Local First-Order Algorithms for Constrained Nonlinear Dynamic Games

Di, Bolei; Lamperski, Andrew

doi:10.23919/acc45564.2020.9147602

Cited by 13 publications

(11 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Nash equilibria have been investigated in [4,5,8,14,15,16,17]. We also take the approach of searching for Nash Fig.…”

Section: A Equilibrium Selectionmentioning

confidence: 99%

“…This behavior can be overly aggressive for the leader (or overly passive for the follower) and does not capture the game-theoretic nature of the problem. Nash equilibria have been investigated in [4], [5], [8], [13], [14], [15], [16]. We also take the approach of searching for Nash equilibria, as this type of equilibrium seems better suited to symmetric, multi-robot interaction scenarios.…”

Section: Equilibrium Selectionmentioning

confidence: 99%

“…Finally, algorithms that are analogous to direct methods in trajectory optimization have also been developed [15], [16]. An algorithm based on a first-order splitting method that is known to have a linear convergence rate was proposed by Di et al [16]. Di's experiments show convergence of the algorithm after typically 10 3 to 10 4 iterations.…”

Section: Game-theoretic Trajectory Optimizationmentioning

confidence: 99%

See 2 more Smart Citations

ALGAMES: A Fast Solver for Constrained Dynamic Games

Cleac’h

Schwager

Manchester

2020

Robotics: Science and Systems XVI

View full text Add to dashboard Cite

Dynamic games are an effective paradigm for dealing with the control of multiple interacting actors. This paper introduces ALGAMES (Augmented Lagrangian GAME-theoretic Solver), a solver that handles trajectory optimization problems with multiple actors and general nonlinear state and input constraints. Its novelty resides in satisfying the first order optimality conditions with a quasi-Newton root-finding algorithm and rigorously enforcing constraints using an augmented Lagrangian formulation. We evaluate our solver in the context of autonomous driving on scenarios with a strong level of interactions between the vehicles. We assess the robustness of the solver using Monte Carlo simulations. It is able to reliably solve complex problems like ramp merging with three vehicles three times faster than a state-of-the-art DDP-based approach. A model predictive control (MPC) implementation of the algorithm, running at more than 60Hz, demonstrates ALGAMES' ability to mitigate the "frozen robot" problem on complex autonomous driving scenarios like merging onto a crowded highway.

show abstract

“…Nash equilibria have been investigated in [4,5,8,14,15,16,17]. We also take the approach of searching for Nash Fig.…”

Section: A Equilibrium Selectionmentioning

confidence: 99%

Section: Equilibrium Selectionmentioning

confidence: 99%

Section: Game-theoretic Trajectory Optimizationmentioning

confidence: 99%

See 1 more Smart Citation

ALGAMES: A Fast Solver for Constrained Dynamic Games

Cleac’h

Schwager

Manchester

2020

Robotics: Science and Systems XVI

View full text Add to dashboard Cite

show abstract

“…To this end, recent works have constructed solvers leveraging different assumptions and approximations to find local equilibria of a Generalized Nash Equilibrium Problem (GNEP) [15]. For instance, [11], [16] solve repeated quadratic games, [9] exploits an augmented Lagrangian approach, and [17] exploits the temporal structure in projected gradient and Douglas-Rachford splitting methods. The peculiarity of urban driving with shared and personal objectives enjoys a more favorable setup than general games (e.g., [18], [19]).…”

Section: Introductionmentioning

confidence: 99%

Urban Driving Games With Lexicographic Preferences and Socially Efficient Nash Equilibria

Zanardi

Mion

Bruschetta

et al. 2021

IEEE Robot. Autom. Lett.

View full text Add to dashboard Cite

We describe Urban Driving Games (UDGs) as a particular class of differential games that model the interactions and incentives of the urban driving task. The drivers possess a "communal" interest, such as not colliding with each other, but are also self-interested in fulfilling traffic rules and personal objectives. Subject to their physical dynamics, the preference of the agents is expressed via a lexicographic relation that puts as first priority the shared objective of not colliding. Under mild assumptions, we show that communal UDGs have the structure of a lexicographic ordinal potential game which allows us to prove several interesting properties. Namely, socially efficient equilibria can be found by solving a single (lexicographic) optimal control problem and iterated best response schemes have desirable convergence guarantees.

show abstract

“…Introduction. There has been a recent growing interest in the application of game-theoretic concepts to applications in automated systems, as explored in [12,19,3,2,8,9,4,7]. Indeed, numerous problems arising in these domains can be modeled as games, and particularly as dynamic or repeated games.…”

mentioning

confidence: 99%

The Computation of Approximate Generalized Feedback Nash Equilibria

Laine¹,

Fridovich-Keil²,

Chiu³

et al. 2021

Preprint

View full text Add to dashboard Cite

We present the concept of a Generalized Feedback Nash Equilibrium (GFNE) in dynamic games, extending the Feedback Nash Equilibrium concept to games in which players are subject to state and input constraints. We formalize necessary and sufficient conditions for (local) GFNE solutions at the trajectory level, which enable the development of efficient numerical methods for their computation. Specifically, we propose a Newton-style method for finding game trajectories which satisfy the necessary conditions, which can then be checked against the sufficiency conditions. We show that the evaluation of the necessary conditions in general requires computing a series of nested, implicitly-defined derivatives, which quickly becomes intractable. To this end, we introduce an approximation to the necessary conditions which is amenable to efficient evaluation, and in turn, computation of solutions. We term the solutions to the approximate necessary conditions Generalized Feedback Quasi Nash Equilibria (GFQNE), and we introduce numerical methods for their computation. In particular, we develop a Sequential Linear-Quadratic Game approach, in which a locally approximate LQ game is solved at each iteration. The development of this method relies on the ability to compute a GFNE to inequality-and equality-constrained LQ games, and therefore specific methods for the solution of these special cases are developed in detail. We demonstrate the effectiveness of the proposed solution approach on a dynamic game arising in an autonomous driving application.

show abstract

Local First-Order Algorithms for Constrained Nonlinear Dynamic Games

Cited by 13 publications

References 13 publications

ALGAMES: A Fast Solver for Constrained Dynamic Games

ALGAMES: A Fast Solver for Constrained Dynamic Games

Urban Driving Games With Lexicographic Preferences and Socially Efficient Nash Equilibria

The Computation of Approximate Generalized Feedback Nash Equilibria

Contact Info

Product

Resources

About