An Iterative Quadratic Method for General-Sum Differential Games with Feedback Linearizable Dynamics

TL;DR

This paper introduces an improved iterative quadratic method for solving general-sum differential games with feedback linearizable dynamics, enhancing convergence reliability and speed in real-time multi-agent motion planning.

Contribution

The paper develops a novel algorithm leveraging feedback linearizability to improve the efficiency and robustness of ILQ methods in multiplayer differential games.

Findings

Converges more reliably than previous methods.

Achieves faster convergence in traffic scenarios.

Demonstrates practical effectiveness in real-time applications.

Abstract

Iterative linear-quadratic (ILQ) methods are widely used in the nonlinear optimal control community. Recent work has applied similar methodology in the setting of multiplayer general-sum differential games. Here, ILQ methods are capable of finding local equilibria in interactive motion planning problems in real-time. As in most iterative procedures, however, this approach can be sensitive to initial conditions and hyperparameter choices, which can result in poor computational performance or even unsafe trajectories. In this paper, we focus our attention on a broad class of dynamical systems which are feedback linearizable, and exploit this structure to improve both algorithmic reliability and runtime. We showcase our new algorithm in three distinct traffic scenarios, and observe that in practice our method converges significantly more often and more quickly than was possible without exploiting the feedback linearizable structure.