Algorithms for Computing Nash Equilibria in Deterministic LQ Games

In this paper we review a number of algorithms to compute Nash equilibria in deterministic linear quadratic differential games.We will review the open-loop and feedback information case.In both cases we address both the finite and the infinite-planning horizon.Algebraic Riccati equations;linear quadratic differential games;Nash equilibria

Algorithms for Computing Nash Equilibria in Deterministic LQ Games

In this paper we review a number of algorithms to compute Nash equilibria in deterministic linear quadratic differential games.We will review the open-loop and feedback information case.In both cases we address both the finite and the infinite-planning horizon.

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

Simulation of interactive motor behaviours in game theory framework for upper-limb rehabilitation

An increasing number of individuals are affected by neurological diseases worldwide. Nowadays, stroke is the leading cause of adult disability in western countries, with upper limb hemiparesis being one of the most common consequences. Therefore, there is a growing interest in developing robotic interfaces to provide neurologically affected individuals the right amount of assistance to guarantee a great recovery. The interactive control of such rehabilitation robots with a stroke survivor is critical to motor recovery, and a successful rehabilitation requires the patient to be engaged in motor task execution. This thesis focuses on the new development of an interactive robot controller, and aims to ensure that differential game theory can be used as a framework to describe various interactive behaviours between a robot and a human user. In this thesis, it will be simulated the interaction between a robot and an injured human user who is recovering after stroke in the game theory framework, demonstrating that it can induce a stable interaction between the two partners by identifying each other’s control law and allow them to successfully perform the task with minimum effort. In this thesis is expected to find a detailed description of the different interactive motor behaviours that exist between a rehabilitation robot and a human user: collaboration, cooperation, competition and co-activity. It will also contain the simulation of these behaviours. In the description of the human-robot interactive motor behaviours, it will be seen that some of these behaviours are modelled in the simulation in the game theory framework, such as collaboration, cooperation and competition, while co-activity consists on a problem where the robot and the human are modelled as two independent linear quadratic regulators. Finally, it will be provided a comparison between the use of a game theory controller and the use of a linear quadratic regulator controller for the development of a rehabilitation robot and it will be demonstrated why a game theory controller is a better option for robots that work in physical contact with humans

Algorithms for computing Nash equilibria in deterministic LQ games

Algebraic Riccati equations, Linear quadratic differential games, Nash equilibria,

Algorithms for Computing Nash Equilibria in Deterministic LQ Games

In this paper we review a number of algorithms to compute Nash equilibria in deterministic linear quadratic differential games.We will review the open-loop and feedback information case.In both cases we address both the finite and the infinite-planning horizon.

Game Theoretic Strategies for Spacecraft Rendezvous and Motion Synchronization

Uno dei possibili sviluppi della guida e del controllo relativo nello spazio è quella di estendere gli algoritmi per operazioni di rendezvous e di docking autonome a più veicoli spaziali che collaborano tra di loro. Il problema del rendezvous tra due veicoli spaziali viene risolto utilizzando la teoria dei giochi differenziali lineari quadratici. La dinamica del gioco viene descritta in un sistema di riferimento cartesiano non inerziale. Per estendere l'utilizzo della teoria dei giochi differenziali lineari quadratici alle equazioni non lineari di moto relativo è stata utilizzata le tecnica di parametrizzazione in funzione dello stato o linearizzazione estesa. Nelle simulazioni è stato valutato il confronto tra le prestazioni e le traiettorie ottenute con l'equilibrio di Pareto e quello di Nash quando entrambi i veicoli spaziali agiscono sotto spinta continua. Una strategia sequenziale è stata utilizzata per estendere il gioco differenziali a più di due giocatori per avere la sincronizzazione del moto relativo durante operazioni di assemblaggio nello spazio. One of the main challenges for autonomous spacecraft relative guidance and control is extending the algorithms for autonomous rendezvous and docking (AR&D) operations to multiple collaborative spacecraft. In this thesis, the autonomous 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 dynamic of the game. The State-Dependent Riccati equation (SDRE) method is applied to extend the Linear Quadratic differential game theory to obtain a feedback control law for nonlinear equation of relative motion. In the simulations both the spacecraft use continuous thrust engines. A comparison among Pareto and Nash equilibrium has been performed. A multiplayer sequential game strategy is used to extend the control law to many spacecraft for relative motion synchronization in an on-orbit self assembly strategy