Stability of Hybrid Position/Force Control Applied to Robots with Flexible
Joints
PhD Thesis by Peter Goldsmith, 1995
Abstract
When a robot arm performs a hybrid task, it applies specified forces to a fixed
surface or mechanism while moving along a prescribed path. To control
simultaneously the contact force and the arm position, three generic feedback
control schemes have been proposed in the literature. This thesis investigates
the stability of these `hybrid controls' in the presence of joint compliance and
contact compliance. While it is well known that compliance produces instability
in robots that use force feedback, it is shown in this thesis that compliance can
destablize certain hybrid controls even when force feedback is not used. First it
is proved that each hybrid control is exponentially stable when no compliance is
present. Then two of the controls are shown to be unstable when compliance is
introduced, while the third control is proved exponentially stable with joint
compliance, contact compliance or both sources present. A novel hybrid control is
proposed that achieves exponential tracking when applied to rigid systems as well
as exponential stability in the presence of compliance. A general theoretical
connection is made between exponential stability and trajectory tracking. The
concept of hybrid control is demonstrated on a 3-degree-of-freedom experimental
manipulator performing a writing task.
The stability analyses presented in this thesis pertain to robots in contact with
arbitrary holonomic constraints. It is shown that Raibert and Craig's established
method for hybrid task specification applies to only a subset of these
constraints. Theoretical justification is provided for Yoshikawa's more general
method for specifying hybrid tasks. This development effectively extends the
scope of previously proposed hybrid controls to arbitrary holonomic constraints.
It is proved that one of these hybrid controls is identical to a control proposed
by McClamroch and Wang for holonomically constrained robots.