Lecture University of Nevada Reno by MikeJenny

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									Computer Science & Engineering, University of Nevada, Reno




                 CS 282
            Simulation Physics

                    Lecture 26:
             Studying a Physics Engine:
            Open Dynamics Engine (ODE)


                    2 December 2010
                    Instructor: Kostas Bekris
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         ODE Manual

 http://opende.sourceforge.net/wiki/index.php/Manual
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         Example

 Run demo_crash
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         What is the Open Dynamics Engine

 Simulates physics of articulated rigid body structures
     • rigid bodies of various shapes are connected together with joints of
         various kinds
         - e.g., a car-like vehicle
            ✓the 4 wheels are connected with joints to the chassis
         - e.g., legged creatures
            ✓the legs are connected to the body
         - e.g., stacks of objects
            ✓that stay together because of friction and contact forces


 Designed to be used in interactive or real-time simulation
     • able to simulate moving objects in changeable virtual environments
     • emphasizes speed and stability over physical accuracy
         - specially-designed scientific simulators are more accurate

 Handling of contacts
     • Hard contacts instead of springs: non-penetration constraint is
         enforced
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         Main Features

 Rigid bodies
     • Bodies with static geometry and mass

 Joints
     • Multiple types: ball-and-socket, hinge, hinge-2, prismatic (slider),
         fixed, angular motor, linear motor, universal


 Forces and Torques
     • Applied to bodies and joints respectively

 Collision Primitives for bodies
     • Sphere, box, cylinder, capsule, plane, ray and triangular mesh

 Collision spaces for culling
     • Different alternatives: Quad Tree, Hash Space and Simple
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         Mains Features

 Simulation Method
     • Lagrangian dynamics instead of Newtonian
     • Integration method
         - fast but introduces errors
     • Multiple time stepping methods
     • Friction model that approximates Coulomb friction

 Written in C/C++
     • Provides a C++ interface
     • Has a native C interface as well

 Many unit tests and demos

 Platform specific optimizations
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         Data Types

 Mathematical data types
     • Quaternions, Matrices and Vectors
     • Necessary to keep track of rigid body configurations

 Important ODE objects
     • dWorld - A dynamics world
     • dSpace - A collision space
     • dBody - A rigid body
     • dGeom - A geometry used for collision checking
     • dJoint - A joint
     • dJointGroup - A group used to track sets of joints
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         Rigid Bodies




 State Parameters
     • Position Vector
     • Orientation
     • Linear Velocity
     • Angular Velocity

 Constant Properties
     • Mass
     • Position of center of mass
     • Inertia Matrix
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         Joints


 Act as interactions between rigid bodies
     • They introduce constraints for the configuration of rigid bodies
     • Some of them they might have motors that generate forces

 Types of joints:
     • Ball-and-socket
     • Hinge
     • Hinge-2
     • Prismatic (slider)
     • Fixed
     • Angular Motor
     • Linear Motor
     • Universal
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         Ball-and-socket and Universal

 Ball and Socket
 Similar to a shoulder joint
     • Not too restrictive

 Constraint
     • There exists a point where the
         connected bodies must remain
         at the same distance
     • 3 DOFs

 Universal
 Similar to B-a-S
 Constraints
     • Like B-a-S but 2nd body
         cannot freely rotate along a
         third axis
     • 2 DOFs
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         Hinge and Hinge-2

 Hinge
 Works like a door hinge

 Constraint:
     • The contact points must pivot
         around a central axis
     • 1 DOF


 Hinge-2
 Works like a car-wheel

 Constraint:
     • Rotation around 2 axes
     • 2 rotations DOFs
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         Prismatic and Piston Joints

 Slider/Prismatic
 Similar to a hydraulic piston
 Constraint:
     • Relative orientations are the same,
         except for distance
     • 1 DOF


 Piston
 Less constrained version of the
  prismatic joint

 Constraint:
     • Like prismatic joint, only that body
         2 can also rotate around the axis
     • 2 DOFs
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         Fixed and Contact Joints


 Fixed
 Just connect 2 rigid bodies into
  one

 0 DOFs

 Contact

 Subclass of fixed joints

     • formed temporarily for collision
         detection purposes
     • just for a single simulation step
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         Linear and Angular Motor joint

 Angular Motor
 Apply torques between two rigid
  bodiers

 No constraints
 3 DOFs



 Linear Motor
 Similar to an angular motor
     • but instead of torques, the
         joints apply forces
         - in a linear fashion

 No constraints
 3 DOFs
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         Combination Joints


 Prismatic Universal Joints
 Combination of prismatic and
  universal joint
     • 3 DOFs
         - 1 from prismatic
         - 2 from universal


 Prismatic Rotational Joints
 Combination of prismatic with
  hinge joint
     • 2 DOFs
         - 1 from prismatic
         - 1 from hinge
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         Joint errors




 As the simulation progresses and
  the rigid bodies move
     • there will be errors in the joints


 ODE uses an error reduction
 parameter (ERP)
     • the higher the ERP, the more will
         ODE try to auto-correct the
         position of the bodies


     • default value is relative low (0.2)
         to reduce computational
         overhead
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         Collision Handling

 Before each simulation step
     • collision detection callbacks are executed
         - to determine what is touching what
     • the callbacks return a list of contact points
     • each contact point specifies:
         - a position in space
         - a surface normal vector
         - a penetration depth
     • for each contact point, a contact joint is created that stores the
         following information (user specified):
         - the friction at the contact surface
         - how bouncy or soft the surfaces are
         - and various other properties
     • all the contact joints are added in a contact joint group
         - easy to add and remove from the simulation quickly
         - the simulation speed goes down as the number of contacts goes up
     • then a simulation step is taken
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         Types of Collisions Handled

 Which collisions are handled?
     • i.e., between which geometric primitives?
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         Physics Simulation




 Abstractions:
     • World
         - takes care of the dynamics, e.g., forces, gravity, etc.
     • Space
         - takes care of the geometry, e.g., collision handling, etc.


 A typical simulation proceeds as follows:
     • Initialize World and Space abstractions
     • Loop
         - Apply simulation step
     • Destroy the World and Space abstractions
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         Initialization


     • Create a dynamics world

     • Create the bodies of the dynamics world

     • Set the configurations of all the bodies

     • Create the joints of the dynamics world

     • Attach the joints to the bodies

     • Set the parameters for the joints

     • Create the corresponding collision world and geometries

     • Create a joint group to hold all collision joints
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         Simulation Loop


     • Apply forces to the bodies in the dynamics world

     • Adjust the joints as necessary

     • Call collision detection

     • Create a contact joint for each contact point
         - Add them to the group

     • Take a simulation step

     • Remove all contact joints from the group
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         Interaction between Dynamics World - Collision Space


 Force are applied to the world
     • and bodies are moved according to physics

 Collisions are detected by the space abstraction
     • if a collision is detected, the simulation backtracks until the point in
         time that the collision occurred
     • two time stepping functions
         - one more accurate and slower     O(m3) time complexity, m: # of
           constraints
         - one faster O(m*N), N: # of iterations that is a user-specified parameter

 At the point of collision, the world abstraction
     • calculates collision joints and forces
     • and progresses the simulation

 This repeats until the simulation step is complete
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         Simulation Physics class


 Why do we need a simulation physics class if there are available
  physics engines?

     • Each engine has a rather narrow area of application
         - e.g., ODE too slow for single rigid body simulation
         - e.g., ODE too inaccurate for scientific simulations and engineering
         - e.g., ODE rather slow for real-time AI algorithms

     • In many (if not most) cases, you will have to:
         - either adapt an existing engine
         - or make a specialized one for your application

     • In any case you need to be aware of the physics in rigid-body
         simulation

								
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