Aiming　at　the　problem　of　self-balancing　control　of　a　cubical　robot,　this　paper　makes　a　research　on　the　dynamic　modeling　of　the　cubical　robot　balancing　on　its　corner.　Using　the　prototype　of　cubical　robot　we　built　as　the　research　object,　the　dynamic　model　is　derived　with　Lagrangian　method　on　foundation　of　analysis　of　coordinate　transformation　relation　of　cubical　robot.　The　correctness　of　the　model　is　verified　in　theory　by　numerical　simulation.　The　controller,　designed　based　on　reaction　torque　characteristic　of　inertia　wheels,　is　used　in　balance　control　of　the　cubical　robot.　The　effectiveness　of　the　controller　is　verified　again　with　the　obtained　expect　effect.　The　dynamic　model　developed　and　controller　can　provide　a　base　for　further　study　of　balance　control　of　a　cubical　robot.　©　The　Authors,　published　by　EDP　Sciences,　2017.