The　users　often　encounter　issues　such　as　difficulty　in　selecting　the　appropriate　number　of　Gaussian　distributions　and　low　accuracy　in　reproducing　trajectories　when　using　Gaussian　mixture　model(GMM)to　plan　robot　trajectories　during　programming　by　demonstration.　To　address　these　concerns，a　composite　strategy　is　proposed，which　integrates　dynamic　time　warping(DTW)algorithm，GMM　and　the　Douglas-Peucker(DP)algorithm.　First，to　address　the　issue　of　varying　time　lengths　in　multiple　trajectories，the　DTW　algorithm　is　used　to　align　the　variation　of　the　demonstrated　trajectories　in　the　time　domain.　Second，the　motion　features　are　learned　from　the　aligned　demonstrated　trajectories　using　GMM，which　can　subsequently　be　reconstructed　into　a　reproduced　trajectory　using　Gaussian　mixture　regression(GMR).　In　this　process，the　number　of　Gaussian　distributions，a　key　parameter　of　GMM，is　estimated　by　DP　algorithm，which　can　derive　a　relatively　precise　parameter　value　simply　and　intuitively　compared　with　the　traditional　method.　Furthermore，the　DP　algorithm　is　employed　to　sparsify　and　optimize　the　data　points　in　the　reproduced　trajectory，ensuring　that　the　final　trajectory　maintains　high　precision　while　drastically　reducing　the　number　of　data　points　in　the　final　trajectory.　Finally，experiments　conducted　on　simulated　welding　trajectories　of　different　shapes　are　carried　out.　The　experimental　results　show　that　the　demonstrated　trajectories　aligned　by　DTW　exhibit　more　pronounced　motion　features，and　the　reproduced　trajectory　generated　using　GMM-GMR　has　great　representation　result；moreover，the　DP　algorithm　effectively　estimates　the　necessary　number　of　Gaussian　distributions　for　GMM-GMR　learning.　The　average　positional　errors　in　final　trajectories　sparsified　by　the　DP　algorithm　are　within　0.500　mm，and　the　maximum　errors　can　be　controlled　within　0.800　mm，meeting　the　precision　requirements　of　welding　trajectory　planning.　It　verifies　the　effectiveness　and　the　superiority　of　the　proposed　strategy.　©　2025　Tianjin　University.　All　rights　reserved.