Some%Bipedal%Control%cs545/CS545_JohnRebula.pdf · Walking%Model%...
Transcript of Some%Bipedal%Control%cs545/CS545_JohnRebula.pdf · Walking%Model%...
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Some Bipedal Control
John Rebula Introduc7on to Robo7cs 2016
March 7
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Controlling nonlinear systems
• Use tools you already know to solve interes7ng nonlinear problems
• For example, bipedal systems are: – Nonlinear (as are all real systems) – Underactuated – Hybrid Dynamic
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Problems with Pendulums:
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Problems with Pendulums:
How much torque do we need to get to top? Can we get to the top with less torque? Some7mes we need to think about trajectories
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Problems with Pendulums:
How much torque do we need to get to top? Can we get to the top with less torque? Some7mes we need to think about trajectories
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Problems with Pendulums:
How much torque do we need to get to top? Can we get to the top with less torque? Some7mes we need to think about trajectories
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Problems with Pendulums:
How much torque do we need to get to top? Can we get to the top with less torque? Some7mes we need to think about trajectories
“Underactuated”
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Problems with Pendulums:
Now, assume we have infinite torque, but finite foot. What happens if we apply the required gravity compensa7on torque?
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Problems with Pendulums:
What does our system look like if we apply the required gravity compensa7on torque?
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Problems with Pendulums:
What does our system look like if we apply the required tau?
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Problems with Pendulums:
What does our system look like if we apply the required tau? What is the effec7ve max torque?
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Problems with Pendulums:
What does our system look like if we apply the required tau? What is the effec7ve max torque? What about really Large tau?
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Problems with Pendulums:
Interes7ng systems might require path planning (or you might be doing exactly the wrong thing)
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Problems with Pendulums:
Interes7ng systems might require path planning Envelopes of opera7on
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Problems with Pendulums:
Interes7ng systems might require path planning Envelopes of opera7on Can find ways to apply our nice linear methods in some cases
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A walking system that requires no sensing, control, computer, etc.
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A walking system that requires no sensing, control, computer, etc.
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A walking system that requires no sensing, control, computer, etc.
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A walking system that requires no sensing, control, computer, etc.
“Hybrid”
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Another walking system
h\ps://www.youtube.com/watch?v=dl7KUUVHC-‐M
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One way to control walking stability
For more detail, a drac of a paper on this project is available at h\ps://dl.dropboxusercontent.com/u/19827221/2014-‐footYawStabilityPaperV3.pdf
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(Wisse 2005) (Kuo 1999)
fix
More info on bicycle stability: h\p://ruina.tam.cornell.edu/research/topics/bicycle_mechanics/papers.php
In par7cular, a very interes7ng bicycle that stabilizes without gyroscopic or caster effects (it uses mass distribu7on to couple lean with steering) h\p://ruina.tam.cornell.edu/research/topics/bicycle_mechanics/stablebicycle/index.htm
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(Wisse 2005) (Kuo 1999)
fix
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(Wisse 2005) (Kuo 1999)
fix
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[Ref] [Ref]
Do people use steering to avoid falls?
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Do people use steering to avoid falls?
Model Human Experiment
Keep this walker icon throughout model sec7on
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Walking Model
Add something technical that says that I’m an irregular person. Eoms?
Eoms were generated analy7cally Hybrid dynamics Collisions are perfectly inelas7c Constraints are enforced using constraint jacobians Limit cycle was found with walking down a gentle slope Using a sequen7al quadra7c programming rou7ne to enforce limit cycle constraints and anthropomorphic gait proper7es
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Walking Model
Add something technical that says that I’m an irregular person. Eoms?
Eoms were generated analy7cally Hybrid dynamics Collisions are perfectly inelas7c Constraints are enforced using constraint jacobians Limit cycle was found with walking down a gentle slope Using a sequen7al quadra7c programming rou7ne to enforce limit cycle constraints and anthropomorphic gait proper7es Analy7cal EOMs
Hybrid dynamics Inelas7c collisions Constraint jacobians SQP à Limit cycle Passive, down slope
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Walking Model
Fix this video
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Linearize Cyclic Dynamics
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Unstable Lateral Falling Mode
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Walking Model
Control to Stabilize Lateral Falling
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Stabilizing the Walking Model
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Stabilizing the Walking Model
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Stabilizing the Walking Model
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Stabilizing the Walking Model
replace
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Stabilizing the Walking Model Foot placement control
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Stabilizing the Walking Model
Perturb to the right
Foot placement control
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Stabilizing the Walking Model
Perturb to the right
Foot placement control
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Stabilizing the Walking Model
Perturb to the right
Foot placement control External rota7on control
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Stabilizing the Walking Model
Perturb to the right Perturb to the right
Foot placement control External rota7on control
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Stabilizing the Walking Model
Perturb to the right Perturb to the right
Foot placement control External rota7on control
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Do people use steering to avoid falls?
Model Human Experiment
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Do people use steering to avoid falls?
Model Human Experiment
Steering stabilizes mechanical model
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Normal Walking Expecta7on plots here (or first? On lec, move traces to right?)
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Normal Walking Expecta7on plots here (or first? On lec, move traces to right?)
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All Stride Correla7ons
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All Stride Correla7ons
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All Stride Correla7ons *, P < 0.05
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All Stride Correla7ons
Have correla7on show up, add p value
*, P < 0.05
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Simple models could be used for planning trajectories
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(Seth 2011)
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(Seth 2011)
(Posa 2013)
(O’Connor ?)
Simple models haven’t told us everything
(Ruina 2005), (Kuo 2005)
(Kuo 1999)
![Page 55: Some%Bipedal%Control%cs545/CS545_JohnRebula.pdf · Walking%Model% Add%something%technical%thatsays%thatI’m%an% irregular%person.%Eoms? Eoms%were%generated%analy7cally% Hybrid%dynamics%](https://reader034.fdocuments.in/reader034/viewer/2022042912/5f477c194d06a46a4b1e755f/html5/thumbnails/55.jpg)
(Seth 2011)
(Posa 2013)
(O’Connor ?)
Simple models haven’t told us everything
• Fundamental Dynamics
• Isolate Mechanisms – Foot placement -‐> Stability – Pushoff -‐> Efficiency
(Ruina 2005), (Kuo 2005)
(Kuo 1999)
![Page 56: Some%Bipedal%Control%cs545/CS545_JohnRebula.pdf · Walking%Model% Add%something%technical%thatsays%thatI’m%an% irregular%person.%Eoms? Eoms%were%generated%analy7cally% Hybrid%dynamics%](https://reader034.fdocuments.in/reader034/viewer/2022042912/5f477c194d06a46a4b1e755f/html5/thumbnails/56.jpg)
(Seth 2011)
(Posa 2013)
(O’Connor ?)
Simple models haven’t told us everything
• Fundamental Dynamics
• Isolate Mechanisms – Foot placement -‐> Stability – Pushoff -‐> Efficiency
(Ruina 2005), (Kuo 2005)
(Kuo 1999)
![Page 57: Some%Bipedal%Control%cs545/CS545_JohnRebula.pdf · Walking%Model% Add%something%technical%thatsays%thatI’m%an% irregular%person.%Eoms? Eoms%were%generated%analy7cally% Hybrid%dynamics%](https://reader034.fdocuments.in/reader034/viewer/2022042912/5f477c194d06a46a4b1e755f/html5/thumbnails/57.jpg)
(Seth 2011)
(Posa 2013)
(O’Connor ?)
Simple models haven’t told us everything
• Fundamental Dynamics
• Isolate Mechanisms – Stability (foot placement) – Efficiecny (Pushoff)
(Ruina 2005), (Kuo 2005)
(Kuo 1999)
![Page 58: Some%Bipedal%Control%cs545/CS545_JohnRebula.pdf · Walking%Model% Add%something%technical%thatsays%thatI’m%an% irregular%person.%Eoms? Eoms%were%generated%analy7cally% Hybrid%dynamics%](https://reader034.fdocuments.in/reader034/viewer/2022042912/5f477c194d06a46a4b1e755f/html5/thumbnails/58.jpg)
(Seth 2011)
(Posa 2013)
(O’Connor ?)
Simple models haven’t told us everything
• Fundamental Dynamics
• Isolate Mechanisms – Stability (foot placement) – Efficiency (Pushoff)
(Ruina 2005), (Kuo 2005)
(Kuo 1999)