This paper proposes a general motion planning and coordination strategy for robot systems. The representation space (RS) of a robot system is constructed to describe the distributions of system attributes. The reachable area in the RS, denoting the attribute set that the system can be of, indicates the system's ability to accomplish tasks. Moreover, it also describes the influences of the internal and external constraints on the system's capability. Task realization is transformed to finding a trajectory in the RS for the system attributes to transit along under constraints. Meanwhile, the realizable conditions of a prescribed task by the robot system of specific configurations are discussed. If the task is realizable, the optimal strategy for task execution could further be figured out. Otherwise, it could be transformed to be realizable via task reassignment or system reconfigurations so that a connected path could be found for the transition of the system attributes from the starting point to the goal in the RS. The proposed scheme contributes to designing, planning, and coordination of the robotic tasks. Experiments on path planning of a robot manipulator and formation movement of a multirobot system, as well as coordination of a mobile manipulator system, are conducted to show the validity and generalization of the proposed method.