PurposeImitation　learning　is　a　powerful　tool　for　planning　the　trajectory　of　robotic　end-effectors　in　Cartesian　space.　Present　methods　can　adapt　the　trajectory　to　the　obstacle;　however,　the　solutions　may　not　always　satisfy　users,　whereas　it　is　hard　for　a　nonexpert　user　to　teach　the　robot　to　avoid　obstacles　in　time　as　he/she　wishes　through　demonstrations.　This　paper　aims　to　address　the　above　problem　by　proposing　an　approach　that　combines　human　supervision　with　the　kernelized　movement　primitives　(KMP)　model.Design/methodology/approachThis　approach　first　extracts　the　reference　database　used　to　train　KMP　from　demonstrations　by　using　Gaussian　mixture　model　and　Gaussian　mixture　regression.　Subsequently,　KMP　is　used　to　modulate　the　trajectory　of　robotic　end-effectors　in　real　time　based　on　feedback　from　its　interaction　with　humans　to　avoid　obstacles,　which　benefits　from　a　novel　reference　database　update　strategy.　The　user　can　test　different　obstacle　avoidance　trajectories　in　the　current　task　until　a　satisfactory　solution　is　found.FindingsExperiments　performed　with　the　KUKA　cobot　for　obstacle　avoidance　show　that　this　approach　can　adapt　the　trajectories　of　the　robotic　end-effector　to　the　user＇s　wishes　in　real　time,　including　trajectories　that　the　robot　has　already　passed　and　has　not　yet　passed.　Simulation　comparisons　also　show　that　it　exhibits　better　performance　than　KMP　with　the　original　reference　database　update　strategy.Originality/valueAn　interactive　learning　approach　based　on　KMP　is　proposed　and　verified,　which　not　only　enables　users　to　plan　the　trajectory　of　robotic　end-effectors　for　obstacle　avoidance　more　conveniently　and　efficiently　but　also　provides　an　effective　idea　for　accomplishing　interactive　learning　tasks　under　constraints.