Lasse Peters

Andrei-Carlo Papuc, Lasse Peters, Sihao Sun et al.

Autonomous drone racing pushes the boundaries of high-speed motion planning and multi-agent strategic decision-making. Success in this domain requires drones not only to navigate at their limits but also to anticipate and counteract competitors' actions. In this paper, we study a fundamental question that arises in this domain: how deeply should an agent strategize before taking an action? To this end, we compare two planning paradigms: the Model Predictive Game (MPG), which finds interaction-aware strategies at the expense of longer computation times, and contouring Model Predictive Control (MPC), which computes strategies rapidly but does not reason about interactions. We perform extensive experiments to study this trade-off, revealing that MPG outperforms MPC at moderate velocities but loses its advantage at higher speeds due to latency. To address this shortcoming, we propose a Learned Model Predictive Game (LMPG) approach that amortizes model predictive gameplay to reduce latency. In both simulation and hardware experiments, we benchmark our approach against MPG and MPC in head-to-head races, finding that LMPG outperforms both baselines.

Yash Jain, Xinjie Liu, Lasse Peters et al.

Many multi-agent interaction scenarios can be naturally modeled as noncooperative games, where each agent's decisions depend on others' future actions. However, deploying game-theoretic planners for autonomous decision-making requires a specification of all agents' objectives. To circumvent this practical difficulty, recent work develops maximum likelihood techniques for solving inverse games that can identify unknown agent objectives from interaction data. Unfortunately, these methods only infer point estimates and do not quantify estimator uncertainty; correspondingly, downstream planning decisions can overconfidently commit to unsafe actions. We present an approximate Bayesian inference approach for solving the inverse game problem, which can incorporate observation data from multiple modalities and be used to generate samples from the Bayesian posterior over the hidden agent objectives given limited sensor observations in real time. Concretely, the proposed Bayesian inverse game framework trains a structured variational autoencoder with an embedded differentiable Nash game solver on interaction datasets and does not require labels of agents' true objectives. Extensive experiments show that our framework successfully learns prior and posterior distributions, improves inference quality over maximum likelihood estimation-based inverse game approaches, and enables safer downstream decision-making without sacrificing efficiency. When trajectory information is uninformative or unavailable, multimodal inference further reduces uncertainty by exploiting additional observation modalities.

Mohammed Irshadh Ismaaeel Sathyamangalam Imran, Lasse Peters, Michael Khayyat et al.

We address the multi-agent motion planning problem where interactions, collisions, and congestion co-exist. Conventional game-theoretic planners capture interactions among agents but often converge to conservative, congested equilibria. Homotopy planners, on the other hand, can explore topologically distinct paths, but lack mechanisms to account for the interdependence of agents' future actions. We propose a unified framework that leverages homotopy classes as structured strategy sets within a receding-horizon setup. At each planning stage, a deterministic homotopy planner generates topologically distinct paths for each agent, conditioned on the joint configuration. To avoid intractable growth of candidate paths, we propose a simple heuristic filtering step that selects a top-$K$ subset of the most suitable congestion-free joint strategies to ensure computational tractability. These serve as initializations for a potential game that enforces homotopy-consistent constraints and yields a generalized open-loop Nash equilibrium (OLNE), with penalties discouraging abrupt strategy shifts in a receding-horizon setting. Simulations with three agents demonstrate improved efficiency (faster completion) and enhanced safety (greater inter-agent clearance, leading to reduced congestion) compared to a local baseline and NH-ORCA that do not reason about homotopies. Hardware trials with two robots and one human demonstrate robustness to irrational behaviors, where our method adapts by switching to alternative feasible equilibria while the baseline game fails.

Dong Ho Lee, Jingqi Li, Lasse Peters et al.

Games of ordered preference (GOOPs) model multi-player equilibrium problems in which each player maintains a distinct hierarchy of strictly prioritized objectives. Existing approaches solve GOOPs by deriving and enforcing the necessary optimality conditions that characterize lexicographically constrained Nash equilibria through a single-level reformulation. However, the number of primal and dual variables in the resulting KKT system grows exponentially with the number of preference levels, leading to severe scalability challenges. We derive a compact reformulation of these necessary conditions that preserves the essential primal stationarity structure across hierarchy levels, yielding a "reduced" KKT system whose size grows polynomially with both the number of players and the number of preference levels. The reduced system constitutes a relaxation of the complete KKT system, yet it remains a valid necessary condition for local GOOP equilibria. For GOOPs with quadratic objectives and linear constraints, we prove that the primal solution sets of the reduced and complete KKT systems coincide. More generally, for GOOPs with arbitrary (but smooth) nonlinear objectives and constraints, the reduced KKT conditions recover all local GOOP equilibria but may admit spurious non-equilibrium solutions. We introduce a second-order sufficient condition to certify when a candidate point corresponds to a local GOOP equilibrium. We also develop a primal-dual interior-point method for computing a local GOOP equilibrium with local quadratic convergence. The resulting framework enables scalable and efficient computation of GOOP equilibria beyond the tractable range of existing exponentially complex formulations.

Lasse Peters, Laura Ferranti, Javier Alonso-Mora et al.

Imitation learning powered by generative models has proven effective for modeling complex single-agent behaviors. However, teaching multi-agent systems, like multiple arms or vehicles, to coordinate through imitation learning is hindered by a fundamental data bottleneck: as the joint state-action space grows exponentially with the number of agents, collecting a sufficient amount of coordinated multi-agent demonstrations becomes extremely costly. In this work, we ask: how can we leverage single-agent demonstration data to learn multi-agent policies? We present Coordinated Diffusion (CoDi), a framework that couples independently trained single-agent diffusion policies through a user-defined multi-agent cost function, without requiring any coordinated demonstrations. We derive a new diffusion-based sampling scheme wherein the diffusion score function decomposes into independent, single-agent pre-trained base policies plus a cost-driven guidance term that coordinates these base policies into cohesive multi-agent behavior. We show that this guidance term can be estimated in a gradient-free manner, making CoDi applicable to black-box, non-differentiable cost functions without additional training. Theoretically and empirically, we analyze the conditions under which this composition can faithfully approximate a target multi-agent behavior. We find a complementary role for demonstration data versus the cost function: single-agent demonstrations must cover the support of the desired multi-agent behavior, while the cost function must promote desired behavior from this product of single-agent policies. Our results in simulation and hardware experiments of a two-arm manipulation task show that CoDi discovers robust coordinated behavior from single-agent data, is more data-efficient than multi-agent baselines, and highlights the importance of joint guidance, base policy support, and cost design.

Pau de las Heras Molins, Beyazit Yalcinkaya, Lasse Peters et al.

Multi-objective reinforcement learning (MORL) allows a user to express preference over outcomes in terms of the relative importance of the objectives, but standard metrics cannot capture whether changes in preference reliably change the agent's behavior in the intended way, a property termed controllability. As a result, preference-conditioned agents can score well on standard MORL metrics while being insensitive to the preference input. If the ability to control agents cannot be reliably assessed, the symbolic interface that MORL provides between user intent and agent behavior is broken. Mainstream MORL metrics alone fail to measure the controllability of preference-conditioned agents, motivating a complementary metric specifically designed to that end. We hope the results spur discussion in the community on existing evaluation protocols to consolidate advances in preference adaptation in MORL to larger and more complex problems.

Kensuke Nakamura, Lasse Peters, Andrea Bajcsy

Hamilton-Jacobi (HJ) reachability is a rigorous mathematical framework that enables robots to simultaneously detect unsafe states and generate actions that prevent future failures. While in theory, HJ reachability can synthesize safe controllers for nonlinear systems and nonconvex constraints, in practice, it has been limited to hand-engineered collision-avoidance constraints modeled via low-dimensional state-space representations and first-principles dynamics. In this work, our goal is to generalize safe robot controllers to prevent failures that are hard--if not impossible--to write down by hand, but can be intuitively identified from high-dimensional observations: for example, spilling the contents of a bag. We propose Latent Safety Filters, a latent-space generalization of HJ reachability that tractably operates directly on raw observation data (e.g., RGB images) to automatically compute safety-preserving actions without explicit recovery demonstrations by performing safety analysis in the latent embedding space of a generative world model. Our method leverages diverse robot observation-action data of varying quality (including successes, random exploration, and unsafe demonstrations) to learn a world model. Constraint specification is then transformed into a classification problem in the latent space of the learned world model. In simulation and hardware experiments, we compute an approximation of Latent Safety Filters to safeguard arbitrary policies (from imitation- learned policies to direct teleoperation) from complex safety hazards, like preventing a Franka Research 3 manipulator from spilling the contents of a bag or toppling cluttered objects.

Xinjie Liu, Lasse Peters, Javier Alonso-Mora et al.

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, agents typically do not have access to a complete model of the game, e.g., due to unknown objectives of other players. Therefore, we consider the inverse game problem, in which some properties of the game are unknown a priori and must be inferred from observations. Existing maximum likelihood estimation (MLE) approaches to solve inverse games provide only point estimates of unknown parameters without quantifying uncertainty, and perform poorly when many parameter values explain the observed behavior. To address these limitations, we take a Bayesian perspective and construct posterior distributions of game parameters. To render inference tractable, we employ a variational autoencoder (VAE) with an embedded differentiable game solver. This structured VAE can be trained from an unlabeled dataset of observed interactions, naturally handles continuous, multi-modal distributions, and supports efficient sampling from the inferred posteriors without computing game solutions at runtime. Extensive evaluations in simulated driving scenarios demonstrate that the proposed approach successfully learns the prior and posterior game parameter distributions, provides more accurate objective estimates than MLE baselines, and facilitates safer and more efficient game-theoretic motion planning.

Lasse Peters, David Fridovich-Keil, Vicenç Rubies-Royo et al.

Robots and autonomous systems must interact with one another and their environment to provide high-quality services to their users. Dynamic game theory provides an expressive theoretical framework for modeling scenarios involving multiple agents with differing objectives interacting over time. A core challenge when formulating a dynamic game is designing objectives for each agent that capture desired behavior. In this paper, we propose a method for inferring parametric objective models of multiple agents based on observed interactions. Our inverse game solver jointly optimizes player objectives and continuous-state estimates by coupling them through Nash equilibrium constraints. Hence, our method is able to directly maximize the observation likelihood rather than other non-probabilistic surrogate criteria. Our method does not require full observations of game states or player strategies to identify player objectives. Instead, it robustly recovers this information from noisy, partial state observations. As a byproduct of estimating player objectives, our method computes a Nash equilibrium trajectory corresponding to those objectives. Thus, it is suitable for downstream trajectory forecasting tasks. We demonstrate our method in several simulated traffic scenarios. Results show that it reliably estimates player objectives from a short sequence of noise-corrupted partial state observations. Furthermore, using the estimated objectives, our method makes accurate predictions of each player's trajectory.

Lasse Peters, David Fridovich-Keil, Claire J. Tomlin et al.

In many settings where multiple agents interact, the optimal choices for each agent depend heavily on the choices of the others. These coupled interactions are well-described by a general-sum differential game, in which players have differing objectives, the state evolves in continuous time, and optimal play may be characterized by one of many equilibrium concepts, e.g., a Nash equilibrium. Often, problems admit multiple equilibria. From the perspective of a single agent in such a game, this multiplicity of solutions can introduce uncertainty about how other agents will behave. This paper proposes a general framework for resolving ambiguity between equilibria by reasoning about the equilibrium other agents are aiming for. We demonstrate this framework in simulations of a multi-player human-robot navigation problem that yields two main conclusions: First, by inferring which equilibrium humans are operating at, the robot is able to predict trajectories more accurately, and second, by discovering and aligning itself to this equilibrium the robot is able to reduce the cost for all players.

David Fridovich-Keil, Ellis Ratner, Lasse Peters et al.

Many problems in robotics involve multiple decision making agents. To operate efficiently in such settings, a robot must reason about the impact of its decisions on the behavior of other agents. Differential games offer an expressive theoretical framework for formulating these types of multi-agent problems. Unfortunately, most numerical solution techniques scale poorly with state dimension and are rarely used in real-time applications. For this reason, it is common to predict the future decisions of other agents and solve the resulting decoupled, i.e., single-agent, optimal control problem. This decoupling neglects the underlying interactive nature of the problem; however, efficient solution techniques do exist for broad classes of optimal control problems. We take inspiration from one such technique, the iterative linear-quadratic regulator (ILQR), which solves repeated approximations with linear dynamics and quadratic costs. Similarly, our proposed algorithm solves repeated linear-quadratic games. We experimentally benchmark our algorithm in several examples with a variety of initial conditions and show that the resulting strategies exhibit complex interactive behavior. Our results indicate that our algorithm converges reliably and runs in real-time. In a three-player, 14-state simulated intersection problem, our algorithm initially converges in < 0.25s. Receding horizon invocations converge in < 50 ms in a hardware collision-avoidance test.