Large-scale,　self-organizing　wireless　ad　hoc　network　deployments　are　being　driven　by　recent　developments　of　the　Internet　of　Things　(IoT)　to　collect　information　from　a　vast　area　or　harsh　environment　efficiently.　How　to　ensure　fast　routing　in　sparse　topology　and　after　node　failure　how　to　ensure　that　the　network　keeps　topology　properties　are　challenging　problems.　In　this　paper,　we　propose　a　Self-stabilizing　dIrected　t-Spanner　for　Autonomous　nodes　problem　(SISA)　and　give　intuitive　solutions　in　both　2D　and　3D　space.　In　the　topology　construction　phase,　sparse　directed　t-spanner　topologies,　without　substantially　degrading　the　path　connecting　any　pair　of　nodes　in　the　original　network,　are　constructed　with　a　minimum　number　of　messages.　In　the　topology　maintenance　phase,　the　self-stabilizing　algorithms　run　in　the　background　to　update　locally　for　keeping　t-spanner　property　when　some　nodes　fail.　In　particular,　our　solutions　have　not　any　central　daemon　and　are　completely　distributed.　Our　experimental　results　demonstrate　the　effectiveness　and　efficiency　of　our　proposed　solutions.　©　2022　Elsevier　B.V.