roboticslab::PadenKahanTwo Class Reference

Second Paden-Kahan subproblem. More...

#include <ScrewTheoryIkSubproblems.hpp>

Inheritance diagram for roboticslab::PadenKahanTwo:

Public Member Functions
	PadenKahanTwo (int id1, int id2, const MatrixExponential &exp1, const MatrixExponential &exp2, const KDL::Vector &p, const KDL::Vector &r)
	Constructor. More...
bool	solve (const KDL::Frame &rhs, const KDL::Frame &pointTransform, Solutions &solutions) const override
	Finds a closed geometric solution for this IK subproblem. More...
int	solutions () const override
	Number of local IK solutions.
const char *	describe () const override
	Return a human-readable description of this IK subproblem.
Public Member Functions inherited from roboticslab::ScrewTheoryIkSubproblem
virtual	~ScrewTheoryIkSubproblem ()=default
	Destructor.

Private Attributes
const int	id1
const int	id2
const MatrixExponential	exp1
const MatrixExponential	exp2
const KDL::Vector	p
const KDL::Vector	r
const KDL::Vector	axesCross
const KDL::Rotation	axisPow1
const KDL::Rotation	axisPow2
const double	axesDot

Additional Inherited Members
Public Types inherited from roboticslab::ScrewTheoryIkSubproblem
using	JointIdToSolution = std::pair< int, double >
	Maps a joint id to a screw magnitude.
using	JointIdsToSolutions = std::vector< JointIdToSolution >
	At least one joint-id+value pair per solution.
using	Solutions = std::vector< JointIdsToSolutions >
	Collection of local IK solutions.

Detailed Description

Dual solution, double revolute joint geometric IK subproblem given by \( e\,^{\hat{\xi_1}\,{\theta_1}} \cdot e\,^{\hat{\xi_2}\,{\theta_2}} \cdot p = k \) (consecutive crossing rotation screws to a point).

Constructor & Destructor Documentation

PadenKahanTwo()

PadenKahanTwo::PadenKahanTwo	(	int	id1,
		int	id2,
		const MatrixExponential &	exp1,
		const MatrixExponential &	exp2,
		const KDL::Vector &	p,
		const KDL::Vector &	r
	)

Parameters

id1	Zero-based joint id of the first product of exponentials (POE) term.
id2	Zero-based joint id of the second POE term.
exp1	First POE term.
exp2	Second POE term.
p	Characteristic point.
r	Point of intersection between both screw axes.

Member Function Documentation

solve()

bool PadenKahanTwo::solve ( const KDL::Frame &  rhs, const KDL::Frame &  pointTransform, Solutions &  solutions  ) const

overridevirtual

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.
solutions	Output vector of local solutions.

Returns

True if all solutions are reachable, false otherwise.

Implements roboticslab::ScrewTheoryIkSubproblem.

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

• libraries/ScrewTheoryLib/ScrewTheoryIkSubproblems.hpp
• libraries/ScrewTheoryLib/PadenKahanSubproblems.cpp