Aiming　at　the　problem　of　self-balancing　control　of　a　cubical　robot,　this　paper　researched　the　dynamic　modeling　of　the　cubical　robot　balancing　on　its　corner.　Using　the　prototype　of　cubical　robot　built　as　the　research　subject,　the　dynamic　model　was　derived　with　Lagrangian　method.　The　correctness　of　the　model　was　verified　in　theory　by　comparison　of　numerical　simulation　and　virtual　prototype　simulation.　A　balancing　controller　is　proposed,　which　parameters　were　confirmed　based　on　the　mathematic　model,　and　was　used　in　balance　control　of　the　cubical　robot　virtual　prototype.　The　effectiveness　of　the　model　was　verified　again　with　the　obtained　expect　effect.　This　dynamic　model　and　controller　can　provide　a　base　for　further　study　for　balancing　control　of　a　cubical　robot.　©　2018　Association　for　Computing　Machinery.