Jeonghyeon Kim, Shinsuk Park (corresponding)

Abstract

A manipulator following a Cartesian reference built from a nominal surface model loses feasibility when the real contact geometry differs. The standard fixes — move to the nearest feasible point, or absorb the mismatch along the estimated surface normal — restore feasibility but can silently drift coordinates the task meant to keep fixed (e.g. progress along a wiping path). This work formulates intent-preserving constraint realization (IPCR): the task specifies both a yield subspace (where the reference may deviate) and the coordinates that must be preserved, and the framework derives the unique realization — and the execution-level controller — that satisfies both, with closed-form guarantees.

Method

• Target-level realization. Given a yield subspace 𝒟 and preserved coordinates y = Lx (with LD = 0), proved the unique feasible point that keeps y unchanged exists and has maximal invariance (Theorem 1) — for affine constraints directly, and for nonlinear ones via a Newton iteration that preserves Lx at every step (Theorem 3)
• Drift of the usual approach. Derived the exact drift of the conventional nearest-feasible realization relative to IPCR, in closed form via the principal angles between the constraint normals and the yield direction (Theorem 2)
• Execution-level condition. Derived the exact null-space requirement on a servo’s absorption subspace, 𝒩_e ⊆ ker L, under which residual constraint mismatch leaves the preserved coordinates untouched regardless of its size (Theorem 4)
• Controller. Built an IPCR-compatible single-contact controller that separates the execution yield direction from the physical force direction — conventional hybrid control conflates both into the same estimated surface normal
• Validation. 15,000 random numerical cases for the theorems; pre-registered experiments on a simulated torque-controlled manipulator with proprioception only, plus a stress test and a curved-constraint boundary test

Results

• On unseen contact constraints, the same geometry produced different, correctly predicted realizations for different tasks
• The executed leak matched the theoretical transfer G(Ñ) quantitatively as the absorption subspace was varied, vanishing exactly where the execution-level condition holds
• A pre-registered replication on further unseen constraints reproduced the result
• A stress test with an oracle-normal intervention isolated high-friction degradation as a contact-geometry estimation effect, not a framework failure

Skills

Python Manipulator Control Contact Mechanics Optimization