The impact of symmetry violations on determining optimal control trajectories for complex robotic systems

Abstract

Complex robotic systems, their properties, features and interactions are considered, the article offers the definition of a complex system on the basis of 5 properties: openness, non-morphic variability of three types (structural, spatial and information), Double-code, event aggregation and violation of physical symmetries. The influence of violations of physical symmetries on the determination of optimal control trajectories is reflected in the paradigm approach to the study of complex robotic systems that are not formalized as mathematical objects. The basic concepts, postulates and hypotheses are formulated. Ideal designs of variability of complex systems; energy causal sets; energies; events, causes, effects and evolution; spacetime, quanta and vacuum; interaction of individuals; operators of physical interactions, aggregated events, text and attachments of words. Three basic models for the study of complex systems - the model of physical interactions, the neurolinguistic model and the model of control at incomplete compatibility are proposed and briefly described. The structure of the kernel of the platform of physical simulation modeling for the researches of complex systems is resulted. Three types of space-time quantum modeling - minimal, semantic and evolutionary - are described. The article provides an illustration of results of application of the proposed approach to the study of actions of complex systems. It is noted that the resulting mathematical structure exhibits fractal properties. Typical trajectories of evolution - «homeostat»; «attenuation of actions»; «invariant»; «accident»; «window of possibilities» have been allocated. The article provides a number of principles of research of complex methodological and methodical systems. Recommendations were made on the scope of the proposed approach.