Multimodal Maximum Entropy Dynamic Games

Oswin, So,; Kyle, Stachowicz,; Theodorou, Evangelos A.

doi:10.48550/arxiv.2201.12925

Cited by 3 publications

(2 citation statements)

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“…The proposed equilibrium formula also enables inverse inference of interaction policy from observations. In [62], [63], the multi-modality in stochastic games is investigated from the perspective of linear-quadratic games and partially observable Markov decision process (POMDP). In [64], an explicit mixed-strategy game formula is proposed, allowing agents to simultaneously optimize for multi-agent pure-strategies, but this formula does not recover the mixed-strategy Nash equilibrium.…”

Section: Game-theoretic Planningmentioning

confidence: 99%

Move Beyond Trajectories: Distribution Space Coupling for Crowd Navigation

Sun¹,

Baldini²,

Trautman³

et al. 2021

Robotics: Science and Systems XVII

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Cooperatively avoiding collision is a critical functionality for robots navigating in dense human crowds, failure of which could lead to either overaggressive or overcautious behavior. A necessary condition for cooperative collision avoidance is to couple the prediction of the agents' trajectories with the planning of the robot's trajectory. However, it is unclear that trajectory based cooperative collision avoidance captures the correct agent attributes. In this work we migrate from trajectory based coupling to a formalism that couples agent preference distributions. In particular, we show that preference distributions (probability density functions representing agents' intentions) can capture higher order statistics of agent behaviors, such as willingness to cooperate. Thus, coupling in distribution space exploits more information about inter-agent cooperation than coupling in trajectory space. We thus introduce a general objective for coupled prediction and planning in distribution space, and propose an iterative best response optimization method based on variational analysis with guaranteed sufficient decrease. Based on this analysis, we develop a sampling-based motion planning framework called DistNav 1 that runs in real time on a laptop CPU. We evaluate our approach on challenging scenarios from both real world datasets and simulation environments, and benchmark against a wide variety of model based and machine learning based approaches. The safety and efficiency statistics of our approach outperform all other models. Finally, we find that DistNav is competitive with human safety and efficiency performance.

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Section: Game-theoretic Planningmentioning

confidence: 99%

Move Beyond Trajectories: Distribution Space Coupling for Crowd Navigation

Sun¹,

Baldini²,

Trautman³

et al. 2021

Robotics: Science and Systems XVII

View full text Add to dashboard Cite

show abstract

“…Several extensions for handling control and/or state constraints with DDP can be found in [23]- [30]. Game theoretic DDP-based methods for multi-agent settings have been presented in [31], [32].…”

Section: Introductionmentioning

confidence: 99%

Distributed Differential Dynamic Programming Architectures for Large-Scale Multi-Agent Control

D.¹,

Aoyama²,

Zhu³

et al. 2022

Preprint

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In this paper, we propose two novel decentralized optimization frameworks for multi-agent nonlinear optimal control problems in robotics. The aim of this work is to suggest architectures that inherit the computational efficiency and scalability of Differential Dynamic Programming (DDP) and the distributed nature of the Alternating Direction Method of Multipliers (ADMM). In this direction, two frameworks are introduced. The first one called Nested Distributed DDP (ND-DDP), is a three-level architecture which employs ADMM for enforcing a consensus between all agents, an Augmented Lagrangian layer for satisfying local constraints and DDP as each agent's optimizer. In the second approach, both consensus and local constraints are handled with ADMM, yielding a two-level architecture called Merged Distributed DDP (MD-DDP), which further reduces computational complexity. Both frameworks are fully decentralized since all computations are parallelizable among the agents and only local communication is necessary. Simulation results that scale up to thousands of vehicles and hundreds of drones verify the effectiveness of the methods. Superior scalability to large-scale systems against centralized DDP and centralized/decentralized sequential quadratic programming is also illustrated. Finally, hardware experiments on a multi-robot platform demonstrate the applicability of the proposed algorithms, while highlighting the importance of optimizing for feedback policies to increase robustness against uncertainty. A video including all results is available here https://youtu.be/tluvENcWldw.

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Mixed strategy Nash equilibrium for crowd navigation

Muchen Sun,

Baldini,

Hughes

et al. 2024

The International Journal of Robotics Research

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Robots navigating in crowded areas should negotiate free space with humans rather than fully controlling collision avoidance, as this can lead to freezing behavior. Game theory provides a framework for the robot to reason about potential cooperation from humans for collision avoidance during path planning. In particular, the mixed strategy Nash equilibrium captures the negotiation behavior under uncertainty, making it well suited for crowd navigation. However, computing the mixed strategy Nash equilibrium is often prohibitively expensive for real-time decision-making. In this paper, we propose an iterative Bayesian update scheme over probability distributions of trajectories. The algorithm simultaneously generates a stochastic plan for the robot and probabilistic predictions of other pedestrians’ paths. We prove that the proposed algorithm is equivalent to solving a mixed strategy game for crowd navigation, and the algorithm guarantees the recovery of the global Nash equilibrium of the game. We name our algorithm Bayesian Recursive Nash Equilibrium (BRNE) and develop a real-time model prediction crowd navigation framework. Since BRNE is not solving a general-purpose mixed strategy Nash equilibrium but a tailored formula specifically for crowd navigation, it can compute the solution in real-time on a low-power embedded computer. We evaluate BRNE in both simulated environments and real-world pedestrian datasets. BRNE consistently outperforms non-learning and learning-based methods regarding safety and navigation efficiency. It also reaches human-level crowd navigation performance in the pedestrian dataset benchmark. Lastly, we demonstrate the practicality of our algorithm with real humans on an untethered quadruped robot with fully onboard perception and computation.

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Multimodal Maximum Entropy Dynamic Games

Cited by 3 publications

References 0 publications

Move Beyond Trajectories: Distribution Space Coupling for Crowd Navigation

Move Beyond Trajectories: Distribution Space Coupling for Crowd Navigation

Distributed Differential Dynamic Programming Architectures for Large-Scale Multi-Agent Control

Mixed strategy Nash equilibrium for crowd navigation

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