An offshore drilling vessel, the vessel comprising: - a floating hull subjected to heave motion, the hull being provided with a moonpool, - a drilling tower at or near the moonpool, - a drilling tubulars storage rack (10,11), e.g. a carousel, adapted for storage of drilling tubulars, e.g. drill pipe stands, in vertical orientation therein, the storage rack being mounted on the hull so as to be subjected to heave motion along with the hull, - a tubulars string slip device, which slip device is adapted to support the weight of a tubulars string, e.g. a drill string, suspended therefrom along a firing line, - a racking device comprising: - a pipe racker system that is adapted to move a tubular between the storage rack and a position in the firing line above the tubulars string slip device in order to allow for making a connection between a new tubular and the suspended tubular string or the removal of a tubular from the tubular string during tripping; - a motion system, in particular a heave motion synchronisation system (200, 160, 161, 162) that is adapted to bring a tubular retrieved from the storage rack into a vertical motion that is synchronous with the heave compensation motion of the tubulars string slip device, thereby allowing for the connection of the tubular to the suspended tubulars string whilst the slip device performs heave compensation motion relative to the heaving hull of the vessel; - in particular a heave motion compensation support that is adapted to support said slip device whilst performing heave compensation motion relative to the heaving hull of the vessel, e.g. a heave motion compensated working deck, wherein the racking device comprises: - vertical rails (145,145'), - at least two separate motion arm assemblies (141, 142, 143; 141',142', 143') mounted on said vertical rails, wherein each motion arm assembly comprises: - an own base (141b, 142b,143b; 141'b, 142'b, 143'b) - a motion arm (141m; 142m) connected to said base, the motion arm of at least one arm assembly being provided with a tubular gripper member (141t; 142t) connected to said arm, and characterised in that the own base is vertically mobile along said vertical rails by a vertical drive including a motor which vertical drive is positioned on said base, wherein each motor of the vertical drive of at least one motion arm assembly (141,142,143) is electrically connected to a controller of the motion system. - a floating hull subjected to heave motion, the hull being provided with a moonpool, - a drilling tower at or near the moonpool, - a drilling tubulars storage rack (10,11), e.g. a carousel, adapted for storage of drilling tubulars, e.g. drill pipe stands, in vertical orientation therein, the storage rack being mounted on the hull so as to be subjected to heave motion along with the hull, - a tubulars string slip device, which slip device is adapted to support the weight of a tubulars string, e.g. a drill string, suspended therefrom along a firing line, - a racking device comprising: - a pipe racker system that is adapted to move a tubular between the storage rack and a position in the firing line above the tubulars string slip device in order to allow for making a connection between a new tubular and the suspended tubular string or the removal of a tubular from the tubular string during tripping; - a motion system, in particular a heave motion synchronisation system (200, 160, 161, 162) that is adapted to bring a tubular retrieved from the storage rack into a vertical motion that is synchronous with the heave compensation motion of the tubulars string slip device, thereby allowing for the connection of the tubular to the suspended tubulars string whilst the slip device performs heave compensation motion relative to the heaving hull of the vessel; - a pipe racker system that is adapted to move a tubular between the storage rack and a position in the firing line above the tubulars string slip device in order to allow for making a connection between a new tubular and the suspended tubular string or the removal of a tubular from the tubular string during tripping; - a motion system, in particular a heave motion synchronisation system (200, 160, 161, 162) that is adapted to bring a tubular retrieved from the storage rack into a vertical motion that is synchronous with the heave compensation motion of the tubulars string slip device, thereby allowing for the connection of the tubular to the suspended tubulars string whilst the slip device performs heave compensation motion relative to the heaving hull of the vessel; - in particular a heave motion compensation support that is adapted to support said slip device whilst performing heave compensation motion relative to the heaving hull of the vessel, e.g. a heave motion compensated working deck, - vertical rails (145,145'), - at least two separate motion arm assemblies (141, 142, 143; 141',142', 143') mounted on said vertical rails, - an own base (141b, 142b,143b; 141'b, 142'b, 143'b) - a motion arm (141m; 142m) connected to said base, the motion arm of at least one arm assembly being provided with a tubular gripper member (141t; 142t) connected to said arm, and characterised in that the own base is vertically mobile along said vertical rails by a vertical drive including a motor which vertical drive is positioned on said base, wherein each motor of the vertical drive of at least one motion arm assembly (141,142,143) is electrically connected to a controller of the motion system.