Systems and methods for controlling transmissions and associated vehicles, machines, equipment, etc., are disclosed. In one case, a transmission control system includes a control unit configured to use a sensed vehicle speed and a commanded, target constant input speed to maintain an input speed substantially constant. The system includes one or more maps that associate a speed ratio of a transmission with a vehicle speed. In one embodiment, one such map associates an encoder position with a vehicle speed. Regarding a specific application, an automatic bicycle transmission shifting system is contemplated. An exemplary automatic bicycle includes a control unit, a shift actuator, various sensors, and a user interface. The control unit is configured to cooperate with a logic module and an actuator controller to control the cadence of a rider. In one embodiment, a memory of, or in communication with, the control unit includes one or more constant cadence maps that associate transmission speed ratios with bicycle speeds.