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





Quaternions




+, -, *, /, = 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





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





Spl_Quaternion




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





Spl_Cubic




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





Spl_path




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





CLIK




q_qdotsets the desired joint position and joint velocity




Table 2.9: Computed_torque_method class member function





Computed_torque_method




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





Resolve_acc




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





Impedance




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





IO_matrix_file




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





Plot2d




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





Plot_file




graphcreate a graphics from a data file






Table 2.15: Config class member functions





Config




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





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