Isobath following using an altimeter
L. Jaulin
IRSC 2018, Southampton September 1, 2018
L. Jaulin Isobath following using an altimeter
La Cordelière and the Regent
Reconstitution de la bataille youtu.be/yP4cM1UGrqY
L. Jaulin Isobath following using an altimeter
Romain Schwab
L. Jaulin Isobath following using an altimeter
L. Jaulin Isobath following using an altimeter
Tests du 7 juillet
youtu.be/cxVs1fDdm1s
Follow an isobath
L. Jaulin Isobath following using an altimeter
Ile des morts experiment
L. Jaulin Isobath following using an altimeter
L. Jaulin Isobath following using an altimeter
24 juillet 2013
L. Jaulin Isobath following using an altimeter
Objective: Follow an isobath with an altimeter, a barometer and a low cost gyroscope.
L. Jaulin Isobath following using an altimeter
Exploration
SLAM paradigm
Bridge-river paradigm
[3]
L. Jaulin Isobath following using an altimeter
Consider an underwater robot:
˙
x = cos ψ
˙
y = sin ψ
˙
z = u 1
ψ ˙ = u 2
The observation function is
y 1 = z − h(x, y)
y 2 = angle(∇h(x, y)) − ψ y 3 = −z
L. Jaulin Isobath following using an altimeter
For the control of the depth:
u 1 = y 3 − y 3
For the heading, we take [1]:
u 2 = tanh (e 2 ) + sawtooth (e 1 )
= − tanh (h 0 + y 3 + y 1 ) + sawtooth (y 2 + π 2 )
L. Jaulin Isobath following using an altimeter
The controller is u =
y 3 −y 3
− tanh (h 0 + y 3 + y 1 ) + sawtooth (y 2 + π 2 )
L. Jaulin Isobath following using an altimeter
The output y 2 = angle(∇h(x,y)) − ψ should thus be estimated [2].
In the robot frame the underneath plane satises z 1 = p 1 x 1 + p 2 y 1 + p 3
L. Jaulin Isobath following using an altimeter
Prediction. We assume the seaoor locally planar. Thus:
p ˙ =
0 ψ ˙ 0
− ψ ˙ 0 0
1 0 0
p .
The prediction for the underneath plane is
p (k + 1 ) =
1 dt · u 2 (k) 0
−dt ·u 2 (k ) 1 0
dt 0 1
p (k) + α (k ) .
L. Jaulin Isobath following using an altimeter
Correction.
−y 1 − y 3 = 0 0 1
p (k ) + β (k ) .
Kalman filter controller
L. Jaulin Isobath following using an altimeter
The controller is thus u =
y 3 − y 3
− tanh (h 0 − p ˆ 3 ) + sawtooth ( atan2 ( ˆ p 2 , p ˆ 1 ) + π 2 )
.
L. Jaulin Isobath following using an altimeter
