The class construction function.

Parameters

type	the type of the system
name	the name of the system

Adds event function for the dynamical system states and inputs.

Parameters

constr

the event function

Adds a holonomic constraint to the dynamical system.

Note

Any holonomic constraint introduces a set of constrained wrenchs to the system (Lagrangian multiplier).

Parameters

constr	the expression of the constraints
load_path	the path from which the symbolic expressions for the input map can be loaded

overload the superclass addState method with fixed state fields

Parameters

x	the state variables
dx	the first order derivative of state variables
ddx	the second order derivative of state variables

Adds unilateral (inequality) constraints on the dynamical system states and inputs.

Parameters

constr

the unilateral constraints

Adds a set of virtual constraints to the dynamical system.

Parameters

constr

the VirtualConstraint object

Append additional vf to the drift vector field Fvec(x) or Fvec(x,dx) of the system.

Parameters

vf

the f(x)

Generated fields of obj:

calculates the mass matrix Fvec(x) or Fvec(x,dx)

Parameters

x	the state variables
dx	the first order derivative of state variables

Todo:

This calculation is slow due to multiple function invoke. Better ideas to improve the speed?

calculate the dynamical equation dx

Parameters

t	the time instant
x	the states
controller	the controller
params	the parameter structure
logger	the data logger object

Return values

xdot	the derivative of the system states

calculates the mass matrix Mmat(x)

Parameters

x	the state variables

Detect the guard condition (event trigger)

Parameters

t	the absolute time
x	the system states
controller	the controller
params	the parameter structure
eventfuncs	a list of event function

Required fields of eventfuncs:

export the symbolic expressions of the system dynamics matrices and vectors and compile as MEX files.

Parameters

export_path	the path to export the file
varargin	variable input parameters compile ( ..., StackVariable, ForceExport, BuildMex, Namespace, NoPrompt ) Required Parameters for varargin: StackVariable whether to stack variables into one ForceExport force the export BuildMex flag whether to MEX the exported file Namespace the namespace of the function NoPrompt answer yes to all prompts

calculate the dynamical equation of the first order dynamical system

Parameters

t	the time instant
x	the states
controller	the controller
params	the parameter structure
logger	the data logger object

Return values

xdot	the derivative of the system states

Required fields of logger:

load the symbolic expression of system dynamical equations from MX binary files for fast loading

Parameters

file_path	the path to the files
vf_names	the names of the drift vectors Fvec
skip_load_vf	indicates whether to skip the loading of drift vectors which could takes a long time

Generated fields of obj:

Remove event functions defined for the system.

Parameters

name	the name of the constraint

Generated fields of obj:

Remove holonomic constraints defined for the system.

Parameters

name	the name of the constraint

Generated fields of obj:

Remove unilateral constraints defined for the system.

Parameters

name	the name of the constraint

Generated fields of obj:

Remove virtual constraints defined for the system.

Parameters

name	the name of the constraint

Generated fields of obj:

save the symbolic expression of system dynamical equations to a MX binary files

Parameters

export_path	the path to export the file
varargin	variable input parameters saveExpression ( ..., ForceExport ) Required Parameters for varargin: ForceExport force the export

calculate the dynamical equation of the second order dynamical system

Parameters

t	the time instant
x	the states
controller	the controller
params	the parameter structure
logger	the data logger object

Return values

xdot	the derivative of the system states

Required fields of logger:

Set the drift vector field Fvec(x) or Fvec(x,dx) of the system.

Parameters

vf

the f(x)

Generated fields of obj:

Set the mass matrix M(x) of the system.

Parameters

M	the mass matrix M(x)

Required fields of M:

Generated fields of obj:

Simulate the dynamical system.

Parameters

t0	the starting time instant
x0	the initial states
tf	the terminating time instant
controller	the controller for the dynamical system
params	extra parameters
logger	the data logger object
eventnames	the name of eventnames to be used
options	simulation options of hybrid system
solver	the ODE solver

Return values

sol	a structure contains the integration result of the ODE solver

Required fields of logger:

References outputfcn(), and str_index().

The event functions.

The event functions are often subset of the unilateral constraints defined on the system. For flexibility, we define them separately.

Note

This property has non-standard access specifiers: SetAccess = Protected, GetAccess = Public

Matlab documentation of property attributes.

The flow (trajectory) from the dynamical system simulation.

Note

This property has non-standard access specifiers: SetAccess = Protected, GetAccess = Public

Matlab documentation of property attributes.

The cell array of the drift vector fields Fvec(x) SymFunction.

We split the Fvec into many sub-vectors Fvec[i], such that

\begin{eqnarray*} Fvec = \sum_i^N Fvec[i] \end{eqnarray*}

Note

This property has non-standard access specifiers: SetAccess = Protected, GetAccess = Public

Matlab documentation of property attributes.

The holonomic constraints of the dynamical system.

Note

This property has non-standard access specifiers: SetAccess = Protected, GetAccess = Public

Matlab documentation of property attributes.

The mass matrix Mmat(x)

Note

This property has non-standard access specifiers: SetAccess = Protected, GetAccess = Public

Matlab documentation of property attributes.

The left hand side of the dynamical equation: M(x)dx or M(x)ddx.

Note

This property has the MATLAB attribute Hidden set to true.

This property has non-standard access specifiers: SetAccess = Private, GetAccess = Public

Matlab documentation of property attributes.

pre-process function handle of the object after the simulation

The function handle should have the syntax

params = postPorcess(sys, sol, controller, params, varargin)

pre-process function handle of the object before the simulation

The function handle should have the syntax

params = preProcess(sys, t, x, controller, params, varargin)

The unilateral constraints of the dynamical system.

Note

This property has non-standard access specifiers: SetAccess = Protected, GetAccess = Public

Matlab documentation of property attributes.

A handle to a function called by a trajectory optimization NLP to enforce system specific constraints.

The function handle should have the syntax

userNlpConstraint(nlp, bounds, varargin)

The virtual constraints of the dynamical system.

Note

This property has non-standard access specifiers: SetAccess = Protected, GetAccess = Public

Matlab documentation of property attributes.