2.19 Summary of functions

Table 2.2: Homogeneous transforms

Homogeneous Transforms

eulzxz transform of Euler angles

ieulzxzEuler angles of a transform

irotk rotation around a unit vector of a transform

irpy roll-pitch-yaw angles of a transform

rotd transform of a rotation around a line segment

rotk transform of a rotation around a unit vector

rpy transform of roll-pitch-yaw angles

rotx transform of a rotation around X axis

roty transform of a rotation around Y axis

rotz transform of a rotation around Z axis

trans transform of a translation

Table 2.3: Quaternion class member functions


+, -, *, /, = operators on quaternions

conjugate, i conjugate (or inverse) of a quaternion

exp, Log, powerexponential, logarithm and power of a quaternion

dot_prod dot product of a quaternion

dot, E quaternion time derivative

unit make a quaternion a unit quaternion

norm, norm_sqrcompute the norm and the square norm of a quaternion

s, v returns the scalar and the vector of a quaternion

set_s, set_v assign values to the scalar and vector part of a quaternion

R, T returns the equivalent rotation matrix (3 × 3 or 4 × 4)

Table 2.4: Quaternion non member functions


Omega returns angular velocity

Slerp Spherical Linear Interpolation

Slerp_prime Spherical Linear Interpolation derivative

Squad Spherical Cubic Interpolation

Squad_primeSpherical Cubic Interpolation derivative

Table 2.5: Spl_Quaternion class member function


quat interpolate the spline at time t to sets the quaternion q.

quat_winterpolate the spline at time t to sets the quaternion q and angular velocity ω.

Table 2.6: Spl_Cubic class member function


interpolating interpolate the spline at time t.

first_derivative interpolate the spline first derivative at time t.

second_derivativeinterpolate the spline second derivative at time t.

Table 2.7: Spl_path class member function


p interpolate the spline at time t to sets the position.

p_pdot interpolate the spline at time t to sets position and velocity.

p_pdot_pddotinterpolate the spline at time t to sets position, velocity and acceleration.

Table 2.8: CLIK class member function


q_qdotsets the desired joint position and joint velocity

Table 2.9: Computed_torque_method class member function


torque_cmdsets the output torque

set_Kd sets the derivative error gain

set_Kp sets the position error gain

Table 2.10: Resolve_acc class member function


torque_cmdsets the output torque

set_Kvp sets the translational velocity error gain

set_Kpp sets the translational position error gain

set_Kvo sets the rotational velocity error gain

set_Kpo sets the rotational position error gain

Table 2.11: Impedance class member function


control sets the compliant trajectory

set_Mpsets the translational impedance inertia matrix

set_Dpsets the translational impedance damping matrix

set_Kpsets the translational impedance stiffness matrix

set_Mosets the rotational impedance inertia matrix

set_Do sets the rotational impedance damping matrix

set_Ko sets the rotational impedance stiffness matrix

Table 2.12: IO_matrix_file class member functions


write create and write data to a file

read read data from a file

read_allread entire data file at once

Table 2.13: Plot2d class member functions


addcommandadd a gnuplot command the 2d graph

addcurve add a curve to the 2d graph

dump dump the content of the graph to stdout

gnuplot plot the graph through a call to gnuplot

settitle sets graph title

setxlabel sets axis X label

setylabel sets axis Y label

set_plot2d “wrapper” function for Plot2d

Table 2.14: Plot_file class member functions


graphcreate a graphics from a data file

Table 2.15: Config class member functions


read_confread configuration file

select assign the value of parameter from a section

add specify the value of parameter for a section

Table 2.16: Robot (and mRobot) class member functions

Joint Variables

get_qget the robot joint variables position

get_qp get the robot joint variables velocity

get_qpp get the robot joint variables acceleration

set_q set the robot joint variables position

set_qp set the robot joint variables velocity

set_qpp set the robot joint variables acceleration

Robot Kinematics

inv_kin inverse kinematics
inv_kin_rhino Rhino inverse kinematics
inv_kin_puma Puma inverse kinematics

jacobian robot Jacobian
jacobian_dot robot Jacobian derivative
jacobian_DLS_invrobot Jacobian DLS inverse

kine, kine_pd forward kinematics

dTdqi partial derivative of forward kinematics

Robot Dynamics

acceleration forward dynamics

inertia robot inertia matrix

torque inverse dynamics

torque_novelocity inverse dynamics without velocity and gravity

G gravity effects

C Coriolis and centrifugal effects

Robot Linearized Dynamics

delta_torque δτ = D(q)δq + S1(q,˙q)δ˙q + S2(q,˙q,q)δq

dq_torque S2(q,˙q,q)δq

dqp_torque S1(q,˙q)δ˙q

dtau_dq ∂τ-
 ∂q = S2(q,q˙,q)

dtau_dqp ∂τ-
 ∂˙q = S1(q,q˙)

Table 2.17: Miscellaneous


odeint adaptive step size Runge-Kutta integrator

Runge_Kutta4fixed step size 4th order Runge-Kutta integrator

Integ_Trap trapezoidal integration

pinv matrix pseudo inverse

vec_dot_prod vector dot product

vec_x_prod vector cross product

x_prod_matrixcross product matrix

perturb_robot perturb robot parameters