Balancing Safety and Comfort in Autonomous Driving: Planning and Control Optimization

Autonomous driving research traditionally emphasizes safety, but passenger comfort is equally important. This article discusses how to achieve both by optimizing the planning and control modules.

Safety and Comfort Definitions – Safety means avoiding collisions and obeying traffic rules, while comfort is quantified by low jerk (acceleration rate) and low curvature rate.

Planning and Control Overview – Planning generates a trajectory (position as a function of time) using inputs like maps, start/end points, obstacles, and perception data. Control receives the planned trajectory and the vehicle’s current state (position, heading, speed, acceleration) and outputs brake/throttle commands and steering angles.

Planning for Safety and Comfort – Planning is formulated as an optimization problem with constraints (vehicle dynamics, road boundaries, obstacle avoidance) and a cost function that penalizes high acceleration, jerk, curvature, and curvature rate. Typical constraints include steering angle limits, acceleration limits, lane‑keeping, and collision avoidance using convex polygons.

Horizontal (Lateral) Optimization – The lateral problem solves for the lateral offset \(l\) from the reference line, subject to lane‑boundary constraints and a cost that minimizes curvature and its rate. This results in a quadratic programming (QP) problem with box constraints, allowing fast solutions.

Longitudinal Optimization – The longitudinal problem solves for the time‑to‑distance function \(t(s)\), ensuring no rear‑end collisions and minimizing acceleration and its derivative for comfort. It uses similar constraints and cost structures as the lateral case.

Reference Line Generation – The reference line (centerline) is generated offline, respecting lane boundaries and curvature limits, with a cost that favors low curvature and curvature rate.

Bicycle Model for Control – A simplified vehicle model assumes the two front wheels and two rear wheels are coincident, allowing the vehicle’s motion to be described by a single steering angle \(\delta\). This model helps derive the relationship between steering angle and turning radius.

Lateral Control – Lateral control tracks the planned trajectory by minimizing lateral error and heading error at a look‑ahead point. The control variable is curvature, turning the problem into another optimization.

Longitudinal Control – Longitudinal control aims to match the vehicle’s speed and position to the planned trajectory, also expressed as an optimization problem.

In summary, both planning and control in autonomous driving can be expressed as constrained optimization problems that balance safety constraints with comfort‑oriented cost functions, enabling vehicles to provide a safe and comfortable ride.