Method for operating a robot for positioning a tool in a target pose, wherein the robot comprises a robot foot and a movable robot arm attached thereto on the distal end of which a robot flange is arranged, on which the tool is held, with the method steps - specification of an axis of the tool, - specification of a Cartesian reference coordinate system originating on the robot foot, - specification of a Cartesian target coordinate system {r} originating on a point of the tool, a z-axis corresponding to the axis of the tool and an x-axis and a y-axis each with initially indeterminate orientations, - specification of 3D spatial coordinates of the point of the tool and an orientation of the axis, expressed in each case in the reference coordinate system, as part of the target pose for the tool, characterised in that the method has the following steps - calculation of the orientations of the x-axis and the y-axis of the target coordinate system {r} expressed in the reference coordinate system by - a first cross product of the specified orientation of the axis and a direction vector, which is not parallel thereto, of a coordinate axis ( x 0, y 0, z 0) of the reference coordinate system, and - a second cross product of a result of the first cross product and the specified orientation of the axis expressed in the reference coordinate system, - creation of a 4x4 matrix, which defines a pose 0 H r of the target coordinate system {r} with reference to the reference coordinate system from the orientations of the coordinate axes ( 0 x r, 0 y r, 0 z r) of the target coordinate system {r} expressed in each case in the reference coordinate system and 3D spatial coordinates ( 0 t r) of the point of the tool and from an additional 1x4 line vector. - specification of an axis of the tool, - specification of a Cartesian reference coordinate system originating on the robot foot, - specification of a Cartesian target coordinate system {r} originating on a point of the tool, a z-axis corresponding to the axis of the tool and an x-axis and a y-axis each with initially indeterminate orientations, - specification of 3D spatial coordinates of the point of the tool and an orientation of the axis, expressed in each case in the reference coordinate system, as part of the target pose for the tool, characterised in that the method has the following steps - calculation of the orientations of the x-axis and the y-axis of the target coordinate system {r} expressed in the reference coordinate system by - a first cross product of the specified orientation of the axis and a direction vector, which is not parallel thereto, of a coordinate axis ( x 0, y 0, z 0) of the reference coordinate system, and - a second cross product of a result of the first cross product and the specified orientation of the axis expressed in the reference coordinate system, - a first cross product of the specified orientation of the axis and a direction vector, which is not parallel thereto, of a coordinate axis ( x 0, y 0, z 0) of the reference coordinate system, and - a second cross product of a result of the first cross product and the specified orientation of the axis expressed in the reference coordinate system, - creation of a 4x4 matrix, which defines a pose 0 H r of the target coordinate system {r} with reference to the reference coordinate system from the orientations of the coordinate axes ( 0 x r, 0 y r, 0 z r) of the target coordinate system {r} expressed in each case in the reference coordinate system and 3D spatial coordinates ( 0 t r) of the point of the tool and from an additional 1x4 line vector.