A　new　method　based　on　virtual　spring-damper　model　is　proposed　for　collision-free　trajectory　planning　of　planar　underactuated　robots.　The　generalized　forces　of　nonholonomic　constraints　equations　are　modified　by　the　virtual　spring-damper　model　when　there　are　obstacles　in　workspace.　The　partly　stable　controllers　are　adopted　and　the　energy　based　fitness　function　is　built,　then　the　best　switching　sequence　of　partly　stable　controllers　are　obtained　by　genetic　algorithm.　Numerical　simulations　which　are　carried　out　on　the　planar　3R　underactuated　robots　show　effectiveness　of　the　proposed　method.