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PseudoSpectralMethodTrajOpt Class Reference

Pseudospectral (PS) method for trajectory optimization. More...

Inheritance diagram for PseudoSpectralMethodTrajOpt:
Collaboration diagram for PseudoSpectralMethodTrajOpt:

Public Member Functions

function PseudoSpectralMethodTrajOpt (plant, N, durations, options)
 
function addDynamicConstraints (obj)
 
function constraint_fun (obj, h1, x, u, varargin)
 dynamic constraint More...
 
function dynamics_data (obj, x, u)
 
function addRunningCost (obj, running_cost_function)
 Adds an integrated cost to all time steps, which is numerical implementation specific this cost is assumed to be time-invariant. More...
 
function reconstructInputTrajectory (obj, z)
 Interpolate all knot points to reconstruct a trajectory using Lagrange interpolation. More...
 
function reconstructStateTrajectory (obj, z)
 Interpolate all knot points to reconstruct a trajectory using Lagrange interpolation. More...
 
- Public Member Functions inherited from DirectTrajectoryOptimization
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...
 
- 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...
 

Public Attributes

Constant Property LGL = 1
 Legendre polynomials on LGL nodes % DEFAULT. More...
 
Constant Property CGL = 2
 chebyshev polynomial on CGL nodes More...
 

Protected Member Functions

function running_fun_end (obj, running_handle, x, u)
 running cost at the first node, which has the subtlety that is this knot point is implicity assosiated with the time step h=0 so feed the running_handle with a constant 0 as the time step instead of passing a variable More...
 
function running_fun_mid (obj, running_handle, h, x, u, weight)
 running cost at nodes 2 to N. More...
 
- Protected Member Functions inherited from DirectTrajectoryOptimization
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 tau
 
Property D
 
Property w
 
- Protected Attributes inherited from DirectTrajectoryOptimization
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

Pseudospectral (PS) method for trajectory optimization.

Constructor & Destructor Documentation

function PseudoSpectralMethodTrajOpt ( plant  ,
N  ,
durations  ,
options   
)
Return values
obj

Member Function Documentation

function addDynamicConstraints ( obj  )
virtual
Return values
obj

Reimplemented from DirectTrajectoryOptimization.

function addRunningCost ( obj  ,
running_cost_function   
)
virtual

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

Parameters
running_cost_functiona function handle of the form running_cost_function(dt,x,u)
Return values
obj

Reimplemented from DirectTrajectoryOptimization.

function constraint_fun ( obj  ,
h1  ,
,
,
varargin   
)

dynamic constraint

Parameters
h1,thefirst time step, used for keeping time-derivative from dynamics at the right scale
x,state,atthe current knot of consideration
u,input,atthe current knot of consideration
varargin,acell of system dynamics and their derivatives at all knot points, i.e., size(varagin)=obj.N
Return values
g
dg
function dynamics_data ( obj  ,
,
 
)
Return values
data
function reconstructInputTrajectory ( obj  ,
 
)

Interpolate all knot points to reconstruct a trajectory using Lagrange interpolation.

Return values
utraj
xtraj
function reconstructStateTrajectory ( obj  ,
 
)

Interpolate all knot points to reconstruct a trajectory using Lagrange interpolation.

Return values
xtraj
function running_fun_end ( obj  ,
running_handle  ,
,
 
)
protected

running cost at the first node, which has the subtlety that is this knot point is implicity assosiated with the time step h=0 so feed the running_handle with a constant 0 as the time step instead of passing a variable

Return values
f
df
function running_fun_mid ( obj  ,
running_handle  ,
,
,
,
weight   
)
protected

running cost at nodes 2 to N.

in case the running cost involves time, force the time steps to be weighted down in the discrete evalaution, and scale back up in the cost. the end result is that the cost in term of time and df/dt won't be weighted, but the cost involving states and inputs will. this trick won't work if the cost is time-variant, i.e., if the cost has terms like u*dt or x*dt

Return values
f
df

Member Data Documentation

Constant Property CGL = 2

chebyshev polynomial on CGL nodes

Property D
protected
Constant Property LGL = 1

Legendre polynomials on LGL nodes % DEFAULT.

Property tau
protected
Property w
protected

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