A robot with large-degree-of-freedom joints is a promising future space robot capable of adapting to various environments and can perform dexterous tasks with multiple manipulators. The attitude dynamics of a free-flying robot shows nonholonomy, which enables the robot to reorient its attitude by moving its body. However, previous studies were not generally able to handle the nonholonomy, especially for robots with large degrees of freedom of joints. In the present study, we analytically investigate a maneuver in which joints are actuated along a parallelogram trajectory in joint angle space and propose an analytical path modification method in joint angle space in order to achieve the target attitude. Parallelogram actuation guarantees that the body configuration is returned to the initial state after one set of maneuvers, and thus the attitude of the robot is independently reoriented to the target maintaining the body configuration. The analytical solution is provided by applying Magnus expansion to the kinematics equation of rotational matrices, and its Lie group structure contributes to concise mathematical expressions. In addition, the analytical solution does not cause numerical difficulties, such as combinatorial explosion, and so can fully make use of the reorientation ability of a robot with large degrees of freedom.

具有大自由度关节的机器人是一种很有前途的未来空间机器人，能够适应各种环境，可以通过多个机械手执行灵巧的任务。自由飞行机器人的姿态动力学表现出非完整性，这使得机器人能够通过移动其身体来重新定位其姿态。然而，以前的研究一般不能处理非完整的，特别是对于关节自由度较大的机器人。在本研究中，我们分析研究了在关节角空间中沿平行四边形轨迹驱动关节的机动，并提出了一种在关节角空间中的解析路径修改方法，以实现目标姿态。平行四边形驱动保证了身体配置在一组动作后恢复到初始状态，因此机器人的姿态独立地重新定向到保持身体配置的目标。通过将马格努斯展开式应用于旋转矩阵的运动学方程提供解析解，其李群结构有助于简洁的数学表达式。此外，解析解不会引起组合爆炸等数值困难，可以充分利用机器人的大自由度重定向能力。