Class implementing a three-tube Concentric Tube Robot (CTR). More...

#include <CTR.hpp>

Collaboration diagram for CTR:

Public Member Functions
	CTR ()=delete
	Removes the default CTR Class constructor.

	CTR (const std::array< std::shared_ptr< Tube >, 3UL > &Tb, blaze::StaticVector< double, 6UL > &q, const double Tol, const mathOp::rootFindingMethod method)
	Implements the overloaded constructor for the CTR class.

	CTR (const CTR &rhs)
	Implements the copy constructor for the CTR class.

	CTR (CTR &&rhs) noexcept
	Implements the move constructor for the CTR class.

	~CTR ()=default
	Destroys the CTR object.

CTR &	operator= (const CTR &rhs)
	Implements the copy assignment operator for the CTR class.

CTR &	operator= (CTR &&rhs) noexcept
	Implements the move assignment operator for the CTR class.

void	reset (const blaze::StaticVector< double, 5UL > &initGuess)
	Resets the std::vector containing all state variables for the CTR at each arc-length.

blaze::StaticVector< double, 5UL >	ODESolver (const blaze::StaticVector< double, 5UL > &initGuess)
	Solves the CTR model equations (system of ODEs) by numerical integration.

blaze::StaticMatrix< double, 5UL, 5UL >	jac_BVP (const blaze::StaticVector< double, 5UL > &initGuess, const blaze::StaticVector< double, 5UL > &residue)
	Computes the finite-differences Jacobian for solving the associated Boundary Value Problem (BVP)

blaze::StaticMatrix< double, 3UL, 6UL >	jacobian (const blaze::StaticVector< double, 5UL > &initGuess, const blaze::StaticVector< double, 3UL > &tipPos)
	Computes the finite-differences Jacobian for the spatial velocities at the distal-end of the CTR.

bool	PowellDogLeg (blaze::StaticVector< double, 5UL > &initGuess)
	Nonlinear root-finding algorithm for solving the shooting method. It implements the Powell's Dog Leg Method to find the zero of the residue function.

bool	Levenberg_Marquardt (blaze::StaticVector< double, 5UL > &initGuess)
	Nonlinear root-finding algorithm for solving the shooting method. It implements the Levenberg-Marquardt Method to find the zero of the residue function.

bool	Broyden (blaze::StaticVector< double, 5UL > &initGuess)
	Nonlinear root-finding algorithm for solving the shooting method. It implements the Broyden's Method (Jacobian inverse is estimated) to find the zero of the residue function.

bool	Broyden_II (blaze::StaticVector< double, 5UL > &initGuess)
	Nonlinear root-finding algorithm for solving the shooting method. It implements the Broyden's Method (Jacobian inverse is estimated) to find the zero of the residue function.

bool	Newton_Raphson (blaze::StaticVector< double, 5UL > &initGuess)
	Nonlinear root-finding algorithm for solving the shooting method. It implements the Newton-Raphson's Method to find the zero of the residue function.

bool	Modified_Newton_Raphson (blaze::StaticVector< double, 5UL > &initGuess)
	Nonlinear root-finding algorithm for solving the shooting method. It implements the modified Newton-Raphson's Method to find the zero of the residue function.

bool	actuate_CTR (blaze::StaticVector< double, 5UL > &initGuess, const blaze::StaticVector< double, 6UL > &q_input)
	Actuates the CTR robot to a configuration determined by the actuation inputs and the associated boundary conditions dictated by the initial guess for the BVP.

bool	posCTRL (blaze::StaticVector< double, 5UL > &initGuess, const blaze::StaticVector< double, 3UL > &target, const double Tol)
	Implements the differential inverse kinematics based on resolved rates motion of the actuators.

std::array< std::shared_ptr< Tube >, 3UL >	getTubes ()
	Returns an std container with smart pointers to the Tube objects comprising the CTR.

blaze::StaticVector< double, 3UL >	getBeta ()
	Returns the current actuation values of the linear joints of the CTR.

blaze::StaticVector< double, 6UL >	getConfiguration ()
	Returns the current actuation values of all the linear and revolute joints of the CTR.

blaze::StaticVector< double, 3UL >	getTipPos ()
	Returns the current end-effector (distal-end) position of the CTR in meters.

blaze::StaticVector< double, 3UL >	getDistalEnds ()
	Returns the arc-lenghts of each tube's distal end in meters.

std::tuple< blaze::HybridMatrix< double, 3UL, 1000UL, blaze::columnMajor >, blaze::HybridMatrix< double, 3UL, 1000UL, blaze::columnMajor >, blaze::HybridMatrix< double, 3UL, 1000UL, blaze::columnMajor > >	getTubeShapes ()
	Implements a getter moethod for acquiring the 3-dimensional shape of each tube in the CTR assembly.

std::tuple< std::vector< double >, std::vector< double >, std::vector< double > >	getShape ()
	Returns a tuple with three std vectors containing the shape of the innermost tube in the CTR assembly.

void	setConfiguration (const blaze::StaticVector< double, 6UL > &q)
	Implements a setter method for setting the actuation joint values. It does not actuate the CTR (does not solve the FK of the CTR)

void	setBVPMethod (mathOp::rootFindingMethod mthd)
	Implements a setter method for chosing wich nonlinear root finding algorithm to use when solving the Boundary Value Problem (BVP)

void	setDistalMoment (const blaze::StaticVector< double, 3UL > &moment)
	Implements a setter method for specifying the point moment acting at the distal-end of the CTR.

void	setDistalForce (const blaze::StaticVector< double, 3UL > &force)
	Implements a setter method for specifying the point force acting at the distal-end of the CTR.

Private Attributes
double	m_accuracy
	Defines the accuracy of the numerical solution for the CTR Boundary Value Problem (BVP).

mathOp::rootFindingMethod	m_method
	Available root-finding methods: Newton-Raphson, Levenberg-Marquardt, Powell (dog-leg), Broyden.

std::array< std::shared_ptr< Tube >, 3UL >	m_Tubes
	Array of smart pointers to the Tube objects comprising the CTR.

blaze::StaticVector< double, 3UL >	m_beta
	Linear actuation values [beta_1, beta_2, beta_3].

blaze::StaticVector< double, 6UL >	m_q
	Joint actuation values [alpha_1, alpha_2, alpha_3].

blaze::StaticVector< double, 3UL >	m_theta_0
	Initial twist angle for all tubes at s = 0.

blaze::StaticVector< double, 4UL >	m_h_0
	Initial orientation of the local frame at s = 0, represented as a quaternion.

blaze::StaticVector< double, 3UL >	m_wf
	External point force at the distal-end of the CTR (force component of the external wrench).

blaze::StaticVector< double, 3UL >	m_wm
	External point moment at the distal-end of the CTR (moment component of the external wrench).

blaze::StaticVector< double, 3UL >	m_e3
	Third canonical basis of R^3.

std::unique_ptr< Segment >	m_segment
	Unique pointer to the segments between transition points along the CTR backbone.

std::vector< state_type >	m_y
	Stores the CTR state vector at each arc-length (spatial integration step).

std::vector< double >	m_s
	Stores the discrete arc-length points (in meters) along the backbone.

std::unique_ptr< ODESystem >	m_stateEquations
	Unique pointer to the ODE system implementing the state differential equations for a three-tube CTR.

std::unique_ptr< Observer >	m_stateObserver
	Unique pointer to the state observer for Boost::odeInt.

Detailed Description

Class implementing a three-tube Concentric Tube Robot (CTR).

Constructor & Destructor Documentation

◆ CTR() [1/3]

CTR::CTR	(	const std::array< std::shared_ptr< Tube >, 3UL > &	Tb,
		blaze::StaticVector< double, 6UL > &	q,
		const double	Tol,
		const mathOp::rootFindingMethod	method )

Implements the overloaded constructor for the CTR class.

Parameters

Tb	A 3-dimensional std::array containing smart pointers to the three tube objects comprising the CTR assembly.
q	A 6-dimensional static Blaze vector containing the actuation input values for the CTR.
Tol	A scalar that dictates the prescribed accuracy (tolerance) for solving the associated Boundary Value Problem (BVP).
method	An enum class specifying the root-finding method. The possible choices are: NEWTON_RAPHSON, LEVENBERG_MARQUARDT, POWELL_DOG_LEG, MODIFIED_NEWTON_RAPHSON, BROYDEN, and BROYDEN_II.

◆ CTR() [2/3]

CTR::CTR ( const CTR & rhs )

Implements the copy constructor for the CTR class.

Parameters

rhs	The source CTR object to copy from.

◆ CTR() [3/3]

CTR::CTR ( CTR && rhs )

noexcept

Implements the move constructor for the CTR class.

Parameters

rhs	The source CTR object to move from.

Member Function Documentation

◆ actuate_CTR()

bool CTR::actuate_CTR	(	blaze::StaticVector< double, 5UL > &	initGuess,
		const blaze::StaticVector< double, 6UL > &	q_input )

Actuates the CTR robot to a configuration determined by the actuation inputs and the associated boundary conditions dictated by the initial guess for the BVP.

Parameters

initGuess	is the initial guess 5-dimensional vector for the boundary value problem (BVP).
q_input	is a 6-dimensional vector of the actuation units The first three entries are the linear joints, the last three are the revolute ones.

Returns: a boolean flag. True: the associated BVP has been solved successfully | False: otherwise

◆ Broyden()

bool CTR::Broyden ( blaze::StaticVector< double, 5UL > & initGuess )

Nonlinear root-finding algorithm for solving the shooting method. It implements the Broyden's Method (Jacobian inverse is estimated) to find the zero of the residue function.

Parameters

initGuess is the initial guess 5-dimensional vector for the boundary value problem (BVP).

Returns: a boolean flag. True: the zero (root) of the residue function has been found | False: the zero (root) of the residue function has not been found

◆ Broyden_II()

bool CTR::Broyden_II ( blaze::StaticVector< double, 5UL > & initGuess )

Nonlinear root-finding algorithm for solving the shooting method. It implements the Broyden's Method (Jacobian inverse is estimated) to find the zero of the residue function.

Parameters

initGuess is the initial guess 5-dimensional vector for the boundary value problem (BVP).

Returns: a boolean flag. True: the zero (root) of the residue function has been found | False: the zero (root) of the residue function has not been found

◆ getBeta()

blaze::StaticVector< double, 3UL > CTR::getBeta ( )

Returns the current actuation values of the linear joints of the CTR.

Returns: a static 3-dimensional Blaze vector with the actuation values for the linear joints [beta_1, beta_2, beta_3]

◆ getConfiguration()

blaze::StaticVector< double, 6UL > CTR::getConfiguration ( )

Returns the current actuation values of all the linear and revolute joints of the CTR.

Returns: a static Blaze vector with the actuation values for all the joints [beta_1, beta_2, beta_3, alpha_1, alpha_2, alpha_3]

◆ getDistalEnds()

blaze::StaticVector< double, 3UL > CTR::getDistalEnds ( )

Returns the arc-lenghts of each tube's distal end in meters.

Returns: a static 3-dimensional Blaze vector with the arc-length distal-end positions of each tube in the CTR assembly

◆ getShape()

std::tuple< std::vector< double >, std::vector< double >, std::vector< double > > CTR::getShape ( )

Returns a tuple with three std vectors containing the shape of the innermost tube in the CTR assembly.

Returns: a tuple with the set of three std::vectors with the shape of the innermost tube in the CTR assembly. The first, second, and third entries in the tuple correspond to the x,y,z coordinates of the tube centerline

◆ getTipPos()

blaze::StaticVector< double, 3UL > CTR::getTipPos ( )

Returns the current end-effector (distal-end) position of the CTR in meters.

Returns: a static 3-dimensional Blaze vector with the position of the distal-end of the CTR

◆ getTubes()

std::array< std::shared_ptr< Tube >, 3UL > CTR::getTubes ( )

Returns an std container with smart pointers to the Tube objects comprising the CTR.

Returns: smart pointers to the tubes comprising the CTR assembly

◆ getTubeShapes()

std::tuple< blaze::HybridMatrix< double, 3UL, 1000UL, blaze::columnMajor >, blaze::HybridMatrix< double, 3UL, 1000UL, blaze::columnMajor >, blaze::HybridMatrix< double, 3UL, 1000UL, blaze::columnMajor > > CTR::getTubeShapes ( )

Implements a getter moethod for acquiring the 3-dimensional shape of each tube in the CTR assembly.

Returns: a set of three 3xN Blaze matrices with the shape of each tube in the CTR assembly. The first, second, and third rows of each matrix correspond to the x,y,z coordinates

◆ jac_BVP()

blaze::StaticMatrix< double, 5UL, 5UL > CTR::jac_BVP	(	const blaze::StaticVector< double, 5UL > &	initGuess,
		const blaze::StaticVector< double, 5UL > &	residue )

Computes the finite-differences Jacobian for solving the associated Boundary Value Problem (BVP)

Parameters

initGuess	is the initial guess 5-dimensional vector for the boundary value problem (BVP).
residue	is the residue (violation of the distal boundary condition) at the current iteration of the shooting problem.

Returns: a 5x5 BVP Jacobian matrix that relates how the residue changes as a function of the initial guesses

◆ jacobian()

blaze::StaticMatrix< double, 3UL, 6UL > CTR::jacobian	(	const blaze::StaticVector< double, 5UL > &	initGuess,
		const blaze::StaticVector< double, 3UL > &	tipPos )

Computes the finite-differences Jacobian for the spatial velocities at the distal-end of the CTR.

Parameters

initGuess	is the initial guess 5-dimensional vector for the boundary value problem (BVP).
tipPos	is the current distal-end position at the current iteration of the inverse kinematics (position control problem).

Returns: a 3x6 BVP Jacobian matrix that relates how the distal spatial velocities residue change as a function of the actuation inputs

◆ Levenberg_Marquardt()

bool CTR::Levenberg_Marquardt ( blaze::StaticVector< double, 5UL > & initGuess )

Nonlinear root-finding algorithm for solving the shooting method. It implements the Levenberg-Marquardt Method to find the zero of the residue function.

Parameters

initGuess is the initial guess 5-dimensional vector for the boundary value problem (BVP).

Returns: a boolean flag. True: the zero (root) of the residue function has been found | False: the zero (root) of the residue function has not been found

◆ Modified_Newton_Raphson()

bool CTR::Modified_Newton_Raphson ( blaze::StaticVector< double, 5UL > & initGuess )

Nonlinear root-finding algorithm for solving the shooting method. It implements the modified Newton-Raphson's Method to find the zero of the residue function.

Parameters

initGuess is the initial guess 5-dimensional vector for the boundary value problem (BVP).

Returns: a boolean flag. True: the zero (root) of the residue function has been found | False: the zero (root) of the residue function has not been found

◆ Newton_Raphson()

bool CTR::Newton_Raphson ( blaze::StaticVector< double, 5UL > & initGuess )

Nonlinear root-finding algorithm for solving the shooting method. It implements the Newton-Raphson's Method to find the zero of the residue function.

Parameters

initGuess is the initial guess 5-dimensional vector for the boundary value problem (BVP).

Returns: a boolean flag. True: the zero (root) of the residue function has been found | False: the zero (root) of the residue function has not been found

◆ ODESolver()

blaze::StaticVector< double, 5UL > CTR::ODESolver ( const blaze::StaticVector< double, 5UL > & initGuess )

Solves the CTR model equations (system of ODEs) by numerical integration.

Parameters

initGuess is the initial guess 5-dimensional vector for the boundary value problem (BVP).

Returns: a 5-dimensional residue vector. The residue is the violation of the distal boundary condition

◆ operator=() [1/2]

CTR & CTR::operator= ( const CTR & rhs )

Implements the copy assignment operator for the CTR class.

Parameters

rhs	The source CTR object to copy from.

Returns: A reference to the assigned CTR object.

◆ operator=() [2/2]

CTR & CTR::operator= ( CTR && rhs )

noexcept

Implements the move assignment operator for the CTR class.

Parameters

rhs	The source CTR object to move from.

Returns: A reference to the assigned CTR object.

◆ posCTRL()

bool CTR::posCTRL	(	blaze::StaticVector< double, 5UL > &	initGuess,
		const blaze::StaticVector< double, 3UL > &	target,
		const double	Tol )

Implements the differential inverse kinematics based on resolved rates motion of the actuators.

Parameters

initGuess	is the initial guess 5-dimensional vector for the boundary value problem (BVP).
target	is a 3-dimensional vector of the target position to where the end-effector (distal-end of the CTR) should be steered to.
Tol	is a scalar indicating the tolerance with which the position control problem should be solved.

Returns: a boolean flag. True: the associated IK has been solved successfully within the prescribed tolerance | False: otherwise

◆ PowellDogLeg()

bool CTR::PowellDogLeg ( blaze::StaticVector< double, 5UL > & initGuess )

Nonlinear root-finding algorithm for solving the shooting method. It implements the Powell's Dog Leg Method to find the zero of the residue function.

Parameters

initGuess is the initial guess 5-dimensional vector for the boundary value problem (BVP).

Returns: a boolean flag. True: the zero (root) of the residue function has been found | False: the zero (root) of the residue function has not been found

◆ reset()

void CTR::reset ( const blaze::StaticVector< double, 5UL > & initGuess )

Resets the std::vector containing all state variables for the CTR at each arc-length.

Parameters

initGuess is the initial guess 5-dimensional vector for the boundary value problem (BVP).

◆ setBVPMethod()

void CTR::setBVPMethod ( mathOp::rootFindingMethod mthd )

Implements a setter method for chosing wich nonlinear root finding algorithm to use when solving the Boundary Value Problem (BVP)

Parameters

mthd	enum class specifying the root-finding method. The possible choices are: NEWTON_RAPHSON, LEVENBERG_MARQUARDT, POWELL_DOG_LEG, MODIFIED_NEWTON_RAPHSON, BROYDEN, and BROYDEN_II.

◆ setConfiguration()

void CTR::setConfiguration ( const blaze::StaticVector< double, 6UL > & q )

Implements a setter method for setting the actuation joint values. It does not actuate the CTR (does not solve the FK of the CTR)

Parameters

q	is a static 6-dimensional Blaze vector containing the actuation values for the CTR joints [beta_1, beta_2, beta_3, alpha_1, alpha_2, alpha_3]

◆ setDistalForce()

void CTR::setDistalForce ( const blaze::StaticVector< double, 3UL > & force )

Implements a setter method for specifying the point force acting at the distal-end of the CTR.

Parameters

force is a static 3-dimensional Blaze vector containing the point force acting at the distal-end of the CTR.

◆ setDistalMoment()

void CTR::setDistalMoment ( const blaze::StaticVector< double, 3UL > & moment )

Implements a setter method for specifying the point moment acting at the distal-end of the CTR.

Parameters

moment is a static 3-dimensional Blaze vector containing the moment acting at the distal-end of the CTR.

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

ctr_library/include/CTR.hpp
ctr_library/src/CTR.cpp

Public Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ CTR() [1/3]

◆ CTR() [2/3]

◆ CTR() [3/3]

Member Function Documentation

◆ actuate_CTR()

◆ Broyden()

◆ Broyden_II()

◆ getBeta()

◆ getConfiguration()

◆ getDistalEnds()

◆ getShape()

◆ getTipPos()

◆ getTubes()

◆ getTubeShapes()

◆ jac_BVP()

◆ jacobian()

◆ Levenberg_Marquardt()

◆ Modified_Newton_Raphson()

◆ Newton_Raphson()

◆ ODESolver()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ posCTRL()

◆ PowellDogLeg()

◆ reset()

◆ setBVPMethod()

◆ setConfiguration()

◆ setDistalForce()

◆ setDistalMoment()