Model Types

abstract type AbstractModel

Abstraction of a model of a dynamical system of the form ẋ = f(x,u), where x is the n-dimensional state vector and u is the m-dimensional control vector.

Any inherited type must define the following interface: ẋ = dynamics(model, x, u) n,m = size(model)

abstract type RigidBody <: AbstractModel

Abstraction of a dynamical system with free-body dynamics, with a 12 or 13-dimensional state vector: [p; q; v; ω] where p is the 3D position, q is the 3 or 4-dimension attitude representation, v is the 3D linear velocity, and ω is the 3D angular velocity.

Interface

Any single-body system can leverage the RigidBody type by inheriting from it and defining the following interface:

forces(::MyRigidBody, x, u)  # return the forces in the world frame
moments(::MyRigidBody, x, u) # return the moments in the body frame
inertia(::MyRigidBody, x, u) # return the 3x3 inertia matrix
inertia_inv(::MyRigidBody, x, u)  # return the 3x3 inverse of the inertia matrix
mass_matrix(::MyRigidBody, x, u)  # return the 3x3 mass matrix

Rotation Parameterization

A RigidBody model must specify the rotational representation being used. Any of the following can be used:

• UnitQuaternion: Unit Quaternion. Note that this representation needs to be further parameterized.
• MRP: Modified Rodrigues Parameters
• RPY: Roll-Pitch-Yaw Euler angles

struct InfeasibleModel{N, M, D<:AbstractModel} <: AbstractModel

An infeasible model is an augmented dynamics model that makes the system artifically fully actuated by augmenting the control vector with n additional controls. The dynamics are handled explicitly in discrete time:

$x_{k+1} = f(x_k,u_k,dt) + w_k$

where $w_k$ are the additional n-dimensional controls. In practice, these are constrained to be zero by the end of the solve.

Constructors

InfeasibleModel(model::AbstractModel)