Collision Concepts | In 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 Concepts | Collision filters are a purely non-physical concept |
Collision Cliques | |
Collision Filter Groups | |
Relationship Between Collision Filter Implementations | In principle, collision cliques and collision filter groups are equivalent implementations of filtering |
Input File Collision Semantics | |
Future Collision Filter Features | |
Multibody Dynamics Concepts | Translating 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 |
Terminology and Notation | Drake uses consistent terminology and notation for multibody mechanics |
Notation Basics | We are interested in representing physical quantities like position, orientation, inertia, and spatial velocity |
Frames and Bodies | The most fundamental object in multibody mechanics is the coordinate frame, or just frame |
Multibody Quantities | Quantities of interest in multibody dynamics have distinct types, which we denote with a single letter |
Spatial Algebra | Multibody dynamics involves both rotational and translational quantities, for motion, forces, and mass properties |
Spatial Pose and Transform | A spatial pose, more commonly just pose, provides the location and orientation of a frame B with respect to another frame A |
Spatial Vectors | Spatial 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 |
Compliant Point Contacts in Drake | Drake is concerned with the simulation of physical phenomena, including contact between simulated objects |
Detecting Contact | Given 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 |
Computing Contact Forces | Consider the definition of a contact with interpenetrating collision elements A and B |
Working with Contacts in Drake | The behavior of a simulation with contact will depend on three factors: |
Formulating and Solving Optimization Problems | Drake 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 |
Modeling Dynamical Systems | Drake uses a Simulink-inspired description of dynamical systems |
Automotive Systems | |
Rigid-Body Systems | |
Control Systems | |
Estimators | |
Primitives | |
Sensors | |