Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!sun-barr!olivea!uunet!mcsun!ukc!reading!minster!george
From: george@minster.york.ac.uk
Newsgroups: comp.ai.neural-nets
Subject: Pole Balancing Problem
Message-ID: <665415070.18755@minster.york.ac.uk>
Date: 1 Feb 91 13:31:10 GMT
Organization: Department of Computer Science, University of York, England
Lines: 54

Has anyone implemented the pole balancing simulator whoses equations are
given in Barto and Sutton "Neuronlike Adaptive Elements That Can Solve
Difficult Learning Control Problems" 1983 IEEE Trans Sys Man & Cyb??? i.e.
the two equations given in the appendix.

I have just coded them (see below), but the behaviour of the simulator is not
reasonable, e.g. pole at angle 10 degrees say, small velocity to left, then
pole should just fall down increasing velocity of cart. However, actually
oscillates between the two - keeping the pole balanced! ;-)

Assumed that sgn() meant a function that returns +1 for +ve numbers (including
0), and -1 for -ve numbers.

Does anyone know what is wrong with the equations?? Otherwise, would be
glad to have alternative equations for cart acceleration and pole
acceleration (taking into account friction at cart/pole and cart/track
interfaces).

Many thanks - George Bolt

pole_acc = ( GRAVITY * sin(pole_angle) +
             cos(pole_angle) *
             ( -1.0 * ((double) impulse_direction) * IMPULSE -
               POLE_MASS * POLE_HLENGTH * pole_vel * pole_vel * sin(pole_angle) +
               CART_FRIC * sgn(cart_vel)
             ) /
             ( CART_MASS + POLE_MASS ) -
             POLE_FRIC * pole_vel / (POLE_MASS * POLE_HLENGTH)
           ) /
           ( POLE_HLENGTH *
             ( 4.0 / 3.0 -
               POLE_MASS * cos(pole_angle) * cos(pole_angle) /
               (CART_MASS + POLE_MASS)
             )
           )

cart_acc = ( ((double) impulse_direction) * IMPULSE +
             POLE_MASS * POLE_HLENGTH *
             ( pole_vel * pole_vel * sin(pole_angle) -
               pole_acc * cos(pole_angle)
             ) -
             CART_FRIC * sgn(cart_vel)
           ) /
           ( CART_MASS + POLE_MASS );

____________________________________________________________
 George Bolt, Advanced Computer Architecture Group,
 Dept. of Computer Science, University of York, Heslington,
 YORK. YO1 5DD.  UK.               Tel: [044] (0904) 432771

 george@uk.ac.york.minster		         JANET
 george%minster.york.ac.uk@nsfnet-relay.ac.uk    ARPA
 george!mcsun!ukc!minster!george		 UUCP
____________________________________________________________