This　article　proposes　convex　optimization　of　mutual　inductance　between　multiantiparallel　coils　(MACs)　for　distance-insensitive　wireless　charging　of　air-ground　robots.　In　order　to　reduce　optimization　costs,　the　proposed　optimization　method　is　developed　by　hybridizing　analytical　and　numerical　models.　First,　it　is　shown　that　the　commonly　used　analytical　model　for　MAC　design　becomes　inaccurate　as　frequency　increases.　Second,　a　trial　mutual　inductance　is　introduced　as　an　optimization　variable.　From　the　trial　mutual　inductance,　an　MAC　is　designed　using　the　analytical　model.　Third,　the　realized　mutual　inductance　of　the　analytically　designed　MAC　is　computed　by　a　numerical　model　to　correct　the　error　of　the　analytical　model.　The　difference　vector　ρ　between　the　realized　and　optimal　mutual　inductances　is　written　as　a　function　of　the　trial　mutual　inductance,　and　the　l_2　-norm　of　ρ　is　minimized　by　changing　the　trial　mutual　inductance.　The　resultant　optimization　problem　is　shown　to　be　convex,　and　it　is　conveniently　solved　by　using　a　local　searching　method.　Simulation　results　show　that　the　proposed　design　method　satisfies　design　specification　much　better　than　the　conventional　analytical-model-based　design　method.　Using　the　proposed　method,　an　MAC　prototype　is　designed　and　fabricated,　and　a　wireless　charging　system　for　air-ground　robots　is　constructed　and　tested.　Measurement　results　show　that　the　efficiency　of　the　designed　MAC　is　maintained　at　around　80%　in　the　transfer　distance　range　of　15-55　mm,　and　stable　efficiency　is　obtained　when　charging　real　air-ground　robots　of　different　heights.　©　2014　IEEE.