## Weight repartition vs torque, balance

Discussions regarding building a walking robot at home. Most of the robots participating at Robo-One competitions are custom fabricated.
24 postsPage 2 of 21, 2
24 postsPage 2 of 21, 2
Hi all,

Before reading your comments, I was rather sharing i-Bot's view:

Based on a static point of view, I still think the ankle servo doesn't need to give that much torque because the only force that applies to the COG when the system is idle is the gravity force.
To get the momentum of resulting from this force on the ankle axis, you need to do a projection of the gravity force on an axis perpendicular to the lever axis. (That is, if my memory serves well). Considering the deviation angle from vertical position is small (be it only because the area of the foot is not big and once the projection of the COG gets out of that area, the biped will just fall, regardless of the ankle's torque), this projection result in a rather small number (approximation of cos(PI/2 +/-alpha) for alpha is alpha .. which is small)

For the hips, the problem is little bit the same but very different because this time, the lever is rather horizontal, so the projection will use alpha, whose cos approximation at small values is 1 - alpha. Here we are nearly facing the maximum momentum.

Something I apparently failed to catch is the dynamic behavior of the system. The following is a summary of what I understood, please correct if I am wrong (you may also confirm if I am correct ).
Here the forces applied are not only the gravity (which is still rather small) but also a force associated to the lateral acceleration of the robot (thanks luison for that missing dot).
Since the lateral acceleration is horizontal, its projection on the level perpenducular is done with a near-one projection ratio. Mass intervene in the lateral acceleration value as inertial term; this is rather here that we find the radius * "weight" expression that impacts the ankle torque.

Now, acceleration is a dynamic behavior, so using kinetic models with low acceleration profile such as S-curves can help reduce the ankle torque (thanks SK for this interesting point)
I don't think the same reasoning applies to the hip torque since its constraint is a static one.

Overall, my mistake was to limit the thinking to static behavior; things are quite different when the robot goes into motion. I am glad to have been corrected early in my design

Nevertheless, the original question remains
I can now reformulate based on the discussion so far. Independently of the respective servo torques (we can assume they all have the same torque to simplify the discussion), the question is "how to adjust the weight repartition in the leg?"
By setting the leg COG higher, I will favor the hips servos because its lever will be smaller. (I am considering only the leg subsystem here. I think that the leg COG position has little impact on how the whole system COG impact the hips work.)
By setting the leg COG lower, I will favor the ankle servos because I will lower the overal COG possion and thus reduce the lever size.

My answer to that would be to favor the hips servos because they are impacted by a static constraint, whereas ankle servos are impacted by a dynamic constraint and we can reduce the dynamic constraint with a better kinematic model.
What do you think?

(All of this is getting my physics back the hard way )

Cheers,

Stéphane
Hi all,

Before reading your comments, I was rather sharing i-Bot's view:

Based on a static point of view, I still think the ankle servo doesn't need to give that much torque because the only force that applies to the COG when the system is idle is the gravity force.
To get the momentum of resulting from this force on the ankle axis, you need to do a projection of the gravity force on an axis perpendicular to the lever axis. (That is, if my memory serves well). Considering the deviation angle from vertical position is small (be it only because the area of the foot is not big and once the projection of the COG gets out of that area, the biped will just fall, regardless of the ankle's torque), this projection result in a rather small number (approximation of cos(PI/2 +/-alpha) for alpha is alpha .. which is small)

For the hips, the problem is little bit the same but very different because this time, the lever is rather horizontal, so the projection will use alpha, whose cos approximation at small values is 1 - alpha. Here we are nearly facing the maximum momentum.

Something I apparently failed to catch is the dynamic behavior of the system. The following is a summary of what I understood, please correct if I am wrong (you may also confirm if I am correct ).
Here the forces applied are not only the gravity (which is still rather small) but also a force associated to the lateral acceleration of the robot (thanks luison for that missing dot).
Since the lateral acceleration is horizontal, its projection on the level perpenducular is done with a near-one projection ratio. Mass intervene in the lateral acceleration value as inertial term; this is rather here that we find the radius * "weight" expression that impacts the ankle torque.

Now, acceleration is a dynamic behavior, so using kinetic models with low acceleration profile such as S-curves can help reduce the ankle torque (thanks SK for this interesting point)
I don't think the same reasoning applies to the hip torque since its constraint is a static one.

Overall, my mistake was to limit the thinking to static behavior; things are quite different when the robot goes into motion. I am glad to have been corrected early in my design

Nevertheless, the original question remains
I can now reformulate based on the discussion so far. Independently of the respective servo torques (we can assume they all have the same torque to simplify the discussion), the question is "how to adjust the weight repartition in the leg?"
By setting the leg COG higher, I will favor the hips servos because its lever will be smaller. (I am considering only the leg subsystem here. I think that the leg COG position has little impact on how the whole system COG impact the hips work.)
By setting the leg COG lower, I will favor the ankle servos because I will lower the overal COG possion and thus reduce the lever size.

My answer to that would be to favor the hips servos because they are impacted by a static constraint, whereas ankle servos are impacted by a dynamic constraint and we can reduce the dynamic constraint with a better kinematic model.
What do you think?

(All of this is getting my physics back the hard way )

Cheers,

Stéphane
Stephane offline
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I can't see if you put pics or not (in my work don't allow some urls ). But reading you, i think you are wrong.
The hip servo, wastes practically all it's torque supporting the momentum force of the chest, not the lever of the other leg.

In general, the best is down your COG or a symmetric leg, but never a high COG, or that is what i think
I can't see if you put pics or not (in my work don't allow some urls ). But reading you, i think you are wrong.
The hip servo, wastes practically all it's torque supporting the momentum force of the chest, not the lever of the other leg.

In general, the best is down your COG or a symmetric leg, but never a high COG, or that is what i think
luison offline
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Well an obvious choice for shifting the COG is placing the batteries either in the feet or somewhere above the legs. Having the batteries in the feet of course results in a lower COG, but doing so the feet have higher mass, which always has to be accelerated and decelerated during walking (from zero velocity when in contact with the ground to twice walking velocity when putting the foot forward). In contrast to this, the upper body typically follows a more regular motion pattern, not requiring this acceleration of battery weight when they are placed there.
I'm thus not quite sure that "never a high COG" is always and in every aspect true. As I mentioned before, it also depends on the geometry/kinematics and gait of the robot one is looking at.
Well an obvious choice for shifting the COG is placing the batteries either in the feet or somewhere above the legs. Having the batteries in the feet of course results in a lower COG, but doing so the feet have higher mass, which always has to be accelerated and decelerated during walking (from zero velocity when in contact with the ground to twice walking velocity when putting the foot forward). In contrast to this, the upper body typically follows a more regular motion pattern, not requiring this acceleration of battery weight when they are placed there.
I'm thus not quite sure that "never a high COG" is always and in every aspect true. As I mentioned before, it also depends on the geometry/kinematics and gait of the robot one is looking at.
SK offline
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SK wrote:Well an obvious choice for shifting the COG is placing the batteries either in the feet or somewhere above the legs. Having the batteries in the feet of course results in a lower COG, but doing so the feet have higher mass, which always has to be accelerated and decelerated during walking (from zero velocity when in contact with the ground to twice walking velocity when putting the foot forward). In contrast to this, the upper body typically follows a more regular motion pattern, not requiring this acceleration of battery weight when they are placed there.
I'm thus not quite sure that "never a high COG" is always and in every aspect true. As I mentioned before, it also depends on the geometry/kinematics and gait of the robot one is looking at.

In some strange case... it's possible higher is better.
SK wrote:Well an obvious choice for shifting the COG is placing the batteries either in the feet or somewhere above the legs. Having the batteries in the feet of course results in a lower COG, but doing so the feet have higher mass, which always has to be accelerated and decelerated during walking (from zero velocity when in contact with the ground to twice walking velocity when putting the foot forward). In contrast to this, the upper body typically follows a more regular motion pattern, not requiring this acceleration of battery weight when they are placed there.
I'm thus not quite sure that "never a high COG" is always and in every aspect true. As I mentioned before, it also depends on the geometry/kinematics and gait of the robot one is looking at.

In some strange case... it's possible higher is better.
luison offline
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Joined: Wed Mar 24, 2010 11:47 am

luison wrote:The hip servo, wastes practically all it's torque supporting the momentum force of the chest, not the lever of the other leg.

Actually, my reasoning was a little bit carried away by this topic, where the robot tries kung fu figures.
In such case, the position of the other leg drags the position of the overall COG away from the supporting hip, and increases the momentum force of the chest + other leg. The more the COG of the other leg is closed to the ankle, the bigger the impact (though I don't have calculations to attach a figure to this impact).

About the "never a high COG" debate, I feel it depends the purpose of the robot:
Seeing Luison's video, he seems to rather target fighting robots, where stability is the key point.
SK is rather participating to socker competition, where mobility is the key point. In that perspective, I find SK's points very interesting (all the more that they precisely challenge the common places of COG position).
luison wrote:The hip servo, wastes practically all it's torque supporting the momentum force of the chest, not the lever of the other leg.

Actually, my reasoning was a little bit carried away by this topic, where the robot tries kung fu figures.
In such case, the position of the other leg drags the position of the overall COG away from the supporting hip, and increases the momentum force of the chest + other leg. The more the COG of the other leg is closed to the ankle, the bigger the impact (though I don't have calculations to attach a figure to this impact).

About the "never a high COG" debate, I feel it depends the purpose of the robot:
Seeing Luison's video, he seems to rather target fighting robots, where stability is the key point.
SK is rather participating to socker competition, where mobility is the key point. In that perspective, I find SK's points very interesting (all the more that they precisely challenge the common places of COG position).
Stephane offline
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Fighting is just the way towards a larger goal
Why i've put a camera?
Fighting is just the way towards a larger goal
Why i've put a camera?
luison offline
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Stephane wrote:SK is rather participating to socker competition, where mobility is the key point. In that perspective, I find SK's points very interesting (all the more that they precisely challenge the common places of COG position).

Well an intuitive analogy would probably be: Would you rather mount 2 3kg weights to your feet or carry the 6kg in a backpack? Carrying them on the feet makes you more statically stable, but as soon as you want to move you´ll definetly notice that overall energy consumption and the torque requirements in your leg "actuators" have increased. Of course the analogy is flawed, because the human balance control and actuation system is much more sophisticated than a robot´s and thus a high COG isn´t so much of a problem for us. Still, as soon as things are supposed to move, dynamics play an important role and should not be ignored.

@Luison:
Your new robot looks pretty good (and the old one too, even if probably a bit hardware limited) , what will be the scenarios it will be used for?
Stephane wrote:SK is rather participating to socker competition, where mobility is the key point. In that perspective, I find SK's points very interesting (all the more that they precisely challenge the common places of COG position).

Well an intuitive analogy would probably be: Would you rather mount 2 3kg weights to your feet or carry the 6kg in a backpack? Carrying them on the feet makes you more statically stable, but as soon as you want to move you´ll definetly notice that overall energy consumption and the torque requirements in your leg "actuators" have increased. Of course the analogy is flawed, because the human balance control and actuation system is much more sophisticated than a robot´s and thus a high COG isn´t so much of a problem for us. Still, as soon as things are supposed to move, dynamics play an important role and should not be ignored.

@Luison:
Your new robot looks pretty good (and the old one too, even if probably a bit hardware limited) , what will be the scenarios it will be used for?
SK offline
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Posts: 105
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Location: near Frankfurt/Main, Germany

Putting two lipos one in each foot (60g each lipo) helped improving my bioloid's stability - less swinging from left to right. He has a total weight of 2.3Kg (including batteries).
Putting two lipos one in each foot (60g each lipo) helped improving my bioloid's stability - less swinging from left to right. He has a total weight of 2.3Kg (including batteries).
F'dan il-passatemp ghandek bzonn zewg affarijiet - FLUS u HIN. Zewg affarijiet li huma skarsi hafna u li jien minnhom ghandi vera ftit!
JavaRN offline
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SK wrote:
Stephane wrote:SK is rather participating to socker competition, where mobility is the key point. In that perspective, I find SK's points very interesting (all the more that they precisely challenge the common places of COG position).

Well an intuitive analogy would probably be: Would you rather mount 2 3kg weights to your feet or carry the 6kg in a backpack? Carrying them on the feet makes you more statically stable, but as soon as you want to move you´ll definetly notice that overall energy consumption and the torque requirements in your leg "actuators" have increased. Of course the analogy is flawed, because the human balance control and actuation system is much more sophisticated than a robot´s and thus a high COG isn´t so much of a problem for us. Still, as soon as things are supposed to move, dynamics play an important role and should not be ignored.

@Luison:
Your new robot looks pretty good (and the old one too, even if probably a bit hardware limited) , what will be the scenarios it will be used for?

Ok SK, that's a really good point.

My first robot, use a BasicX running at 8MHz, with only 400bytes of RAM... now i use a chip more powerfull, running my code, i'm complete sure that the AXON will not be the problem (second core or chip for sensors ), the real problem in power is the CMUcamp3... i still haven't programmed it, and i have some really good ideas for it, but only ideas.

Scenarios: I use robo-one tournaments for teach my robot how to move., so this year, only robo-one tournaments, like http://bipedolandia.com/sites/default/f ... CAMUBI.png . The next year... i don't know, everything is on the air (if i go, for example, to robocup, i would go only with one robot, pay all the trip... i don't know)
SK wrote:
Stephane wrote:SK is rather participating to socker competition, where mobility is the key point. In that perspective, I find SK's points very interesting (all the more that they precisely challenge the common places of COG position).

Well an intuitive analogy would probably be: Would you rather mount 2 3kg weights to your feet or carry the 6kg in a backpack? Carrying them on the feet makes you more statically stable, but as soon as you want to move you´ll definetly notice that overall energy consumption and the torque requirements in your leg "actuators" have increased. Of course the analogy is flawed, because the human balance control and actuation system is much more sophisticated than a robot´s and thus a high COG isn´t so much of a problem for us. Still, as soon as things are supposed to move, dynamics play an important role and should not be ignored.

@Luison:
Your new robot looks pretty good (and the old one too, even if probably a bit hardware limited) , what will be the scenarios it will be used for?

Ok SK, that's a really good point.

My first robot, use a BasicX running at 8MHz, with only 400bytes of RAM... now i use a chip more powerfull, running my code, i'm complete sure that the AXON will not be the problem (second core or chip for sensors ), the real problem in power is the CMUcamp3... i still haven't programmed it, and i have some really good ideas for it, but only ideas.

Scenarios: I use robo-one tournaments for teach my robot how to move., so this year, only robo-one tournaments, like http://bipedolandia.com/sites/default/f ... CAMUBI.png . The next year... i don't know, everything is on the air (if i go, for example, to robocup, i would go only with one robot, pay all the trip... i don't know)
luison offline
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24 postsPage 2 of 21, 2
24 postsPage 2 of 21, 2