ALGAMES: A Fast Solver for Constrained Dynamic Games

Cleac’h, Simon Le; Schwager, Mac; Manchester, Zachary

doi:10.15607/rss.2020.xvi.091

Cited by 31 publications

(40 citation statements)

References 40 publications

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“…A similar iterative method was proposed in [21] for planning interactive trajectories in the presence of uncertainties where equilibria of risk-sensitive dynamic games were sought. In [22], a solver was developed for interactive trajectory planning in the presence of general nonlinear state and input constraints.…”

Section: B Approximate Solutions To Differential Gamesmentioning

confidence: 99%

“…Proof: We prove this by showing that under assumption (21), cost structures ( 13) and ( 14) satisfy the conditions ( 8) and ( 9) in Theorem 1. Let p, ands be defined as introduced in (22). For each agent i, we define the agentspecific term c i in (8) to be…”

Section: Interactive Trajectory Planningmentioning

confidence: 99%

“…Note that in the above, c i and s i are only a function of the states and inputs of agents other than agent i. Using the potential function (22) and the cost functions ( 23) and (24), it is easy to verify that for each agent i, we have…”

Section: Interactive Trajectory Planningmentioning

confidence: 99%

“…where the potential functions p ands are as defined in (22). The significance of this result is that now we can use standard single-agent trajectory optimization algorithms to solve (28).…”

Section: Interactive Trajectory Planningmentioning

confidence: 99%

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Potential iLQR: A Potential-Minimizing Controller for Planning Multi-Agent Interactive Trajectories

Kavuncu¹,

Ayberk²,

Mehr³

2021

Robotics: Science and Systems XVII

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Many robotic applications involve interactions between multiple agents where an agent's decisions affect the behavior of other agents. Such behaviors can be captured by the equilibria of differential games which provide an expressive framework for modeling the agents' mutual influence. However, finding the equilibria of differential games is in general challenging as it involves solving a set of coupled optimal control problems. In this work, we propose to leverage the special structure of multi-agent interactions to generate interactive trajectories by simply solving a single optimal control problem, namely, the optimal control problem associated with minimizing the potential function of the differential game. Our key insight is that for a certain class of multi-agent interactions, the underlying differential game is indeed a potential differential game for which equilibria can be found by solving a single optimal control problem. We introduce such an optimal control problem and build on single-agent trajectory optimization methods to develop a computationally tractable and scalable algorithm for planning multi-agent interactive trajectories. We will demonstrate the performance of our algorithm in simulation and show that our algorithm outperforms the state-of-the-art game solvers. To further show the real-time capabilities of our algorithm, we will demonstrate the application of our proposed algorithm in a set of experiments involving interactive trajectories for two quadcopters.

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Section: B Approximate Solutions To Differential Gamesmentioning

confidence: 99%

Section: Interactive Trajectory Planningmentioning

confidence: 99%

Section: Interactive Trajectory Planningmentioning

confidence: 99%

“…where the potential functions p ands are as defined in (22). The significance of this result is that now we can use standard single-agent trajectory optimization algorithms to solve (28).…”

Section: Interactive Trajectory Planningmentioning

confidence: 99%

See 2 more Smart Citations

Potential iLQR: A Potential-Minimizing Controller for Planning Multi-Agent Interactive Trajectories

Kavuncu¹,

Ayberk²,

Mehr³

2021

Robotics: Science and Systems XVII

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“…Coupled prediction and planning approaches explicitly capture the mutual dependencies between human and robot. An important body of work is game theoretic planning [13,7], these planners typically assume agent objectives are known, but recent works introduce online estimation of human agents' objectives [36,25]. Further, [36] uses the social value orientation (SVO) to quantify the degree of agents' selfishness or altruism.…”

Section: Related Workmentioning

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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Physical scene understanding

2024

AI Magazine

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Current AI systems still fail to match the flexibility, robustness, and generalizability of human intelligence: how even a young child can manipulate objects to achieve goals of their own invention or in cooperation, or can learn the essentials of a complex new task within minutes. We need AI with such embodied intelligence: transforming raw sensory inputs to rapidly build a rich understanding of the world for seeing, finding, and constructing things, achieving goals, and communicating with others. This problem of physical scene understanding is challenging because it requires a holistic interpretation of scenes, objects, and humans, including their geometry, physics, functionality, semantics, and modes of interaction, building upon studies across vision, learning, graphics, robotics, and AI. My research aims to address this problem by integrating bottom‐up recognition models, deep networks, and inference algorithms with top‐down structured graphical models, simulation engines, and probabilistic programs.

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ALGAMES: A Fast Solver for Constrained Dynamic Games

Cited by 31 publications

References 40 publications

Potential iLQR: A Potential-Minimizing Controller for Planning Multi-Agent Interactive Trajectories

Potential iLQR: A Potential-Minimizing Controller for Planning Multi-Agent Interactive Trajectories

Move Beyond Trajectories: Distribution Space Coupling for Crowd Navigation

Physical scene understanding

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