Motion Synthesis for Articulated Human Bodies

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Motion Synthesis for Articulated Human Bodies
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Contents

• Human motion synthesis Zoo
• Articulated body mechanics
• Optimization based motion synthesis
• Feedback based balance control

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Human motion components

• 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

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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

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Human motion model (II)

• Deformable model
• Skin mesh motored by skeleton or captured skin
  animation
• Muscle shape representation

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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!
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Human motion model (IV)

• Visible Human data set (realistic musculature and
  flesh) Teran05

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Methods for motion synthesis (I)

• Data-driven based synthesis
• 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

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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

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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

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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

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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

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Contents

• Human motion synthesis Zoo
• Articulated body mechanics
• Optimization based motion synthesis
• Feedback based balance control

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Articulated body dynamics

• Each joint i is 1 DoF
• Ball-and-socket and saddle can
• be represented by some 1 DoF

• Ball-and-socket 3 DoF
• Saddle 2 DoF
• Hinge 1 Dof

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A special case of multi-body dynamics
Yins work gives an example
Joint makes impulse and penalty difficult
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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

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Inverse dynamics

• Known q, ,
• Unknown f, t
• 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)
• Roots p, v, a
• End effectors force and torque

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Forward dynamics

• Known q, , f, t
• Unknown
• More difficult
• 3 loops
• Evangelos04

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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 well-studied
  problem for rigid body simulation.
• See David Baraffs papers and note.

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Linear complementarity problem (LCP) Andreas

• One of the standard methods to handle contact and
  constraints.

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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

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Solution to LCP iterative method

• LCP can be represented by QP, so can be solved by
  iterative methods, like Gauss-Seidel, Newton

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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

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LCP model for constraints

• Unilateral constraint (force exists only when
  contacting)
• Joint Limit
• LCP guarantees zero virtual work for contact
  forces
• w Mz q?

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LCP model for constraints

• Use velocity-level dynamics equations, because
  acceleration-level dynamics equations will fail
  to obtain a solution in some configurations.
• Can be implemented in both reduced coordinate or
  full coordinate. But full coordinate need
  stabilization.

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Mixed LCP

• Sometimes LCP must be solved simultaneously with
  other equations without complementary constraints
  (e.g. dynamics equation and joint constraints)

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Solve mixed LCP

• Eliminate non LCP variables ( x )
• Directly modify pure LCP solver
• E.g. for pivot method non LCP variables are
  always in basic vector and does not take part in
  minimum ratio test.

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Extended LCP model for frictions

• Coulomb cone
• Dynamic friction Static friction

• Solved by extending iterative LCP solver

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Other possible solutions

• Extension to LCP
• Staggered Projections for Frictional Contact in
  Multibody Systems Danny08
• Velocity based shock propagationKenny09
• Implicit Contact Handling for Deformable Objects
  Miguel09

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Impact constraints

• Non-interpenetrate constraint
• Collision reaction
• Impulse or force modeling
• See David Baraffs papers and note.

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Simulation loops
LCP solver
forward dynamics
Ode solver
Collision detector
Impact response
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Contents

• Human motion synthesis Zoo
• Articulated body mechanics
• Optimization based motion synthesis
• Feedback based balance control

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Optimization based motion synthesis Sumit09
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System overview
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Lagrange mechanics
Generalized force
Lagrange function

• Lagrange mechanics for rigid body
• Lagrange mechanics for articulated body

Gravity, contact force, external force
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Complete force modeling Liu05
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Actuated and non actuated joint

• Root joint non (passive) actuated
• Its configuration (position and rotation) is
  actuated by joint constraints.
• Other joints (active) actuated
• Its configuration is actuated by muscle energy

Muscle force
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Passive controller

• Muscle controller
• Limited torque / force
• Limited torque / force change rate
• Contact controller
• Static friction
• Dynamic friction
• Non-penetration

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Optimization with passive controller

• Why (minimize q variation)?
• Avoid trivial solution, like sliding or break-off
• Zero virtual work guarantee
• Roll back

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User controller specification

• Balance controller
• Climb controller
• Swing controller
• Multiple controller composition
• controller example

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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.

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Balance controller
balance
takeStep
relaxFoot
p target position qv slow spline
perpendicular to ground cp CoM balance cf
support feet position c friction
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Climb controller
relaxHand
relaxFoot
allSupport
moveHand
moveFoot
com change CoM
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Swing controller
trySwing
passiveSwing
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Visual sensor

• Reachable objects search

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Contents

• Human motion synthesis Zoo
• Articulated body mechanics
• Optimization based motion synthesis
• Feedback based balance control

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Human motion control model
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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

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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 generalized-coordinate
  form and full-coordinate form

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Full-coordinate constrained matrix form (I)

• Constraint i between body a and b
• Constraint system (each item in J is 33 matrix)

Here f is dim-12 vector, every 3 sub-vector is
force for body (a, b, c, or d), J is 912
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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 is torque on all objects

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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

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Simulation result

• Perturbation by a ball

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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)

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Motion FSM

• Difference with FSM in Sumit09
• For control torque heuristics
• More robust (precision, static)

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Feed-forward Feed-back error learning

• Cyclic motion (function of phase)
• Learn inverse model dynamically (system
  identification)

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Feed-back control (I)

• PD control
• Contact control (support leg)

Low gain
Follow mocap data high gain
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Feed-back control (II)

• COM feedback

COM velocity
COM position
vgt0 or d gt 0 ? forward step quickly
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Feed-back control (III)

• CoM feedback

Basic controller (default target)
Continuous feedback
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Control summary

• 2D to 3D
• sagittal and coronal planes

Feedback and feedforward torques
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Simulation result

• demo
• Overview
• Downhill
• Drunk
• Limp
• Spin
• Boxes
• Different friction

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Reference

• 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 Physics-based 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
• Shinschiro07 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