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.