tag:blogger.com,1999:blog-35412705.post7541535280188126843..comments2022-07-18T06:46:28.554-05:00Comments on Jake Beal's Next Step: How resilient is it anyway? Jacob Bealhttp://www.blogger.com/profile/03294188694250217754noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-35412705.post-42504369632725419592012-09-11T01:36:56.199-05:002012-09-11T01:36:56.199-05:00I do talk about this some in the paper... one of t...I do talk about this some in the paper... one of the advantages of the way I've set up the proposed metric is that it <i>is</i> invariant to linear transformations. So changes of units, scaling, etc., should not affect the metric.<br /><br />Nonlinear transformations are a different matter. For example, switching a measurement from side length to area to volume, or switching from linear scale to log scale all do change the values.<br /><br />I'm not sure that's a bad thing, though, if the measures you choose are the ones that you are choosing to regulate.<br /><br />For example, I'm intending to apply this metric to the robotic redesign problem we've working in in the <a href="http://madv.bbn.com/" rel="nofollow">MADV project</a>. There, we have controllers that will need to be acting semi-independently on the robot's mass and on various dimensions. These are, of course, coupled, but since we're acting on them semi-independently, I want to know about whichever type of incremental steps are most likely to get us into trouble, whether that be mass (cubic) or side length (linear). My guess is that we'll find mass to be more sensitive when going down and side length to be more sensitive when going up...Jacob Bealhttps://www.blogger.com/profile/03294188694250217754noreply@blogger.comtag:blogger.com,1999:blog-35412705.post-54799594469353055362012-09-10T20:27:08.580-05:002012-09-10T20:27:08.580-05:00Are you not going to have severe problems relating...Are you not going to have severe problems relating to measurement? It doesn't seem like this is going to be invariant to various simple transformations of the systems that don't really affect its behavior. [This is based on the description in your blog post; I have not read the paper.]rifhttps://www.blogger.com/profile/09408465377684869050noreply@blogger.com