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ts
Then you have to, for example, after it gives you a supposed minimum,
drop the minimization software and look at the landscape in the
neighborhood of a supposed minimum. My guess is
that it is relatively flat in some direction(s), and maybe has
a kinked valley.
You might try your software on some test problems to see how well
it works. You can look up tricky optimizaton test functions.
Try for example
Z = |(x^2 + y^2 -1)| + e*x
where e = (say) 10^-6.
Naively, I would worry that a defective underlying model might not do a very good job of fitting real data. I.e., suppose riders have variable delay, or variable gain, depending on what they are daydreaming about?
Jim Papadopoulos
________________________________
From: st...@googlegroups.com [st...@googlegroups.com] on behalf of Jason Moore [moore...@gmail.com]
Sent: Friday, December 09, 2011 11:52 AM
To: Single Track Vehicle Dynamics
Subject: [stvdy] System ID experts
Hi,
Jason
--
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Sports Biomechanics Lab<http://biosport.ucdavis.edu>, UC Davis
Davis Bike Collective<http://www.davisbikecollective.org> Minister, Davis, CA
BikeDavis.info<http://BikeDavis.info>
Office: +01 530-752-2163<tel:530-752-2163>
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Home: +01 530-753-0794<tel:530-753-0794>
I'm glad you are alert to the non-tight vs tight distinction -- the latter I guess is where the crossover model should work. [I'm guessing the former represents 99.9% of normal bike riding, but of course it has no bearing on ability to recover from or avoid a sudden, bad situation.]
I have nothing to contribute to your methodology which is beyond me.
As you mention the Whipple model, I do wonder: what if the tires substantially modified the steering torque? I would think you'd want to do some riding with no external disturbances, to see if steer torque and steer angle are accurately related by the model. If they weren't, the model would not be the right thing to use.... right?
Jim P.
Jason, thanks for the links and impressive fits.
I'm glad you are alert to the non-tight vs tight distinction -- the latter I guess is where the crossover model should work. [I'm guessing the former represents 99.9% of normal bike riding, but of course it has no bearing on ability to recover from or avoid a sudden, bad situation.]
I have nothing to contribute to your methodology which is beyond me.
As you mention the Whipple model, I do wonder: what if the tires substantially modified the steering torque? I would think you'd want to do some riding with no external disturbances, to see if steer torque and steer angle are accurately related by the model. If they weren't, the model would not be the right thing to use.... right?
Jim P.
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Thanks for your patience in responding. I will snip and answer back selectively, for easy reading:
Subject: Re: [stvdy] System ID experts
Jim,
>99.9% is bold claim. This is surely debatable.
I feel I have to say something to get serious attention. I think that when I ride my bike to work 45 minutes, there are no more than 10 seconds when I really try to steer precisely, between two cars or threading a rapid series of potholes. OK, 10sec/2700sec is .4%, so 99.6%. Well, each time I start from rest I have a little skilled balancing for 2 sec. But the rest of the time, I am not aware of doing anything. What might that mean?
>Here are my thoughts on whether we do this pulsive control as you describe or something else:
I have thought at length about 'pulsivity' and I am not wedded to it for non-tight control. It just looks like an easy explanation. Along the lines of how we throw a ball, how much feedback control is exerted in the 0.2-0.4 seconds of hand acceleration?
If we are going to make a quick move, I guess it should be open loop. But the lazy person might apply a more moderate torque for an open-loop period to change roll angle. Still hard to make the case that much feedback is operating, unless you are cornering in a pack and striving to maintain a 6" gap to your neighbor.
>Even if you have these day dreaming moments while riding a bike,
>where it is pretty much "open loop", you still have to employ control
>at these sporadic moments and that control has to be governed by
>some law, which crossover type models may be a good choice.
Umm -- on the face of it, that does not seem convincing. The sporadic control can be a gross correction, with no attempt to make it precise. E.g., wandering off the road in a car, wrench the wheel a little, and then make subsequent corrections only if needed. (Narrow lane.)
Isn't it true that the crossover model is only a representation of human behavior near the limit of performance?
>I'm not sure I'm even on board with the sporadic control theory* because
>I don't necessarily believe that the bicycle + rider is ever open loop stable.
Well, I think this is a great point. I think if we have a rigidified rider and hard tires the whipple model might be reasonable. But with a real rider, a dead person can't sit up, so of course a free-torso system can't be stable. And as soon as a person controls their torso, they are of course affecting (controlling) the bike.
>Meaning that we have to employ some form of control at all times.
I don't really buy that. Or at least, there are many versions of this idea.
For example, suppose we have an internal program for sitting upright.
Running that program shouldn't necessarily be charged against the bicycling activity.
Maybe once that program runs, the bike is either stable, OR (like the whipple model) it is simply
HEAVILY damped in roll. In that case, you observe the roll angle once in a while, and occasionally apply
some pressure with a roughly appropriate total steering impulse.
>This control can certainly, and may be dominated by, learned
>unconscious control which is taken care of in our spinal cord,
>but it is still control which is governed by some model, which
>seems more probable to me to be continuous.
Philosophically, I have fallen away from the continuous idea
because of the obvious delays. In my experience, only when
really needing to exert tight control do I have any sense of *continually*
processing input and producing output. Otherwise, my idea and sometimes
sensation is of discrete sampling with reaction when a threshold is exceeded.
>These kinds of theories surely need to be tested. I find that
>there is little evidence for the pulsive control but a lot for a more continuous framework.
What would you offer as evidence for continuous control, for example of a standing still person?
As opposed to a detection of threshold exceedance, and setting into motion a distinct corrective.
Oops, I see I am anticipating your words here!
>Does anyone know of any work on just a human standing or sitting?
>Do we have a constantly activated control system that makes sure
>we don't fall over? Or is it more like control is enacted only when
>when our lean angle reaches some threshold?
A lot of work has been done, and I think Andy is pretty familiar with the ideas.
>*btw I haven't studied the Doyle work yet or the work you've done to explain it
Nor have I, sadly. It just seems really relevant!
>I think this test you describe would only be true in the case without a human rider.
>For a given steer torque applied by the rider if you compare the measured roll and
>steer to the roll and steer predicted by the Whipple model with the same measured
>steer torque you are not guaranteed to get matches. This is not only because the
>tire model might be bad, but because of many other things including but not limited
>to: noise (human remnant and other noise) in the inputs and the outputs, a bad human
>model or other deficiencies in the Whipple model such as rider rigidity.
Model deficiencies: I totally agree. That is why I believe in your approach of rigidifying
the rider. But that is all subject to test: rigidify the rider, pump the tires hard, measure
the steer torque, and see if steer angle and roll angle are accurately predicted.
Human remnant noise: I don't agree at all!! If that is just an input steer torque,
measure it.
Wind noise: must avoid.
Bottom line, I claim it is possible to test the goodness of the whipple model as long as the rider is rigidified. Unfortunately, I bet it is not all that good when tires are 'normally' loaded.
>To properly
>test what you suggest would require eliminating the human from the system and
>applying steer torque via a a motor (i.e. a robotic bicycle). This is precisely what
>Luke is working on here
Don't have to eliminate the human, just rigidify and measure the torque input accurately.
>The best assumption I can make is based off of work like Jodi's MS thesis
>which says the Whipple model predicts the motion of rider-less torque free
>bicycle between 4 and 6 m/s and trying to make good modeling assumptions,
>of which it certainly may be a good idea to entertain a tire model.
Those words sound like something I advocated, because indeed his bicycle had relatively
undeformed tires and no floppy rider.
I think the NEED for a tire model should best be SHOWN by testing with tires loaded to real-world levels. Luke's bike is one way, but a rigidified human rider is another.
Jason, thanks for engaging, and please be assured that I am openminded about possible logical errors in my 'worldview'!
Regards
Jim P.
I am not all into the details of this conversation. But let me add a couple
quick thoughts.
Not having any awareness of actively balancing says _Nothing_ about what advanced controls
you may be using. You are not aware of balancing when standing and that requires a busy
feedback look. You are not aware of the incredible neural processing to recognize a face,
and that is probably much more advance a sensory process than is involved in bicycle
balance. People walk robustly, and I don't see how they could possibly do that without
a busy feedback loop. But I don't sense this in action at all when I walk. Remember
that fruitflies can fly pretty well. And maybe fruitfly flight control is about as
hard as human walking or biking control. What awareness do you think the fruitfly
has of its control in normal commuting flight?
BTW, there is a whole literature about how people stand still. I went to a whole meeting
basically about that. Perhaps some people know how people stand still, candidates
are people named Kimmel (in Maryland) and Peterka (in Oregon). But there was certainly
no concensus about how it is done or if, for example, there are two regimes: one for
near vertical and one for large excursions. Same for how people balance sticks
on their finger tips.
If you bike guys (Davis, Delft) do a good job I can well imagine you would be advancing
the state of the art. On the other hand I think you should know the Kimmel and Peterka
stuff well before you publish anything. Both nice smart fellows, by the way.
-Andy
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-Andy Ruina, ru...@cornell.edu, http://ruina.tam.cornell.edu
Yes, you are surely right. But seems to me we can conclude something from the fact that (a) sensing-computing-actuating delay is inescapable (b) there is some distinction between un-noticeable control (riding on a 10-ft wide path) and conscious, tight control (riding on a 4" wide stripe).
Isn't it fair to say that on the narrow path we are more attentive, and do things more quickly, and can have less reliance on letting a learned response play out? Or in other words, that whatever 'advanced' controls we use in the wide-path or 'easy' activities, they are not high-gain or rapid?
This should at least suggest that there are distinctly different modes of controlling a bike, of which Jason and others are arguably studying the former (and normally much less used).
JMP
________________________________________
From: st...@googlegroups.com [st...@googlegroups.com] on behalf of Andy Ruina [ru...@cornell.edu]
Sent: Friday, December 16, 2011 4:18 AM
To: st...@googlegroups.com
Subject: Re: [stvdy] System ID experts
Jim:
I agree that attentive tight-tolerance riding feels different than lower tolerance
subconscious balancing. Whether this is a mode change or just a slight improvement that
crosses into consciousness I wouldn't bet on one way or another. My guess, not strongly
felt, is that it is not a big change in system behavior. But it will be great when
we know more.
-Andy
The idea I now feel comfortable with (but it is derived from a rigid bike model so leaves out all postural dynamics) is that of 'apparent roll damping' -- that after any disturbance by steer input (possibly intentional) or by wind, the stable weave mode drops the roll rate approximately to zero, leaving the bike nearly balanced (in a steady turn) with slowly growing or decaying capsize. Automatically having the roll rate damp in this way seems tailor-made for occasional or generally uncalibrated steer inputs, because the result is so benign -- at worst an inappropriate turn radius.
For a system like that, in which steer torque correlates to roll rate, it is hard to see a question of balancing -- most riding would be a matter of altering roll angle to achieve approximately desired path curvature.
Jim
________________________________________
From: st...@googlegroups.com [st...@googlegroups.com] on behalf of Andy Ruina [ru...@cornell.edu]
Sent: Friday, December 16, 2011 3:53 PM
Hi Jason,
Thanks for your patience in responding. I will snip and answer back selectively, for easy reading:
Subject: Re: [stvdy] System ID experts
Jim,
I feel I have to say something to get serious attention. I think that when I ride my bike to work 45 minutes, there are no more than 10 seconds when I really try to steer precisely, between two cars or threading a rapid series of potholes. OK, 10sec/2700sec is .4%, so 99.6%. Well, each time I start from rest I have a little skilled balancing for 2 sec. But the rest of the time, I am not aware of doing anything. What might that mean?
>99.9% is bold claim. This is surely debatable.
I have thought at length about 'pulsivity' and I am not wedded to it for non-tight control. It just looks like an easy explanation. Along the lines of how we throw a ball, how much feedback control is exerted in the 0.2-0.4 seconds of hand acceleration?
>Here are my thoughts on whether we do this pulsive control as you describe or something else:
If we are going to make a quick move, I guess it should be open loop. But the lazy person might apply a more moderate torque for an open-loop period to change roll angle. Still hard to make the case that much feedback is operating, unless you are cornering in a pack and striving to maintain a 6" gap to your neighbor.
>Even if you have these day dreaming moments while riding a bike,Umm -- on the face of it, that does not seem convincing. The sporadic control can be a gross correction, with no attempt to make it precise. E.g., wandering off the road in a car, wrench the wheel a little, and then make subsequent corrections only if needed. (Narrow lane.)
>where it is pretty much "open loop", you still have to employ control
>at these sporadic moments and that control has to be governed by
>some law, which crossover type models may be a good choice.
Isn't it true that the crossover model is only a representation of human behavior near the limit of performance?
Well, I think this is a great point. I think if we have a rigidified rider and hard tires the whipple model might be reasonable. But with a real rider, a dead person can't sit up, so of course a free-torso system can't be stable. And as soon as a person controls their torso, they are of course affecting (controlling) the bike.
>I'm not sure I'm even on board with the sporadic control theory* because
>I don't necessarily believe that the bicycle + rider is ever open loop stable.
I don't really buy that. Or at least, there are many versions of this idea.
>Meaning that we have to employ some form of control at all times.
For example, suppose we have an internal program for sitting upright.
Running that program shouldn't necessarily be charged against the bicycling activity.
Maybe once that program runs, the bike is either stable, OR (like the whipple model) it is simply
HEAVILY damped in roll. In that case, you observe the roll angle once in a while, and occasionally apply
some pressure with a roughly appropriate total steering impulse.
Don't have to eliminate the human, just rigidify and measure the torque input accurately.
>To properly
>test what you suggest would require eliminating the human from the system and
>applying steer torque via a a motor (i.e. a robotic bicycle). This is precisely what
>Luke is working on here
Those words sound like something I advocated, because indeed his bicycle had relatively
>The best assumption I can make is based off of work like Jodi's MS thesis
>which says the Whipple model predicts the motion of rider-less torque free
>bicycle between 4 and 6 m/s and trying to make good modeling assumptions,
>of which it certainly may be a good idea to entertain a tire model.
undeformed tires and no floppy rider.
I think the NEED for a tire model should best be SHOWN by testing with tires loaded to real-world levels. Luke's bike is one way, but a rigidified human rider is another.
Jason, thanks for engaging, and please be assured that I am openminded about possible logical errors in my 'worldview'!
Regards
Jim P.
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________________________________
>Like I said earlier, I more on board with feedback happening *all*
>the time. Although I couldn't point you to any proof.
Isn't it true that the crossover model is only a representation of human behavior near the limit of performance?
>I'm not sure that that is a given about the crossover model.
Well, I'm not smart enough (yet) to understand it. But I think in several explanations, I have recurringly seen a statement like (or that I interpret like): "Near the boundary of system stability, the human operator asymptotic behavior seems to take a simple form that makes system behavior approximate 1/s", or something like that. The clear idea that I got is that as humans try hard, with various kinds of plant to control, they do their best to shape it into a certain form, and "the result 'at the crossover' (I thought maybe that meant, 'at the stability boundary') can be characterized by a simple form." This is probably near some fairly consistent upper frequency limit...
If you don't think this is right I will put in some library time to find the sources for that hazy recollection.
>I agree that this is a control strategy and can surely work, but
>some kind of nice experimental validation of this is needed.
>Of all the data I've seen whether hands on riding or hands off,
>the steer angle and roll angle are very jittery which seems to
>lead me to believe we are constantly correcting. I never have
>seem smooth values and the occasional correcting, but maybe
>I've never done the right experiment, or I'm viewing the data wrong.
AMEN AND HALLELUJAH! This is the discussion that I feel is needed. I don't know the answers. I haven't noticed the most relevant details. I don't know a way to prove or decide. What I was hoping from you and others, and I feel you have done it here, is an acknowledgement that some of the fairly big questions are not really settled. (Whereas, some others probably ARE settled, by your work or Weir's work...) So we need to dig around in the muck of ignorance in search of a little more clarity.
>Ok, ... I think I spoke too soon about the human remnant. I had
>convinced myself for some reason. I'm going to run these simulations
>with respect to my measured input data to check the Whipple model
>validation.
As long as there is no wind...!
>There are a few potential model deficiencies with the Whipple model
>and my rigidified rider experiments. One being the tire model, the other
>is the rider's arm motion
Do you mean the contribution of the rider's arms as passive elements, namely
inertia, damping, and load-stiffening? Or something more sophisticated?
I am happy to explore with you potentially reasonable mechanical approximations
to the impedance 'added' by the arms, as I have given it some thought.
>and the third is how well I estimate the physical parameters of the bicycle/rider.
Well, THIS seems like it could be a fruitful area for parameter 'fitting',
along with critical review of the thought process. In that arena, it could be good to add
masses to the handlebar ends, to see if they show up in the coefficients as expected. Or to
use a torque motor to apply a simple balancing program while the rider or the
pile of bricks is inactive.
>Currently, the steer torques I measured are higher than the ones
>predicted by the Whipple model for a given roll and steer.
I invite you to share some of that data and seek input. Higher by a factor,
or is there a 'transfer function' i.e. higher in some frequency ranges with
some phase shift?
>Any one of these issues Iisted could contribute to the higher
>steer torques with the tire and arm model more likely candidates.
>Our riders' torso and legs are rigidly affixed to the frame but the
>arms still move when controlling the bicycle. Turns out that
>simply adding the inertial effects of the arms is significant and
>pushes capsize eigenmode from mildly unstable to very unstable.
GREAT TO KNOW!!!!! That is a major result in my mind.
Would be very interested to hear how you made that model.
On the other hand, capsize is the simplest mode to predict, so should
be a piece of cake to attribute and wrap this up.
>I'm working on checking the outputs of the Whipple model and
>Whipple model with arms with respect to the experimental steer
>torque I measured. As far as a tire model goes, I don't have one
>easily available to check things with, but would welcome anyone
>that wants to look into that or can provide a tire model.
You could resolve some things quickly by giving the rider a fixed hand support, and allowing steering through
the fingertips. If the problem goes away then you know the cause for sure.
Jim P.
Jason, thanks for the responses, here are brief rejoinders:
________________________________
>Like I said earlier, I more on board with feedback happening *all*
>the time. Although I couldn't point you to any proof.
Isn't it true that the crossover model is only a representation of human behavior near the limit of performance?Well, I'm not smart enough (yet) to understand it. But I think in several explanations, I have recurringly seen a statement like (or that I interpret like): "Near the boundary of system stability, the human operator asymptotic behavior seems to take a simple form that makes system behavior approximate 1/s", or something like that. The clear idea that I got is that as humans try hard, with various kinds of plant to control, they do their best to shape it into a certain form, and "the result 'at the crossover' (I thought maybe that meant, 'at the stability boundary') can be characterized by a simple form." This is probably near some fairly consistent upper frequency limit...
>I'm not sure that that is a given about the crossover model.
If you don't think this is right I will put in some library time to find the sources for that hazy recollection.
AMEN AND HALLELUJAH! This is the discussion that I feel is needed. I don't know the answers. I haven't noticed the most relevant details. I don't know a way to prove or decide. What I was hoping from you and others, and I feel you have done it here, is an acknowledgement that some of the fairly big questions are not really settled. (Whereas, some others probably ARE settled, by your work or Weir's work...) So we need to dig around in the muck of ignorance in search of a little more clarity.
>I agree that this is a control strategy and can surely work, but
>some kind of nice experimental validation of this is needed.
>Of all the data I've seen whether hands on riding or hands off,
>the steer angle and roll angle are very jittery which seems to
>lead me to believe we are constantly correcting. I never have
>seem smooth values and the occasional correcting, but maybe
>I've never done the right experiment, or I'm viewing the data wrong.
>Ok, ... I think I spoke too soon about the human remnant. I had
>convinced myself for some reason. I'm going to run these simulationsAs long as there is no wind...!
>with respect to my measured input data to check the Whipple model
>validation.
Do you mean the contribution of the rider's arms as passive elements, namely
>There are a few potential model deficiencies with the Whipple model
>and my rigidified rider experiments. One being the tire model, the other
>is the rider's arm motion
inertia, damping, and load-stiffening? Or something more sophisticated?
I am happy to explore with you potentially reasonable mechanical approximations
to the impedance 'added' by the arms, as I have given it some thought.
Well, THIS seems like it could be a fruitful area for parameter 'fitting',
>and the third is how well I estimate the physical parameters of the bicycle/rider.
along with critical review of the thought process. In that arena, it could be good to add
masses to the handlebar ends, to see if they show up in the coefficients as expected. Or to
use a torque motor to apply a simple balancing program while the rider or the
pile of bricks is inactive.
I invite you to share some of that data and seek input. Higher by a factor,
>Currently, the steer torques I measured are higher than the ones
>predicted by the Whipple model for a given roll and steer.
or is there a 'transfer function' i.e. higher in some frequency ranges with
some phase shift?
GREAT TO KNOW!!!!! That is a major result in my mind.
>Any one of these issues Iisted could contribute to the higher
>steer torques with the tire and arm model more likely candidates.
>Our riders' torso and legs are rigidly affixed to the frame but the
>arms still move when controlling the bicycle. Turns out that
>simply adding the inertial effects of the arms is significant and
>pushes capsize eigenmode from mildly unstable to very unstable.
Would be very interested to hear how you made that model.
On the other hand, capsize is the simplest mode to predict, so should
be a piece of cake to attribute and wrap this up.
You could resolve some things quickly by giving the rider a fixed hand support, and allowing steering through
>I'm working on checking the outputs of the Whipple model and
>Whipple model with arms with respect to the experimental steer
>torque I measured. As far as a tire model goes, I don't have one
>easily available to check things with, but would welcome anyone
>that wants to look into that or can provide a tire model.
the fingertips. If the problem goes away then you know the cause for sure.
Jim P.
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>I asked Ron Hess your question and this was his response:
>"Not really. I can describe the dynamics of the human at various "crossover" frequencies
>and various performance levels. It's true, that it has been verified in many laboratory and
>vehicle control tasks where good performance was required."
>So it doesn't seem that your recollection is necessarily fact.
>It'd be nice to find some references that say this more explicitly.
OK, that's a big one for me. I'm honored that Ron took the time to think it over. I'll put that issue in my queue.
What is "A" crossover frequency, I thought there was only "ONE" for a given plant.
>I've played around with checking this and it seems to be that a given measured steer torque
>that controlled the real system will not necessarily stabilize the Whipple model. So simulating
>the Whipple model seems to always blow up, but sometimes with "bad" initial condition estimates
>it will be stable but the comparisons of the experimental outputs with the simulation outputs is
>poor due to bias. But I'm not sure how to choose the right initial conditions. I was hoping that
>this would be easy to check, but it may not be. I'm probably won't spend much time on this,
>as Luke will be tackling specifically with better data very soon.
Errrr --- This is a good place for the diff eq experts to jump in. Does one validate a differential equation by looking
at the solution, or is it better to simply check whether the highest order derivative is instantaneously quite accurate.
I can see the issue that putting the measured torque as an open loop input into the Whipple
model could have an increasing divergence as time progressed, including a blowup
if the hands free model is not stable at that speed.
So maybe the better question is: for given state (steer and steer rate; lean and lean rate)
what are the steer acceleration and roll acceleration? That could either be with applied steer
torque or with no applied steer torque -- just use the measured torque.
If the equations are applicable, the linear relation between state plus torque, and the two output variables,
should be linear with coefficients constant at a given speed. Seems like many seconds of data should
permit a strong test of this idea. Then if the linear model DOES match most data, are the coefficients
close to predictions from the equations of motion?
Of course, WHERE the torque is measured (middle of steerer, or top of steerer below handlebars, or
applied to handlebars) changes the equations a little. If you imagine a flywheel disk
mounted either above or below the torque sensor, the measured torque for a given bicycle
motion will change. More complex conditions if the sensor is below the handlebar, and the handlebar has a mass
offset from the steer axis....
>I add passive arms with spherical joints at the shoulders and the hand to handlebar grip connection.
>Revolutes at the elbows. I then constrain them to basically hang down. It's similar to a model Arend
>presented at the conference in Delft. See my rough explanation here:
> http://moorepants.github.com/dissertation/extensions.html#rider-arms
>If you have thoughts on an arm model that may be more realistic, I'm interested.
I guess I have to read that.....
>From a preliminary glance it seems to be be higher by a factor. The data is available for use on my website.
>If you want a csv file of a particular run, just let me know what run number and I'll send it. I'll send you the
>Whipple parameters I estimated too. Run details are here:
> http://biosport.ucdavis.edu/research-projects/bicycle/instrumented-bicycle/run-information-table
> But this graph basically shows the bad torque predictions:
> http://biosport.ucdavis.edu/research-projects/bicycle/instrumented-bicycle/run-information-table
>Look at the tDelta curve.
Aargh, more work if I want to be responsible! Thanks for the links.
>See: http://moorepants.github.com/dissertation/extensions.html#rider-arms
MORE? (MOORE?)
OK, many thanks, this is very fruitful for me.
Jim
Jim responded:
> Errrr --- This is a good place for the diff eq experts to jump in. Does one validate a differential equation by looking
> at the solution, or is it better to simply check whether the highest order derivative is instantaneously quite accurate.
I am not that expert, the the class of expertise would be system identification, not ODEs.
For a system that is passively unstable, or nearly so, the usual approach of simulating forwards
in time and looking at the errors (or trying to minimize them if doing, rather than checking,
system ID) can't work.
A) SYSTEM ID FOR UNSTABLE SYSTEMS
Two approaches that I have thought of, and again I don't know the subject well, are below.
One semi-expert listened to what I wrote below a couple of months ago and used it when he was similarly stumped with
system ID for an unstable system. The two ideas are so natural that they both must be
standard practice in some community.
1) Look at how well the ODE is satisfied at every instant in time
and try to minimize that error. If the ODE is written as a single nth order equation this is
equivalent to Jim's idea of seeing how well you predict the highest order term.
2) Take a set of data and analyze it like this. Start one simulation at each data point.
Integrate forward in time from each. Take the difference between the simulated free variables
and the data. This much is what Jason did already. But now multiply by a weighting function
that discounts the future. This could be an exponential decay, a gaussian or a box function.
If the weighting function decays very fast this method is equivalent to (1) above. But if
it is substantially non-zero for some reasonable time into the future, it gives more weight
to fitting the difficult (unstable) modes. But you kill off the unstable divergence problem.
The divergence is still there between the simulation and the data, but in your measurement of
the error it is killed off by the weighting function.
Finally, it seems to me that you should NOT be using a Whipple model with set measured parameters.
Rather you should be fitting the coefficients in the Whipple model (the K's, C and M) as part
of your system ID. Then you can, for your curiosity, see how close that is to your more directly
measured Whipple model. I think Jim was saying that also, but I am not sure.
Jason: hoping to converge with fewer responses each time!
OK, that's a big one for me. I'm honored that Ron took the time to think it over. I'll put that issue in my queue.
>I asked Ron Hess your question and this was his response:
>"Not really. I can describe the dynamics of the human at various "crossover" frequencies
>and various performance levels. It's true, that it has been verified in many laboratory and
>vehicle control tasks where good performance was required."
>So it doesn't seem that your recollection is necessarily fact.
>It'd be nice to find some references that say this more explicitly.
What is "A" crossover frequency, I thought there was only "ONE" for a given plant.
Errrr --- This is a good place for the diff eq experts to jump in. Does one validate a differential equation by looking
>I've played around with checking this and it seems to be that a given measured steer torque
>that controlled the real system will not necessarily stabilize the Whipple model. So simulating
>the Whipple model seems to always blow up, but sometimes with "bad" initial condition estimates
>it will be stable but the comparisons of the experimental outputs with the simulation outputs is
>poor due to bias. But I'm not sure how to choose the right initial conditions. I was hoping that
>this would be easy to check, but it may not be. I'm probably won't spend much time on this,
>as Luke will be tackling specifically with better data very soon.
at the solution, or is it better to simply check whether the highest order derivative is instantaneously quite accurate.
I can see the issue that putting the measured torque as an open loop input into the Whipple
model could have an increasing divergence as time progressed, including a blowup
if the hands free model is not stable at that speed.
So maybe the better question is: for given state (steer and steer rate; lean and lean rate)
what are the steer acceleration and roll acceleration? That could either be with applied steer
torque or with no applied steer torque -- just use the measured torque.
If the equations are applicable, the linear relation between state plus torque, and the two output variables,
should be linear with coefficients constant at a given speed. Seems like many seconds of data should
permit a strong test of this idea. Then if the linear model DOES match most data, are the coefficients
close to predictions from the equations of motion?
Of course, WHERE the torque is measured (middle of steerer, or top of steerer below handlebars, or
applied to handlebars) changes the equations a little. If you imagine a flywheel disk
mounted either above or below the torque sensor, the measured torque for a given bicycle
motion will change. More complex conditions if the sensor is below the handlebar, and the handlebar has a mass
offset from the steer axis....
I guess I have to read that.....
>I add passive arms with spherical joints at the shoulders and the hand to handlebar grip connection.
>Revolutes at the elbows. I then constrain them to basically hang down. It's similar to a model Arend
>presented at the conference in Delft. See my rough explanation here:
> http://moorepants.github.com/dissertation/extensions.html#rider-arms
>If you have thoughts on an arm model that may be more realistic, I'm interested.
>From a preliminary glance it seems to be be higher by a factor. The data is available for use on my website.
>If you want a csv file of a particular run, just let me know what run number and I'll send it. I'll send you the
>Whipple parameters I estimated too. Run details are here:
> http://biosport.ucdavis.edu/research-projects/bicycle/instrumented-bicycle/run-information-table
> But this graph basically shows the bad torque predictions:
> http://biosport.ucdavis.edu/research-projects/bicycle/instrumented-bicycle/run-information-table
Aargh, more work if I want to be responsible! Thanks for the links.
>Look at the tDelta curve.
>See: http://moorepants.github.com/dissertation/extensions.html#rider-arms
MORE? (MOORE?)
OK, many thanks, this is very fruitful for me.
Jim
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2) Take a set of data and analyze it like this. Start one simulation at each data point.
Integrate forward in time from each. Take the difference between the simulated free variables
and the data. This much is what Jason did already. But now multiply by a weighting function
that discounts the future. This could be an exponential decay, a gaussian or a box function.
If the weighting function decays very fast this method is equivalent to (1) above. But if
it is substantially non-zero for some reasonable time into the future, it gives more weight
to fitting the difficult (unstable) modes. But you kill off the unstable divergence problem.
The divergence is still there between the simulation and the data, but in your measurement of
the error it is killed off by the weighting function.
Finally, it seems to me that you should NOT be using a Whipple model with set measured parameters.
Rather you should be fitting the coefficients in the Whipple model (the K's, C and M) as part
of your system ID. Then you can, for your curiosity, see how close that is to your more directly
measured Whipple model. I think Jim was saying that also, but I am not sure.
-Andy Ruina, ru...@cornell.edu, http://ruina.tam.cornell.edu
USA cell: +1 607 821-1442,
Skype: andyruina
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Jason: January 23, 2012This is all very good and clear but I don't quite understand it. Somecomments/questions.1) In all of the curves you show you take the torque as input and then integrateforward in time to get the angles vs time, using the best fit for the initial conditions. In your previous emails you seemed unable to do this because the equations were unstable so you got divergences. How did you get around this?
2) Have you tried the opposite, and tried to calculate the torque and then makethe comparison at the level of the torque? I realize this takes smoothingand differentiation, but you seem to have pretty good data. I am not sayingit is so, but I would like to be assured that the natural bike instabilityis not contaminating your fits.
3) Assuming your conclusions hold up, I think your wording at the end is a bittoo strong. The Whipple model equations seem to be good, but the Whipple physicalmeaning of the parameters seems to be not accurate.
But I would still want to check even that. For example have you played withtrail, something tricky to measure or even define when there is extended contact,as a free parameter? If you want to take the masses and geometry as givenand use your data for tire-model identification, I think you might want todo that anyway, as well as putting in a viscous contact torque that scales with1/v. At least these are two tire-model terms that fit into the Whipple model.
More than that, and you have to leave the Whipple dynamics equations, I believe,and put in lateral ground motions (slip) for which you have to reformulatethe dynamics equations a bit.
All in all it's a great project.
I'll interleave here, but leave out the things for which I have
no new comments.
On Jan 23, 2012, at 01/23/12 | 9:10 AM , Jason Moore wrote:
> Andy,
>
> On Sun, Jan 22, 2012 at 10:29 PM, Andy Ruina <ru...@cornell.edu> wrote:
> Jason: January 23, 2012
>
> This is all very good and clear but I don't quite understand it. Some
> comments/questions.
>
> 1) In all of the curves you show you take the torque as input and then integrate
> forward in time to get the angles vs time, using the best fit for the initial conditions. In your previous emails you seemed unable to do this because the equations were unstable so you got divergences. How did you get around this?
>
> In my first attempts I was wrongly trying to impose initial conditions (i.e. ones that cause the system to blow up). I didn't understand what I was doing. So now, I integrate forward in time with the measured steer torque, but search for the set of initial conditions that give the best least squares fit on of the model outputs compared to the measured outputs. In this case, you can find a set of initial conditions which give a stable output for the supplied torque input. So the instability I originally brought up previously seems to be a non-issue.
Let's say that you are in a regime where the Whipple model is unstable.
The problem would not be removed by your approach here, just delayed.
That is, if you simulated long enough you would have the same issues you
have previously. You just minimize them in the short run by fishing for
good initial conditions.
Now if your integration time is short enough, which yours seems to be,
then maybe all is maybe fine. But that your best initial conditions are
actually a poor match at t=0 seems to indicate a problem.
I would prefer if you model fit wasn't based on long integration times but on
a short window, as per my email of some weeks ago, or on the instantaneous
fit to the equations, which a calculation of torques from measured angles
would do (note that you have to calculate a lean torque also which hopefully
will be close to zero).
> btw - Your past student, Manoj, visited two weeks ago and we had some great discussions. We talked at length about this project and he was very helpful.
A smart thoughtful creative and helpful guy, in my experience.
-Andy Ruina, ru...@cornell.edu, http://ruina.tam.cornell.edu
Åland phone: +358 40 778-3435
USA phone: 607 821-1442 (forwards to Finland, no charge)
Skype: andyruina
I have been reading your post on the system identification and Andy's reply. Your guess is that its mainly tires that you are missing. Instead of starting from total darkness, have you considered adding tires to your model? For the tire model you only need a lateral slip coefficient, some initial guesses on this are in Roland, Kyle or recently Dressel.
Yours,
-Arend L. Schwab
a.l.s...@tudelft.nl
http://bicycle.tudelft.nl/schwab/
06 2852 7539
Season's Greetings http://bicycle.tudelft.nl/schwab/Xmas2011/
-----Original Message-----
From: st...@googlegroups.com [mailto:st...@googlegroups.com] On Behalf Of Andy Ruina
Sent: Monday, January 23, 2012 8:22 AM
To: st...@googlegroups.com
Subject: Re: [stvdy] System ID experts
Jason: January 23, 2012
--
Hi Jason,
I understand your concern about complex tire modeling but I’m proposing a very simple model: Flateral=Ca*alpha where alpha is the slip angle i.e. the angle between the wheel rolling direction and the velocity of the wheel, see f.i. Pacejka for a proper definition. So you add only one degree of freedom and only one constant Ca. You could consider adding also a tire model at the rear but I would start with only the front.
With the instruments you and Luke have it will be super easy to get your linearized Whipple model plus one extra degree of freedom for the lateral motion of the front wheel, right?
Wouldn't lateral slip destroy the form of the equations? Wouldn't a
viscous torsional contact damping be a simpler term to put in? Also,
taking the trail as a fit variable (because the contact patch is long)?
I am not saying these two things are best, but they are the easiest
to plug in, aren't they? If they don't work, then the next term in
the tire model is a lateral slip. But isn't the structure of the Whipple
equations then destroyed?
-Andy
Yes, assuming only scrub torque at the tire can be modeled by adding viscous torsional damping and that's only adding terms in the Whipple equation but I got the impression from Jason that the Whipple equations were not enough to fit his data. Modeling lateral tire slip adds an extra degree of freedom to the Whipple model, the structure is extended.
Hi Jason,
Hum, so you think the tire adds mainly spin torque stiffness and little spin torque damping? Note that the rider can add considerable stiffness by stiffening up his arms.
Research Scientist
Department Integrated Safety
Technical Sciences / Automotive
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