Practical Search Techniques in Path Planning for Autonomous Driving

We describe a practical path-planning algorithm that generates smooth paths for an autonomous vehicle operating in an unknown environment, where obstacles are detected online by the robot’s sensors. This work was motivated by and experimentally validated in the 2007 DARPA Urban Challenge, where robotic vehicles had to autonomously navigate parking lots. Our approach has two main steps. The first step uses a variant of the well-known A* search algorithm, applied to the 3D kinematic state space of the vehicle, but with a modified state-update rule that captures the continuous state of the vehicle in the discrete nodes of A* (thus guaranteeing kinematic feasibility of the path). The second step then improves the quality of the solution via numeric non-linear optimization, leading to a local (and frequently global) optimum. The path-planning algorithm described in this paper was used by the Stanford Racing Teams robot, Junior, in the Urban Challenge. Junior demonstrated flawless performance in complex general path-planning tasks such as navigating parking lots and executing U-turns on blocked roads, with typical fullcycle replaning times of 50–300ms. Introduction and Related Work We address the problem of path planning for an autonomous vehicle operating in an unknown environment. We assume the robot has adequate sensing and localization capability and must replan online while incrementally building an obstacle map. This scenario was motivated, in part, by the DARPA Urban Challenge, in which vehicles had to freely navigate parking lots. The path-planning algorithm described below was used by the Stanford Racing Team’s robot, Junior in the Urban Challenge (DARPA 2007). Junior (Figure 1) demonstrated flawless performance in complex general path-planning tasks—many involving driving in reverse—such as navigating parking lots, executing Uturns, and dealing with blocked roads and intersections with typical full-cycle replanning times of 50–300ms on a modern PC. One of the main challenges in developing a practical path planner for free navigation zones arises from the fact that the space of all robot controls—and hence trajectories—is continuous, leading to a complex continuous-variable optimization landscape. Much of prior work on search algorithms for Copyright c © 2008, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. Figure 1: Junior, our entry in the DARPA Urban Challenge, was used in all experiments. Junior is equipped with several LIDAR and RADAR units, and a high-accuracy inertial measurement system. path planning (Ersson and Hu 2001; Koenig and Likhachev 2002; Ferguson and Stentz 2005; Nash et al. 2007) yields fast algorithms for discrete state spaces, but those algorithms tend to produce paths that are non-smooth and do not generally satisfy the non-holonomic constraints of the vehicle. An alternative approach that guarantees kinematic feasibility is forward search in continuous coordinates, e.g., using rapidly exploring random trees (RRTs) (Kavraki et al. 1996; LaValle 1998; Plaku, Kavraki, and Vardi 2007). The key to making such continuous search algorithms practical for online implementations lies in an efficient guiding heuristic. Another approach is to directly formulate the path-planning problem as a non-linear optimization problem in the space of controls or parametrized curves (Cremean et al. 2006), but in practice guaranteeing fast convergence of such programs is difficult due to local minima. Our algorithm builds on the existing work discussed above, and consists of two main phases. The first step uses a heuristic search in continuous coordinates that guarantees kinematic feasibility of computed trajectories. While lacking theoretical optimality guarantees, in practice this first