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

2026-09-19

AI Summary

本文提出了一种预定时间性能成形控制方法，通过引入笛卡尔曲率表示和双变换技术来解决单段柔性臂的曲率跟踪问题，确保在预定时间内达到非零终端精度。

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.

Problem

• Prescribed-Time
• Curvature Tracking
• Flexible Arm
• Tendon-Driven
• Performance Boundary

Innovation

• prescribed-time performance-shaping control
• Cartesian curvature representation
• cubic performance boundary
• dual transformation
• asymptotic convergence