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. More...

#include <manipulability.h>

Inheritance diagram for exotica::Manipulability:

Collaboration diagram for exotica::Manipulability:

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

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

int	TaskSpaceDim () override

Public Member Functions inherited from exotica::TaskMap
virtual void	InstantiateBase (const Initializer &init)

virtual void	AssignScene (ScenePtr scene)

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

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

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)

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 int	TaskSpaceJacobianDim ()

virtual void	PreUpdate ()

virtual std::vector< TaskVectorEntry >	GetLieGroupIndices ()

std::vector< KinematicFrameRequest >	GetFrames () const

Public Member Functions inherited from exotica::Object
	Object ()

virtual	~Object ()

virtual std::string	type () const
	Type Information wrapper: must be virtual so that it is polymorphic... More...

std::string	GetObjectName ()

void	InstantiateObject (const Initializer &init)

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

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

virtual	~InstantiableBase ()=default

virtual std::vector< Initializer >	GetAllTemplates () const =0

Public Member Functions inherited from exotica::Instantiable< ManipulabilityInitializer >
void	InstantiateInternal (const Initializer &init) override

Initializer	GetInitializerTemplate () override

std::vector< Initializer >	GetAllTemplates () const override

const ManipulabilityInitializer &	GetParameters () const

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
std::vector< KinematicSolution >	kinematics = std::vector<KinematicSolution>(1)

int	id = -1

int	start = -1

int	length = -1

int	start_jacobian = -1

int	length_jacobian = -1

bool	is_used = false

Public Attributes inherited from exotica::Object
std::string	ns_

std::string	object_name_

bool	debug_

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

ScenePtr	scene_ = nullptr

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.