In　order　to　meet　the　requirements　of　high　positioning　accuracy　and　trajectory　accuracy　of　industrial　robots　in　the　field　of　high-precision　operation,　this　paper　studied　the　real-time　compensation　method　of　the　robot　trajectory　error　used　laser　tracker　to　measure　the　end　position　of　robot　in　real　time.　This　real-time　error　calculation　method　of　robot　trajectory　based　on　continuous　dynamic　time　warping　(CDTW),　which　was　studied　to　determine　the　position　error　of　robot　trajectory　at　each　moment.　Moreover,　this　paper　researched　the　PID　parameter　tuning　technology　of　response　surface　model　method　based　on　gray　analysis　and　got　a　real-time　compensation　method.　The　compensation　value　was　fed　back　to　the　robot　for　motion　compensation　in　real　time　through　KUKA　RSI.　The　last,　the　influence　of　compensation　parameters　and　period　was　analyzed　and　the　error　compensation　experiment　of　positioning,　linear　trajectory　and　arc　trajectory　were　carried　out.　After　compensation,　the　absolute　positioning　error　of　the　robot　was　less　than　0.06　mm　and　the　trajectory　position　error　was　less　than　0.15　mm,　which　greatly　improved　the　position　accuracy　of　the　robot.