Prescribed-Time Contracting-Boundary Control of a Tendon-Driven Flexible Arm

Abstract:This study develops a prescribed-time performance-shaping control method for curvature tracking of a single-segment flexible arm actuated by three antagonistic tendon pairs. A Cartesian curvature representation is introduced to avoid the undefined bending direction at the straight configuration and to establish an explicit six-tendon kinematic mapping. A cubic performance boundary contracts smoothly from an initially admissible error bound to a nonzero terminal accuracy bound within a prescribed time. Based on this boundary, a dual transformation combining static symmetric error scaling and time-varying behavior shaping maps the tracking error into a fixed unit box. The resulting controller guarantees boundary invariance, prescribed-time entry into the terminal accuracy region, and subsequent asymptotic convergence. Numerical evaluations with Python and OpenCR--MuJoCo, together with a supervised reduced-order experiment on a two-section, four-channel platform, provide complementary validation. Across six experimental trials, no violation of the prescribed boundary is observed, and the proposed controller reduces the mean terminal curvature RMSE by 32.5% relative to a matched baseline, with comparable terminal-band entry times. These results support the feasibility of the proposed approach in the reduced-order experimental setting.

Robotics (cs.RO)

arXiv:2609.22963 [cs.RO]

(or arXiv:2609.22963v1 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2609.22963 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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