Singularity Avoidance in Inverse Kinematics: A Unified Treatment of Classical and Learning-based Methods

arXiv cs.RO / 4/16/2026

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Key Points

The paper proposes a unified framework for handling singularities in inverse kinematics by connecting classical techniques (e.g., Jacobian regularization, Riemannian manipulability tracking, constrained optimization) with modern learning-based approaches.
It introduces a taxonomy that organizes IK methods by which geometric structure they preserve and whether robustness is backed by formal guarantees or relies on empirical performance.
To close an evaluation gap, the authors define a benchmarking protocol and test 12 IK solvers on the Franka Panda for position-only IK using multiple panels (condition-number-driven error, velocity amplification, out-of-distribution robustness, and compute cost).
Experimental results indicate that pure learning methods can fail catastrophically even on well-conditioned targets (e.g., an MLP achieves 0% success and ~10 mm mean error), while hybrid warm-start systems can significantly improve success rates through classical refinement.
The study highlights deeper evaluation in the singularity regime as immediate future work, given the observed limitations of learning-only methods versus hybrid approaches.

Abstract

Singular configurations cause loss of task-space mobility, unbounded joint velocities, and solver divergence in inverse kinematics (IK) for serial manipulators. No existing survey bridges classical singularity-robust IK with rapidly growing learning-based approaches. We provide a unified treatment spanning Jacobian regularization, Riemannian manipulability tracking, constrained optimization, and modern data-driven paradigms. A systematic taxonomy classifies methods by retained geometric structure and robustness guarantees (formal vs. empirical). We address a critical evaluation gap by proposing a benchmarking protocol and presenting experimental results: 12 IK solvers are evaluated on the Franka Panda under position-only IK across four complementary panels measuring error degradation by condition number, velocity amplification, out-of-distribution robustness, and computational cost. Results show that pure learning methods fail even on well-conditioned targets (MLP: 0% success, approx. 10 mm mean error), while hybrid warm-start architectures - IKFlow (59% to 100%), CycleIK(0% to 98.6%), GGIK (0% to 100%) - rescue learned solvers via classical refinement, with DLS converging from initial errors up to 207 mm. Deeper singularity-regime evaluation is identified as immediate future work.