SYSTEM AND METHOD FOR ESTIMATING STATES OF SPACECRAFT IN PLANET-MOON ENVIRONMENT

A method estimates a state of a spacecraft in a planet-moon environment by executing iteratively a particle filter. The particle filter comprising integrates individually states of each particle of the particle filter according to a probability-evolution equation using a model of the state of the spacecraft represented as a planar circular restricted three-body problem and determines a prior probability of each particle as a previous posterior probability of a corresponding particle during a previous iteration. A joint probability distribution of the state of the spacecraft is determines using the states of each particle and the prior probabilities of each particle and the states and the prior probabilities of each particle are updated according to the joint probability distribution of the state of the spacecraft and a measurement of the state of the spacecraft to produce posterior probabilities of each particle

MULTI-AGENT CONTROL SYSTEM AND METHOD

Motion of multiple agents with identical non - linear dynamics is controlled to change density of the agents from the initial to the final density . A first control problem is formulated for optimizing a control cost of changing density of the agents from the initial density to the final density subject to dynamics of the agents in a density space . The first control problem , which is a non - linear non - convex problem over a multi - agent control and a density of the agents , is trans formed into a second control problem over the density of the agents and a product of the multi - agent control and the density of the agents . The second control problem is a non - linear convex problem that is solved to produce the control input for each section of the state space. A motion of each agent is controlled according to a control input corresponding to its section of the state space

Phase space analysis of nonlinear wave propagation in a bistable mechanical metamaterial with a defect

We study the dynamics of solitary waves traveling in a one-dimensional chain of bistable elements in the presence of a local inhomogeneity (`defect\u27). Numerical simulations reveal that depending upon its initial speed, an incoming solitary wave can get transmitted, captured or reflected upon interaction with the defect. The dynamics are dominated by energy exchange between the wave and a breather mode localized at the defect. We derive a reduced-order two degree of freedom Hamiltonian model for wave-breather interaction, and analyze it using dynamical systems techniques. Lobe dynamics analysis reveals the fine structure of phase space that leads to the complicated dynamics in this system. This work is a step towards developing a rational approach to defect engineering for manipulating nonlinear waves in mechanical metamaterials

Mechanochemical Topological Defects in an Active Nematic

We propose a reaction-diffusion system that converts topological information of an active nematic into chemical signals. We show that a curvature-dependent reaction dipole is sufficient for creating a system that dynamically senses topology by producing a scalar order parameter possessing local extrema coinciding with $\pm\frac{1}{2}$ defects. We consider two possible physical origins of such dipoles: (i) curved molecules that preferentially bind to nematic regions matching their curvature and (ii) nematic molecules that become reaction dipoles when deformed. We demonstrate the behavior of this system for stationary defects and in the presence of hydrodynamic flows as seen in active nematics. The model can help generate testable hypotheses for biological phenomena and motivate the creation of bioinspired materials that dynamically couple nematic structure with biochemistry

Phase space analysis of nonlinear wave propagation in a bistable mechanical metamaterial with a defect

We study the dynamics of solitary waves traveling in a one-dimensional chain of bistable elements in the presence of a local inhomogeneity (“defect”). Numerical simulations reveal that depending upon its initial speed, an incoming solitary wave can get transmitted, captured, or reflected upon interaction with the defect. The dynamics are dominated by energy exchange between the wave and a breather mode localized at the defect. We derive a reduced-order two degree of freedom Hamiltonian model for wave-breather interaction and analyze it using dynamical systems techniques. Lobe dynamics analysis reveals the fine structure of phase space that leads to the complicated dynamics in this system. This work is a step toward developing a rational approach to defect engineering for manipulating nonlinear waves in mechanical metamaterials

Fuel-Optimal Trajectories in a Planet-Moon Environment Using Multiple Gravity Assists

For low energy spacecraft trajectories such as multi-moon orbiters for the Jupiter system, multiple gravity assists by moons could be used in conjunction with ballistic capture to drastically decrease fuel usage. In this paper, we outline a procedure to obtain a family of zero-fuel multi-moon orbiter trajectories, using a family of Keplerian maps derived by the first author previously. The maps capture well the dynamics of the full equations of motion; the phase space contains a connected chaotic zone where intersections between unstable resonant orbit manifolds provide the template for lanes of fast migration between orbits of different semimajor axes. Patched three body approach is used and the four body problem is broken down into two three-body problems, and the search space is considerably reduced by the use of properties of the Keplerian maps. We also introduce the notion of Switching Region where the perturbations due to the two perturbing moons are of comparable strength, and which separates the domains of applicability of the corresponding two Keplerian maps