Nullspace Computation for Estimated Inverse Jacobians

Determine how to compute and use the Jacobian nullspace when only an inverse Jacobian is estimated, so that redundant robotic structures can be controlled with nullspace-based stabilization.

Background

The paper contrasts its forward-Jacobian estimator with prior methods that estimate the inverse Jacobian directly. Direct inverse estimation provides a task-to-command mapping without explicitly inverting a matrix, but redundancy requires access to the Jacobian nullspace for posture or grip regulation. The unresolved issue limits the extension of inverse-Jacobian approaches to redundant robotic hands and other redundant systems.

References

However, as only its inverse is estimated, it is not clear how to compute and utilize the nullspace of the Jacobian, limiting the extendability to redundant structures.

— Rapid Learning of Dexterous In-Hand Pen Writing through Real-Time Jacobian Estimation  (2609.11775 - Stewart et al., 10 Sep 2026) in Section 2, Related Work, subsection “Online Jacobian estimation and visual servoing”