The drone (10) comprises an onboard video camera (14) picking up a sequence of images to be transmitted to a remote control. The user selects an exposure mode such as forward or sideways, panoramic or boom plane, tracking, defining a trajectory to be transmitted to the drone. Corresponding setpoint values are generated and applied to a processing subsystem controlling the motors of the drone. Once the drone is stabilized on the prescribed trajectory (38), the exposure by the video camera (14) is activated and the trajectory is stabilized by an open loop control avoiding the oscillations inherent in a servocontrol with feedback loop.