The constructor function.

Parameters

name	the name of the problem
plant	the dynamical system plant
num_grid	the number of grids along the trajectory
bounds	a structed data stores the boundary information of the NLP variables
varargin	user-defined options for the problem TrajectoryOptimization ( ..., [ "CollocationScheme", CollocationScheme_value ] [, "DistributeParameters", DistributeParameters_value ] [, "DistributeTimeVariable", DistributeTimeVariable_value ] [, "ConstantTimeHorizon", ConstantTimeHorizon_value ] [, "DerivativeLevel", DerivativeLevel_value ] [, "EqualityConstraintBoundary", EqualityConstraintBoundary_value ] ) Named Parameters for varargin: CollocationScheme CollocationScheme ( Default: HermiteSimpson ) DistributeParameters DistributeParameters ( Default: true ) DistributeTimeVariable DistributeTimeVariable ( Default: true ) ConstantTimeHorizon ConstantTimeHorizon ( Default: nan(2,1) ) DerivativeLevel DerivativeLevel ( Default: 1 ) EqualityConstraintBoundary EqualityConstraintBoundary ( Default: 0 )

Add direct collocation equations as a set of equality constraints.

Todo:

implement pseudospectral method

Add NLP constraints constraints.

See also

NlpFunction, removeConstraint

Note

Parameters

label	the label name (column) of the constraints
nodes	the node list of the variable
cstr_array	an array of structures that could be used to construct the NlpFunction object.

Add NLP object functions.

See also

NlpFunction, removeCost

Note

Parameters

label	the label name (column) of the cost
nodes	the node list of the variable
cost_array	an array of structures that could be used to construct the NlpFunction object.

Add system dynamics equations as a set of equality constraints.

Adds input variables as the NLP decision variables to the problem.

Note

The input variables may includes the control inputs, as well as external forces such as disturbance or contact wrenches.

Parameters

bounds

a structed data stores the boundary information of the NLP variables

Required fields of bounds:

Add NLP constraint function that only depends on variables at a particular node. The input argument 'nodes' will specify at which nodes the function is defined.

Note

This function provides a simple type of constraints function which dependends only on variables at same particular node.

Attention

In the case the constraints function dependes on variables at different nodes, please use the basic 'addCost' method directly.

This method can be used to add any terminal constraint by specify 'nodes' as either 'first' or 'last'.

Parameters

func	a symbolic function of the constraint
deps	a list of dependent variables
nodes	an indicator of first or last node
lb	the lower bound of the constraints
ub	the upper bound of the constraints
type	the type of the constraints ('Linear' or 'Nonlinear')
auxdata	auxilary constant data to be feed in the function

Required fields of func:

References implode().

Add a cost function that only depends on variables at a particular node. The input argument 'nodes' will specify at which nodes the function is defined.

Note

This function provides a simple type of cost function which dependends only on variables at some particular node. If multiple nodes are specified, the final cost function will be the sum of the function computated at each node.

Attention

In the case the cost function dependes on variables at different nodes, please use the basic 'addCost' method directly.

This method can be used to add any terminal cost function by specify 'nodes' as either 'first' or 'last'.

Parameters

func	a symbolic function to be integrated
deps	a list of dependent variables
auxdata	auxilary constant data to be feed in the function
node	an indicator of first or last node

Required fields of func:

References implode().

Adds parameters as the NLP decision variables to the problem.

Parameters

bounds

a structed data stores the boundary information of the NLP variables

Add a running cost to the problem.

Parameters

func	a symbolic function to be integrated
deps	a list of dependent variables
auxdata	auxilary constant data to be feed in the function

Required fields of func:

Adds state variables as the NLP decision variables to the problem.

Parameters

bounds

a structed data stores the boundary information of the NLP variables

Adds time as the NLP decision variables to the problem.

Parameters

bounds

a structed data stores the boundary information of the NLP variables

Required fields of bounds:

Adds NLP decision variables.

See also

NlpVariable, removeVariable

Parameters

label	the label name (column) of the variable
nodes	the node list of the variable
varargin	variable input arguments for property values non-empty NlpVariables This function updates the properties of the class object based on the input name-value pair arguments.
varargin	variable nama-value pair input arguments, in detail: updateProp ( lb, ub, x0 ) Required Parameters for varargin: lb lower limit ub upper limit x0 a typical value of the variable

Check the violation of the constraints.

Check the value of const function.

Check the violation of the constraints.

Compile and export symbolic expression and derivatives of all NLP functions.

Note

If constr is emtpy, then it will compile all constraints.

Parameters

constr	a list of constraints to be compiled
export_path	the path to export the file
exclude	a list of functions to be excluded
varargin	variable input parameters compileConstraint ( ..., StackVariable, ForceExport, BuildMex, Namespace ) 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

Compile and export symbolic expression and derivatives of all NLP functions.

Note

If cost is emtpy, then it will compile all cost functions.

Parameters

cost	the cost function to be compiled
export_path	the path to export the file
exclude	a list of functions to be excluded
varargin	variable input parameters compileObjective ( ..., ForceExport, BuildMex ) Required Parameters for varargin: ForceExport force the export BuildMex flag whether to MEX the exported file

configure the trajectory optimizatino NLP problem

This process will add NLP variables based on the information of the dynamical system object, impose dynamical and collocation constraints, then call the system constraints callback function to add any system-specific constraints.

Parameters

bounds

a struct data contains the boundary values

Note

If the number of node equals 1, then the system is either discrete event system or a ternimal node of a hybrid system. For this type of system, the problem is actually not a trajectory optimization problem. Hence no need to enforce the collocation constraint and dynamics constraint.

This function configures the structure of the optimization variable by adding (registering) them to the optimization variable table.

A particular project might inherit the class and overload this function to achieve custom configuration of the optimization variables

Parameters

bounds

a structed data stores the boundary information of the NLP variables

Required fields of bounds:

Return the SymFunction object of the direct collocation constraint given the state (x) and derivatives (dx).

Parameters

name	the name suffix of the function
x	the state SymVariable
dx	the derivative of states

Analyzes the solution of the NLP problem.

Parameters

sol	The solution vector of the NLP problem
t0	the initial time

Return values

tspan	the time span of the trajectory
states	the state trajectories
inputs	the input variable trajectories
params	the parameter variables

Removes a group of NLP constraints.

See also

addConstraint

Parameters

label

the label name (column) of the constraints

Removes a group of NLP cost functions.

See also

addCost

Parameters

label

the label name (column) of the cost function

Removes a NLP optimization variable.

See also

addVariable

Parameters

label

the label name (column) of the variable

Updates the NLP problems before load it to NLP solver.

Note

Overload the superclass (NonlinearProgram) for additional updates

Generated fields of obj:

This function updates the properties of the constraint objects based on the input name-value pair arguments.

Note

The note identifier can be either the numbers of node indices

or the following string to specify particular nodes

• first: the first node
• last: the last node
• all: all nodes
• cardinal: all cardinal (odd) nodes, only effective if HermiteSimpson scheme is used
• interior: all interior (even) nodes, only effective if HermiteSimpson scheme is used

Parameters

label	the row name of the constraints
node	the identifier of the node list
varargin	variable nama-value pair input arguments, in detail: updateConstrProp ( ..., lb, ub ) Required Parameters for varargin: lb lower limit ub upper limit

This function updates the properties of the cost function objects based on the input name-value pair arguments.

Note

The note identifier can be either the numbers of node indices

or the following string to specify particular nodes

• first: the first node
• last: the last node
• all: all nodes
• cardinal: all cardinal (odd) nodes, only effective if HermiteSimpson scheme is used
• interior: all interior (even) nodes, only effective if HermiteSimpson scheme is used

Parameters

label	the row name of the constraints
node	the identifier of the node list
varargin	variable nama-value pair input arguments, in detail: updateCostProp ( ..., lb, ub ) Required Parameters for varargin: lb lower limit ub upper limit

This function updates the boundary conditions of the optimization variable by updating corresponding NLP variables.

Parameters

bounds

a structed data stores the boundary information of the NLP variables

Required fields of bounds:

This function updates the properties of the NLP variable objects based on the input name-value pair arguments.

Note

The note identifier can be either the numbers of node indices

or the following string to specify particular nodes

• first: the first node
• last: the last node
• all: all nodes
• cardinal: all cardinal (odd) nodes, only effective if HermiteSimpson scheme is used
• interior: all interior (even) nodes, only effective if HermiteSimpson scheme is used

Parameters

label	the row name of the constraints
node	the identifier of the node list
varargin	variable nama-value pair input arguments, in detail: updateVariableProp ( ..., lb, ub, x0 ) Required Parameters for varargin: lb lower limit ub upper limit x0 a typical value of the variable

A table of NLP constraints. The row determines the identity of the constraint, and the column determines at which node the constraint is defined.

Note

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

Matlab documentation of property attributes.

A table of cost functions. The row determines the identity of the function, and the column determines at which node the variable is defined.

Attention

We assume the cost functioin (or objective) of a NLP is the sum of these cost functions.

Note

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

Matlab documentation of property attributes.

The default number of collocation grids.

Note

This property has the MATLAB attribute Hidden set to true.

Matlab documentation of property attributes.
Default: 10

The number of discrete nodes　along the trajectory.

Note

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

Matlab documentation of property attributes.

A table of NLP decision variables. The row determines the identity of the variable, and the column determines at which node the variable is defined.

Note

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

Matlab documentation of property attributes.

The dynamical system plant of the interest.

Note

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

Matlab documentation of property attributes.