Self-Organizing Multi-Resolution Grid for Motion Planning and Control

A fully self-organizing neural network approach to low-dimensional control problems is described. We consider the problem of learning to control an object and solving the path planning problem at the same time. Control is based on the path planning model that follows the gradient of the stationary solution of a diffusion process working in the state space. Previous works are extended by introducing a self-organizing multigrid-like discretizing structure to represent the external world. Diffusion is simulated within a recurrent neural network built on this multigrid system. The novelty of the approach is that the diffusion on the multigrid is fast. Moreover, the diffusion process on the multigrid fits well the requirements of the path planning: it accelerates the diffusion in large free space regions while still keeps the resolution in small bottleneck-like labyrinths along the path. Control is achieved in the usual way: associative learning identifies the inverse dynamics of the system in a direct fashion. To this end there are introduced interneurons between neighboring discretizing units that detect the strength of the steady-state diffusion and forward control commands to the control neurons via modifiable connections. This architecture forms the Multigrid Position-and-Direction-to-Action (MPDA) map. The architecture integrates reactive path planning and continuous motion control. It is also shown that the scheme leads to population coding for the actual command vector.