Aiming　at　the　balancing　control　problem　of　a　cubical　robot,　a　system　balancing　on　its　corner　was　modeled　by　taking　the　physical　prototype　as　research　object,　and　least　system　variables　were　defined　for　expressing　system　movement　attributes.　The　energy　function　and　generalized　forces　of　the　system　were　calculated,　and　the　dynamic　model　of　the　cubical　robot　balancing　on　its　corner　was　derived　based　on　Lagrange　method.　The　correctness　of　the　model　was　analyzed　in　theory　by　numerical　simulation,　and　the　model　precision　was　verified　with　basically　indetical　response　results　about　zero-input　experiment　in　comparision　betweeen　the　model　and　virtual　prototype.　A　balancing　controller　designed　based　on　the　dynamic　model　was　applied　in　balancing　control　of　the　virtual　prototype.　The　experiment　results　show　that　the　cubical　robot　can　balance　effectively　by　the　controller,　then　the　effectiveness　of　the　model　is　verified　further.　The　dynamic　model　provides　an　important　foundation　for　the　further　research　on　balancing　control　of　the　cubical　robot.　©　2019,　Editorial　Department　of　Journal　of　Beijing　University　of　Technology.　All　right　reserved.