Underwater Robots - Gianluca Antonelli.pdf

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8.5 Explicit Force Control 215
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Fig. 8.7. External force control. Roll and pitch vehicle’s angles (top) and q 2 as
manipulability measure (bottom). Solid: without exploiting redundancy; Dashed:
exploiting redundancy with the proposed scheme
The first scheme isobtained byusing the transpose of the Jacobian to
project the force error from the task space directly to the control input space,
i.e., force/moments for the vehicle and torques for the manipulator, leading
to an evident physical interpretation.
In the second scheme, instead, the force error is projected from the task
space to the body-fixed velocities. This is done to avoid the need to directly
access the control input; in many cases, in fact, avelocity controller is
implemented on the manipulator and control torques are not accessible [119].
Forboth the control schemes, the kinematic control applied is the same as
the algorithm exploited in the external force control scheme, already shown
in Section 8.4.1.