The geometry of the trajectories

In this paper, we use of the geometry of a class of the nature flows to define trajectory manifolds. Trajectory connections as a generalization of the Levi-Civita connections are considered. A method for determining the geometry of the flows created by the integral curves of a vector field is presented. The method contains two steps, the first step is finding the connection by the trajectories of a vector field, and the second step is finding a trajectory metric corresponding to the deduced connection. We show that doing the first step is possible, but for some of the vector fields, the second step may not be possible. In the case of existence of a trajectory manifold a new kind of curvature which we called it “trajectory curvature scalar” appears. We calculate trajectory connections for some vector fields and by an example we show that the trajectory curvature scalar for a trajectory manifold may not be equal to the curvature scalar of it. We find trajectory connection for a vector field close to the Schwarzschild black hole.

Intelligence Dumping into Autonomous Robotic Systems for Higher Autonomy

More global decision making delegation should be given today man made systems with large number of heterogeneous components and high complexity. A new paradigm is proposed for mix of power and information fluxes at task control level for goal accomplishment, with associated trajectory manifold resulting from system self-organization. It rests upon system invariants characterizing Complex Systems (CS) dynamics, and uses qualitative methods independent of system state dimension privileging robustness to compensate impreciseness of system parameters and functional variations. A well defined control law is constructed in explicit terms from mathematical representation of system dynamics, guaranteeing both asymptotic stability and robustness. A “determinism” criterion for autonomous system is considered with evaluation of resulting constraints on system parameters. Proposed merging of Complex Systems with Information Technologies (IT) provides a first step toward system autonomous intelligence.