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From: acc@hatstand.cee.hw.ac.uk (Andrew Clegg)
Subject: Re: Some questions about adaptive robot control
In-Reply-To: rbh@gambit.utias.utoronto.ca's message of 21 Sep 94 16:28:32 GMT
Message-ID: <ACC.94Sep26104059@hatstand.cee.hw.ac.uk>
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Organization: Ocean Systems Lab. Heriot-Watt University, Edinburgh
References: <35n3q7$r8s@news.iastate.edu> <1994Sep21.122831.20770@jarvis.cs.toronto.edu>
Date: Mon, 26 Sep 1994 09:40:59 GMT
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[Sorry about the previous blank message - I was a bit too keen]

In article <1994Sep21.122831.20770@jarvis.cs.toronto.edu> rbh@gambit.utias.utoronto.ca (Roger Barry Hertz) writes:

> >There are several ways to develop this control law.  One way would
> >be to linearize the dynamics about the nominal trajectory to get
> >the classic formulation for the perturbation state variables of
> >
> >           delta (q dot) = A*(delta q) + B*(delta u)        (1)
> >
> >Then pole placement or some optimal control scheme could be used to
> >develop the feedback gains.  BUT, since A and B are time varying
> >(sometimes rapidly if the robot moves at high speed) the feedback
> >gains will need to be periodically updated based on a new
> >linearization.  My question is IF one is updating a control law
> >based on changing parameters (not kinematic D-H parameters etc.,
> >but the parameters resulting from changing A and B above) in this
> >fashion, would this be considered an "adaptive" control scheme even
> >though there is no "adaptation law" per se.  The robotics
> >literature is full of so-called adaptive control algorithms but I
> >haven't been able to determine a definition of what exactly is
> >meant when you say you have an "adaptive" controller for your
> >robot.

This is a form of adaptive control, basically an advanced form of
'gain scheduling', since (I assume) A and B are determined from a
fixed dynamic model that is determined a-priori. If you wanted to get
clever (or maybe you are) you would have an on-line identification
block updating your model and the A and B parameters - so that it
could track any unmodelled dynamics, such as changes in payload.

> I would agree with you -- allot of people write wonderful papers
> in control, but yet fail to apply it to real life situations.
> You therefore get only very simple examples in the literature of
> its application, which leaves some doubt whether it can apply to
> real-life problems.  

Very true. My own work is application drive - so my adaptive control
laws have been developed so as to be implementable. They are simple
(yet effective) independent self-tuning pole-placement controllers,
one for each joint. It works well in my application, large hydraulic
manipulator,  where coupling between joints is not a major effect.

> >pole placement ... stability should be guaranteed so
> >long as you put them in the left half of the real/imaginary plane.
> 
> Sounds very reasonable, but gain margin could be quite slim depending
> on how fast you update the model (A and B matrix) and the gains.

I update my model every sample period - 50 to 100Hz.

Andy Clegg________________________________________acc@cee.hw.ac.uk___

Ocean Systems Lab, Dept of Computing & Electrical Engineering,
Heriot-Watt University, Edinburgh, EH14 4AS	  Tel : 031 451 3506
http://www.cee.hw.ac.uk/~acc/acc.html		  Fax : 031 451 3327
_____________________________________________________________________
