Barrier States Embedded Iterative Dynamic Game for Robust and Safe Trajectory Optimization

TL;DR

This paper introduces a novel trajectory optimization method that integrates barrier states into a differential game framework to ensure safety and robustness in uncertain, safety-critical control systems, demonstrated on pendulum and quadrotor models.

Contribution

It develops a game-theoretic differential dynamic programming approach with barrier states and a Stackleberg line-search strategy for robust, safe trajectory optimization under uncertainties.

Findings

Effective in high-uncertainty scenarios

Ensures safety constraints through barrier states

Successful implementation on quadrotor in windy conditions

Abstract

Considering uncertainties and disturbances is an important, yet challenging, step in successful decision making. The problem becomes more challenging in safety-constrained environments. In this paper, we propose a robust and safe trajectory optimization algorithm through solving a constrained min-max optimal control problem. The proposed method leverages a game theoretic differential dynamic programming approach with barrier states to handle parametric and non-parametric uncertainties in safety-critical control systems. Barrier states are embedded into the differential game's dynamics and cost to portray the constrained environment in a higher dimensional state space and certify the safety of the optimized trajectory. Moreover, to find a convergent optimal solution, we propose to perform line-search in a Stackleberg (leader-follower) game fashion instead of picking a constant learning rate. The proposed algorithm is evaluated on a velocity-constrained inverted pendulum model in a moderate and high parametric uncertainties to show its efficacy in such a comprehensible system. The algorithm is subsequently implemented on a quadrotor in a windy environment in which sinusoidal wind turbulences applied in all directions.