# LUCIDGames: Online Unscented Inverse Dynamic Games for Adaptive Trajectory Prediction and Planning

arXiv: https://arxiv.org/abs/2011.08152 · HTML: https://mlsanity.com/paper/2011.08152/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2020.

## Built on by (most cited first, 17 of 17)

- [UMBRELLA: Uncertainty-Aware Model-Based Offline Reinforcement Learning Leveraging Planning](https://mlsanity.com/paper/2111.11097/) (2021)
- [Individual-Level Inverse Reinforcement Learning for Mean Field Games](https://mlsanity.com/paper/2202.06401/) (2022)
- [Energy-based Potential Games for Joint Motion Forecasting and Control](https://mlsanity.com/paper/2312.01811/) (2023)
- [Learning Interaction-aware Guidance Policies for Motion Planning in Dense Traffic Scenarios](https://mlsanity.com/paper/2107.04538/) (2021)
- [Blending Data-Driven Priors in Dynamic Games](https://mlsanity.com/paper/2402.14174/) (2024)
- [Multi-Agent Inverse Reinforcement Learning in Real World Unstructured Pedestrian Crowds](https://mlsanity.com/paper/2405.16439/) (2024)
- [On a Connection between Differential Games, Optimal Control, and Energy-based Models for Multi-Agent Interactions](https://mlsanity.com/paper/2308.16539/) (2023)
- [Auto-Encoding Bayesian Inverse Games](https://mlsanity.com/paper/2402.08902/) (2024)
- [Mixed Strategy Nash Equilibrium for Crowd Navigation](https://mlsanity.com/paper/2403.01537/) (2024)
- [Distributed Differentiable Dynamic Game for Multi-robot Coordination](https://mlsanity.com/paper/2207.08892/) (2022)
- [A Two-stage Based Social Preference Recognition in Multi-Agent Autonomous Driving System](https://mlsanity.com/paper/2310.03303/) (2023)
- [Constraint Learning in Multi-Agent Dynamic Games from Demonstrations of Local Nash Interactions](https://mlsanity.com/paper/2508.19945/) (2025)
- [NashFormer: Leveraging Local Nash Equilibria for Semantically Diverse Trajectory Prediction](https://mlsanity.com/paper/2305.17600/) (2023)
- [Online Parameter Identification of Generalized Non-cooperative Game](https://mlsanity.com/paper/2310.09511/) (2023)
- [Distributed Fractional Bayesian Learning for Adaptive Optimization](https://mlsanity.com/paper/2404.11354/) (2024)
- [PACE: A Framework for Learning and Control in Linear Incomplete-Information Differential Games](https://mlsanity.com/paper/2504.17128/) (2025)
- [Peer-Aware Cost Estimation in Nonlinear General-Sum Dynamic Games for Mutual Learning and Intent Inference](https://mlsanity.com/paper/2504.17129/) (2025)

## Abstract (arXiv)

Existing game-theoretic planning methods assume that the robot knows the objective functions of the other agents a priori while, in practical scenarios, this is rarely the case. This paper introduces LUCIDGames, an inverse optimal control algorithm that is able to estimate the other agents' objective functions in real time, and incorporate those estimates online into a receding-horizon game-theoretic planner. LUCIDGames solves the inverse optimal control problem by recasting it in a recursive parameter-estimation framework. LUCIDGames uses an unscented Kalman filter (UKF) to iteratively update a Bayesian estimate of the other agents' cost function parameters, improving that estimate online as more data is gathered from the other agents' observed trajectories. The planner then takes account of the uncertainty in the Bayesian parameter estimates of other agents by planning a trajectory for the robot subject to uncertainty ellipse constraints. The algorithm assumes no explicit communication or coordination between the robot and the other agents in the environment. An MPC implementation of LUCIDGames demonstrates real-time performance on complex autonomous driving scenarios with an update frequency of 40 Hz. Empirical results demonstrate that LUCIDGames improves the robot's performance over existing game-theoretic and traditional MPC planning approaches. Our implementation of LUCIDGames is available at https://github.com/RoboticExplorationLab/LUCIDGames.jl.