Some%Bipedal%Control%cs545/CS545_JohnRebula.pdf · Walking%Model%...

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Some Bipedal Control John Rebula Introduc7on to Robo7cs 2016 March 7

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)  

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(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)  

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(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)  

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(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)  

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(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)