ROS2 Velocity Profiling for Smooth Stops

Problem Statement

Implement generate_velocity_profile(distance, max_vel, accel, dt) that returns a list of velocity setpoints for moving a robot a given distance.

Function Signature

def generate_velocity_profile(distance: float, max_vel: float, accel: float, dt: float) -> list[float]:

Requirements

Generate a trapezoidal velocity profile:

1. Ramp up: increase velocity by accel * dt each step until max_vel is reached
2. Cruise: maintain max_vel until deceleration must begin
3. Ramp down: decrease velocity by accel * dt each step until velocity reaches 0
4. The profile must not overshoot the target distance (total distance ≤ target + 0.01m tolerance)
5. The last velocity value must be 0 (robot stops at target)
6. All velocities must be ≥ 0

Deceleration distance

The robot needs d_decel = v² / (2 * accel) metres to decelerate from velocity v to 0. Start decelerating when remaining distance ≤ d_decel.

🤖 Why This Matters in Real Robots

Trapezoidal profiles are built into every industrial servo drive (Beckhoff, Siemens, Fanuc). In ROS2, the joint_trajectory_controller and follow_joint_trajectory action server both interpolate between waypoints using exactly this profile. Understanding it from scratch is prerequisite to working with ros2_control's trajectory execution.