腱驱动柔性臂的预定时间收缩边界控制

中文摘要 AI 辅助

本研究开发了一种预定时间性能整形控制方法，用于由三对拮抗腱驱动的单段柔性臂的曲率跟踪。引入笛卡尔曲率表示，以避免在直线构型时弯曲方向未定义的问题，并建立显式的六腱运动学映射。一个三次性能边界在预定时间内从初始允许误差界平滑收缩到非零终端精度界。基于该边界，结合静态对称误差缩放和时变行为整形的双重变换，将跟踪误差映射到固定的单位盒内。所得控制器保证边界不变性、预定时间内进入终端精度区域以及随后的渐近收敛。使用Python和OpenCR--MuJoCo进行的数值评估，以及在两段四通道平台上的监督降阶实验，提供了互补验证。在六次实验试验中，未观察到预定边界的违反，所提出的控制器相对于匹配基线将平均终端曲率RMSE降低了32.5%，且终端带进入时间相当。这些结果支持了所提出方法在降阶实验设置中的可行性。

英文摘要

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.

发表机构

• Hubei University of Economics（湖北经济学院）
• Ocean University of China（中国海洋大学）

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