Transcript Motion Synthesis for Articulated Bodies

Motion Synthesis for
Articulated Human Bodies
Contents
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Human motion synthesis: Zoo
Articulated body mechanics
Optimization based motion synthesis
Feedback based balance control
Human motion components
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Bone (skeleton): ~206 (motion invariant)
Joint (articulation): limitation
Tendon and ligament: elasticity / plasticity
Muscle: ~639, works in group, limitation
– uni-articulate and bi-articulate (passive
inefficiency)
– parallel or perpendicular shape
• Neuron-system: reflection speed
Neuron  Muscle  Tedon  Bone
Human motion model (I)
• Pure articulated model
– Simplified skeleton (hand / foot / tibia-fibula)
– Directly control force and torque on joints
– Convenient for high-level control
Human motion model (II)
• Deformable model
– Skin mesh motored by skeleton or captured
skin animation
– Muscle shape representation
Human motion model (III)
• Tendons and muscles model
– Musculoskeletal models and simulation
– Muscle-tendon model (strand)
Hand can have similar DoF with coarse
whole body!
Human motion model (IV)
• Visible Human data set (realistic
musculature and flesh) [Teran05]
Methods for motion synthesis (I)
• Data-driven based synthesis
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Captured motion skeleton data
Captured deformable data (face / skin)
Motion dynamics and naturalness is trivial
Limited response to environment
• Blending, Editing, Style transfer; no guarantee for physics
correctness
– Captured data is sparse
• [pose, time] space is huge
– Difficult to obtain data
• High dynamic motion
• Outdoor environment
Methods for motion synthesis (II)
• Pure generative-based synthesis
– Physics constraint can be guaranteed
– Easy to interact with dynamic environment
– Hard to be natural
• Naturalness is a subset of physics correctness
– Dynamics simulator complexity
• E.g. stable / dynamic frictions
– Computational complexity and stableness
• High gain means high stiffness
– Controller design
• Mutual controller is difficult to design and hard to generalize
Methods for motion synthesis (III)
• Pure motion planning
– Can obtain solution in constrained
environment
– High-level path planning
– Solution has no continuous or physics
guarantee
– Still time consuming
• High dimension of human skeleton
Combined methods
• Mocap data + physics: better controller
– Controller for hand [Nancy05]
– Controller for whole body [Yin08]
• Mocap data + motion planning: high level
motion:
– Manipulating [Katsu04]
– Tangling [Edmond08]
• Dynamics + motion
planning (for articulated model) [Russell07]
Other related
• Robotics [Kris06]
– Primitive based motion planning use transition
motion to balance natural motion and
environment constraints.
• Biomechanics
– Provides many principles
for motion control: balance,
Locomotion, neuroscience. [Alexandrov05] [Christine07]
Contents
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Human motion synthesis: Zoo
Articulated body mechanics
Optimization based motion synthesis
Feedback based balance control
Articulated body dynamics
• Ball-and-socket: 3 DoF
• Saddle: 2 DoF
• Hinge: 1 Dof
• Each joint i is 1 DoF
• Ball-and-socket and saddle can
be represented by some 1 DoF
A special case of multi-body
dynamics
Yin’s work gives
an example
Joint makes impulse
and penalty difficult
Parameters for articulated body
• State of root (position, rotation, linear /
angular velocity)
• Configuration of joints (q, , )
• Inertia matrix (for articulated body, inertia
matrix is an equivalent inertia matrix: give
a test force, get an acceleration  inertia)
• Lecture in COMP 790-058
Inverse dynamics
• Known: q, ,
• Unknown: f, τ
• Simple: recursive [Featherstone]
– Compute v and a; compute net force on a link,
similar to f = ma (downwards)
– Compute force and torque on a joint (upwards)
– Root’s p, v, a
– End effector’s force and torque
Forward dynamics
• Known: q, , f, τ
• Unknown:
• More difficult
– 3 loops
[Evangelos04]
Limitation of basic algorithms
• Many things are simplified in algorithms
– Joint limitation
– Unilateral constraint (ground constraint)
– Friction (kinetic, static, rolling and spinning)
– Non-interpenetrate constraint
– Collision response
• Modeling contact and constraint is a wellstudied problem for rigid body simulation.
– See David Baraff’s papers and note.
Linear complementarity problem
(LCP) [Andreas]
• One of the standard methods to handle
contact and constraints.
Solution to LCP: pivot method
• Basic idea: if q is positive or zero, solution
is trivial: (w = q, z = 0)
• Pivot q and w to make it true
• where
Solution to LCP: iterative method
• LCP can be represented by QP, so can be
solved by iterative methods, like GaussSeidel, Newton
Pros and Cons
• Pivot method
– Convergence is guaranteed after limited steps
– suffer from numerical problem, especially for
large-scale and/or ill-conditioned problems
• Iterative method
– easier to implement and
– numerically robust
– convergence is proven only for a limited class
of M matrix
LCP model for constraints
• Unilateral constraint (force exists only when contacting)
• Joint Limit
• LCP guarantees zero virtual work for
contact forces
• w = Mz + q?
Extended LCP model for frictions
• Coulomb cone
• Dynamic friction
Static friction
• Solved by extending iterative LCP solver
Other possible solutions
• Recent there are many new algorithms
other than LCP to deal with unilateral
constraints and friction
– Nonconvex Rigid Bodies with Stacking [Eran03]
• Extension to LCP
– Staggered Projections for Frictional Contact in
Multibody Systems [Danny08]
– Velocity based shock propagation[Kenny09]
– Implicit Contact Handling for Deformable
Objects [Miguel09]
Impact constraints
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Non-interpenetrate constraint
Collision reaction
Impulse or force modeling
See David Baraff’s papers and note.
Simulation loops
LCP solver
forward dynamics
Ode solver
Collision detector
Contact response
Contents
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Human motion synthesis: Zoo
Articulated body mechanics
Optimization based motion synthesis
Feedback based balance control
Optimization based motion
synthesis [Sumit09]
System overview
Lagrange
function
Lagrange mechanics
Generalize
d force
• Lagrange mechanics for rigid body
• Lagrange mechanics for articulated body
Gravity, contact force, external force
Complete force modeling [Liu05]
Actuated and non actuated joint
• Root joint: non (passive) actuated
– It’s configuration (position and rotation) is
actuated by joint constraints.
• Other joints: (active) actuated
– It’s configuration is actuated by muscle
energy
Muscle force
Passive controller
• Muscle controller
– Limited torque / force
– Limited torque / force change rate
• Contact controller
– Static friction
– Dynamic friction
– Non-penetration
Optimization with passive controller
• Why
(minimize q variation)?
– Avoid trivial solution, like sliding or break-off
• Zero virtual work guarantee
– Roll back
User controller specification
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Balance controller
Climb controller
Swing controller
Multiple controller composition
controller example
Controller protocol
• Finite State Machine
• Each state has its own constraints (in
objective form)
• State transition happens when feasible
solution can not find or contact breaks.
Balance controller
balance
takeStep
p: target position
qv: slow
spline: perpendicular to ground
cp: CoM balance
cf: support feet position
c: friction
relaxFoot
Climb controller
relaxFoot
relaxHand
allSupport
moveFoot
moveHand
com: change CoM
Swing controller
trySwing
passiveSwing
Visual sensor
• Reachable objects search
Contents
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Human motion synthesis: Zoo
Articulated body mechanics
Optimization based motion synthesis
Feedback based balance control
Human motion control model
Feedback based balance control
• Balance control under small perturbation
[Yin03]
• Balance control under large perturbation
[Yin08]
• Similar strategy: feed-back + feed-forward,
large perturbation  step strategy
System description
• The dynamics system does not use
generalized coordinate
• Instead, use full-coordinate constrained
form for dynamics
• Traditional style (based on Barraf 1996
paper)
• Control is a hybrid of generalizedcoordinate form and full-coordinate form
Full-coordinate constrained matrix
form (I)
• Constraint i between body a and b
• Constraint system (each item in J is 3*3
matrix)
Here f is dim-12 vector, every 3
sub-vector is force for body (a, b, c, or d), J is 9*12
Full-coordinate constrained matrix
form (II)
• For torque, similar
• row number of H is number of freedom, its
column number is 3 * object number.
• Each term is joint i’s torque on all objects
Balance control under small
perturbation
• Preprocess: use inverse dynamics to
compute force for original motion
• In each step of dynamic simulation
– Forward dynamics: current state
– Feedback control
– Feedforward control
– Net control
Simulation result
• Perturbation by a ball
Balance control under large
perturbation
• Two differences:
– Motion is modeled by finite state machine
– Under large perturbation, a pre-computed
feed-forward input is not suitable (using
adaptive control instead)
Motion FSM
• Difference with FSM in [Sumit09]
– For control torque heuristics
– More robust (precision, static)
Feed-forward: Feed-back error
learning
• Cyclic motion (function of phase)
• Learn inverse model dynamically (system
identification)
Feed-back control (I)
• PD control
Low gain
Follow mocap data: high gain
• Contact control (support leg)
Feed-back control (II)
• COM feedback
COM velocity
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v
v
v=0
d<0
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+ v=0
COM position
d>0
v>0 or d > 0  forward step quickly
Feed-back control (III)
• CoM feedback
Basic controller
(default target)
Continuous feedback
General form for multiple joints (matrix form)
Control summary
• 2D to 3D:
– sagittal and coronal planes
Feedback and feedforward torques
Simulation result
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demo
Overview
Downhill
Drunk
Limp
Spin
Boxes
Different friction
Reference
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[Edmond08] Planning tangling motions for humanoids
[Nancy05] Physically Based Grasping Control from Example
[Yin08] SIMBICON: Simple Biped Locomotion Control
[Katsu04] Synthesizing Animations of Human Manipulation Tasks
[Russell07] Efficient Motion Planning of Highly Articulated Chains using Physicsbased sampling
[Kris06] Using motion primitives in probabilistic sample-based planning for humanoid
robots
[Teran05] Creating and Simulating Skeletal Muscle from the Visible Human Data Set
[Alexandrov05] Feedback equilibrium control during human standing
[Christine07] Bipedal locomotion: toward unified concepts in robotics and
neuroscience
[Evangelos04] Practical Physics for Articulated Characters
[Shin’schiro07] Constraint-based dynamics simulator for humanoid robots with shock
absorbing mechanics
[Featherstone] Robot Dynamics Algorithms
[Andreas] Practical Optimization
[Eran03] Nonconvex Rigid Bodies with Stacking
[Danny08] Staggered Projections for Frictional Contact in Multibody Systems
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[Sumit09] Optimization-based interactive motion synthesis
[Liu05] Towards a generative model of natural motion
[Baraff89] Analytical methods for dynamics simulation of non-penetrating rigid bodies
[Yin03] Motion Perturbation Based on Simple Neuromotor Control Models
[Kenny09] Velocity-based shock progagation for multibody dynamics animation
[Miguel09] Implicit Contact Handling for Deformable Objects