Optimal trajectory planning for autonomous driving integrating logical constraints: An MIQP perspective

Abstract

This paper considers the problem of optimal trajectory generation for autonomous driving under both continuous and logical constraints. Classical approaches based on continuous optimization formulate the trajectory generation problem as a nonlinear program, in which vehicle dynamics and obstacle avoidance requirements are enforced as nonlinear equality and inequality constraints. In general, gradient-based optimization methods are then used to find the optimal trajectory. However, these methods are ill-suited for logical constraints such as those raised by traffic rules, presence of obstacles and, more generally, to the existence of multiple maneuver variants. We propose a new formulation of the trajectory planning problem as a Mixed-Integer Quadratic Program. This formulation can be solved efficiently using widely available solvers, and the resulting trajectory is guaranteed to be globally optimal. We apply our framework to several scenarios that are still widely considered as challenging for autonomous driving, such as obstacle avoidance with multiple maneuver choices, overtaking with oncoming traffic or optimal lane-change decision making. Simulation results demonstrate the effectiveness of our approach and its real-time applicability.