无导数广义多变量超螺旋控制用于受约束的欧拉-拉格朗日系统

中文摘要 AI 辅助

执行负载提升和转移任务的机器人操作器必须在突然的负载变化下跟踪预定轨迹，同时受限于执行器饱和和不准确的系统模型。这类系统本质上由多变量欧拉-拉格朗日（EL）动力学描述，其交叉耦合通过惯性项和科里奥利项建立。超螺旋算法（STA）是此类系统中调节一阶滑模（FOSM）的标准方法，然而现有设计大多局限于标量滑模变量，并依赖于EL系统不满足的扰动导数假设。特别是，FOSM动力学依赖于扰动，并在负载接合和释放产生的阶跃变化下变得不连续，导致该导数无定义。本研究通过一种无导数广义多变量超螺旋框架解决了这两个问题。不连续的符号函数积分项被替换为连续的分数幂项，其动力学独立于扰动导数，同时将已知的状态相关扰动缩放纳入控制律和自适应增益更新中。时间平移屏障函数保证在独立于初始条件的情况下，预设时间内收敛到用户指定的界限，设计仅依赖于质量矩阵范数界限。在7自由度操作器上，在执行器饱和条件下进行的仿真和实验结果验证了所提方案的有效性。

英文摘要

Robotic manipulators performing payload lift-and-transfer must track prescribed trajectories under abrupt load changes, with limited actuation and inaccurate plant knowledge. Such plants are inherently described by multivariable Euler--Lagrange~(EL) dynamics with cross-coupling established through inertial and Coriolis terms. The super-twisting algorithm~(STA) is the standard approach to regulating a first-order sliding mode~(FOSM) in such settings, yet existing designs are largely restricted to scalar sliding variables, and rest on a disturbance-derivative assumption that EL systems violate. In particular, the FOSM dynamics depend on the disturbance and become discontinuous under the step changes in load produced by payload engagement and release, rendering that derivative ill-defined. This study resolves both with a derivative-free generalized multivariable super-twisting framework. The discontinuous sign-function integral term is replaced with a continuous fractional-power term whose dynamics are independent of the disturbance derivative, while the known state-dependent scaling of the perturbation is incorporated into both the control law and the adaptive gain update. A time-shifting barrier function guarantees prescribed-time convergence to a user-specified bound independently of initial conditions, with the design relying only on mass-matrix norm bounds. Simulation and experimental results on a 7-DoF manipulator under actuator saturation are used to validate the proposed scheme.

发表机构

• Indian Institute of Science（印度科学学院）

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