Autonomous racing control algorithms are the link between a planned racing line and the physical actions of a race car. They decide how much to steer, accelerate, and brake many times per second while the car is moving near the limit of tire grip. This matters because a small delay or an overaggressive command can make the car miss the apex, lose traction, or become unstable.
Racing is a demanding test bed for robotics, control theory, sensing, and vehicle dynamics.
Key Facts
- Lateral error e_y is the sideways distance between the car and the planned path.
- Heading error e_psi is the angle between the car direction and the path tangent.
- A simple steering law can be delta = k_y e_y + k_psi e_psi, where delta is steering angle.
- Vehicle speed update can be approximated by v_next = v + a dt, where a is acceleration and dt is time step.
- Tire grip is limited by the friction circle: F_x^2 + F_y^2 <= (mu F_z)^2.
- Model predictive control chooses commands by minimizing J = path error + speed error + control effort over a future time horizon.
Vocabulary
- Racing line
- The planned path around a track that balances shortest distance, cornering speed, and smooth vehicle motion.
- Feedback control
- A control method that compares the car's measured state with the desired state and corrects the difference.
- Model predictive control
- An algorithm that predicts future vehicle motion and chooses commands that best satisfy goals and constraints.
- Actuator command
- A numerical instruction sent to a physical system such as the steering motor, throttle, or brake.
- Friction circle
- A model showing that a tire has a limited total grip shared between acceleration, braking, and cornering.
Common Mistakes to Avoid
- Treating the planned path as the final answer. The path only gives a target, and the controller must still correct errors caused by speed, tire grip, delay, and disturbances.
- Ignoring speed when choosing steering. The same steering angle is much more dangerous at high speed because lateral force demand grows with v^2.
- Using full throttle and maximum steering at the same time. This is wrong because the tires must share limited grip between forward force and sideways cornering force.
- Forgetting actuator delay. Commands do not affect the car instantly, so a controller that ignores delay may turn or brake too late.
Practice Questions
- 1 A car is 0.40 m to the outside of the planned path and has a heading error of 0.08 rad. Using delta = k_y e_y + k_psi e_psi with k_y = 0.50 rad/m and k_psi = 1.20, find the steering command delta in radians.
- 2 An autonomous race car is traveling at 35 m/s and brakes with acceleration a = -6 m/s^2 for 1.5 s. Using v_next = v + a dt, find its new speed.
- 3 A controller is entering a corner and requests hard braking while also requesting a large steering angle. Explain why the friction circle suggests the controller may need to reduce one of these commands.