roboticslab::PardosGotorEight Class Reference

Eighth Pardos-Gotor subproblem. More...

#include <ScrewTheoryIkSubproblems.hpp>

Inheritance diagram for roboticslab::PardosGotorEight:

Public Member Functions
	PardosGotorEight (const MatrixExponential &exp1, const MatrixExponential &exp2, const MatrixExponential &exp3, const KDL::Vector &p, const int firstID, const int lastId, const PoeExpression poe)
	Constructor.
bool	solve (const KDL::Frame &rhs, const KDL::Frame &pointTransform, const JointConfig &reference, Solutions &solutions, const KDL::Frame &H_S_T, const KDL::JntArray &c_solutions, const KDL::Frame &H_S_T_0) const override
bool	solve (const KDL::Frame &rhs, const KDL::Frame &pointTransform, const JointConfig &reference, Solutions &solutions) const override
	Finds a closed geometric solution for this IK subproblem.
int	solutions () const override
	Number of local IK solutions.
const char *	describe () const override
	Return a human-readable description of this IK subproblem.
virtual bool	solve (const KDL::Frame &rhs, const KDL::Frame &pointTransform, const JointConfig &reference, Solutions &solutions) const=0
	Finds a closed geometric solution for this IK subproblem.
virtual bool	solve (const KDL::Frame &rhs, const KDL::Frame &pointTransform, const JointConfig &reference, Solutions &solutions, const KDL::Frame &H_S_T, const KDL::JntArray &c_solutions) const
virtual bool	solve (const KDL::Frame &rhs, const KDL::Frame &pointTransform, const JointConfig &reference, Solutions &solutions, const KDL::Frame &H_S_T, const KDL::JntArray &c_solutions, const KDL::Frame &H_S_T_0) const
bool	solve (const KDL::Frame &rhs, const KDL::Frame &pointTransform, Solutions &_solutions) const
Public Member Functions inherited from roboticslab::ScrewTheoryIkSubproblem
virtual	~ScrewTheoryIkSubproblem ()=default
	Destructor.
bool	solve (const KDL::Frame &rhs, const KDL::Frame &pointTransform, Solutions &_solutions) const

Private Attributes
const MatrixExponential	exp1
const MatrixExponential	exp2
const MatrixExponential	exp3
const KDL::Vector	p
const KDL::Vector	n
const KDL::Rotation	axisPow
const int	firstID
const int	lastID
const PoeExpression	poe

Additional Inherited Members
Public Types inherited from roboticslab::ScrewTheoryIkSubproblem
using	JointConfig = std::vector< double >
	Joint configurations.
using	Solutions = std::vector< JointConfig >
	Collection of local IK solutions.

Detailed Description

Triple solution, triple revolute joint geometric IK subproblem given by \( e\,^{\hat{\xi_1}\,{\theta_1}} \cdot e\,^{\hat{\xi_2}\,{\theta_2}} \cdot e\,^{\hat{\xi_3}\,{\theta_3}} \cdot Hp = Hk \) (rotation around three subsequent parallel axes applied to a pose or coordinate system, see [3]).

Constructor & Destructor Documentation

PardosGotorEight()

PardosGotorEight::PardosGotorEight	(	const MatrixExponential &	exp1,
		const MatrixExponential &	exp2,
		const MatrixExponential &	exp3,
		const KDL::Vector &	p,
		const int	firstID,
		const int	lastId,
		const PoeExpression	poe
	)

Parameters

exp1	First POE term.
exp2	Second POE term.
exp3	Third POE term.
p	Characteristic point.
firstID	ID of first axis
lastID	ID of third axis
poe	POE terms

Member Function Documentation

describe()

const char * roboticslab::PardosGotorEight::describe ( ) const

inlineoverridevirtual

Implements roboticslab::ScrewTheoryIkSubproblem.

solutions()

int roboticslab::PardosGotorEight::solutions ( ) const

inlineoverridevirtual

Implements roboticslab::ScrewTheoryIkSubproblem.

solve() [1/5]

bool roboticslab::PardosGotorEight::solve ( const KDL::Frame &  rhs, const KDL::Frame &  pointTransform, const JointConfig &  reference, Solutions &  solutions  ) const

inlineoverridevirtual

Given the product of exponentials (POE) formula \( \prod_i e\,^{\hat{\xi}_i\,{\theta_i}} \cdot H_{ST}(0) = H_{ST}(\theta) \), invariant and known terms are rearranged to the right side (rhs) as follows:

\[ \prod_{i=j}^{j+k} e\,^{\hat{\xi}_i\,{\theta_i}} = \left [ \prod_{i=1}^{j-1} e\,^{\hat{\xi}_i\,{\theta_i}} \right ]^{-1} \cdot H_{ST}(\theta) \cdot \left [ H_{ST}(0) \right ]^{-1} \cdot \left [ \prod_{i=j+k+1}^{N} e\,^{\hat{\xi}_i\,{\theta_i}} \right ]^{-1} \]

where \( j = \{1, 2, ..., N\} \), \( k = \{1, 2, ..., N-1\} \), \( 1 <= j+k <= N \).

Given \( N \) terms in the POE formula, \( j \) of which are unknowns, any characteristic point \( p \) postmultiplying this expression could be rewritten as \( p' \) per:

\[ \prod_{i=1}^j e\,^{\hat{\xi}_i\,{\theta_i}} \cdot \prod_{i=j+1}^N e\,^{\hat{\xi}_i\,{\theta_i}} \cdot p = \prod_{i=1}^j e\,^{\hat{\xi}_i\,{\theta_i}} \cdot p' \]

where pointTransform is the transformation matrix that produces \( p' \) from \( p \).

Parameters

rhs	Right-hand side of the POE formula prior to being applied to the right-hand side of this subproblem.
pointTransform	Transformation frame applied to the first (and perhaps only) characteristic point of this subproblem.
reference	Known nearby solutions to be used as reference in case a singularity is found.
solutions	Output vector of local solutions.

Returns

True if all solutions are reachable, false otherwise.

Implements roboticslab::ScrewTheoryIkSubproblem.

solve() [2/5]

virtual bool roboticslab::ScrewTheoryIkSubproblem::solve ( const KDL::Frame &  rhs, const KDL::Frame &  pointTransform, const JointConfig &  reference, Solutions &  solutions  ) const

virtual

Given the product of exponentials (POE) formula \( \prod_i e\,^{\hat{\xi}_i\,{\theta_i}} \cdot H_{ST}(0) = H_{ST}(\theta) \), invariant and known terms are rearranged to the right side (rhs) as follows:

\[ \prod_{i=j}^{j+k} e\,^{\hat{\xi}_i\,{\theta_i}} = \left [ \prod_{i=1}^{j-1} e\,^{\hat{\xi}_i\,{\theta_i}} \right ]^{-1} \cdot H_{ST}(\theta) \cdot \left [ H_{ST}(0) \right ]^{-1} \cdot \left [ \prod_{i=j+k+1}^{N} e\,^{\hat{\xi}_i\,{\theta_i}} \right ]^{-1} \]

where \( j = \{1, 2, ..., N\} \), \( k = \{1, 2, ..., N-1\} \), \( 1 <= j+k <= N \).

Given \( N \) terms in the POE formula, \( j \) of which are unknowns, any characteristic point \( p \) postmultiplying this expression could be rewritten as \( p' \) per:

\[ \prod_{i=1}^j e\,^{\hat{\xi}_i\,{\theta_i}} \cdot \prod_{i=j+1}^N e\,^{\hat{\xi}_i\,{\theta_i}} \cdot p = \prod_{i=1}^j e\,^{\hat{\xi}_i\,{\theta_i}} \cdot p' \]

where pointTransform is the transformation matrix that produces \( p' \) from \( p \).

Parameters

rhs	Right-hand side of the POE formula prior to being applied to the right-hand side of this subproblem.
pointTransform	Transformation frame applied to the first (and perhaps only) characteristic point of this subproblem.
reference	Known nearby solutions to be used as reference in case a singularity is found.
solutions	Output vector of local solutions.

Returns

True if all solutions are reachable, false otherwise.

Implements roboticslab::ScrewTheoryIkSubproblem.

solve() [3/5]

virtual bool roboticslab::ScrewTheoryIkSubproblem::solve ( const KDL::Frame &  rhs, const KDL::Frame &  pointTransform, const JointConfig &  reference, Solutions &  solutions, const KDL::Frame &  H_S_T, const KDL::JntArray &  c_solutions  ) const

inlinevirtual

Reimplemented from roboticslab::ScrewTheoryIkSubproblem.

solve() [4/5]

virtual bool roboticslab::ScrewTheoryIkSubproblem::solve ( const KDL::Frame &  rhs, const KDL::Frame &  pointTransform, const JointConfig &  reference, Solutions &  solutions, const KDL::Frame &  H_S_T, const KDL::JntArray &  c_solutions, const KDL::Frame &  H_S_T_0  ) const

inlinevirtual

Reimplemented from roboticslab::ScrewTheoryIkSubproblem.

solve() [5/5]

bool PardosGotorEight::solve ( const KDL::Frame &  rhs, const KDL::Frame &  pointTransform, const JointConfig &  reference, Solutions &  solutions, const KDL::Frame &  H_S_T, const KDL::JntArray &  c_solutions, const KDL::Frame &  H_S_T_0  ) const

overridevirtual

Reimplemented from roboticslab::ScrewTheoryIkSubproblem.

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

• libraries/ScrewTheorySolvers/ScrewTheoryIkSubproblems.hpp
• libraries/ScrewTheorySolvers/PardosGotorSubproblems.cpp