Interface shared by all IK subproblems found in Screw Theory applied to Robotics. More...
#include <ScrewTheoryIkProblem.hpp>
Public Types | |
| using | JointConfig = std::vector< double > |
| Joint configurations. | |
| using | Solutions = std::vector< JointConfig > |
| Collection of local IK solutions. | |
Public Member Functions | |
| virtual | ~ScrewTheoryIkSubproblem ()=default |
| Destructor. | |
| 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. | |
| bool | solve (const KDL::Frame &rhs, const KDL::Frame &pointTransform, Solutions &_solutions) |
| 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
◆ describe()
|
pure virtual |
◆ solutions()
|
pure virtual |
◆ 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. 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.
Implemented in roboticslab::PadenKahanOne, roboticslab::PadenKahanTwo, roboticslab::PadenKahanThree, roboticslab::PardosGotorOne, roboticslab::PardosGotorTwo, roboticslab::PardosGotorThree, roboticslab::PardosGotorFour, roboticslab::PadenKahanOne, roboticslab::PadenKahanTwo, roboticslab::PadenKahanThree, roboticslab::PardosGotorOne, roboticslab::PardosGotorTwo, roboticslab::PardosGotorThree, and roboticslab::PardosGotorFour.
The documentation for this class was generated from the following file:
- libraries/ScrewTheoryLib/ScrewTheoryIkProblem.hpp
