Math related to robotics calculations. More...

Classes
class	arl::primitive::JointTrajectory
	Stores a Robot Joint Trajectory, providing interfaces with Armadillo or ROS msgs. You can provide the class with several points and it will interpolate returning position, velocity, acceleration in any given time. More...

class	arl::primitive::Trajectory< T >
	Represent a simple fifth order polynomial trajectory. Its a templated class that can be used with multiple types. More...

class	arl::math::Admittance
	Integrates the dynamical system for admittance control. More...

class	arl::math::Clik
	Calculates joint velocities given desired task velocities by implementing Closed Loop Inverse Kinematics. More...

Functions
EIGEN_DEVICE_FUNC Matrix < Scalar, 3, 3 >	skewSymmetric () const
	Returns the skew symmetric matrix from an Eigen Vector. More...

EIGEN_DEVICE_FUNC Matrix < Scalar, internal::traits < Derived >::ColsAtCompileTime, internal::traits< Derived > ::RowsAtCompileTime >	pinv (Scalar tolerance=Scalar{NumTraits< Scalar >::epsilon()}) const
	Calculates the pseudoinverse of a matrix. More...

double	arl::math::getTranslationalManipulabilityMeasureStrongSense (const arma::mat &jac)
	Calculates the translational manipulability measure in the strong sense as this is defined in Yoshikawa, Tsuneo. "Translational and rotational manipulability of robotic manipulators." American Control Conference, 1990. IEEE, 1990. APA. More...

double	arl::math::getTranslationalManipulabilityMeasureStrongSense (const arma::mat &jac, const arma::mat &choose)
	Calculates the translational manipulability measure in the strong sense as this is defined in Yoshikawa, Tsuneo. "Translational and rotational manipulability of robotic manipulators." American Control Conference, 1990. IEEE, 1990. APA. More...

arma::mat	arl::math::getScrewTransformation (const arma::mat &homogen)
	Returns the screw transformation. More...

arma::mat	arl::math::getTwistTransformation (const arma::mat &homogen)
	Calculates the twist transformation as defined in Eq. (4.23) p. 117 [2] using Armadillo. More...

Eigen::Matrix6d	arl::math::getTwistTransformation (const Eigen::Affine3d &transformation)
	Calculates the twist transformation as defined in Eq. (4.23) p. 117 [2] using Eigen. More...

arma::mat	arl::math::get6x6Rotation (const arma::mat &rotation)
	Returns the 6x6 matrix which the upper left and the down right sumbmatrices are the given 3x3 rotation matrix. More...

void	arl::math::skewSymmetric (const KDL::Vector &v, KDL::Rotation *skew)
	Calculates the skew symmetrix given a 3D vector using KDL. More...

void	arl::math::skewSymmetric (const Eigen::Matrix< double, 3, 1 > &v, Eigen::Matrix< double, 3, 3 > *skew)
	Calculates the skew symmetrix given a 3D vector using Eigen. More...

void	arl::math::skewSymmetric (const arma::vec &v, arma::mat *skew)
	Calculates the skew symmetrix given a 3D vector using Armadillo. More...

arma::mat	arl::robot::trajectory::get5thOrder (double t, arma::vec p0, arma::vec pT, double totalTime)
	Designs a 5th order trajectory. More...

arma::mat	arl::robot::trajectory::get5thOrderRotationMatrix (double t, arma::mat R0, arma::mat Rt, double totalTime)
	Designs a 5th order trajectory for orientation. More...

arma::mat	arl::robot::trajectory::get3rdOrder (double t, arma::vec p0, arma::vec pT, double totalTime)
	Designs a 3th order trajectory. More...

arma::mat	arl::robot::trajectory::getMinJerk (const arma::mat &state, const arma::vec &goal, double tau, double dt)
	Computes minimum jerk trajectory step given that we are currently in x, xd, xdd and that we have tau time before we reach the goal. More...

Detailed Description

Math related to robotics calculations.

Function Documentation

arma::mat arl::robot::trajectory::get3rdOrder	(	double	t,
		arma::vec	p0,
		arma::vec	pT,
		double	totalTime
	)

Designs a 3th order trajectory.

Parameters

t	For the current time instance
p0	From this point (initial)
pT	To the target
totalTime	If the total duaration of motion is this

Returns: The exact position, velocity and acceleration for that time instance, as columns [p][pdot][pddot]

arma::mat arl::robot::trajectory::get5thOrder	(	double	t,
		arma::vec	p0,
		arma::vec	pT,
		double	totalTime
	)

Designs a 5th order trajectory.

Parameters

t	For the current time instance
p0	From this point (initial)
pT	To the target
totalTime	If the total duaration of motion is this

Returns: The exact position, velocity and acceleration for that time instance, as columns [p][pdot][pddot]

arma::mat arl::robot::trajectory::get5thOrderRotationMatrix	(	double	t,
		arma::mat	R0,
		arma::mat	Rt,
		double	totalTime
	)

Designs a 5th order trajectory for orientation.

Parameters

t	For the current time instance
R0	Initial orientation
Rt	Target orientation
totalTime	If the total duration of motion is this

Returns: The exact orientation[3x3], angular velocity[3x1] and angular acceleration[3x1] for that time instance, as columns [R][qdot][qddot]

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arma::mat arl::math::get6x6Rotation ( const arma::mat & rotation )

Returns the 6x6 matrix which the upper left and the down right sumbmatrices are the given 3x3 rotation matrix.

Parameters

rotation The given rotation matrix

Returns: The 6x6 rotation matrix

arma::mat arl::robot::trajectory::getMinJerk	(	const arma::mat &	state,
		const arma::vec &	goal,
		double	tau,
		double	dt
	)

Computes minimum jerk trajectory step given that we are currently in x, xd, xdd and that we have tau time before we reach the goal.

Parameters

state	The current state. A matrix with 3 columns for position, velocity and acceleration
goal	The goal state
tau	The time until we reach the goal
dt	The time step

arma::mat arl::math::getScrewTransformation ( const arma::mat & homogen )

Returns the screw transformation.

The screw transformation (gamma matrix) for transforming a wrench applied on frame {B} and expressed in frame {B} to the wrench applied on frame {A} and expressed in frame {A}, as given in given by 4.27 in Doulgeri Robotics. The calculation is based on a 3x4 matrix storing the homogeneous transformation from tranferring something expressed in frame {B} to something expressed in frame {A}. The first three columns should contain the rotation matrix and the last column the translation.

Parameters

homogen The homogeneous transformation

Returns: The screw transformation matrix

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double arl::math::getTranslationalManipulabilityMeasureStrongSense ( const arma::mat & jac )

Calculates the translational manipulability measure in the strong sense as this is defined in Yoshikawa, Tsuneo. "Translational and rotational manipulability of robotic manipulators." American Control Conference, 1990. IEEE, 1990. APA.

Parameters

jac	The full jacobian matrix of the arm

Returns: The TMM in the strong sense

double arl::math::getTranslationalManipulabilityMeasureStrongSense	(	const arma::mat &	jac,
		const arma::mat &	choose
	)

Calculates the translational manipulability measure in the strong sense as this is defined in Yoshikawa, Tsuneo. "Translational and rotational manipulability of robotic manipulators." American Control Conference, 1990. IEEE, 1990. APA.

Parameters

jac	The full jacobian matrix of the arm
choose	A matrix for choosing a specific row of the jacobian (e.g. if you need only the manipulability in the z-axis (3rd row)

Returns: The TMM in the strong sense

arma::mat arl::math::getTwistTransformation ( const arma::mat & homogen )

Calculates the twist transformation as defined in Eq. (4.23) p. 117 [2] using Armadillo.

Returns the matrix:

$\Gamma_{bc} = \begin{bmatrix}R_{bc} & \hat{p}_{bc}R_{bc} \\ 0 & R_{bc}\end{bmatrix}$

where the rotation and the translation are taken from the given homogeneous matrix.

If you want to transfer a twist from frame c to frame b you can do it by multiplying the output with the twist from the right.

Parameters

homogen The homogeneous transformation between the two frames

Returns: The twist transformation

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Eigen::Matrix6d arl::math::getTwistTransformation ( const Eigen::Affine3d & transformation )

Calculates the twist transformation as defined in Eq. (4.23) p. 117 [2] using Eigen.

Returns the matrix:

$\Gamma_{bc} = \begin{bmatrix}R_{bc} & \hat{p}_{bc}R_{bc} \\ 0 & R_{bc}\end{bmatrix}$

where the rotation and the translation are taken from the given homogeneous matrix.

If you want to transfer a twist from frame c to frame b you can do it by multiplying the output with the twist from the right.

Parameters

homogen The homogeneous transformation between the two frames

Returns: The twist transformation

EIGEN_DEVICE_FUNC Matrix<Scalar, internal::traits<Derived>::ColsAtCompileTime, internal::traits<Derived>::RowsAtCompileTime> pinv ( Scalar tolerance = Scalar{NumTraits<Scalar>::epsilon()} ) const

inline

Calculates the pseudoinverse of a matrix.

Parameters

tolerance Any singular values less than tolerance are treated as zero. The default value is the machine precision given by NumTraits<Scalar>::epsilon()

Returns: The pseudoinverse matrix.

,

EIGEN_DEVICE_FUNC Matrix<Scalar, 3, 3> skewSymmetric ( ) const

inline

Returns the skew symmetric matrix from an Eigen Vector.

Returns: The 3x3 skew symmetric matrix

,

void arl::math::skewSymmetric	(	const KDL::Vector &	v,
		KDL::Rotation *	skew
	)

inline

Calculates the skew symmetrix given a 3D vector using KDL.

Parameters

v	A KDL vector
skew	A KDL rotation matrix as output

Deprecated:: Use EIGEN_DEVICE_FUNC inline Matrix<Scalar, 3, 3> skewSymmetric() const instead.

void arl::math::skewSymmetric	(	const Eigen::Matrix< double, 3, 1 > &	v,
		Eigen::Matrix< double, 3, 3 > *	skew
	)

inline

Calculates the skew symmetrix given a 3D vector using Eigen.

Parameters

v	An Eigen 3D vector
skew	An Eigen 3x3 matrix as output

Deprecated:: Use EIGEN_DEVICE_FUNC inline Matrix<Scalar, 3, 3> skewSymmetric() const instead.

void arl::math::skewSymmetric	(	const arma::vec &	v,
		arma::mat *	skew
	)

inline

Calculates the skew symmetrix given a 3D vector using Armadillo.

Parameters

v	An arma 3D vector
skew	An arma 3x3 matrix as output

Deprecated:: Use EIGEN_DEVICE_FUNC inline Matrix<Scalar, 3, 3> skewSymmetric() const instead.

Classes

Functions

Detailed Description

Function Documentation