Game Theoretic Strategies for Spacecraft Rendezvous and Motion Synchronization

The rendezvous problem between two active spacecraft is formulated as a two player nonzero-sum differential game. The local-vertical local-horizontal (LVLH) rotating reference frame is used to describe the dynamics of the game. Linear quadratic cooperative and noncooperative differential games are applied to obtain a feedback control law. A comparison between Pareto and Nash equilibria was then performed. The state-dependent Riccati equation (SDRE) method is applied to extend the Linear Quadratic differential game theory to obtain a feedback controller in the case of nonlinear relative motion dynamics. Finally, a multiplayer sequential game strategy is synthesized to extend the control law to the relative motion synchronization of multiple vehicles

Realistic Guidance Performance during Lunar Rendezvous with Third Body Perturbation

The paper describes the performance of a guidance law based on the Adjoint and SDRE methods in presence of reality representative models of sensors and actuators during the rendezvous phase of the proposed Heracles mission to the Moon. In recent years, the increased interest in returning to the Moon has motivated the necessity to develop accurate models for the analysis of missions that takes into account realistic system components. The paper reviews the mission’s details, the rendezvous/berthing guidance algorithm with third body perturbation, and sensor’s and actuators state of the art models. A Montecarlo analysis is used to validate the models in order to satisfy the safety of the trajectory. The results show that the proposed guidance and control are capable of maintaining safe relative motion between the vehicles

Relative Motion Equations in the local-vertical local-Horizon Frame for Rendezvous in lunar Orbits

In this paper, a set of equations for relative motion description in lunar orbits is presented. The local-vertical local-horizon frame is selected to describe the relative dynamics of a chaser approaching a target in lunar orbit, allowing the development of relative guidance and navigation systems for rendezvous and docking. The model considers the Earth and Moon gravitational influence on the two spacecraft, which are assumed to have negligible masses. The proposed equations are intended for the study of rendezvous missions with a future cis-lunar space station, whose development is currently investigated by several space agencies as the next step for space exploration

Distributed Cooperative Deployment of Heterogeneous Autonomous Agents: A Pareto Suboptimal Approach

The paper presents a distributed cooperative control law for autonomous deployment of a team of heterogeneous agents. Deployment problems deal with the coordination of groups of agents in order to cover one or more assigned areas of the operational space. In particular, we consider a team composed by agents with different dynamics, sensing capabilities, and resources available for the deployment. Sensing heterogeneity is addressed by means of the descriptor function framework, an abstraction that provides a set of mathematical tools for describing both agent sensing capabilities and the desired deployment. A distributed cooperative control law is then formally derived nding a suboptimal solution of a cooperative dierential game, where the agents are interested in achieving the requested deployment, while optimizing the resources usage according to their dynamics. The control law eectiveness is proven by theoretical arguments, and supported by numerical simulations

Synchronization Patterns in Networks of Kuramoto Oscillators: A Geometric Approach for Analysis and Control

Synchronization is crucial for the correct functionality of many natural and man-made complex systems. In this work we characterize the formation of synchronization patterns in networks of Kuramoto oscillators. Specifically, we reveal conditions on the network weights and structure and on the oscillators' natural frequencies that allow the phases of a group of oscillators to evolve cohesively, yet independently from the phases of oscillators in different clusters. Our conditions are applicable to general directed and weighted networks of heterogeneous oscillators. Surprisingly, although the oscillators exhibit nonlinear dynamics, our approach relies entirely on tools from linear algebra and graph theory. Further, we develop a control mechanism to determine the smallest (as measured by the Frobenius norm) network perturbation to ensure the formation of a desired synchronization pattern. Our procedure allows us to constrain the set of edges that can be modified, thus enforcing the sparsity structure of the network perturbation. The results are validated through a set of numerical examples

Distributed Real-Time Hardware- and Man-in-the-loop Simulation for the ICARO II Unmanned Systems Autopilot

The autopilot market for small and research UAVs offers several products, but most of them, although widely configurable or even open-source, do not constitute a practical and safe development system for custom guidance, navigation and control systems. The ICARO project aims at providing the small UAV community with a valid autopilot alternative. The ICARO autopilot exploits rapid control system prototyping techniques and immersive manned simulation with the possibility of testing the autopilot using the Hardware- In-the-Loop (HIL) approach. This paper describes the hardware-in-the-loop and man-in-the-loop simulator for the ICARO II platform together with the synchronization protocol we developed to keep simulator and autopilot synchronized. Experimental evidence of the effectiveness of the synchronization protocol is given

Cooperative Control for Multiple Autonomous Vehicles Using Descriptor Functions

The paper presents a novel methodology for the control management of a swarm of autonomous vehicles. The vehicles, or agents, may have different skills, and be employed for different missions. The methodology is based on the definition of descriptor functions that model the capabilities of the single agent and each task or mission. The swarm motion is controlled by minimizing a suitable norm of the error between agents’ descriptor functions and other descriptor functions which models the entire mission. The validity of the proposed technique is tested via numerical simulation, using different task assignment scenarios

Swarm Obstacle and Collision Avoidance using Descriptor Functions

The descriptor function framework is used as tool for the control management of a swarm of dynamic agents. In this framework, a provision is made for obstacle and collision avoidance, thus improving the potential of the methodology from previous results. Obstacle and collision avoidance terms are added to the overall mission performance index, and the resulting control law moves the agents along obstacle and collision free trajectories. The analytical derivation is validated via numerical simulations

Synchronization Patterns in Networks of Kuramoto Oscillators: A Geometric Approach for Analysis and Control

Synchronization is crucial for the correct functionality of many natural and man-made complex systems. In this work we characterize the formation of synchronization patterns in networks of Kuramoto oscillators. Specifically, we reveal conditions on the network weights and structure and on the oscillators’ natural frequencies that allow the phases of a group of oscillators to evolve cohesively, yet independently from the phases of oscillators in different clusters. Our conditions are applicable to general directed and weighted networks of heterogeneous oscillators. Surprisingly, although the oscillators exhibit nonlinear dynamics, our approach relies entirely on tools from linear algebra and graph theory. Further, we develop a control mechanism to determine the smallest (as measured by the Frobenius norm) network perturbation to ensure the formation of a desired synchronization pattern. Our procedure allows us to constrain the set of edges that can be modified, thus enforcing the sparsity structure of the network perturbation. The results are validated through a set of numerical example

Inhibition of ?±-class cytosolic human carbonic anhydrases I II IX and XII and ?²-class fungal enzymes by carboxylic acids and their derivatives: New isoform-I selective nanomolar inhibitors

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