So it sounds like the environment (the room) doesn’t change and your camera doesn’t move. So you are right: why render the room over and over again if the only thing that changes is the robot.
Light the robot as you wish and render all his frames with just him with an alpha channel and the room turned off.
Then apply a shadowcatcher material (R19 and above) to the floor object and render all the frames of your floor, the robot with no materials on him, only the lights that cast shadows and a compositing tag on the robot with “seen by camera: set to off. The robot will not show in the render but his shadow will (as an alpha), and only the shadow. So you don’t need materials on the room objects and you only need to have the objects that will receive shadows visible.
Then render just the room in full color but just one frame.
Composite the robot, the shadow and the room together in a compositing program, extending the one room frame to cover the entire length of the robot’s animation