Modern Robotics Print-Only Errata

Printed Version Errata, February 3, 2022

Chapter 3

• At the end of the introduction Exercise 3.16, it says "origin of {b} is at (0,2,0) is {s}", but "is {s}" should be "in {s}".
• Exercise 3.20, Figure 3.26: In the figure, the y and z axes for the {a}, {b}, and {c} frames are switched (y should point forward and z should point up). Also, the space frame is located at the bottom of the small wheel, directly below the {a} frame.
• Exercise 3.25(a): the element in the third row and third column of the matrix $A$ should be 0. (It is incorrectly written as 1.)

Chapter 4

• Exercise 4.21: The question should begin "For each $T$ below..." instead of "For each $T\in SE(3)$ below...". (Since the first part of the problem is determining whether Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T} is indeed an element of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle SE(3)} .

Chapter 8

• Equation (8.74): the first two plus signs should be minus signs.

Chapter 10

• Second displayed equation of Chapter 10.6.3 (Workspace Potential): As it is written, this equation (which involves a partial derivative with respect to the robot's configuration Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q} ) already gives the repulsive generalized force Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F_{ij}(q)} , i.e., the Jacobian is already embedded, obviating the subsequent development. To fit the rest of the development, the partial derivative in this equation should be with respect to Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f_i(q)} . So the equation should read:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F^\prime_{ij}(q) = -\frac{\partial P^\prime_{ij}}{\partial f_i(q)} = \frac{k}{\|f_i(q) - c_j\|^4} (f_i(q) - c_j) \in \mathbb{R}^3. }

Chapter 11

• The one-sentence paragraph near the beginning of Chapter 11.3.3, after Equation (11.16): Change "As in Section 11.3.2 ... where Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle k_{p},k_{i}>0} ." to "The diagonal entries of the diagonal gain matrices Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K_p, K_i \in \mathbb{R}^{6 \times 6}} should be positive." (Currently it says that these matrices shold have the form Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k_p I} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k_i I} , but the units for a twist are different (first three units are angular velocities, last three units are linear velocities). So you may wish to use one positive value for the top three elements on the diagonal and a different positive value for the bottom three elements on the diagonal.)
• Chapter 11.5, Equations (11.52) and (11.53) (and nearby text): The term Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K_{fp}} in Equations (11.52) and (11.53) should be Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (K_{fp}+I)} . (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle I} is the identity matrix.) In the text immediately after Equation (11.51), the term "positive-definite" should be eliminated. In the text immediately after Equation (11.53), Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle K_{fp}} should be replaced by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (K_{fp}+I)} .

Minor typos, etc., no danger of misunderstanding

Throughout the book

• The V-REP simulator has been discontinued and replaced by the CoppeliaSim simulator. Replace every instance of "V-REP" with "CoppeliaSim."

Chapter 2

• Figure 2.9 (left): the bold segment of the line should not extend beyond the closing parenthesis at b.

Chapter 3

• Proposition 3.10: "satisifies" should be "satisfies"

Chapter 5

• Chapter 5.3, Case V: For maximum clarity, the title should be "Case V: Six Revolute Joint Axes Intersecting a Common Line." Similarly, fifth bullet of Chapter 5.5: item (v) on the list should say "six revolute joint axes intersecting..." instead of just "six revolute joints intersecting..."

Chapter 6

• Chapter 6.2.2, Example 6.1: just before the matrix Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T_{sd}} , "corresponds to to" should be "corresponds to."
• Chapter 6.3, first sentence after Equation (6.7): "however small" should be written "however, small" to avoid ambiguity.

Chapter 8

• First bullet of Chapter 8.10: In the displayed equation, the math italic Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle L} should be in the calligraphic font Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathcal{L}} , for the Lagrangian.

Chapter 13

• In Equation (13.37), and twice in the following sentence, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathcal{V}} should be Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathcal{V}_e} .