In this paper, we present a model for the inverse dynamics of underactuated manipulators that is free from inertial coupling singularities. The framework’s main idea is to include a small-amplitude wave on the trajectory of the rotating active joints. First, we derive the modified nonlinear dynamics for the multijoint manipulators with multiple degrees-of-freedom (DoF). Next, a 4-DoF mass-rotating underactuated manipulator with two passive and two active joints is chosen. Then, a condition assuming the positive definiteness of the inertia matrix is developed to have the singularity-free inverse dynamics. Finally, we analytically study how singularities can be avoided and show an example simulation with a feed-forward control at the singular configuration.

在本文中，我们为欠惯性机械手的逆动力学提供了一个模型，该模型没有惯性耦合奇异性。该框架的主要思想是在旋转的活动关节的轨迹上包括一个小振幅波。首先，我们推导了具有多个自由度（DoF）的多关节机械手的修改后的非线性动力学。接下来，选择具有两个被动和两个主动关节的4自由度质量旋转欠驱动机械手。然后，将假设惯性矩阵为正定的条件发展为具有无奇点逆动力学。最后，我们分析研究如何避免奇异点，并在奇异配置下显示具有前馈控制的示例仿真。