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DirectTrajectoryOptimization Class Reference

DIRECTTRAJECTORYOPTIMIZATION An abstract class for direct method approaches to trajectory optimization. More...

Inheritance diagram for DirectTrajectoryOptimization:
Collaboration diagram for DirectTrajectoryOptimization:

Public Member Functions

function DirectTrajectoryOptimization (plant, N, durations, options)
 function obj = DirectTrajectoryOptimization(plant,initial_cost,running_cost,final_cost, % t_init,traj_init,T_span,constraints, options) Trajectory optimization constructor More...
 
function getN (obj)
 
function getXinds (obj)
 
function getHinds (obj)
 
function addInputConstraint (obj, constraint, time_index)
 Add constraint (or composite constraint) that is a function of the input at the specified time or times. More...
 
function addStateConstraint (obj, constraint, time_index, x_indices)
 Add constraint (or composite constraint) that is a function of the state at the specified time or times. More...
 
function addTrajectoryDisplayFunction (obj, display_fun)
 add a dispay function that gets called on every iteration of the algorithm More...
 
function solveTraj (obj, t_init, traj_init)
 Solve the nonlinear program and return resulting trajectory. More...
 
function getInitialVars (obj, t_init, traj_init)
 evaluates the initial trajectories at the sampled times and constructs the nominal z0. More...
 
function setupVariables (obj, N)
 Default implementation, Assumes, if time is not fixed, that there are N-1 time steps N corresponding state variables and N-1 corresponding input variables Overwrite to change. More...
 
function addInitialCost (obj, initial_cost)
 Adds a cost to the initial state f(x0) More...
 
function addFinalCost (obj, final_cost_function)
 adds a cost to the final state and total time More...
 
function reconstructInputTrajectory (obj, z)
 default behavior is to use first order holds, but this can be re-implemented by a subclass. More...
 
function reconstructStateTrajectory (obj, z)
 default behavior is to use first order holds, but this can be re-implemented by a subclass. More...
 
function extractFirstInput (obj, z)
 When using trajectory optimization a part of a model-predictive control system, we often only need to extract u(0). More...
 
virtual function addRunningCost (obj, running_cost_function)
 Adds an integrated cost to all time steps, which is numerical implementation specific (thus abstract) this cost is assumed to be time-invariant. More...
 
virtual function addDynamicConstraints (obj)
 
- Public Member Functions inherited from NonlinearProgram
function NonlinearProgram (num_vars, x_name)
 
function addCompositeConstraints (obj, cnstr, xind, data_ind)
 add a CompositeConstraint to the object, change the constraint evalation of the program. More...
 
function addConstraint (obj, cnstr, varargin)
 obj = addConstraint(obj,cnstr,varargin) Queries the constraint type and calls the appropriate addConstraint method (e.g. More...
 
function addNonlinearConstraint (obj, cnstr, xind, data_ind)
 add a NonlinearConstraint to the object, change the constraint evalation of the program. More...
 
function addLinearConstraint (obj, cnstr, xind)
 add a LinearConstraint to the program More...
 
function addBoundingBoxConstraint (obj, cnstr, xind)
 add a BoundingBoxConstraint to the program More...
 
function addCost (obj, cnstr, xind, data_ind)
 Add a cost to the objective function. More...
 
function addQuadraticCost (obj, Q, x_desired, xind)
 helper function for the very common case of adding the objective g(x) = (x-xd)'Q(x-xd), Q = Q' >= 0 More...
 
function getArgumentArray (obj, x, xind)
 Retrieves the elements from the vector x related to xind and returns them as a cell array where: args{i} = x(xind{i}) More...
 
function nonlinearConstraints (obj, x)
 evaluate the nonlinear constraints More...
 
function objective (obj, x)
 return the value of the objective More...
 
function objectiveAndNonlinearConstraints (obj, x)
 evaluate the objective and the nonlinear constraints altogher More...
 
function addDecisionVariable (obj, num_new_vars, var_name)
 appending new decision variables to the end of the current decision variables More...
 
function replaceCost (obj, cost, cost_idx, xind)
 replace the cost_idx'th cost in the original problem with a new cost More...
 
function addSharedDataFunction (obj, user_fun, xind)
 Adds the specified shared data function to be evaluated within each iteration of the program. More...
 
function getNumSharedDataFunctions (obj)
 
function evaluateSharedDataFunctions (obj, x)
 Evaluate all shared data functions and return the data object. More...
 
function addDisplayFunction (obj, display_fun, indices)
 add a dispay function that gets called on every iteration of the algorithm More...
 
function setCheckGrad (obj, check_grad)
 
function setConstraintErrTol (obj, tol)
 
function setSolver (obj, solver)
 
function setSolverOptions (obj, solver, optionname, optionval)
 
function getNonlinearGradientSparsity (obj)
 This function sets the nonlinear sparsity vector iGfun and jGvar based on the nonlinear sparsity of the objective, nonlinear inequality constraints and nonlinear equality constraints. More...
 
function bounds (obj)
 return the bounds for all the objective function, nonlinear constraints and linear constraints More...
 
function solve (obj, x0)
 
function compareSolvers (obj, x0, solvers)
 
function isNonlinearConstraintID (obj, cnstr_id)
 Given an ID, determine if any of the nonlinear constraint obj.nlcon has that ID. More...
 
function isLinearConstraintID (obj, cnstr_id)
 Given an ID, determine if any of the linear constraint obj.lcon has that ID. More...
 
function isBoundingBoxConstraintID (obj, cnstr_id)
 Given an ID, determine if any of the bounding box constraint obj.bbcon has that ID. More...
 
function deleteConstraint (obj, delete_cnstr_id)
 delete a constraint from the program More...
 
function updateConstraint (obj, varargin)
 update a Constraint of the program. More...
 
function deleteNonlinearConstraint (obj, delete_cnstr_id)
 delete a nonlinear constraint from the program More...
 
function updateNonlinearConstraint (obj, varargin)
 updateNonlinearConstraint(obj,cnstr_id,cnstr,xind,data_ind) update the nonlinear constraint whose id=cnstr_id with a new Constraint object cnstr, the newly added Constraint cnstr has the ID new_cnstr_id More...
 
function deleteLinearConstraint (obj, delete_cnstr_id)
 delete the LinearConstraint obj.lcon{cnstr_idx} from the program More...
 
function updateLinearConstraint (obj, varargin)
 updateLinearConstraint(obj,cnstr_id,cnstr,xind) update the linear constraint whose id=cnstr_id with a new Constraint object cnstr, the newly added Constraint cnstr has the ID new_cnstr_id More...
 
function deleteBoundingBoxConstraint (obj, cnstr_id)
 delete the BoundingBoxConstraint in obj.bbcon with ID=cnstr_id from the program More...
 
function updateBoundingBoxConstraint (obj, varargin)
 updateBoundingBoxConstraint(obj,cnstr_id,cnstr,xind) update the BoundingBoxConstraint whose id=cnstr_id with a new BoundingBoxConstraint cnstr More...
 

Protected Member Functions

function final_cost (obj, final_cost_function, h, x)
 
- Protected Member Functions inherited from NonlinearProgram
function snopt (obj, x0)
 
function fmincon (obj, x0)
 if (obj.num_cin + obj.num_ceq) nonlinearConstraints = .nonlinearConstraint; else nonlinearConstraints = []; end More...
 
function ipopt (obj, x0)
 
function setVarBounds (obj, lb, ub)
 
function mapSolverInfo (obj, exitflag, x)
 Based on the solver information and solution, re-map the info. More...
 

Protected Attributes

Property N
 
Property options
 
Property plant
 
Property h_inds
 
Property x_inds
 
Property u_inds
 
Property dynamic_constraints
 
Property constraints
 
- Protected Attributes inherited from NonlinearProgram
Property num_vars
 
Property num_cin
 
Property num_ceq
 
Property Ain
 
Property bin
 
Property Ain_name
 
Property Aeq
 
Property beq
 
Property Aeq_name
 
Property cin_lb
 
Property cin_ub
 
Property cin_name
 
Property ceq_name
 
Property x_lb
 
Property x_ub
 
Property x_name
 
Property solver
 
Property solver_options
 
Property display_funs
 
Property display_fun_indices
 
Property check_grad
 
Property constraint_err_tol
 numerical gradient at the begining and end of the nonlinear optimization More...
 
Property nlcon
 
Property lcon
 
Property bbcon
 
Property cost
 
Property nlcon_xind
 
Property bbcon_xind
 nlcon{i}.eval(x(nlcon_xind{i}{1},x(nlcon_xind{i}{2},) cost_xind_cell % A cell array, cost_xind{i} is a cell array of int vectors recording the indices of x that is used in evaluating obj.cost{i} More...
 
Property shared_data_xind_cell
 a cell array like nlcon_xind, where shared_data_xind_cell{i} is a cell array of int vectors recording indices used in evaluating the shared_data_function More...
 
Property nlcon_dataind
 a cell array of function handles, each of which returns a data object so that shared_data{i} = shared_data_functions(x(shared_data_xind_cell{i}{1}),x(shared_data_xind_cell{i}{2}),) shared_data_functions More...
 
Property cost_dataind
 
Property iFfun
 2 if user has their own snopt in MATLAB path More...
 
Property iCinfun
 
Property iCeqfun
 

Detailed Description

DIRECTTRAJECTORYOPTIMIZATION An abstract class for direct method approaches to trajectory optimization.

Generally considers cost functions of the form: e(x0) + int(f(x(t),u(t)) + g(T,xf)

Subclasses must implement the two abstract methods: obj = addRunningCost(obj,running_cost); where running_cost is a NonlinearConstraint f(h,x,u) and obj = addDynamicConstraints(obj); which add the constraints to enforce xdot = f(x,u)

This class assumes that there are a fixed number (N) time steps, and that the trajectory is discreteized into timesteps h (N-1), state x (N), and control input u (N)

To maintain nominal sparsity in the optimization programs, this implementation assumes that all constraints and costs are time-invariant.

Constructor & Destructor Documentation

function DirectTrajectoryOptimization ( plant  ,
N  ,
durations  ,
options   
)

function obj = DirectTrajectoryOptimization(plant,initial_cost,running_cost,final_cost, % t_init,traj_init,T_span,constraints, options) Trajectory optimization constructor

Parameters
plant
Nthe number of time samples
durationThe lower and upper bounds on total time for the trajectory [lb ub]
options(optional) options.time_option {1: all time steps are constant, 2: all time steps are independent}
Return values
obj

Member Function Documentation

function addFinalCost ( obj  ,
final_cost_function   
)

adds a cost to the final state and total time

Parameters
final_cost_functiona function handle f(T,xf)
Return values
obj
function addInitialCost ( obj  ,
initial_cost   
)

Adds a cost to the initial state f(x0)

Return values
obj
function addInputConstraint ( obj  ,
constraint  ,
time_index   
)

Add constraint (or composite constraint) that is a function of the input at the specified time or times.

Parameters
constrainta Constraint or CompositeConstraint
time_indexa cell array of time indices ex1., time_index = {1, 2, 3} means the constraint is applied individually to knot points 1, 2, and 3. For convenience, [1,2,3] is also interpreted as {1,2,3}. ex2,. time_index = {[1 2], [3 4]} means the constraint is applied to knot points 1 and 2 together (taking the combined state as an argument) and 3 and 4 together.
Return values
obj
virtual function addRunningCost ( obj  ,
running_cost_function   
)
virtual

Adds an integrated cost to all time steps, which is numerical implementation specific (thus abstract) this cost is assumed to be time-invariant.

Parameters
running_cost_functiona function handle

Reimplemented in ContactImplicitTrajectoryOptimization, PseudoSpectralMethodTrajOpt, DircolTrajectoryOptimization, and DirtranTrajectoryOptimization.

function addStateConstraint ( obj  ,
constraint  ,
time_index  ,
x_indices   
)

Add constraint (or composite constraint) that is a function of the state at the specified time or times.

Parameters
constrainta CompositeConstraint
time_indexa cell array of time indices ex1., time_index = {1, 2, 3} means the constraint is applied individually to knot points 1, 2, and 3. For convenience, [1,2,3] is also interpreted as {1,2,3}. ex2,. time_index = {[1 2], [3 4]} means the constraint is applied to knot points 1 and 2 together (taking the combined state as an argument) and 3 and 4 together.
x_indexoptional subset of the state vector x which this constraint depends upon
Default: 1:num_x
Return values
obj
function addTrajectoryDisplayFunction ( obj  ,
display_fun   
)

add a dispay function that gets called on every iteration of the algorithm

Parameters
display_funa function handle of the form displayFun(t,x,u) where t is a 1-by-N, x is n-by-N and u is m-by-N
Return values
obj
function extractFirstInput ( obj  ,
 
)

When using trajectory optimization a part of a model-predictive control system, we often only need to extract u(0).

This method does exactly that.

Return values
u0
function final_cost ( obj  ,
final_cost_function  ,
,
 
)
protected
Return values
f
df
function getHinds ( obj  )
Return values
h_inds
function getInitialVars ( obj  ,
t_init  ,
traj_init   
)

evaluates the initial trajectories at the sampled times and constructs the nominal z0.

Overwrite to implement in a different manner

Return values
z0
function getN ( obj  )
Return values
N
function getXinds ( obj  )
Return values
x_inds
function reconstructInputTrajectory ( obj  ,
 
)

default behavior is to use first order holds, but this can be re-implemented by a subclass.

Return values
utraj
function reconstructStateTrajectory ( obj  ,
 
)

default behavior is to use first order holds, but this can be re-implemented by a subclass.

Return values
xtraj
function setupVariables ( obj  ,
N   
)

Default implementation, Assumes, if time is not fixed, that there are N-1 time steps N corresponding state variables and N-1 corresponding input variables Overwrite to change.

Generates num_vars total number of decision variables h_inds (N-1) x 1 indices for timesteps h so that z(h_inds(i)) = h(i) x_inds N x n indices for state u_inds N x m indices for time

Parameters
Nnumber of knot points
Return values
obj
function solveTraj ( obj  ,
t_init  ,
traj_init   
)

Solve the nonlinear program and return resulting trajectory.

Parameters
t_initinitial timespan for solution. can be a vector of length obj.N specifying the times of each segment, or a scalar indicating the final time.
traj_init(optional) a structure containing Trajectory objects specifying the initial guess for the system inputs traj_init.u , traj_init.x, %
Default: small random numbers
Return values
xtraj
utraj
z
F
info
infeasible_constraint_name

Member Data Documentation

Property constraints
protected
Property dynamic_constraints
protected
Property h_inds
protected
Property N
protected
Property options
protected
Property plant
protected
Property u_inds
protected
Property x_inds
protected

The documentation for this class was generated from the following file: