A Theory for Motion Primitive Adaptation

A Theory For Motion Primitive

Adaptation

A Theory For Motion Primitive

Adaptation

Richard SouthernNational Centre for

Computer Animation

Richard SouthernNational Centre for

Computer Animation

Liu, F.; Southern, R.; Guo, S.; Yang, X.; Zhang, J. J.; , "Motion Adaptation With Motor Invariant Theory," Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on, 2013

Talk StructureTalk Structure

● Background● Overview● Theory for Motion Adaptation● Entrainment for Structural Stability● Local Controllers for State Stability● Walking model● Results


Motivation: Character AnimationMotivation: Character Animation

● Still lots of problems in game character animation– Handling lots of character collisions (crowds)– Repetition of pre-recorded animations– Sliding when running into walls

● Still lots of problems in game character animation– Handling lots of character collisions (crowds)– Repetition of pre-recorded animations– Sliding when running into walls

The following clips thanks to David Greer @ NaturalMotion

Motivation: RoboticsMotivation: Robotics

“At present there is no accepted theory of how animals can, or robots might, be energy-stingy, robust, versatile and adaptable. Finding plausible schemes for the organization of a controller that has these features is, I think, the key problem in locomotion research today."

Andy Ruina, Cornell Robotics Group

“At present there is no accepted theory of how animals can, or robots might, be energy-stingy, robust, versatile and adaptable. Finding plausible schemes for the organization of a controller that has these features is, I think, the key problem in locomotion research today."

Andy Ruina, Cornell Robotics Group

Basic Assumptions of Low Level Motor ControlBasic Assumptions of Low Level Motor Control

● Brain not used much in low level locomotion ● Motion Primitives: building blocks of complex motion (e.g. frog

wave)● Body+Environment=Motion – animals don't move the way they

want, but the way they can (e.g. whale vs fish)● The central nervous system (CNS) only controls final motion

result, not process (equilibrium point hypothesis)

● Brain not used much in low level locomotion ● Motion Primitives: building blocks of complex motion (e.g. frog

wave)● Body+Environment=Motion – animals don't move the way they

want, but the way they can (e.g. whale vs fish)● The central nervous system (CNS) only controls final motion

result, not process (equilibrium point hypothesis)M. Latash, Neurophysiological Basis of Movement. Champaign, IL: Human Kinetics Publ., 2008.E. Bizzi, S. Giszter, E. Loeb, F. Mussa-Ivaldi, and P. Saltiel, “Modular organization of motor behavior in the frog’s spinal cord,” Trends Neurosci.,vol. 18, no. 10, pp. 442–446, Oct. 1995.A. G. Feldman, “Once more on the equilibrium-point hypothesis (λ model) for motor control,” J. Motor Behav., vol. 18(1), 17–54, Mar. 1986.

Basic Assumptions cont.Basic Assumptions cont.

● All interesting motion is periodic● Motion adaptation: CNS “tweaks” these primitives to adapt

to environmental changes● We're going to describe “tweaking” mathematically

● All interesting motion is periodic● Motion adaptation: CNS “tweaks” these primitives to adapt

to environmental changes● We're going to describe “tweaking” mathematically

What we don't do (yet)What we don't do (yet)

● High level motion planning– Computer vision– Adaptation selection

● Use complex biomechanical models (no ankles, muscles, running)

● Build robots● Rigorously test hypothesis on humans subjects

● High level motion planning– Computer vision– Adaptation selection

● Use complex biomechanical models (no ankles, muscles, running)

● Build robots● Rigorously test hypothesis on humans subjects

State (Dynamic) StabilityState (Dynamic) Stability

● How well does it respond to perturbations in state space? (e.g. walker is pushed)

● Region of stability = basin of attraction

● How well does it respond to perturbations in state space? (e.g. walker is pushed)

● Region of stability = basin of attraction

Structural StabilityStructural Stability

● If we change the system (e.g. add a term to the function), does the topology change?

● If we change the system (e.g. add a term to the function), does the topology change?




OverviewOverview

OverviewOverview

No input – not much happening

OverviewOverview

Global controller ensures stable periodic system

OverviewOverview

Local controller to alters limit cycle




The Motor InvariantThe Motor Invariant

● The motor invariant we want to preserve is the topology of the dynamic system.

● Type and Number of attractors do not change.● Shape of attractor and basin may change.

● The motor invariant we want to preserve is the topology of the dynamic system.

● Type and Number of attractors do not change.● Shape of attractor and basin may change.

Theory of Valid Motion AdaptationTheory of Valid Motion Adaptation

● For example: walker continues to walk, ball keeps bouncing ● Evidence: motion capture analysis, handwriting

adaptation*● Realised through Lie group symmetry

● For example: walker continues to walk, ball keeps bouncing ● Evidence: motion capture analysis, handwriting

adaptation*● Realised through Lie group symmetry

*Affine differential geometry analysis of human arm movementsTamar Flash and Amir A. Handzel, Biol Cybern. 2007 June; 96(6): 577–601.

A valid motion adaptation is one which preserves the motor invariant

What does this mean?What does this mean?

● These are validity conditions for motion adaptation● We can construct energy efficient controllers to make a

system more stable under certain environmental conditions

● These are validity conditions for motion adaptation● We can construct energy efficient controllers to make a

system more stable under certain environmental conditions




Application 1: Global ControllerApplication 1: Global Controller

● Design a controller to enhance state stability, or grow the basin of attraction

● Without changing the type or number of attractors

● Design a controller to enhance state stability, or grow the basin of attraction

● Without changing the type or number of attractors

EntrainmentEntrainment

● Couple an unconditionally stable oscillator with a potentially unstable one

● Stable oscillator controls unstable one● Both oscillators assume same period● Strong biological evidence

● Couple an unconditionally stable oscillator with a potentially unstable one

● Stable oscillator controls unstable one● Both oscillators assume same period● Strong biological evidence

A. H. Cohen, “Evolution of the vertebrate central pattern generator forlocomotion,” in Neural Control of Rhythmic Movements in Vertebrates.Hoboken, NJ: Wiley, 1988, pp. 129–166.

Oscillator couplingOscillator coupling● We use Matsuoka oscillator: exactly one periodic attractor.● F is mechanical system● S neural oscillator● Controller u input/output derived from oscillator

parameters / mechanical system parameters● h in/out user entrainment parameters

● We use Matsuoka oscillator: exactly one periodic attractor.● F is mechanical system● S neural oscillator● Controller u input/output derived from oscillator

parameters / mechanical system parameters● h in/out user entrainment parameters

K. Matsuoka. Sustained oscillations generated by mutuallyinhibiting neurons with adaptation. BiologicalCybernetics, 52(1):345–353, 1985.

Results: greater structural stabilityResults: greater structural stability

Results: enforces periodicityResults: enforces periodicity




Application 2: Local ControllerApplication 2: Local Controller

● Reasons to transform the dynamic system:– Move system so current state is within basin of attraction,

accounting for terrain variation– Change frequency of system (walk faster, bounce ball faster)– Change style of motion (more energetic, bounce ball higher)

● Effectively realised as a local affine transform to the state space.

● Reasons to transform the dynamic system:– Move system so current state is within basin of attraction,

accounting for terrain variation– Change frequency of system (walk faster, bounce ball faster)– Change style of motion (more energetic, bounce ball higher)

● Effectively realised as a local affine transform to the state space.

Local controller derivationLocal controller derivation

Divergence Shooting Our Method

Lie Group Control SymmetryLie Group Control Symmetry● Transforming a motion by a function g is equivalent

to transforming every state by g.● For each action g there is a corresponding “lift”

action Tg applied to tangential space● Control symmetry: solve Euler-Legrange equations

for transformed and untransformed systems

● Transforming a motion by a function g is equivalent to transforming every state by g.

● For each action g there is a corresponding “lift” action Tg applied to tangential space

● Control symmetry: solve Euler-Legrange equations for transformed and untransformed systems

Invariant Preserving OperatorsInvariant Preserving Operators

Controller DerivationController Derivation




Motion PrimitivesMotion Primitives

● Difficult to decouple motion primitives from complex motion

● Walking triggers little brain activity, uses very little energy● Passive Dynamic Walker (with knees) from robotics● Mechanical, physics based model, not a muscle model

● Difficult to decouple motion primitives from complex motion

● Walking triggers little brain activity, uses very little energy● Passive Dynamic Walker (with knees) from robotics● Mechanical, physics based model, not a muscle model

The following clip from the Cornell Robotics Group

Passive Dynamic WalkerPassive Dynamic Walker

● We use Chen's passive dynamic walker with knees● We use Chen's passive dynamic walker with knees

V. F. H. Chen. Passive dynamic walking with knees: Apoint foot model. Master’s thesis, Massachusetts Instituteof Technology, 2007.

Enhancing stabilityEnhancing stability

Slope 0.03 radsSlope 0.06 rads

+Neural Oscillator +Local Control

Motion AdaptationMotion Adaptation




ResultsResults

● Controller design choice influences state stability while maintaining structure

● Computationally trivial – a couple of matrix multiplications at each time step

● Very energy efficient – cost of transport 0.02 (half of Cornell Ranger, tenth of a human)

● Controller design choice influences state stability while maintaining structure

● Computationally trivial – a couple of matrix multiplications at each time step

● Very energy efficient – cost of transport 0.02 (half of Cornell Ranger, tenth of a human)

ApplicationsApplications

● Robot controller design● Rehabilitation: understanding human motion adaptation● One day: in character synthesis for games

● Robot controller design● Rehabilitation: understanding human motion adaptation● One day: in character synthesis for games

ChallengesChallenges

● Describing complex mechanical systems with solvable dynamic models (ankles, running and muscles)

● More complex (not affine transform) local controllers● Isolating motion primitives

● Describing complex mechanical systems with solvable dynamic models (ankles, running and muscles)

● More complex (not affine transform) local controllers● Isolating motion primitives

Questions?Questions?

AppendicesAppendices

Why Periodic Motion?Why Periodic Motion?

Using Degallier and Ijspeert 2010 as a reference, we argued that most motion is probably periodic, on a biological level at least.

Of the three types of attractors, chaos is not applicable to motion control problems, and fxed point attractors can be easily modeled using a traditional proportional derivative controller,which in many cases is a trivial problem.

For these reasons, periodic motion is of most interest to biology and robotics researchers, and are the most difficult to explain.

Using Degallier and Ijspeert 2010 as a reference, we argued that most motion is probably periodic, on a biological level at least.

Of the three types of attractors, chaos is not applicable to motion control problems, and fxed point attractors can be easily modeled using a traditional proportional derivative controller,which in many cases is a trivial problem.

For these reasons, periodic motion is of most interest to biology and robotics researchers, and are the most difficult to explain.

Matsuoka OscillatorMatsuoka Oscillator

Chen's model for passive dynamic walking with kneesChen's model for passive dynamic walking with knees

PD Controllers for Periodic MotionPD Controllers for Periodic Motion

● Problems with methods from Van De Panne et al.:– High gain (leading to stiffness)– Reference trajectory– Overshooting

● Problems with methods from Van De Panne et al.:– High gain (leading to stiffness)– Reference trajectory– Overshooting

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A Theory for Motion Primitive Adaptation

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