Nonholonomic Reorientation of Free-Flying Space Robots Using Parallelogram Actuation in Joint Space

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.