Motivated by the energy shaping framework and the properties of homogeneous systems, we introduce a methodology to derive strict Lyapunov Functions (LFs) for a class of global finite-time (FT) controllers for robot manipulators. As usual in the energy shaping methodology, these controllers are described by the gradient of the controller potential energy plus the gradient of (nonlinear) energy dissipation-like functions. Sufficient conditions on the controller potential energy and energy dissipation-like functions are provided in order to obtain, in a straightforward manner, strict LFs ensuring global FT stability at the desired equilibrium. As an important practical outcome, we illustrate the proposed methodology by constructing strict LFs for some particular FT controllers. The construction of such strict LFs allows us to solve the open problem of FT trajectory tracking of robot manipulators with continuous control laws to track any bounded trajectory.

受能量整形框架和齐次系统特性的启发，我们引入了一种方法来为机器人操纵器的一类全局有限时间 (FT) 控制器导出严格的李雅普诺夫函数 (LF)。通常在能量整形方法中，这些控制器由控制器势能的梯度加上（非线性）类似能量耗散的函数的梯度来描述。提供了关于控制器势能和类似能量耗散的函数的充分条件，以便以简单的方式获得严格的 LF，确保在所需平衡下的全局 FT 稳定性。作为一个重要的实际结果，我们通过为某些特定的 FT 控制器构建严格的 LF 来说明所提出的方法。