In　the　automatic　polishing　process　by　industrial　robot,　the　curvature　variation　at　the　polishing　point　will　cause　the　problem　of　uneven　polishing　quality.　To　solve　the　problem,　polishing　methods　based　on　constant　down　displacement　and　constant　downforce　are　analyzed　according　to　elliptical　Hertzian　contact　theory.　Then,　the　constant　stress　polishing　methods　based　on　displacement　and　force　are　proposed.　Simulations　are　performed　by　finite　element　analysis　software.　The　stress　changes　of　four　polishing　methods　during　the　polishing　process　are　compared.　Finally,　a　force　control　strategy　based　on　speed　regulation　and　impedance　control　algorithm　is　adopted　to　ensure　the　stability　of　the　tool　and　workpiece　contact　during　machining.　The　results　show　that　stable　polishing　stress　can　be　obtained　by　the　constant　stress　polishing　methods　based　on　down　displacement　and　downforce.　Therefore,　it　is　feasible　to　control　the　uniformity　of　polishing　quality　by　adjusting　the　displacement　or　downforce　of　an　industrial　robot.　©　2021　IEEE.