Topology Representing Network in Robotics

We consider the visually guided control of the grasping movements of a highly hysteretic five- joint pneumatic robot arm. For this purpose we apply a modified version of the so-called topology representing network algorithm, a vector quantization algorithm that also learns to represent neighborhood relationships. The notion of neighborhood relationships allowed us to average the behavior of neurons which represent similar tasks, both during the training and in generating control signals in the mature state. Based on visual information provided by two cameras, the robot learns to position and orient its end effector properly for the object to be grasped. For simplicity, we consider the grasping of cylindrical objects only. The control is comprised of two stages. In the first stage, the end effector approaches the side of the cylinder facing the robot base; and in the second stage, the end effector grasps the cylinder. Training of the first stage involves a brief episode of supervised learning to prime the network. The control is achieved through a visual feedback loop: for both stages of the motion the system detects the error to target and applies a linear correction. This correction is achieved through a training that yields a vector-quantized representation of a zero-order signal of joint pressures and a first-order correction through Jacobian tensors which relate the error, expressed in terms of camera coordinates, to correct joint pressures. The network is trained satisfactorily after about 300 trial movements, with a residual average error of 1.35 camera pixels. Besides a demonstration of the technical feasibility of control through topology representing networks, this chapter provides a tutorial for technical applications of such networks. The algorithm behind a topology representing network, its training and employment for task control, is described in complete detail to provide the reader with a comprehensive view of this important class of neural networks in the context of a technical application.

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