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 $T$ is indeed an element of $SE(3)$.

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 $q$) already gives the repulsive generalized force $F_{ij}(q)$, 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 $f_{i}(q)$. So the equation should read:

$F_{ij}^{\prime }(q)=-{\frac {\partial P_{ij}^{\prime }}{\partial f_{i}(q)}}={\frac {k}{\|f_{i}(q)-c_{j}\|^{4}}}(f_{i}(q)-c_{j})\in \mathbb {R} ^{3}.$

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 $k_{p},k_{i}>0$." to "The diagonal entries of the diagonal gain matrices $K_{p},K_{i}\in \mathbb {R} ^{6\times 6}$ should be positive." (Currently it says that these matrices shold have the form $k_{p}I$ and $k_{i}I$, 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 $K_{fp}$ in Equations (11.52) and (11.53) should be $(K_{fp}+I)$. ($I$ 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), $K_{fp}$ should be replaced by $(K_{fp}+I)$.

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 use of "V-REP" with "CoppeliaSim." There is one reference to V-REP in the Preface and one in Figure 1.1; those may be the only uses.

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 $T_{sd}$, "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 $L$ should be in the calligraphic font ${\mathcal {L}}$, for the Lagrangian.

Chapter 13

• In Equation (13.37), and twice in the following sentence, ${\mathcal {V}}$ should be ${\mathcal {V}}_{e}$.