Swarm assignment and trajectory optimization using variable-swarm, distributed auction assignment and sequential convex programming

This paper presents a distributed, guidance and control algorithm for reconfiguring swarms composed of hundreds to thousands of agents with limited communication and computation capabilities. This algorithm solves both the optimal assignment and collision-free trajectory generation for robotic swarms, in an integrated manner, when given the desired shape of the swarm (without pre-assigned terminal positions). The optimal assignment problem is solved using a distributed auction assignment that can vary the number of target positions in the assignment, and the collision-free trajectories are generated using sequential convex programming. Finally, model predictive control is used to solve the assignment and trajectory generation in real time using a receding horizon. The model predictive control formulation uses current state measurements to resolve for the optimal assignment and trajectory. The implementation of the distributed auction algorithm and sequential convex programming using model predictive control produces the swarm assignment and trajectory optimization (SATO) algorithm that transfers a swarm of robots or vehicles to a desired shape in a distributed fashion. Once the desired shape is uploaded to the swarm, the algorithm determines where each robot goes and how it should get there in a fuel-efficient, collision-free manner. Results of flight experiments using multiple quadcopters show the effectiveness of the proposed SATO algorithm

Review of Formation Flying and Constellation Missions Using Nanosatellites

Small satellites are enabling multisatellite missions that were not otherwise possible because of their small size and modular nature [1]. Multiple small satellites can be flown instead of a much bigger and costlier conventional satellite for distributed sensing applications such as atmospheric sampling, distributed antennas [2], and synthetic apertures [3,4]. Missions with multiple small satellites can deliver a comparable or greater mission capability than a monolithic satellite, but with significantly enhanced flexibility (adaptability, scalability, evolvability, and maintainability) and robustness (reliability, survivability, and fault tolerance) [1,5]. Small satellites that weigh less than 10 kg can be broadly classified into nanosatellites (mass between 1 and 10 kg), picosatellites (mass between 0.1 and 1 kg), and femtosatellites (mass less than 100 g) [1,6]

Review of Formation Flying and Constellation Missions Using Nanosatellites

Small satellites are enabling multisatellite missions that were not otherwise possible because of their small size and modular nature [1]. Multiple small satellites can be flown instead of a much bigger and costlier conventional satellite for distributed sensing applications such as atmospheric sampling, distributed antennas [2], and synthetic apertures [3,4]. Missions with multiple small satellites can deliver a comparable or greater mission capability than a monolithic satellite, but with significantly enhanced flexibility (adaptability, scalability, evolvability, and maintainability) and robustness (reliability, survivability, and fault tolerance) [1,5]. Small satellites that weigh less than 10 kg can be broadly classified into nanosatellites (mass between 1 and 10 kg), picosatellites (mass between 0.1 and 1 kg), and femtosatellites (mass less than 100 g) [1,6]

A Review of Impending Small Satellite Formation Flying Missions

Small satellites, like popular nanosatellite platforms called CubeSats, are suitable for formation flying missions because of their modular nature and low cost. This paper presents a review of thirty-nine missions, using multiple small satellites, in various stages of development. These missions are categorized based on their mission type, mission status, number of satellites, leading organization, funding source, and requirement for constellation or formation flying. We conclude that Earth science related missions are the most popular, while most multi-satellite missions only require a constellation. Although six missions aim to demonstrate formation flying capability in space using two to three small satellites, there are currently only two formation flying missions planning to use four or more small satellites

Initial hardness response and hardness profiles in the study of Woodward-Hoffmann rules for electrocyclizations

The fundamental principles of pericyclic reactions are governed by the Woodward-Hoffmann rules, which state that these reactions can only take place if the symmetries of the reactants' molecular orbitals and the products' molecular orbitals are the same. As such, these rules rely on the nodal structure of either the wave function or the frontier molecular orbitals, so it is unclear how these rules can be recovered in the density functional reactivity theory (or "conceptual DFT"), where the basic quantity is the strictly positive electron density. A third, nonsymmetry based approach to predict the outcome of pericyclic reactions is due to Zimmerman which uses the concept of the aromatic transition states: allowed reactions possess aromatic transition states, while forbidden reactions possess antiaromatic transition states. Based on our recent work on cycloadditions, we investigate the initial response of the chemical hardness, a central DFT based reactivity index, along the reaction profiles of a series of electrocyclizations. For a number of cases, we also compute complete initial reaction coordinate (IRC) paths and hardness profiles. We find that the hardness response is always higher for the allowed modes than for the forbidden modes. This suggests that the initial hardness response along the IRC is the key for casting the Woodward-Hoffmann rules into conceptual DFT

Information-Driven Systems Engineering Study of a Formation Flying Demonstration Mission using Six CubeSats

Small satellites are suitable for formation flying missions where a large number of spacecraft serve as distributed sensors for applications like synthetic aperture radar, interferometry, etc. A survey of existing or proposed small satellite missions concludes that there is a dearth of formation flying missions using four or more spacecraft that require formation maintenance. This paper presents a systems engineering based design of a formation flying technology demonstration mission that requires precise formation maintenance and reconfigurations and highlights the challenges that need to be overcome for its successful implementation. The goal of this paper is to provide directions for future research and development in spacecraft formation flying technologies