Global IK branch tracking for unsorted inverse-kinematics solutions

Develop a method for tracking inverse-kinematics solutions into globally consistent branches when the solver does not globally sort its solutions into branches, including for IK-Geo subproblems 5 and 6 and polynomial or eigenvalue inverse-kinematics methods.

Background

The paper differentiates through analytic inverse-kinematics mappings using the inverse function theorem, enabling constrained trajectory optimization in minimal coordinates without modifying black-box IK implementations. This framework requires consistent handling of the discrete and continuous self-motion parameters exposed by an IK solver.

The authors identify unresolved difficulties for solvers whose solutions cannot be globally organized into branches. They specifically cite IK-Geo subproblems 5 and 6 and polynomial or eigenvalue IK methods, for which reliable solution tracking remains an open issue relevant to deploying the proposed parameterization framework.

References

Open questions remain in this space, especially related to IK solution tracking for solvers that do not globally sort IK solutions into ``branches'' -- examples include IK-Geo's subproblems 5 and 6 and polynomial/eigenvalue IK methods.

— Planning along Differentiable Charts of Constraint Manifolds with General-Purpose IK Solvers  (2609.10905 - Cohn et al., 9 Sep 2026) in Section Discussion

For cuspidal manipulators, such challenges are present independent of the IK algorithm, and path planning for such robots in the minimal-coordinates framework remains an open problem.

— Planning along Differentiable Charts of Constraint Manifolds with General-Purpose IK Solvers  (2609.10905 - Cohn et al., 9 Sep 2026) in Section Discussion

Although inverse kinematics is ubiquitous in robotics, it remains an open challenge for redundant kinematic chains, with many approaches in parallel for different use cases.

— MorphIK: Morphology-Conditioned Neural Inverse Kinematics for Unknown Robots  (2609.29908 - Clasmeier et al., 24 Sep 2026) in Section 1, Introduction