Manipulability measure. The manipulability measure for a robot at a given joint configuration indicates dexterity, that is, how isotropic the robot's motion is with respect to the task space motion. The measure is high when the manipulator is capable of equal motion in all directions and low when the manipulator is close to a singularity. This task map implements Yoshikawa's manipulability measure

$m(x) = \sqrt{J(x)J(x)^T}$

that is based on the shape of the velocity ellipsoid where $J(x)$ is the manipulator Jacobian matrix.. The task map is expressed by

$\phi(x) := -m(x).$

. More...

#include <manipulability.h>

Inheritance diagram for exotica::Manipulability:

[legend]

Public Member Functions
void	Instantiate (const ManipulabilityInitializer &init) override

int	TaskSpaceDim () override

void	Update (Eigen::VectorXdRefConst x, Eigen::VectorXdRef phi) override

Public Member Functions inherited from exotica::TaskMap
virtual void	AssignScene (ScenePtr scene)

std::vector< KinematicFrameRequest >	GetFrames () const

virtual std::vector< TaskVectorEntry >	GetLieGroupIndices ()

virtual void	InstantiateBase (const Initializer &init)

virtual void	PreUpdate ()

virtual int	TaskSpaceJacobianDim ()

virtual void	Update (Eigen::VectorXdRefConst q, Eigen::VectorXdRef phi, Eigen::MatrixXdRef jacobian)

virtual void	Update (Eigen::VectorXdRefConst x, Eigen::VectorXdRefConst u, Eigen::VectorXdRef phi, Eigen::MatrixXdRef dphi_dx, Eigen::MatrixXdRef dphi_du)

virtual void	Update (Eigen::VectorXdRefConst x, Eigen::VectorXdRefConst u, Eigen::VectorXdRef phi)

virtual void	Update (Eigen::VectorXdRefConst x, Eigen::VectorXdRefConst u, Eigen::VectorXdRef phi, Eigen::MatrixXdRef dphi_dx, Eigen::MatrixXdRef dphi_du, HessianRef ddphi_ddx, HessianRef ddphi_ddu, HessianRef ddphi_dxdu)

virtual void	Update (Eigen::VectorXdRefConst q, Eigen::VectorXdRef phi, Eigen::MatrixXdRef jacobian, HessianRef hessian)

Public Member Functions inherited from exotica::Object
std::string	GetObjectName ()

void	InstantiateObject (const Initializer &init)

	Object ()

virtual std::string	Print (const std::string &prepend) const

virtual std::string	type () const

virtual	~Object ()

Public Member Functions inherited from exotica::InstantiableBase
	InstantiableBase ()=default

virtual	~InstantiableBase ()=default

Public Member Functions inherited from exotica::Instantiable< ManipulabilityInitializer >
std::vector< Initializer >	GetAllTemplates () const override

Initializer	GetInitializerTemplate () override

const ManipulabilityInitializer &	GetParameters () const

void	InstantiateInternal (const Initializer &init) override

Private Attributes
int	n_end_effs_
	Number of end-effectors. More...

int	n_rows_of_jac_
	Number of rows from the top to extract from full jacobian. Is either 3 (position) or 6 (position and rotation). More...

Additional Inherited Members
Public Attributes inherited from exotica::TaskMap
int	id

bool	is_used

std::vector< KinematicSolution >	kinematics

int	length

int	length_jacobian

int	start

int	start_jacobian

Public Attributes inherited from exotica::Object
bool	debug_

std::string	ns_

std::string	object_name_

Protected Attributes inherited from exotica::TaskMap
std::vector< KinematicFrameRequest >	frames_

ScenePtr	scene_

Protected Attributes inherited from exotica::Instantiable< ManipulabilityInitializer >
ManipulabilityInitializer	parameters_

Detailed Description

Manipulability measure. The manipulability measure for a robot at a given joint configuration indicates dexterity, that is, how isotropic the robot's motion is with respect to the task space motion. The measure is high when the manipulator is capable of equal motion in all directions and low when the manipulator is close to a singularity. This task map implements Yoshikawa's manipulability measure

$m(x) = \sqrt{J(x)J(x)^T}$

that is based on the shape of the velocity ellipsoid where $J(x)$ is the manipulator Jacobian matrix.. The task map is expressed by

$\phi(x) := -m(x).$

.

To use the task map as an inequality constraint the lower bound for $\phi$ should be set as a goal and each element should be negative.

Note that

the associated value for $\rho$ must be negative in order to maximize the manipulability, and
derivatives of $\Phi$ are computed using finite differences.

Todo

Update user options, that is allow user to specify to compute based on translation, rotation, all, yoshikawa, or asada as in Peter Corkes' toolbox (cf. https://github.com/petercorke/robotics-toolbox-matlab/blob/0ca01aac26b4475094845982b9a5e80b02c024fd/%40SerialLink/maniplty.m#L27).

Definition at line 61 of file manipulability.h.

Member Function Documentation

void exotica::Manipulability::Instantiate ( const ManipulabilityInitializer & init )

overridevirtual

Reimplemented from exotica::Instantiable< ManipulabilityInitializer >.

Definition at line 47 of file manipulability.cpp.

int exotica::Manipulability::TaskSpaceDim ( )

overridevirtual

Implements exotica::TaskMap.

Definition at line 62 of file manipulability.cpp.

void exotica::Manipulability::Update	(	Eigen::VectorXdRefConst	x,
		Eigen::VectorXdRef	phi
	)

overridevirtual

Implements exotica::TaskMap.

Definition at line 36 of file manipulability.cpp.

Member Data Documentation

int exotica::Manipulability::n_end_effs_

private

Number of end-effectors.

Definition at line 69 of file manipulability.h.

int exotica::Manipulability::n_rows_of_jac_

private

Number of rows from the top to extract from full jacobian. Is either 3 (position) or 6 (position and rotation).

Definition at line 70 of file manipulability.h.

The documentation for this class was generated from the following files:

Public Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Member Function Documentation

Member Data Documentation