A Real-Time Game Theoretic Planner for Autonomous Two-Player Drone Racing

In this article, we propose an online 3-D planning algorithm for a drone to race competitively against a single adversary drone. The algorithm computes an approximation of the Nash equilibrium in the joint space of trajectories of the two drones at each time step, and proceeds in a receding horizon fashion. The algorithm uses a novel sensitivity term, within an iterative best response computational scheme, to approximate the amount by which the adversary will yield to the ego drone to avoid a collision. This leads to racing trajectories that are more competitive than without the sensitivity term. We prove that the fixed point of this sensitivity enhanced iterative best response satisfies the first-order optimality conditions of a Nash equilibrium. We present results of a simulation study of races with 2-D and 3-D race courses, showing that our game theoretic planner significantly outperforms amodel predictive control (MPC) racing algorithm. We also present results of multiple drone racing experiments on a 3-D track in which drones sense each others'' relative position with onboard vision. The proposed game theoretic planner again outperforms the MPC opponent in these experiments where drones reach speeds up to 1.25m/s

GTP-SLAM: Game-Theoretic Priors for Simultaneous Localization and Mapping in Multi-Agent Scenarios

Robots operating in complex, multi-player settings must simultaneously model the environment and the behavior of human or robotic agents who share that environment. Environmental modeling is often approached using Simultaneous Localization and Mapping (SLAM) techniques; however, SLAM algorithms usually neglect multi-player interactions. In contrast, a recent branch of the motion planning literature uses dynamic game theory to explicitly model noncooperative interactions of multiple agents in a known environment with perfect localization. In this work, we fuse ideas from these disparate communities to solve SLAM problems with game theoretic priors. We present GTP-SLAM, a novel, iterative best response-based SLAM algorithm that accurately performs state localization and map reconstruction in an uncharted scene, while capturing the inherent game-theoretic interactions among multiple agents in that scene. By formulating the underlying SLAM problem as a potential game, we inherit a strong convergence guarantee. Empirical results indicate that, when deployed in a realistic traffic simulation, our approach performs localization and mapping more accurately than a standard bundle adjustment algorithm across a wide range of noise levels.Comment: 6 pages, 3 figure

ALGAMES: A Fast Solver for Constrained Dynamic Games

Dynamic games are an effective paradigm for dealing with the control of multiple interacting actors. This paper introduces ALGAMES (Augmented Lagrangian GAME-theoretic Solver), a solver that handles trajectory optimization problems with multiple actors and general nonlinear state and input constraints. Its novelty resides in satisfying the first order optimality conditions with a quasi-Newton root-finding algorithm and rigorously enforcing constraints using an augmented Lagrangian formulation. We evaluate our solver in the context of autonomous driving on scenarios with a strong level of interactions between the vehicles. We assess the robustness of the solver using Monte Carlo simulations. It is able to reliably solve complex problems like ramp merging with three vehicles three times faster than a state-of-the-art DDP-based approach. A model predictive control (MPC) implementation of the algorithm demonstrates real-time performance on complex autonomous driving scenarios with an update frequency higher than 60 Hz.Comment: 10 pages, 8 figures, submitted to Robotics: Science and Systems Conference (RSS) 202

A Sequential Quadratic Programming Approach to the Solution of Open-Loop Generalized Nash Equilibria

Dynamic games can be an effective approach to modeling interactive behavior between multiple non-cooperative agents and they provide a theoretical framework for simultaneous prediction and control in such scenarios. In this work, we propose a numerical method for the solution of local generalized Nash equilibria (GNE) for the class of open-loop general-sum dynamic games for agents with nonlinear dynamics and constraints. In particular, we formulate a sequential quadratic programming (SQP) approach which requires only the solution of a single convex quadratic program at each iteration. Central to the robustness of our approach is a non-monotonic line search method and a novel merit function for SQP step acceptance. We show that our method achieves linear convergence in the neighborhood of local GNE and we derive an update rule for the merit function which helps to improve convergence from a larger set of initial conditions. We demonstrate the effectiveness of the algorithm in the context of car racing, where we show up to 32\% improvement of success rate when comparing against a state-of-the-art solution approach for dynamic games. \url{https://github.com/zhu-edward/DGSQP}

Game-theoretic Objective Space Planning

Autonomous Racing awards agents that react to opponents' behaviors with agile maneuvers towards progressing along the track while penalizing both over-aggressive and over-conservative agents. Understanding the intent of other agents is crucial to deploying autonomous systems in adversarial multi-agent environments. Current approaches either oversimplify the discretization of the action space of agents or fail to recognize the long-term effect of actions and become myopic. Our work focuses on addressing these two challenges. First, we propose a novel dimension reduction method that encapsulates diverse agent behaviors while conserving the continuity of agent actions. Second, we formulate the two-agent racing game as a regret minimization problem and provide a solution for tractable counterfactual regret minimization with a regret prediction model. Finally, we validate our findings experimentally on scaled autonomous vehicles. We demonstrate that using the proposed game-theoretic planner using agent characterization with the objective space significantly improves the win rate against different opponents, and the improvement is transferable to unseen opponents in an unseen environment.Comment: Submitted to 2023 IEEE International Conference on Robotics and Automation (ICRA 2023

Winning the 3rd Japan Automotive AI Challenge -- Autonomous Racing with the Autoware.Auto Open Source Software Stack

The 3rd Japan Automotive AI Challenge was an international online autonomous racing challenge where 164 teams competed in December 2021. This paper outlines the winning strategy to this competition, and the advantages and challenges of using the Autoware.Auto open source autonomous driving platform for multi-agent racing. Our winning approach includes a lane-switching opponent overtaking strategy, a global raceline optimization, and the integration of various tools from Autoware.Auto including a Model-Predictive Controller. We describe the use of perception, planning and control modules for high-speed racing applications and provide experience-based insights on working with Autoware.Auto. While our approach is a rule-based strategy that is suitable for non-interactive opponents, it provides a good reference and benchmark for learning-enabled approaches.Comment: Accepted at Autoware Workshop at IV 202