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# Motion profiling and advanced movement

Motion profiling gives a controller a smooth target over time instead of an abrupt position jump.

### The trapezoidal profile

A trapezoidal profile has three phases:

1. accelerate
2. cruise
3. decelerate

```java
public static double motionProfilePosition(double maxAccel, double maxVel,
                                            double distance, double elapsedTime) {
    double accelTime = maxVel / maxAccel;
    double accelDist = 0.5 * maxAccel * accelTime * accelTime;

    if (accelDist > distance / 2.0) {
        accelTime = Math.sqrt(distance / maxAccel);
        accelDist = distance / 2.0;
    }

    double cruiseDist = distance - 2 * accelDist;
    double cruiseTime = cruiseDist / maxVel;
    double decelTime  = accelTime;
    double totalTime  = accelTime + cruiseTime + decelTime;

    double t = Math.min(elapsedTime, totalTime);

    if (t < accelTime) {
        return 0.5 * maxAccel * t * t;
    } else if (t < accelTime + cruiseTime) {
        double cruiseElapsed = t - accelTime;
        return accelDist + maxVel * cruiseElapsed;
    } else {
        double decelElapsed = t - accelTime - cruiseTime;
        return accelDist + cruiseDist
                + maxVel * decelElapsed
                - 0.5 * maxAccel * decelElapsed * decelElapsed;
    }
}
```

### Combining profile, PID, and feedforward

```java
double targetPos = motionProfilePosition(MAX_ACCEL, MAX_VEL, distance, timer.seconds());

double power = pid.calculate(targetPos, motor.getCurrentPosition())
             + kV * targetVelocity
             + kA * targetAcceleration;

motor.setPower(power);
```

This is especially useful for lifts, arms, and slides.

Trapezoidal profiles are the right place to start. Use S-curves only if you still need smoother motion.


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