2004 IEEERSJ International Conference on intelligent Robots and Systems

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2004 IEEE/RSJ International Conference on
intelligent Robots and Systems
IROS 2004
Generation of Multi-step limit cycles for Rabbit
using a low dimensional nonlinear predictive
control scheme
A. CHEMORI M. ALAMIR
Laboratoire d'Automatique de Grenoble. UMR
5528 BP46,Domaine Univesitaire, 38402 Saint
Martin d'Hères, France. Ahmed.Chemori(Mazen.Alami
r)_at_inpg.fr
September, 28th, 2004 Sendai International
Center, Sendai, Japan
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Outline of the presentation

• Rabbit prototype

• Walking control problem formulation

• The robot dynamic

• The proposed control nonlinear predictive
  scheme

• The stability issue

• Illustrative simulations

• General conclusion

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• 5 limbs a torso 2 legs with knees
• Without ankles punctual contact
• Up to 7 d.o.f
• 4 actuators (DC motors with speed reducers)
• Under-actuated biped walking robot
• 4 sensors to measure the joint angles

• Walking in a circular path, and
• Lateral stabilization
• Thanks to

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• Objective stable dynamic walking control of
  the biped
• Assumptions

• Friction forbids any sliding (to be checked a
  posteriori)
• The walking takes place in the sagittal plan,
  on a level
• surface without obstacles

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• 7 d.o.f nonlinear dynamic model

• the system is
  under-actuated

• The single support phase model

holonomic constraints

• The impact phase model (rigid impact)

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- Summary of the approach -
7 d.o.f Nonlinear Dynamic
Single support assumption
Holonomic constraints
Independent coordinates
Dependent coordinates
Under-actuation
Completely controllable
uncontrollable
Zero dynamic trajectories
Parameterized trajectories
Optimization
Prediction
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- Details -
impact
impact
. . . . . .
. . . . . .

• boundary conditions (at ith sample time)

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with the impact map
using the prediction
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(No Transcript)
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since
then the overall stability depends on the
stability of the sequence
using and the impact map leads to
the prediction over gives
In multi-step (k0 step) form
A key quantity in stability analysis, see the
following
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Example of typical situation
___ convergence
bisector
___ divergence
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Example of typical situation
bisector
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Walking at constant mean velocity starting from
rest
Actuated coordinates
Femurs
Tibias
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Unactuated coordinates
Cartesian coordinates of the hips
x coordinate of the hips
y coordinate of the hips
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Unactuated coordinates
Coordinates of the torso
Its phase portrait
Its position and velocity
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Foot contact forces and control inputs
Foot contact forces
Control inputs
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Stability analysis according to proposition
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MPEG movie of the robot animation
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• Addressed Problem walking control of an
  under-actuated biped robot

• Confronted with Nonlinear open-loop unstable
  system
• Under-actuation
• Hybrid dynamic

• Proposed control scheme a nonlinear
  predictive control approach

• Closed-loop system stability analysis
  Poincaré section method

• Future work implementation on the real plant
  testbed

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Thank you for your attention