1,050 research outputs found
Game-theoretic Occlusion-Aware Motion Planning: an Efficient Hybrid-Information Approach
We present a novel algorithm for motion planning in complex, multi-agent
scenarios in which occlusions prevent all agents from seeing one another. In
this setting, the fundamental information that each agent has, i.e., the
information structure of the interaction, is determined by the precise
configurations in which agents come into view of one another. Occlusions
prevent the use of existing pure feedback solutions, which assume availability
of the state information of all agents at every time step. On the other hand,
existing open-loop solutions only assume availability of the initial agent
states. Thus, they do not fully utilize the information available to agents
during periods of unhampered visibility. Here, we first introduce an algorithm
for solving an occluded, linear-quadratic (LQ) dynamic game, which computes
Nash equilibrium by using hybrid information and switching between feedback and
open-loop information structures. We then design an efficient iterative
algorithm for decision-making which exploits this hybrid information structure.
Our method is demonstrated in overtaking and intersection traffic scenarios.
Results confirm that our method outputs trajectories with favorable running
times, converging much faster than recent methods employing reachability
analysis
Deep Q-Learning for Nash Equilibria: Nash-DQN
Model-free learning for multi-agent stochastic games is an active area of
research. Existing reinforcement learning algorithms, however, are often
restricted to zero-sum games, and are applicable only in small state-action
spaces or other simplified settings. Here, we develop a new data efficient
Deep-Q-learning methodology for model-free learning of Nash equilibria for
general-sum stochastic games. The algorithm uses a local linear-quadratic
expansion of the stochastic game, which leads to analytically solvable optimal
actions. The expansion is parametrized by deep neural networks to give it
sufficient flexibility to learn the environment without the need to experience
all state-action pairs. We study symmetry properties of the algorithm stemming
from label-invariant stochastic games and as a proof of concept, apply our
algorithm to learning optimal trading strategies in competitive electronic
markets.Comment: 16 pages, 4 figure
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
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