Generic Prototype

The purpose of the project is to develop a generic software Prototype of the full scale Linguistic Geometry Tools. This Prototype will be tuned to the specific problem domain to generate applications. Initially this Prototype is intended to generate soft ware for the class of pursuit-evasion robot control problems. Specifically, the Prototype will be tested on concurrent multiagent robotic systems.

The first step of the development is an introduction of the hierarchical system. Employing the LG approach a new multi-goal, multi-level system will substitute for the original one-goal one-level system by introducing intermediate goals and breakin g the system down into subsystems striving to attain these goals. The goals of the subsystems are individual but coordinated within the main global goal. For example, each second-level subsystem includes entities of both opposing sides. In robot control, it means the selection of a couple of robots of opposing sides: one - as a pursuer and the other - as an evader, generation of the local paths for approaching the evader, as well as the paths of other robots supporting the pursuit or protecting the evader .

The next step is implementation of the hierarchy of formal languages which represents a hierarchy of subsystems. Each sentence - a group of words or symbols - of the lower level language corresponds to a word in the higher level one. The lowest lev el subsystem is represented by a Language of Trajectories in which expressions are trajectories denoted as strings of parametric symbols a(x₁)a(x₂)...a(x_n), in which the parameters incorporate the semantics of some proble m domain. Strings of the type represent paths - trajectories - of system's elements. For a robotic model, x_i are coordinates of the robot's planning path. The second-level subsystem is represented by a Language of Trajectory Networks in which e xpressions are trajectory networks, denoted as strings composed of parametric symbols t(p_1,t₁,t₁) t(p₂, t₂,t₂) ...t(p_k,t_k,t_k), where p_i is an ele ment of the system, a robot, t_i is an entire trajectory, t_i are problem domain-specific parameters. These networks represent a framework for dynamic tactical planning. The elements move along the network trajectories attempting to ac hieve local goals, while advancing the achievement of the strategic goal of the entire system. In various problems there may be many levels of Trajectory Network Languages representing a hierarchy of subsystems.

The entire system operates by changing from one state to another. That is, the motion of an element from one location to another causes an adjustment of the hierarchy of languages. This adjustment is represented as a mapping or translation from one hierarchy to another, or to a new state of the same hierarchy. Thus, in the system operation, the search process generates a tree of translations of the hierarchy of languages. The top-level language to be implemented is the Language of Translations. It contains all the trees of translations represented as strings of parametric symbols. Each arc of the search tree, i.e., each symbol, represents the movement of a robot from one location to another along the trajectory network. Expressions in the Language of Translations represent searches for an optimal (suboptimal) operation, such as the optimal plan for a robot control problem. Generation in this language is controlled by interaction of trajectory networks. This generation results in a dramatically red uced search tree which yields a solution of the problem.

The development and the following experiments with the Prototype for various control problems will generate an extremely interesting data set that would allow to us to plan the development of the industrial software.