Real-Time Collision Avoidance: Differential Game, Numerical Solution, and Synthesis of Strategies

Lachner, Rainer; Breitner, Michael H.; Pesch, Hans Josef

doi:10.1007/978-1-4612-1336-9_6

Cited by 8 publications

(9 citation statements)

References 20 publications

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“…promising for complex dynamic game problems, see also B. (2000), B. et al (2001) and Lachner et al (2000). Four important approaches are outlined, compared and discussed.…”

Section: Discussionmentioning

confidence: 99%

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Coarse-Grained Parallelization of the Advanced Neurosimulator Faun 1.0 With PVM and the Enhanced Cornered Rat Game Revisited

Mettenheim

Breitner

2005

Int. Game Theory Rev.

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Today artificial neural networks are very useful to solve complex dynamic games of various types, i.e., to approximate optimal strategies with sufficient accuracy. Exemplarily four synthesis approaches for the solution of zero-sum, noncooperative dynamic games are outlined and discussed. Either value function, adjoint vector components or optimal strategies can be synthesized as functions of the state variables. In principle all approaches enable the solution of dynamic games. Nevertheless every approach has advantages and disadvantages which are discussed. The neural network training usually is very difficult and computationally very expensive. The coarse-grained parallelization FAUN 1.0-HPC-PVM of the advanced neurosimulator FAUN uses PVM subroutines and runs on heterogeneous and decentralized networks interconnecting general-purpose workstations, PCs and also high-performance computers. Computing times of days, weeks or months can be cut down to hours. An enhanced cornered rat game -formulated and analyzed in 1993 -serves as an example. Optimal strategies for cat and rat are synthesized. For this purpose open-loop representations of optimal strategies on an equidistant grid in the state space are used. An important end game modification is presented.

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“…promising for complex dynamic game problems, see also B. (2000), B. et al (2001) and Lachner et al (2000). Four important approaches are outlined, compared and discussed.…”

Section: Discussionmentioning

confidence: 99%

“…(1996), B. (1994), B. et al (2001), B. et al (2000), Järmark and Bengtsson (1989), Lachner et al (2000), Shinar (1991) and Siemens AG et al (1998).…”

Section: Introductionmentioning

confidence: 99%

Coarse-Grained Parallelization of the Advanced Neurosimulator Faun 1.0 With PVM and the Enhanced Cornered Rat Game Revisited

Mettenheim

Breitner

2005

Int. Game Theory Rev.

Self Cite

View full text Add to dashboard Cite

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“…With this assumption (which still eludes any rigorous mathematical proof), the optimal open-loop representations (u * P , u * E ) of the closed-loop strategies are introduced as It is worth remarking that the determination of open-loop representations is relevant for zero-sum games, because it represents an essential premise for the successive synthesis of feedback strategies. Pesch et al [19], Breitner and Pesch [20], and Lachner et al [21] computed a relevant number of open-loop solutions and employed them for the synthesis of feedback strategies by means of special techniques (e.g., with the use of neural networks).…”

Section: Formulation Of the Zero-sum Dynamic Gamementioning

confidence: 99%

Numerical Solution of Orbital Combat Games Involving Missiles and Spacecraft

Pontani

2011

Dyn Games Appl

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“…On an abstract level, the guidance of cooperative vehicles can be related to problems in game theory, namely, cooperative, antagonistic, and Stackelberg (follower‐leader) games. Antagonistic games are primarily used for worst‐case scenarios. Since they result in rather pessimistic strategies, they are not used for modeling cooperative vehicles in road traffic.…”

Section: Introductionmentioning

confidence: 99%

A generalized Nash equilibrium approach for optimal control problems of autonomous cars

Dreves

Gerdts

2017

Optim Control Appl Methods

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SummaryWe consider optimal control problems with ordinary differential equations that are coupled by shared, possibly nonconvex, constraints. For these problems, we use the generalized Nash equilibrium approach and provide a reformulation of normalized Nash equilibria as solutions to a single optimal control problem. By this reformulation, we are able to prove existence, and in some settings, exploiting convexity properties, we also get a limited number or even uniqueness of the normalized Nash equilibria. Then, we use our approach to discuss traffic scenarios with several autonomous vehicles, whose dynamics is described through differential equations, and the avoidance of collisions couples the optimal control problems of the vehicles. For the solution to the discretized problems, we prove strong convergence of the states and weak convergence of the controls. Finally, using existing optimal control software, we show that the generalized Nash equilibrium approach leads to reasonable results for a crossing scenario with different vehicle models. KEYWORDS autonomous vehicles, existence of an equilibrium, generalized Nash equilibrium problem, optimal control, ordinary differential equations, traffic scenarios

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Real-Time Collision Avoidance: Differential Game, Numerical Solution, and Synthesis of Strategies

Cited by 8 publications

References 20 publications

Coarse-Grained Parallelization of the Advanced Neurosimulator Faun 1.0 With PVM and the Enhanced Cornered Rat Game Revisited

Coarse-Grained Parallelization of the Advanced Neurosimulator Faun 1.0 With PVM and the Enhanced Cornered Rat Game Revisited

Numerical Solution of Orbital Combat Games Involving Missiles and Spacecraft

A generalized Nash equilibrium approach for optimal control problems of autonomous cars

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