A Self-Organizing Neural Model of Motor Equivalent Reaching and Tool Use by a Multijoint Arm

Abstract

This paper describes a self-organizing neural model for eye-hand coordination. Called the DIRECT model, it embodies a solution of the classical motor equivalence problem. Motor equivalence computations allow humans and other animals to flexibly employ an arm with more degrees of freedom than the space in which it moves to carry out spatially defined tasks under conditions that may require novel joint configurations. During a motor babbling phase, the model endogenously generates movement commands that activate the correlated visual, spatial, and motor information that are used to learn its internal coordinate transformations. After learning occurs, the model is capable of controlling reaching movements of the arm to prescribed spatial targets using many different combinations of joints. When allowed visual feedback, the model can automatically perform, without additional learning, reaches with tools of variable lengths, with clamped joints, with distortions of visual input by a prism, and with unexpected perturbations. These compensatory computations occur within a single accurate reaching movement. No corrective movements are needed. Blind reaches using internal feedback have also been simulated. The model achieves its competence by transforming visual information about target position and end effector position in 3-D space into a body-centered spatial representation of the direction in 3-D space that the end effector must move to contact the target. The spatial direction vector is adaptively transformed into a motor direction vector, which represents the joint rotations that move the end effector in the desired spatial direction from the present arm configuration. Properties of the model are compared with psychophysical data on human reaching movements, neurophysiological data on the tuning curves of neurons in the monkey motor cortex, and alternative models of movement control.

Training a spiking neural network to control a 4-DoF robotic arm based on Spike Timing-Dependent Plasticity

“…The sequence of the joint angles that fix the end-effector at the intermediate points can then be followed, forcing the end-effector to trace the desired path. As discussed in [1], this approach has two main shortcomings. Since there could be multiple joint configurations that can result to the same spatial position of the end-effector, it is possible to have discontinuity in the joint space, and encounter, for example, two non-adjacent angles between consecutive steps along the path for the same joint.…”

“…1 We will denote for the rest of the paper the i-th input layer and the j-th output layer by L input i and L output j , respectively. We use a population of 1200 neurons for each input layer, and a population of 800 neurons for each output layer.…”

“…While the process of encoding the value of a variable into spike trains is important for the input layers, as well as for the output 1 In this paper, we use the term "layer" when referring to a group of input/output neurons. ϑ2 ϑ3 ϑ4 e1 e2 e3 ϑ2 ϑ3 ϑ4 ϑ1 plastic, all-to-all Fig.…”

“…Bullock et al [1] presented the DIRECT (Direction-toRotation Effector Control Transform) model which is a self-organizing neural network that learns, during a motor babbling period, the mapping between joint commands and the resulting spatial displacements of the end-effector. (Motor babbling can be observed in babies, where a repetitive actionperception cycle generates associative information between the various representations.)…”

Learning for the Control of Dynamical Motion Systems

“…Among them, several significant contributions highlight two main approaches: those which are looking for an a priori analogy with biological systems (identification of functions of the cerebellum) [1][2][3], and the others which are looking for an a posteriori analogy with biological systems [4][5].…”