MR Second Printing

Overall

Updates in red were added Aug 2019 or later, after the list of changes was given to David.

In the "partial list of errata contributors," perhaps add "and" before the last name. Also, "posted in October, 2016" should be "posted online in October, 2016" to be more specific.

There are a few places in the book where we have an italic T instead of a roman T for transpose, often where they are preceded by a negative (inverse) sign. These should be corrected. The ones we're aware of are listed below:

Equation (5.4) p149
Fifth line of p163
p168 third line of Eq (5.27)
Last line of p216
p239: eq (8.21) and equation just above.

p254: Eqs (8.75), (8.76), (8.78), (8.79), 8.80)

pp256-7: several instances in Ch 8.6. Just after eq (8.87) (two times), four times in eq (8.88), just after (8.88), and (8.90) and (8.91).
p272, in each of the two displayed equations in the 2nd bullet

p491, second-to-last bullet, in each of the two displayed equations and the in-line equation just after.

Preface

p xiv: Video lectures that accompany the textbook will also be available --> Video lectures that accompany the textbook are also available

(This is a very minor change, so I don't think we have to re-date the preface or provide a separate update.)

p xv: Several updates at the end of the preface. Change "A partial list of errata contributors." in the preface to "Notes on the second printing." Then have:

Readers are encouraged to consult the companion website \url{http://modernrobotics.org} for more information on the Modern Robotics software library, videos, online courses, robot simulations, practice problems with solutions, errata, a linear algebra refresher chapter, and more.

Then thanking the errata contributors.

Chapter 1

p3, middle: Change "convenient way to calculate a lower bound on the dof" to "convenient way to calculate the dof"

Chapter 2

Proposition 2.2, p16: "This formula holds only if all joint constraints are independent. If they are not independent then the formula provides a lower bound on the number of degrees of freedom." should be "This formula holds in "generic" cases, but it fails under certain configurations of the links and joints, such as when the joint constraints are not independent." (In your correction, you say ... "generic cases", ... as opposed to the suggested ... "generic" cases, ... . I prefer my suggested ... "generic" cases, ... but if there is a reason why your wording is better, shouldn't the comma be inside the quotes?)

Chapter 2.2.2, Example 2.3, p16: "Substituting" is misspelled.

Eliminate two sentences on p19: "Grubler's formula provides ... are discussed in Chapter 7."

Fifth bullet of Chapter 2.6 p32: Eliminate the last sentence "If the constraints enforced ... degrees of freedom."

Chapter 3

In the caption of Figure 3.3 p53, $(0.5,1/{\sqrt {2}})$ 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 (1/2, \sqrt{3}/2)} , 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 (-1/\sqrt{2},0.5)} 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 (-\sqrt{3}/2, 1/2)} .

Under "Representing a configuration" in Chapter 3.3.1.2 p78 near the bottom, the text says "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_{bc} = (R_{bc},p_{bc})} represents {b} relative to {c}" but it should say "represents {c} relative to {b}".
There is a typo in the final 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_{ce}} , of Example 3.19, p82. 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 130/\sqrt{2}} 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 160/\sqrt{2}} .
In the displayed equation just after Equation (3.76) p85, the left-hand side 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}_s]} (the brackets are missing).
Near the end of Chapter 3.6 Software p97, the function "AxisAng" should be written "AxisAng6."
Exercise 3.16(i) p103 asks for "the" 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,\hat{s},h\}} representation but it should say "a" 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,\hat{s},h\}} representation (since 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} is not unique). Replace "the" with "a".

Chapter 4

Example 4.1, last row of the table (screw axis for joint 3), middle of p122: The linear component 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 v_i} 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 (0, -L_2, 0)} (the 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 -} sign is missing).

Chapter 5

Equation (5.7) p153: The the first two terms on the right-hand side of the equation 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 J_{s1} \dot{\theta}_1 + J_{s2}(\theta) \dot{\theta}_2} .

Exercise 5.2(b) p173: Change (a) to "Suppose that the last link must apply a wrench corresponding to a force of ..." (then continue as current, "5 N in the..."). In (b), change "the tip" to "the last link". One more thing: let's add to the end of the first sentence in (b), so it is now "...direction, with zero components in other wrench directions."

Figure 5.15(b) p174: The circular arrow indicating the rotation of joint 3 is slightly misplaced. Kevin can provide.

Exercise 5.11(a) p178: Change "What are the..." to "Is this motion possible? If so, what are the ..."

Exercise 5.16 p180: change "PRRRRR" to "PRPRRR". Similarly, caption of Figure 5.26, p181, change "PRRRRR" to "PRPRRR."

Exercise 5.25(b) p186: At the end of part (b), add the sentence "Comment on why it is usually preferred to use the body Jacobian instead of the space Jacobian for the manipulability ellipsoid."

Chapter 6

Chapter 6.3, first sentence after Eq (6.7), p199: the 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 T_{sd}^{-1} \dot{T}_{sd}} 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 \dot{T}_{sd} T_{sd}^{-1}} are referred to as twists, but these are the se(3) matrix representations of the twists. Change the beginning of this sentence to "The matrix 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 [\mathcal{V}_d(t)]} of the desired twist is either 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}^{-1}(t) \dot{T}_{sd}(t)} (the matrix form of the body twist of the desired trajectory at time 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} ) or 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 \dot{T}_{sd}(t) T_{sd}^{-1}(t)} (the matrix form of the spatial twist), depending ..." and then complete the sentence as is.

Chapter 7

p218 displayed equation after (7.12): replace 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 \phi_5} with 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 \psi_5} in 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_p} to be consistent with definition 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 q_a} .

Just below caption for Figure 7.8 p222: There is an extraneous dot.

Chapter 8

In Equation (8.14) p236, 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{K}(\theta)} 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 \mathcal{K}(\theta,\dot{\theta})} .

Figure 8.5 p244 says the volume of the rectangular parallelepiped is 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 abc} but it 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 hlw} .

End of first sentence after Eq (8.26) in Section 8.2.1 p244 should read "... columns 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 R_{bc}} correspond to the eigenvectors 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 \mathcal{I}_b} ." (The word "eigenvalues" should be replaced by "eigenvectors.")

pp 249-50, between equations (8.46) and (8.47): We would like to clarify this derivation by replacing the text beginning "Then" and ending just before "Substituting" with the latex below, which can be cut-and-pasted. This is a pdf of what the revision should look like. The new text (replacing the old text) is in blue. Here is a latex'able zip directory to create the pdf file; the main file to be latex'ed is modern_robotics.tex.

From the fact $\dot{T}_{i,i-1} T_{i,i-1}^{-1}= -[\mathcal{A}_i \dot{\theta}_i]$, we have
\[
\dot{R}_{i,i-1} = -[\omega\dot{\theta}_i]R_{i,i-1}, \quad \dot{p} = -[\omega\dot{\theta}_i]p -v\dot{\theta}_i.
\]
Then 
\begin{align*}
\frac{d}{dt} & ([\text{Ad}_{T_{i,i-1}}])\mathcal{V}_{i-1} \\
& = \frac{d}{dt} 
\begin{bmatrix}
R_{i,i-1} && 0\\
[p]R_{i,i-1} && R_{i,i-1}
\end{bmatrix} \mathcal{V}_{i-1}\\
& = \begin{bmatrix}
-[\omega\dot{\theta}_i]R_{i,i-1} && 0\\
[-[\omega\dot{\theta}_i]p -v\dot{\theta}_i] R_{i,i-1}-[p][\omega\dot{\theta}_i]R_{i,i-1} && -[\omega\dot{\theta}_i]R_{i,i-1}
\end{bmatrix}\mathcal{V}_{i-1}\\
& = \underbrace{\begin{bmatrix}
-[\omega\dot{\theta}_i] && 0\\
-[v\dot{\theta}_i] && -[\omega\dot{\theta}_i]
\end{bmatrix}}_{-[\operatorname{ad}_{\mathcal{A}_i \dot{\theta}_i}]}
\underbrace{\begin{bmatrix}
R_{i,i-1} && 0\\
[p]R_{i,i-1} && R_{i,i-1}
\end{bmatrix}}_{[\operatorname{Ad}_{T_{i,i-1}}]} \mathcal{V}_{i-1} \\
& = -[\text{ad}_{\mathcal{A}_i\dot\theta_i}] \mathcal{V}_i\\
& = [\text{ad}_{\mathcal{V}_i}] \mathcal{A}_i\dot\theta_i,
\end{align*}
where the transition from the second equality to the third follows from the Jacobi identity
$a \times (b \times c) + b \times (c \times a) + c \times (a \times b) = 0$ for all $a, b, c \in \real^3$,
and the transition from the fourth equality to the fifth follows from the identity
$[\operatorname{ad}_{\twist_1}] \twist_2 = - [\operatorname{ad}_{\twist_2}] \twist_1$.

p258: In the parenthetical text a few lines before Equation (8.95): "...there is an equality constraint..." should instead be "...there is also an inequality constraint..."

Update Chapter 8.7 with an example and clearer text describing the equations, as in the Dropbox directory "Robotics Textbook Second Edition Sandbox".

Caption of Figure 8.10 p264: The operating region is light gray and the continuous operating region is dark gray (swap the two parenthetical statements).

Exercise 8.6(a) p276: The expression 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 \text{ad}_{J_i}(J_j)} has the indices switched; the correct expression is 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 \text{ad}_{J_j}(J_i)} .

Exercise 8.7 p276: The expression should be written:

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 \dot{M} = -\mathcal{A}^{\rm T} \mathcal{L}^{\rm T} \mathcal{W}^{\rm T} [\mbox{ad}_{\mathcal{A} \dot{\theta}}]^{\rm T} \mathcal{L}^{\rm T} \mathcal{GLA} - \mathcal{A}^{\rm T} \mathcal{L}^{\rm T} \mathcal{GL} [\mbox{ad}_{\mathcal{A} \dot{\theta}}] \mathcal{WLA} }

Chapter 10

Equation (10.4) p332 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 u = F(q) - B \dot{q}} (the plus sign in the book should be a minus sign).

p335, first line of chapter 10.6.4: 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 u = F(q) - B \dot{q}} (plus sign should be a minus sign). In the second-to-last line on the same page, the plus sign should be a minus sign.

Chapter 11

In the displayed equation after Equation (11.18) p360, the vector 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 X_e(t)} is a six-vector. The bottom three elements are written correctly, but the top three elements, an angular velocity, are written instead in their 3x3 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 so(3)} form. Also, the term written 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 R^{\text{T}}(d)} should be written 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 R^{\text{T}}(t)} . So, replace the top three elements in the vector 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 \omega_e(t)} , make the period after the equation a comma, and insert a line immediately following saying "where 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 [\omega_e(t)] = \log(R^{\text{T}}(t) R_d(t))} ."

In Equation (11.33) p366, the right-hand side should be zero, not 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 c} .

Figure 11.24 p384, the Robonaut 2 series elastic actuator, fourth sentence of the caption: The words "outer" and "inner" should be switched, so the new sentence reads "The inner ring of hole mounts connects to the harmonic gearhead output, and the outer ring of hole mounts is the output of the SEA, connecting to the next link."

Chapter 12

In Example 12.4 p404, the elements of the wrenches 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{F}_1, \mathcal{F}_2, \mathcal{F}_3} are erroneously written in the order 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_x,f_y,m_z)} ; they should be written in the order 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 (m_z,f_x,f_y)} . In other words, change these 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 (-2,0,1)} , 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 (1,-1,0)} , 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 (1,1,0)} , respectively. Also, I think the word "yield" right after 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{F}_3} should be "yielding."
In Chapter 12.1.6, just before Example 12.5, mention that point at infinity on the contact normal line correspond to translations and have +/- labels. Parallel contact normals for multiple contacts leave that point at infinity still with the +/- label after intersecting their feasible CoRs.
Caption of Figure 12.14 p412, second-to-last sentence: "rotation if possible" should be "rotation is possible."

Chapter 13

Equation (13.29) p467: 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 y_p} 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 y_P} (P is capitalized).

p469, first line just below the figure: get rid of the absolute value signs, so should be $v_d \neq 0$. The statement is equivalent with and without the absolute value signs, so we got rid of them.

Appendix C

Section C.3, Equation (C.5) p507: All four instances 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 \phi_{i-1}} 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 \phi_i} .

In Equation (C.12) p510, two instances 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 M_{i-1}} 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 M_i} .

A partial list of errata contributors

Thanks to the following people who provided corrections, starting from the preliminary version of the book posted in October, 2016:

H. Andy Nam, Eric Lee, Yuchen Rao, Chainatee Tanakulrongson, Mengjiao Hong, Kevin Cheng, Jens Lundell, Elton Cheng, Michael Young, Jarvis Schultz, Logan Springgate, Sofya Akhmametyeva, Aykut Onol, Josh Holcomb, Yue Chen, Mark Shi, AJ Ibraheem, Yalun Wen, Seongjae Jeong, Josh Mehling, Felix Wang, Drew Warren, Chris Miller, Clemens Eppner, Zack Woodruff, Jian Shi, Jixiang Zhang, Shachar Liberman, Will Wu, Dirk Boysen, Awe Wang, Ville Kyrki, John Troll, Andrew Taylor, and Nikhil Bakshi