Autonomous racing path planning is the process of choosing where a race car should drive on the track to finish a lap as fast as possible while staying safe. The car must account for track boundaries, tire grip, speed limits in curves, and its own ability to steer, brake, and accelerate. This matters because a path that looks short is not always fastest if it forces the car to slow down too much.
A good racing line balances distance, curvature, and speed.
Key Facts
- Lateral acceleration in a turn is a_y = v^2 / r, where v is speed and r is turn radius.
- Maximum cornering speed is approximately v_max = sqrt(mu g r), where mu is tire friction coefficient.
- Curvature is kappa = 1 / r, so tighter turns have larger curvature.
- A trajectory includes both path position and timing, such as x(t), y(t), v(t), and a(t).
- The fastest safe path often uses outside, apex, outside geometry to increase turn radius and reduce curvature.
- Model predictive control minimizes a cost such as lap time plus penalties for leaving the track, high acceleration, or unstable steering.
Vocabulary
- Racing line
- The racing line is the planned path through a track segment that allows high speed while staying within track limits.
- Trajectory
- A trajectory is a time-based plan that tells the car where to be, how fast to go, and how to control its motion at each moment.
- Curvature
- Curvature measures how sharply a path bends, with larger curvature requiring more lateral acceleration at the same speed.
- Friction circle
- The friction circle is a model showing the limited tire grip shared between braking, accelerating, and cornering.
- Model predictive control
- Model predictive control is a control method that repeatedly predicts future motion and chooses the best control inputs over a short time horizon.
Common Mistakes to Avoid
- Choosing the shortest path, which is wrong because the shortest path may have tight turns that force a much lower speed.
- Ignoring tire grip limits, which is wrong because the car cannot brake, accelerate, and corner beyond the available friction without sliding.
- Planning only a path and not a velocity profile, which is wrong because the same path can be safe or unsafe depending on speed.
- Treating the track as perfectly known and static, which is wrong because sensor noise, opponents, changing grip, and localization error require continuous replanning.
Practice Questions
- 1 A car enters a curve with radius 60 m on tires with mu = 1.2. Using g = 9.8 m/s^2, estimate the maximum cornering speed in m/s from v_max = sqrt(mu g r).
- 2 At 30 m/s, a car follows a path with radius 75 m. Calculate the lateral acceleration using a_y = v^2 / r, then express it in g by dividing by 9.8 m/s^2.
- 3 Explain why an autonomous race car might choose a longer outside, apex, outside racing line instead of hugging the inside edge of a corner.