Introduction to Path Planning Algorithms
Path planning is a critical component in self-driving cars, enabling the vehicle to generate safe and efficient trajectories from a starting point to a goal while avoiding obstacles. It builds on prerequisites like SLAM for mapping the environment and odometry/IMU for localization.
In this lesson, we focus on two foundational algorithms: A (A-star) and RRT* (Rapidly-exploring Random Tree). These methods generate feasible trajectories by searching through the configuration space, which represents possible vehicle positions and orientations.
- A* is a deterministic, grid-based search algorithm that finds the optimal path in terms of cost (e.g., distance or time).
- RRT is a probabilistic, sampling-based method ideal for high-dimensional spaces and dynamic environments.
Both are essential for decision-making in autonomous driving, ensuring collision-free paths. For example, in urban settings, A* might plan a route on a pre-mapped grid, while RRT handles unstructured off-road scenarios.
The general path planning problem can be formulated as finding a sequence of states $q(t)$ from $q_{start}$ to $q_{goal}$ that minimizes a cost function: $$\min \int_{0}^{T} c(q(t), \dot{q}(t)) \, dt$$ where $c$ includes factors like distance, speed, and obstacle proximity.