Purpose:　This　paper　aims　to　investigate　the　distributed　formation　control　problem　for　a　multi-quadrotor　unmanned　aerial　vehicle　system　without　linear　velocity　feedbacks.　Design/methodology/approach:　A　nonlinear　controller　is　proposed　based　on　the　orthogonal　group　SE(3)　to　obviate　singularities　and　ambiguities　of　the　traditional　parameterized　attitude　representations.　A　cascade　structure　is　applied　in　the　distributed　controller　design.　The　inner　loop　is　responsible　for　attitude　control,　and　the　outer　loop　is　responsible　for　translational　dynamics.　To　ensure　a　linear-velocity-free　characteristic,　some　auxiliary　variables　are　introduced　to　construct　virtual　signals　in　distributed　controller　design.　The　stability　analysis　of　the　proposed　distributed　control　method　by　the　Lyapunov　function　is　provided　as　well.　Findings:　A　group　of　four　quadrotors　with　constant　reference　linear　velocity　and　a　group　of　six　quadrotors　with　varying　reference　linear　velocity　are　adopted　to　verify　the　effectiveness　of　the　proposed　strategy.　Originality/value:　This　is　a　new　innovation　for　multi-robot　formation　control　method　to　improve　assembly　automation.　©　2021,　Emerald　Publishing　Limited.