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As a kind of space robot, the two-arm cascade combination system (TACCS) has been applied to perform auxiliary operations at different locations outside space cabins. The motion coupling relation of two arms and complex surrounding obstacles make the collision-free trajectory planning optimization of TACCS more difficult, which has become an urgent problem to be solved. For the above problem, this paper proposed collision-free and time–energy–minimum trajectory planning optimization algorithms, considering the motion coupling of two arms. In this method, the screw-based inverse kinematics (IK) model of TACCS is established to provide the basis for the motion planning in joint space by decoupling the whole IK problem into two IK sub-problems of two arms; the minimum distance calculation model is established based on the hybrid geometric enveloping way and basic distance functions, which can provide the efficient and accurate data basis for the obstacle-avoidance constraint condition of the trajectory optimization. Moreover, the single and bi-layer optimization algorithms are presented by taking motion time and energy consumption as objectives and considering obstacle-avoidance and kinematics constraints. Finally, through example cases, the results indicate that the bi-layer optimization has higher convergence efficiency under the premise of ensuring the optimization effect by separating variables and constraint terms. This work can provide theoretical and methodological support for the efficient and intelligent applications of TACCS in the space arena. [ABSTRACT FROM AUTHOR]