Concept 02: Acceleration, Jerk & S-Curves

▶ Interactive Demo: Elevator Motion & Jerk Visualizer

Open the interactive demo below to compare an instant acceleration step against a smooth S-Curve profile and watch the sloshing coffee / carriage forces in real time.

1. The Real-World Problem: The Coffee-Spill Elevator

Imagine you are standing inside an elevator holding a full cup of hot coffee filled to the very brim:

1. Position x (Where you are): Which floor you are on.
2. Velocity v (How fast you move): At a steady cruising speed of 3 m/s, the coffee stays completely flat. Velocity creates no extra force.
3. Acceleration a (Rate of speed change): When the elevator speeds up, your knees feel heavier. The coffee presses down into the cup with force F = m·a. Steady acceleration keeps the surface level.
4. Jerk j (Rate of acceleration change): If the motor instantly slams full voltage in 0 milliseconds, the floor violently jerks upward. The sudden jump in force sloshes boiling coffee all over your hand!

2. Solving It in Code (Java & WPILib)

Production WPILib Equivalent: Motion Profiling

In WPILib, motion constraints are generated and evaluated via TrapezoidProfile:

import edu.wpi.first.math.trajectory.TrapezoidProfile;

// Constrain Max Velocity to 3.0 m/s, Max Acceleration to 6.0 m/s²
TrapezoidProfile.Constraints constraints = 
    new TrapezoidProfile.Constraints(3.0, 6.0);

TrapezoidProfile profile = new TrapezoidProfile(constraints);

// Set current state (at 0 m) and desired goal (at 5 m)
TrapezoidProfile.State current = new TrapezoidProfile.State(0.0, 0.0);
TrapezoidProfile.State goal = new TrapezoidProfile.State(5.0, 0.0);

// Calculate setpoint for the next 20ms robot loop
TrapezoidProfile.State nextSetpoint = profile.calculate(0.020, current, goal);

System.out.printf("Target Position: %.3f m, Target Velocity: %.3f m/s%n",
    nextSetpoint.position, nextSetpoint.velocity);

3. Review Checkpoints

Checkpoint 1

A robot elevator’s velocity is given by v(t) = 3·t². What is the acceleration a(t) at t = 2.0 seconds?

Solution:

1. Differentiate velocity: a(t) = dv/dt = 6·t.
2. Evaluate at t = 2.0: a(2.0) = 6(2.0) = 12.0 m/s².

Checkpoint 2

Why do modern FRC elevator feedforward controllers include kA · a?

Solution: Because accelerating a heavy mechanism requires extra motor voltage (F = m·a). Providing voltage proportionally to target acceleration (kA · a) cancels out inertia and eliminates lag.