An asymmetric two-link robot supported atop a flat platform by wheels that roll and pivot freely, but do not slip laterally, will develop forward momentum if the joint between the links is actuated internally. In particular, oscillations in the joint angle will generate undulatory locomotion suggesting fishlike swimming. If two such robots surmount a common platform that's free to translate with its own inertial dynamics, then the individual robots' dynamics will be coupled so that the locomotion of either robot is affected by that of the other. We develop a mathematical model for this system and present simulations demonstrating its behavior. We then consider a single robot with an unactuated joint rolling atop a platform that moves under control, and show that actuation of the platform is sufficient to dictate the robot's behavior. In particular, with the acceleration of the platform as an input, the robot's heading can be made to track a chosen function of time. This is sufficient to guarantee that the robot can be induced to orbit a fixed point on the platform or to locomote persistently in a desired direction.