A construction robot for attaching building blocks against a vertical surface of a vertical wall, wherein the robot comprises a group of components, the group of components including - a magazine of building blocks, the building blocks being defined by an attachment side for attachment to the vertical wall, an opposite second side which after attachment faces away from the wall, and edges surrounding the attachment side and the second side; - a glue container; - a glue dispenser configured for automatically dispensing glue from the glue container onto the attachment side while it is facing upwards; - a conveyor for automatically receiving a building block from the magazine and for moving the building block from the magazine to the glue dispenser in an orientation where the attachment side of the building block is facing upwards for receiving glue by the glue dispenser; characterised in that the construction robot further comprises: - a gripper station comprising a rotationally suspended gripper and arranged for receiving the building block from the conveyor and for gripping the building block by the gripper, wherein the gripper is configured for holding the building block during a rotation of the building block by the gripper station until the attachment side is vertical and facing the vertical surface of the vertical wall; and wherein the gripper station is configured for moving the attachment side towards the wall and with the glue into contact with the wall while the building block is held by the gripper; wherein the robot also comprises a frame comprising a vertical beam and a horizontal beam for suspending the group and motors for moving the group horizontally and vertically along the wall and for moving the gripper towards the wall for attachment of the building block onto the wall, wherein the motors are controlled by a controller programmed with computer instructions for sequentially attaching one building block after the other against the wall at predetermined locations; wherein the gripper comprises clamp jaws configured for engaging with opposite edges of the building block and holding the building block clamped between the clamp jaws by a force against the edges; wherein the gripper station is configured for receiving the building block from the conveyor in a first orientation and for clamping the edges by the clamp jaws, and subsequently, while clamping the edges, turning the clamp jaws together with the building block from the received first orientation to a second orientation where the attachment side is vertical and facing the wall, wherein the construction robot comprises a contact flange that is movable in a direction towards the wall independently of the gripper station for contact with the wall prior to a movement of the clamp jaws with the building block towards and against the wall, wherein a mechanical link (30C, 33) between the gripper station and the contact flange defines the movement of the clamp jaws towards the wall relatively to the contact flange, wherein the mechanical link comprises a guide roller as part of the gripper station and a slot as part of the contact flange for taking up the guide roller inside the slot during advance of the clamp jaws towards the wall. - a magazine of building blocks, the building blocks being defined by an attachment side for attachment to the vertical wall, an opposite second side which after attachment faces away from the wall, and edges surrounding the attachment side and the second side; - a glue container; - a glue dispenser configured for automatically dispensing glue from the glue container onto the attachment side while it is facing upwards; - a conveyor for automatically receiving a building block from the magazine and for moving the building block from the magazine to the glue dispenser in an orientation where the attachment side of the building block is facing upwards for receiving glue by the glue dispenser; characterised in that the construction robot further comprises: - a gripper station comprising a rotationally suspended gripper and arranged for receiving the building block from the conveyor and for gripping the building block by the gripper, wherein the gripper is configured for holding the building block during a rotation of the building block by the gripper station until the attachment side is vertical and facing the vertical surface of the vertical wall; and wherein the gripper station is configured for moving the attachment side towards the wall and with the glue into contact with the wall while the building block is held by the gripper;