Many problems in robotics involve multiple decision making agents. To operate efficiently such settings, a robot must reason about the impact of its decisions on behavior other Differential games offer an expressive theoretical framework for formulating these types multi-agent problems. Unfortunately, most numerical solution techniques scale poorly with state dimension and are rarely used real-time applications. For this reason, it is common to predict future agents solve resulting...

Contingency planning, wherein an agent generates a set of possible plans conditioned on the outcome uncertain event, is increasingly popular way for robots to act under uncertainty. In this work we take game-theoretic perspective contingency tailored multi-agent scenarios in which robot's actions impact decisions other agents and vice versa. The resulting <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">contingency game</i> allows robot...

Hamilton-Jacobi (HJ) reachability is a rigorous mathematical framework that enables robots to simultaneously detect unsafe states and generate actions prevent future failures. While in theory, HJ can synthesize safe controllers for nonlinear systems nonconvex constraints, practice, it has been limited hand-engineered collision-avoidance constraints modeled via low-dimensional state-space representations first-principles dynamics. In this work, our goal generalize robot failures are hard --...

Many autonomous agents, such as intelligent vehicles, are inherently required to interact with one another. Game theory provides a natural mathematical tool for robot motion planning in interactive settings. However, tractable algorithms problems usually rely on strong assumption, namely that the objectives of all players scene known. To make tools applicable ego-centric only local information, we propose an adaptive model-predictive game solver, which jointly infers other players' online...

Robots and autonomous systems must interact with one another their environment to provide high-quality services users.Dynamic game theory provides an expressive theoretical framework for modeling scenarios involving multiple agents differing objectives interacting over time.A core challenge when formulating a dynamic is designing each agent that capture desired behavior.In this paper, we propose method inferring parametric objective models of based on observed interactions.Our inverse solver...

Robots deployed to the real world must be able interact with other agents in their environment. Dynamic game theory provides a powerful mathematical framework for modeling scenarios which have individual objectives and interactions evolve over time. However, key limitation of such techniques is that they require priori knowledge all players’ objectives. In this work, we address issue by proposing novel method learning continuous dynamic games from noise-corrupted, partial state observations....

In many settings where multiple agents interact, the optimal choices for each agent depend heavily on of others. These coupled interactions are well-described by a general-sum differential game, in which players have differing objectives, state evolves continuous time, and play may be characterized one equilibrium concepts, e.g., Nash equilibrium. Often, problems admit equilibria. From perspective single such this multiplicity solutions can introduce uncertainty about how other will behave....

In multi-agent settings, game theory is a natural framework for describing the strategic interactions of agents whose objectives depend upon one another's behavior.Trajectory games capture these complex effects by design.In competitive this makes them more faithful interaction model than traditional "predict then plan" approaches.However, current game-theoretic planning methods have important limitations.In work, we propose two main contributions.First, introduce an offline training phase...

When multiple agents interact in a common environment, each agent's actions impact others' future decisions, and noncooperative dynamic games naturally capture this coupling. In interactive motion planning, however, typically do not have access to complete model of the game, e.g., due unknown objectives other players. Therefore, we consider inverse game problem, which some properties are priori must be inferred from observations. Existing maximum likelihood estimation (MLE) approaches solve...

Robots must operate safely when deployed in novel and human-centered environments, like homes. Current safe control approaches typically assume that the safety constraints are known a priori, thus, robot can pre-compute corresponding controller. While this may make sense for some (e.g., avoiding collision with walls by analyzing floor plan), other more complex spills), inherently personal, context-dependent, only be identified at deployment time is interacting specific environment person...

We study noncooperative games, in which each agent's objective is composed of a sequence ordered-and potentially conflicting-preferences. Problems this type naturally model wide variety scenarios: for example, drivers at busy intersection must balance the desire to make forward progress with risk collision. Mathematically, these problems possess nested structure, and behave properly agents prioritize their most important preference, only consider less preferences extent that they do not...

In many problems that involve multiple decision making agents, optimal choices for each agent depend on the of others. Differential game theory provides a principled formalism expressing these coupled interactions and recent work offers efficient approximations to solve non-cooperative equilibria. iLQGames.jl is framework designing solving differential games, built around iterative linear-quadratic method. It written in Julia programming language allow flexible prototyping integration with...

In multi-agent dynamic games, the Nash equilibrium state trajectory of each agent is determined by its cost function and information pattern game. However, may be unavailable to other agents. Prior work on using partial observations infer costs in games assumes an open-loop pattern. this work, we demonstrate that feedback concept more expressive encodes complex behavior. It desirable develop specific tools for inferring players' objectives games. Therefore, consider game inference problem...

Decision-making in multi-player games can be extremely challenging, particularly under uncertainty. In this work, we propose a new sample-based approximation to class of stochastic, general-sum, pure Nash games, where each player has an expected-value objective and set chance constraints. This scheme inherits the accuracy from established sample average (SAA) method enjoys feasibility guarantee derived scenario optimization literature. We characterize complexity game-theoretic scheme,...

Many problems in robotics involve multiple decision making agents. To operate efficiently such settings, a robot must reason about the impact of its decisions on behavior other Differential games offer an expressive theoretical framework for formulating these types multi-agent problems. Unfortunately, most numerical solution techniques scale poorly with state dimension and are rarely used real-time applications. For this reason, it is common to predict future agents solve resulting...

Robots deployed to the real world must be able interact with other agents in their environment. Dynamic game theory provides a powerful mathematical framework for modeling scenarios which have individual objectives and interactions evolve over time. However, key limitation of such techniques is that they require a-priori knowledge all players' objectives. In this work, we address issue by proposing novel method learning continuous dynamic games from noise-corrupted, partial state...

Decision-making in multi-player games can be extremely challenging, particularly under uncertainty. In this work, we propose a new sample-based approximation to class of stochastic, general-sum, pure Nash games, where each player has an expected-value objective and set chance constraints. This scheme inherits the accuracy from established sample average (SAA) method enjoys feasibility guarantee derived scenario optimization literature. We characterize complexity game-theoretic scheme,...

Contingency planning, wherein an agent generates a set of possible plans conditioned on the outcome uncertain event, is increasingly popular way for robots to act under uncertainty. In this work we take game-theoretic perspective contingency tailored multi-agent scenarios in which robot's actions impact decisions other agents and vice versa. The resulting game allows robot efficiently interact with by generating strategic motion multiple intents actors scene. games are parameterized via...

In multi-agent settings, game theory is a natural framework for describing the strategic interactions of agents whose objectives depend upon one another's behavior. Trajectory games capture these complex effects by design. competitive this makes them more faithful interaction model than traditional "predict then plan" approaches. However, current game-theoretic planning methods have important limitations. work, we propose two main contributions. First, introduce an offline training phase...

Many autonomous agents, such as intelligent vehicles, are inherently required to interact with one another. Game theory provides a natural mathematical tool for robot motion planning in interactive settings. However, tractable algorithms problems usually rely on strong assumption, namely that the objectives of all players scene known. To make tools applicable ego-centric only local information, we propose an adaptive model-predictive game solver, which jointly infers other players' online...

Robots and autonomous systems must interact with one another their environment to provide high-quality services users. Dynamic game theory provides an expressive theoretical framework for modeling scenarios involving multiple agents differing objectives interacting over time. A core challenge when formulating a dynamic is designing each agent that capture desired behavior. In this paper, we propose method inferring parametric objective models of based on observed interactions. Our inverse...