Underwater Robots - Gianluca Antonelli.pdf

XXII Notation
η q =[η T 1 ε T η ] T ∈ IR 7
ν 1 =[u v w ] T ∈ IR 3
ν 2 =[p q r ] T ∈ IR 3
ν =[ν T 1
R β 3 × 3
α ∈ IR
ν T 2 ] T ∈ IR 6
3 × 3
J k,o ( η 2 ) ∈ IR
4 × 3
J k,oq( Q ) ∈ IR
6 × 6
J e ( η 2 ) ∈ IR
7 × 6
J e,q( Q ) ∈ IR
τ 1 =[X Y Z ] T ∈ IR 3
τ 2 =[K M N ] T ∈ IR 3
τ v =[τ T 1
τ � v ∈ IR 6
τ T 2 ] T ∈ IR 6
body(vehicle) position/orientation with the
orientation expressed byquaternions
vector representing the linear velocity ofthe
origin ofthe body(vehicle)-fixed frame with
respect to the origin of the inertial frame expressed
in the body(vehicle)-fixed frame (see
Figure 2.1)
vector representing the angular velocityofthe
body(vehicle)-fixed frame with respect to the
inertial frame expressed in the body(vehicle)fixed
frame (see Figure 2.1)
vector representing the linear/angular velocity
inthe body(vehicle)-fixed frame
rotation matrix expressing the transformation
from frame α to frame β
Jacobian matrix defined in (2.2)
Jacobian matrix defined in (2.10)
Jacobian matrix defined in (2.19)
Jacobian matrix defined in (2.23)
vector representing the resultantforcesacting
on the rigid body(vehicle) expressed in the
body(vehicle)-fixed frame
vector representing the resultant moment acting
on the rigid body(vehicle) expressed in
the body(vehicle)-fixed frame to the pole O b
generalized forces: forces and moments acting
on the vehicle
generalized forces in the earth-fixed-framebased
model defined in (2.53)
n degrees offreedom ofthe manipulator
q ∈ IR n
τ q ∈ IR n
τ =[τ T v
u ∈ IR p
τ T q ] T ∈ IR 6+n
joint positions
joint torques
generalizedforces: vehicle forcesand moments
and joint torques
control inputs, τ = Bu (see (2.72))