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| code Name |
LaTeX |
Description |
Dimensions |
pos_a_b |
$p^ {a}_ {a,b}$ |
Position Vector |
[3,1] |
pos_a_b_c |
$p^ {a}_ {b,c}$ |
Position Vector |
[3,1] |
rotm_a_b |
$R^ {a}_ {b}$ |
Rotation Matrix |
[3,3] |
tform_a_b |
$T^ {a}_ {b}$ |
Homogeneous Matrix |
[4,4] |
quat |
$q$ |
Quaternion vector |
[4,1] |
linkPos_0 |
$p^ {0}_ {0,i}$ |
link i position wrt inertial frame |
[3,1] |
linkQuat_0 |
$q^ {0}_ {i}$ |
link i orientation (quaternion) |
[4,1] |
linkEul_0 |
|
link i orientation (euler angles) |
[3,1] |
linkAngVel_0 |
$\omega^ {0}_ {0,i}$ |
link i angular velocity |
[3,1] |
linkTwist_0 |
$\begin{bmatrix} \dot{p}^ {0}_ {0,i} \\ \omega^ {0}_ {0,i} \end{bmatrix}$ |
link i twist |
[6,1] |
linkPosQuat_0 |
$\begin{bmatrix} p^ {0}_ {0,i} \\ q^ {0}_ {i} \end{bmatrix}$ |
link i position and orientation (quaternion) |
[7,1] |
jAngVel_PJ |
$\omega^ {pj}_ {pj,cj}$ |
joint j angular velocity |
[3,1] |
mBodyTwist_0 |
$v$ |
vector links twists |
[6*nLink,1] |
mBodyTwAcc_0 |
$\dot{v}$ |
vector links acceleration twists |
[6*nLink,1] |
mBodyPosQuat_0 |
$x$ |
kinematic state wrt inertial frame |
[7*nLink,1] |
mBodyVelQuat_0 |
$\dot{x}$ |
kinematic state derivative |
[7*nLink,1] |
mBodyLinVel_0 |
$\begin{bmatrix} \vdots \\ \dot{p}^ {0}_ {0,i} \\ \vdots \end{bmatrix}$ |
vector links linear velocity |
[3*nLink,1] |
mBodyAngVel_0 |
$w = \begin{bmatrix} \vdots \\ \omega^ {0}_ {0,i} \\ \vdots \end{bmatrix}$ |
vector links angular velocity |
[3*nLink,1] |
jointsAngVel_PJ |
$\omega = \begin{bmatrix} \vdots \\ \omega^ {pj}_ {pj,cj} \\ \vdots \end{bmatrix}$ |
vector of joints angular velocity |
[3*nJoints,1] |
jointsAngVelBase_0 |
|
vector of joints angular velocity + base |
[3*nJoints+6,1] |
mBodyPosVel_0 |
$\chi = \begin{bmatrix} x \\ v \end{bmatrix}$ |
|
[(7+6)*nLink,1] |
mBodyPosVel_0_g |
$\chi_ g$ |
|
[(7+6)*nLink,1] |
mBodyVelAcc_0 |
$\dot{\chi} = \begin{bmatrix} \dot{x} \\ \dot{v} \end{bmatrix}$ |
|
[(7+6)*nLink,1] |
motorsAngVel |
$\omega_ {act}= \begin{bmatrix} \vdots \\ \omega^ {pj}_ {pj,cj} \\ \vdots \end{bmatrix}$ |
angular velocity actuated joints |
[nMotors,1] |
motorsCurrent |
|
|
[nMotors,1] |
Jc |
$J_ {c}$ |
jacobian of constraints |
[nConstraints,6*nLink] |
dJc |
$\dot{J}_ {c}$ |
jacobian of constraints time derivative |
[nConstraints,6*nLink] |
mBodyWrenchExt_0 |
|
|
|
jointsWrenchConstr_PJ |
|
|
[nConstraints,1] |
| Frames |
Description |
0 |
inertial frame |
b |
body frame |
g |
CoM frame |
p |
body frame located at the center of the parent link |
c |
body frame located at the center of the child link |
pj |
body frame located at the connection point (relative to joint j) of the parent link |
cj |
body frame located at the connection point (relative to joint j) of the child link |
Extra
| Name |
Description |
nLink |
number of links |
nJoints |
number of joints |
nMotors |
number of motors |
nConstraints |
number of constraints |