Connectionist modeling for arm kinematics using visual information

The self-organizing adaptive map algorithm is adopted to learn all possible postures for an artificial arm of arbitrary configuration placed in a three-dimensional workspace. Arm postures are represented through their projections onto a set of image planes. Based on the link orientation and link length extracted from these images, a topological state space Q is generated. Arm kinematics is expressed as a transformation of topological hypersurfaces, the intersections of which represents the multiple postures of the arm in the workspace for a given end effector position. The self-organizing feature map learns how the topological hypersurfaces transform in the state space during arbitrary movements of the arm in the workspace. During the learning phase, the neural network generates clusters of neurons, each neuron being responsible for reproducing an arm posture in the workspace. The neural clusters map the hypersurfaces' intersection in the topological Q-space to any position of the arm gripper in the workspace. Simulations for planar and nonplanar multiple degrees of freedom arms are presented.