General Modeling for Space Robot Proximity Relative Motion by Using Dual Operator With Hybrid Coordinates

With the increasing demand for space missions, task robots have evolved from rigid bodies to rigid‐flexible coupling in close‐range approach missions, such as flexible module in‐orbit assembly missions and flexible spacecraft formation missions proposed in recent years. This poses a challenge to the dynamic modeling of space proximity tasks that are more concise, efficient, and have engineering practicality. In this paper, a six‐degree‐of‐freedom representation of space robot proximity relative dynamics is developed by using the algebra of dual numbers, whether the space robot is a rigid body or a rigid‐flexible coupling system. The main work of this paper lies in the following three aspects: First, this paper develops a six‐dimensional screw representation of dual number–based general dynamics that allows model parameters (dual inertia operator) to be directly matched with space robot engineering parameters (mass and moment of inertia) to replace its classical three‐dimensional motor form. This work improves the convenience of the engineering application of the general model. Second, by combining hybrid coordinate modeling methods with dual algebra, the general expression is extended from the motion of a rigid body to a flexible body; on this basis, the integrated dynamic model of the rigid‐flexible coupling space robot is developed. This effort solves the problem of compact representation and computational efficiency of relative dynamic models between two rigid‐flexible coupling space robots. Third, the derivative rule of a space robot with time‐varying configuration is provided; this work enables the general model to be applied to certain specific scenarios, such as space robot proximity missions under the premise of rotating solar panels, rotating optical lenses, or other rotating structures. Based on the above relative dynamics, a PD controller is adopted, and the successful application of the proposed models is verified.