Authors Page 450, tble 13.1, line 15 Q should be replaced by Q^{-1} Page 450 Zach Dodds Page 450, tble 13.1, lines 9 and 14 In line 9 and line 14 the subscript 'n' on Sigma should be replaced with 'j', that is, \Sigma^{[k]}_{ n ,t-1 } should be \Sigma^{[k]}_{ j ,t-1 }. Page 450 Kamil Wnuk Pages 450 (line 16), 461 (line 22), and 464 (line 30) Unnecessary transposes: ( z_t - \hat{z}_{\hat{c}} )^T should be ( z_t - \hat{z}_{\hat{c}} ). Pages 446-464 Kamil Wnuk Page 452, 3rd line One of the two occurrences of "dm_c_t" should be omitted. Pages 452 Authors Pages 446-464 In chapter 13 on FastSLAM, there is a typo that effects many different equations. The chapter erroneously states the measurement covariance to be R_t, whereas in the remainder of this book it has been defined as Q_t. The affected equations and tables are: eq. 13.16 (page 446); eq. 13.25 (page 448); lines 9 and 14 in table 13.1 (page 450); eq. 13.27 (page 452); eq. 13.35 (page 453) eq. 13.43 (page 454); eq. 13.45 (page 454); eq. 13.52-53 (page 456); eq. 13.58 (page 458); eq. 13.62 (page 459); lines 8 and 18 in table 13.2 (page 461); lines 9, 24, and 33 in table 13.3 (page 463-464); Pages 446-464 Jorge Costa (and Authors) Pages 446-464 There is another typo in chapter 13 on FastSLAM: g and h are used exactly the wrong way, and so are the Jacobians G and H. This problem ocurrs in the following places: text before and after eq. 13.15 (page 446) eq. 13.15-18 (page 446) eq. 13.25 (page 448) and reference to g in the subsequent paragraph lines 7-9, 12-15, and 17 in table 13.1 (page 450) eq. 13.27-48 (pages 452-455) and accommodating text eq. 13.52-53 (page 456) and accommodating text eq. 13.58-62 (pages 458-459) and accommodating text lines 6-8, 17-18, 21, and 23 in table 13.2 (page 461) lines 5-11, 13, 22-24, 29, 31, and 33 in table 13.3 (pages 463-464) Pages 446-464 Authors Page 459, Eq (13.62) and Page 461, line 18. There is no suitable definition of H_c or H_j. On Page 461, we added the following H_j = h'(\mu_{j,t}^{[k]},x_t^{[k]}), which is essentialy the one given in line 7. Pages 446-464 Jan Oberlaender Page 463, Lines 9, 11, 13, 22, 23, 24. Replace H_{m,t} by H_{m,j}. Swap lines 22 and 23. Replace H_j by H_{m,j} in line 24. Replace Q_j by Q_j^{-1} in line 11. Use \mu_{j,t-1}^{[k]} in line 13, instead of \mu_{x_t,j}. Pages 446-464 Jan Oberlaender Page 463, Lines 12 and 28 Cache sampled pose into auxiliary variable x_{t,j}^{[k]} (line 12), and use this sampled pose in line 28, not the predicted pose \hat{x}_{j,t}. Pages 446-464 Jan Oberlaender Page 464, Line 33 Swap Q and R and fix a transpose. Pages 446-464 Jan Oberlaender Page 453, Eq. 13.37 replace R_t^{[k]} with P_t^{[k]} Pages 453 Authors Page 456, Eq. 13.52 the firt probability in the last line of tihs equation has as a mean g(\hat{x}_{t-1}^{[k]},u_t), not just \hat{x}_{t-1}^{[k]} Pages 456 Authors Page 463, Table 13.3 The term Q_j in line 10 should be inverted: Q_j^{-1} Pages 463 Authors Page 466, Fig. 13.8 The lower rights tests on j should be: j<=5 and j<=7. Page 466 Jochen Sprickerhof Page 514, sentence following Eg. 15.2 There is the function "r" missing in the definition of V_1(b): E_x[r(x,u)] Page 514 Stefano Carpin Page 572, Eq. 17.3 This is truly just a Jensen bound, and in the context of this text it is meant as an approximation, since the expectation of a log replaces a sum and a log. The equality should therefore be replaced by an approximate sign. Page 572 Gabe Hoffman Page 572, Eq. 17.6 Remove orphan ")" Page 572 Tapio Taipalus