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[detail level 123]
oCollision ConceptsIn the real world, we can rely on the axiom that no two objects can occupy the same space at the same time; the universe provides this constraint for free
|\Collision Filter ConceptsCollision filters are a purely non-physical concept
| oCollision Cliques
| oCollision Filter Groups
| oRelationship Between Collision Filter ImplementationsIn principle, collision cliques and collision filter groups are equivalent implementations of filtering
| oInput File Collision Semantics
| \Future Collision Filter Features
oMultibody Dynamics ConceptsTranslating from the mathematics of multibody mechanics to correct code is a difficult process and requires careful discipline to ensure that the resulting code is correct
|oTerminology and NotationDrake uses consistent terminology and notation for multibody mechanics
||oNotation BasicsWe are interested in representing physical quantities like position, orientation, inertia, and spatial velocity
||oFrames and BodiesThe most fundamental object in multibody mechanics is the coordinate frame, or just frame
||\Multibody QuantitiesQuantities of interest in multibody dynamics have distinct types, which we denote with a single letter
|\Spatial AlgebraMultibody dynamics involves both rotational and translational quantities, for motion, forces, and mass properties
| oSpatial Pose and TransformA spatial pose, more commonly just pose, provides the location and orientation of a frame B with respect to another frame A
| oSpatial VectorsSpatial vectors are 6-element quantities that are pairs of ordinary 3-vectors
| \Spatial Mass Matrix (Spatial Inertia)A Spatial Mass Matrix (also called Spatial Inertia) M represents the mass, center of mass location, and inertia in a single 6×6 symmetric, mass-weighted positive definite matrix that logically consists of four 3×3 submatrices
oCompliant Point Contacts in DrakeDrake is concerned with the simulation of physical phenomena, including contact between simulated objects
|oDetecting ContactGiven two posed geometric shapes in a common frame, the collision detection system is responsible for determining if those shapes are penetrating and characterizing that penetration
|oComputing Contact ForcesConsider the definition of a contact with interpenetrating collision elements A and B
|\Working with Contacts in DrakeThe behavior of a simulation with contact will depend on three factors:
oFormulating and Solving Optimization ProblemsDrake wraps a number of commercial solvers (+ a few custom solvers) to provide a common interface for convex optimization, mixed-integer convex optimization, and other non-convex mathematical programs
oModeling Dynamical SystemsDrake uses a Simulink-inspired description of dynamical systems
|oAutomotive Systems
|oRigid-Body Systems
|oControl Systems