Interface shared by all IK subproblems found in Screw Theory applied to Robotics. More...
#include <ScrewTheoryIkProblem.hpp>
Public Types | |
| 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. | |
Public Member Functions | |
| virtual | ~ScrewTheoryIkSubproblem ()=default |
| Destructor. | |
| virtual bool | solve (const KDL::Frame &rhs, const KDL::Frame &pointTransform, Solutions &solutions) const =0 |
| Finds a closed geometric solution for this IK subproblem. More... | |
| virtual int | solutions () const =0 |
| Number of local IK solutions. | |
| virtual const char * | describe () const =0 |
| Return a human-readable description of this IK subproblem. | |
Detailed Description
Derived classes are considered to be immutable.
Member Function Documentation
◆ solve()
|
pure 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. solutions Output vector of local solutions.
- Returns
- True if all solutions are reachable, false otherwise.
Implemented in roboticslab::PardosGotorFour, roboticslab::PardosGotorThree, roboticslab::PardosGotorTwo, roboticslab::PardosGotorOne, roboticslab::PadenKahanThree, roboticslab::PadenKahanTwo, and roboticslab::PadenKahanOne.
The documentation for this class was generated from the following file:
- libraries/ScrewTheoryLib/ScrewTheoryIkProblem.hpp
