Cognitive map learners (CML) have been shown to enable hierarchical, compositional machine learning. That is, interpedently trained CML modules can be arbitrarily composed together to solve more complex problems without task-specific retraining. This work applies this approach to control the movement of a multi-jointed robot arm, whereby each arm segment's angular position is governed by an independently trained CML. Operating in a 2D Cartesian plane, target points are encoded as phasor hypervectors according to fractional power encoding (FPE). This phasor hypervector is then factorized into a set of arm segment angles either via a resonator network or a modern Hopfield network. These arm segment angles are subsequently fed to their respective arm segment CMLs, which reposition the robot arm to the target point without the use of inverse kinematic equations. This work presents both a general solution for both a 2D robot arm with an arbitrary number of arm segments and a particular solution for a 3D arm with a single rotating base.