This paper proposes a switched control algorithm for distributed cooperative manipulation of rigid bodies in a planar setting. More specifically, we consider the problem of making a grasped object follow a desired position and orientation path. The system contains N robots, possibly of heterogeneous designs, each of which consists of a manipulator arm and a nonholonomic mobile platform. Control is based on local information, is carried out on a kinematic level and partly utilizes inverse kinematics. We use Lyapunov-like arguments to prove that the algorithm is almost globally stable and also show that its parameters can be chosen so that any input saturation level is met. The time between certain switches is proved to be bounded below, and the system is shown to be free of any Zeno behavior.