Controlling robotic arms is important for real, physical world applications. Such control is hard because movement of one joint affects the position of many of the rest. In this paper we present an algorithm that finds plans of motion from one arm configuration to a goal arm configuration in 2D space. Our algorithm is unique in two ways: (a) It takes time that is only polynomial in the number of joints, thus allowing scaling up to complex arms; and (b) it decomposes the control problem to that of the separate joints, thus enabling future development of reactive modules. The algorithm leaves each joint somewhat independent of the rest by reformulating the domain description and re-partitioning it. Our algorithm is sound and complete given mild assumptions: it finds a plan, if there is one, and every returned plan leads to the goal. Also, it has bounded error with respect to the optimal path in the discretized environment. Our approach is promising because it leads naturally to a subsumption-architecture-like control of robotic arms.