Multi-robot systems have substantially increased capabilities over single robots and can handle very large or peculiar objects. The paper presents a differential (incremental) motion planning algorithm for an m-robot system (m⩾2) to cooperatively transfer an object from an initial to a desired final position by rigidly holding it at given m points. One of the robots plays the role of a ‘master’, while other robots operate in the ‘slave’ mode, maintaining invariant their relative positions and orientations during system motion. The method employs the differential displacements of the end effector of each robot arm. Then, the differential displacements of the joints of the m robots are computed for application of incremental motion control. The algorithm was tested on numerous examples. One of them is shown, concerning three STAUBLI RX-90L robots similar to 6-dof PUMA robots. The results obtained show the practicality and effectiveness of the method, which, however, needs particular care for completely eliminating the cumulative errors that may occur.