🚀 go-pugleaf

I am trying to determine the state of the art in the field of
robot modelling methods.  I shall present a view that there is
little in the way of practical achievement and hope to be proved
wrong!

There are a number of graphical robot simulation systems about. 
These only use kinematic modelling and are very good as planning
tools, but any generated off-line programs need some tweaking
before they can be used.

The main question I am interested in is how to derive the
kinematic and dynamic parameters for a particular robot.  The
situation as I see it at the moment follows:


Kinematic equations

There have been a number of papers describing methods of
compensating for errors in kinematic parameters, usually based
upon the Denavit-Hartenberg representation.  These are based on
the premise that the robot contoller's nominal kinematic model
differs from the actual kinematic parameters of the robot. 
Positions can be corrected by passing them through the actual
inverse kinematics and then the nominal forward kinematics to
'fool' ther controller into sending the robot to the correct
position.

The main issue associated with this approach is to obtain values
for the actual kinematic parameters.  Researchers have described
various methods of measuring robot positions, but there is little
evidence of actual results.  There is also the problem of getting
very large values for the Denavit-Hartenberg d parameter for
joint axes which are 'not quite parallel' - solutions to this
have only been hinted at.

My own research has shown that the only significant kinematic
parameter errors are offsets in the joint angles due to
inaccurate resolver calibration, and minor misalignments in
spherical wrists.


Dynamic equations

The area of dynamics is even more obscure than that of
kinematics.  Researchers have published ideas and some of the
basic equations, but again there is little evidence of practical
results.  There are two sets of dynamic parameters which are very
difficult to obtain, namely moments of inertia and compliance. 
I would be interested to hear of any methods of determining the
moment of inertia of a robot arm short of dismantling it so as
to determine the mass distribution.

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Dr Phill Edwards, Lecturer in IT, University of Nottingham, UK