Underwater Robots - Gianluca Antonelli.pdf

8.5 Explicit Force Control 217
where k f,p , k f,v , k f,i are scalar positive gains, and ˜ f e = f e,d − f e is the force
error. Equation (8.17), thus, is aforce control action in the task space that
is further projected, via the transpose of the Jacobian, onthe vehicle/joint
space.
x p,d, x s,d
IK
ζ d
− 1
J k
� +
Fig. 8.9. Explicit force control scheme 1
−
Motion
Control
+
+
UVMS
+env.
J T posu F
Explicit force control, scheme 2. Asketch ofthe implemented scheme is
provided in Figure 8.10. The force control action iscomposed oftwo loops;
the action − J T posf e is aimed at compensating the end-effector contact force
(included in the block labeled “UVMS +env.”). The input of the motion
control is asuitable integration of the velocity vector:
ζ r = ζ d + ζ F = ζ d + J T pos( k ∗ f,p ˜ f e − k ∗ f,v ˙ f e + k ∗ f,i
� t
0
f e,d
˜f e ( σ ) dσ) ,
where k ∗ f,p , k ∗ f,v , k ∗ f,i are positive gains, and ζ d is the output ofthe inverse
kinematics algorithm described inprevious Section.
x p,d, x s,d
IK
ζ d +
+
− 1
J k
� +
J T pos
−
η , q
Fig. 8.10. Explicit force control scheme 2
8.5.1 Robustness
Motion
Control
J T pos
+ − UVMS
+env.
In the following, the robustness of the schemes to react against unexpected
impacts or errors in planning desired force/position directions is discussed.
PID
+
η , q
−
f e
f e
f e,d