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Feature: Detect and/or cope with redundant manipulators  #17

@OstermD

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@OstermD

As mentioned in issues #16 and #15, EAIK is currently unable to detect 6R manipulators that are singular in every configuration.

While we often succeed in providing LS solutions if such manipulator is decomposable into SP 1-4 (LS solutions), decompositions into SP5 and SP6 typically yield no solution if they are faced with redundant kinematic chains.

In my opinion, there are two ways to cope with this issue:

  • Empirical detection, e.g., by (exhaustive?) set of configurations causing redundancy:
    There is a set of known configurations that will be singular in every configuration:
    Geometric Interpretation of Manipulator Singularities by Paden and Sastry:
    https://www2.eecs.berkeley.edu/Pubs/TechRpts/1984/378.html
  • Further robustification of the subproblems w.r.t. these chains

If the first option is chosen, this should go along with a numeric fallback that intervenes in such situations or an empirical selection of the redundant joint and user-side parametrization.

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