Eric Whitman 72009 Outline Existing controller Evaluation Resistance to perturbations Speed Control Proposed controller and work towards it 3D Biped Complex System 5 Rigid Links 24 dimensional state space ID: 637166
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Slide1
Multi-Policy Control of Biped Walking
Eric Whitman
7/20/09Slide2
Outline
Existing controller
Evaluation
Resistance to perturbations
Speed Control
Proposed controller and work towards itSlide3
3D Biped (Complex System)
5
Rigid Links
24 dimensional state space
12 control
dimensionsTorque-controlled jointsStatic friction with groundμ=1.0Slide4
Dividing the System
Simplified Coronal Model
Simplified Sagittal ModelSlide5
Sagittal Plane Dynamics
Forward Kinematics
Newton’s Second Law
Non-rotating Torso
For Leg
Substituting:
Simplifying:Slide6
Sagittal Plane Dynamics (Touch Down)
Commanded as an action at any time
Slide7
Sagittal Plane Policy Generation
Ankle Torque Policy
Touchdown PolicySlide8
Full System Sagittal ControlSlide9
Sagittal System Comparison
Major Discrepancies:
Swing Leg Acceleration – Negative initial acceleration
Torso Bob – High late-step accelerationSlide10
Touchdown Prediction
Ankle Torque Policy
Touchdown Policy
Duration of Simulation:Slide11
Time Until Touch DownSlide12
Predicted Angle and Angular Velocity at Touch DownSlide13
Swing Leg Requirements
Must reach touchdown angle at touchdown time
Must touch down without slipping (velocity matching)
Must not accelerate rapidly
Must not touch ground during swingSlide14
Trajectory Generation
Cubic
Spline
Start at current leg angle and angular velocity
Go to predicted touch down angle and angular velocitySlide15
Trajectory Update
Start at currently desired angle and angular velocity
End at new estimate of touch down angle and angular velocity
T
ime
AngleSlide16
Swing Leg Trajectory TrackingSlide17
Swing Knee
Use knee to control swing leg length
Must not touch down during swing
Command foot to 5 cm above ground
Must touch down at appointed time with a straight leg
Command knee angle to straighten linearly:Slide18
Swing Foot Height and Knee AngleSlide19
Coronal Plane Control
Similar dynamics to sagittal plane
Touchdown is different
Switch sides
Pick angle of touch down
Small anglesState not actionSimplified system – counts down and reset to nominal periodFull system – provided by sagittal policySlide20
Full and Simple Coronal ComparisonSlide21
Coronal Swing Leg
Simulate forward to get desired touch down angle
Track with PD servoSlide22
Yaw Control
PD controller on the ankle rotation axis – axis parallel to shin
Does not work well due to large coupling
Must use low gainsSlide23
Perturbation Resistance by TimeSlide24
Failure ModesSlide25
Speed Control by LeaningSlide26
Speed Control By PoliciesSlide27
Parameters
Sagittal Stance
Cost function weights – 2
Nominal Speed
Speed lost at touchdown
Sagittal SwingFoot heightKnee extension rate
Coronal Plane
Cost function weights – 3
Nominal leg angle
Speed lost at touchdown
PD servos
Stance hip – 2Swing hip – 2Swing kneeYaw ankleSlide28
Planned Improvements
Collaborative Coordination
Swing leg policy
More sophisticated sagittal and coronal models
Arms
Better Yaw ControlSlide29
Collaborative Coordination
Each policy supplies V(
t
td
)
Select ttd to minimize sum(V(ttd)) at each time stepEach policy must then know how to act optimally given that
t
td
Slide30
Sagittal Policy with t
tdSlide31
Sagittal Policy with t
tdSlide32
Swing Hip Policy
Dynamic programming
5D state
Angle
Angular velocity
Target AngleTarget Angular VelocityTarget TimeCost Model for TrajectoriesSlide33
Upgraded Simple Models
Unrestrict
the torso angle
Adds 2 more states
Adds an action
Better touch down modelEffect on velocity depends on angleSlide34
Arms
Add an arm swing policy
Probably does not need to participate in collaborative coordination – can be subordinate
Add an estimate of arm swing effect to sagittal policySlide35
Improved Yaw Control
Use adjusted pitch and roll ankle torques to cancel the coupled portion of the rotation torques
Change gain with step
High gain mid-step
Low gain at touchdown
Coordinate with leaning or foot placement?Slide36
Coronal Swing
Can cause trouble if it does not reach its target by touch down
Make a model of tracking error
PD rise time or slew speed
Report expected error to coronal controller
Coronal controller knows cost of this errorSlide37
Robust DP
Normally:
Use:
Or: