Skip to content

Integral errors

The Mellinger controller uses integral terms to reject steady-state errors. Because every controller in crazyflow.control is a pure function, integral state cannot be stored inside the function. It is an explicit return value that you pass back on the next call.

Initialisation

You have two ways to start the integral error at zero:

  1. Pass None (or omit the argument). The controller then creates the zero array internally.
  2. Create the zero array yourself and pass it explicitly. The integral error has the same shape as the position (for pos_err_i) or angular velocity (for r_int_error), so a zero array of that shape works.
import numpy as np
from crazyflow.control import parametrize
from crazyflow.control.mellinger import state2attitude

ctrl = parametrize(state2attitude, "cf2x_L250")
pos = np.zeros(3)
quat = np.array([0.0, 0.0, 0.0, 1.0])
vel = np.zeros(3)
cmd = np.zeros(13)

# Option 1: let the controller initialise the integral error.
rpyt, pos_err_i = ctrl(pos, quat, vel, cmd, pos_err_i=None)

# Option 2: initialise it yourself.
rpyt, pos_err_i = ctrl(pos, quat, vel, cmd, pos_err_i=np.zeros(3))

Under jax.jit, prefer option 2. Passing None on the first call and an array on the following calls changes the argument structure, so JAX traces and compiles the function twice. Passing a zero array from the start keeps the input structure constant and compiles only once.

Carrying errors across timesteps

Pass the returned error straight back as pos_err_i on the next call:

import numpy as np
from crazyflow.control import parametrize
from crazyflow.control.mellinger import state2attitude

ctrl = parametrize(state2attitude, "cf2x_L250")
pos = np.zeros(3)
quat = np.array([0.0, 0.0, 0.0, 1.0])
vel = np.zeros(3)
cmd = np.zeros(13)
cmd[0] = 1.0  # 1 m setpoint error in x

pos_err_i = None
for _ in range(10):
    rpyt, pos_err_i = ctrl(pos, quat, vel, cmd, pos_err_i=pos_err_i)  # carry forward

# After 10 steps at 100 Hz, integral error is approximately 10 * 0.01 = 0.1 m.

Both stages have integral errors

state2attitude tracks position error via pos_err_i. attitude2force_torque tracks angular velocity error via r_int_error. Manage them independently:

import numpy as np
from crazyflow.control import parametrize
from crazyflow.control.mellinger import attitude2force_torque, state2attitude

state_ctrl = parametrize(state2attitude, "cf2x_L250")
att_ctrl = parametrize(attitude2force_torque, "cf2x_L250")

pos = np.zeros(3)
quat = np.array([0.0, 0.0, 0.0, 1.0])
vel = np.zeros(3)
ang_vel = np.zeros(3)
cmd = np.zeros(13)

pos_err_i = None
r_int_error = None

for _ in range(5):
    rpyt, pos_err_i = state_ctrl(pos, quat, vel, cmd, pos_err_i=pos_err_i)
    force, torque, r_int_error = att_ctrl(quat, ang_vel, rpyt, r_int_error=r_int_error)