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LQRTree Class Reference
Inheritance diagram for LQRTree:
Collaboration diagram for LQRTree:

Public Member Functions

function LQRTree (xG, uG, tilqr, V)
 
function addTrajectory (obj, xtraj, utraj, tvlqr, Vtv, parentID, parentT)
 
function getSampleTime (obj)
 
function inAnyFunnelGuard (obj, t, ignoredArg, x)
 
function transitionIntoAnyFunnel (obj, m, t, ignoredArg, x)
 
function checkFunnels (obj, x)
 find lowest V for this x, by searching over ti and tv funnels. More...
 
function onTreeConstraint (obj, x)
 note: the input x is in the plant state frame (everything else inside this class is stored in the input frame of the controller) More...
 
- Public Member Functions inherited from HybridDrakeSystem
function HybridDrakeSystem (num_u, num_y)
 
function addMode (obj, mode_sys, name)
 
function addTransition (obj, from_mode_num, guard, transition, directFeedthrough, timeInvariant, to_mode_num)
 guard is a function pointer with style: phi = guard(fsm_obj,t,mode_x,u) with phi a scalar, which indicates a transition when phi<=0. More...
 
function andGuards (obj, varargin)
 produces a single guard that is a logical 'and' of the variable number of guards input. More...
 
function notGuard (obj, orig_guard)
 
function drawModeGraph (obj)
 depends on having graphviz2mat installed (from matlabcentral) todo: make that a dependency in configure? More...
 
function getMode (obj, mode_num)
 
function getInitialMode (obj)
 
function getInitialState (obj)
 
function getInitialStateWInput (obj, t, x, u)
 
function dynamics (obj, t, x, u)
 
function update (obj, t, x, u)
 
function output (obj, t, x, u)
 
function zeroCrossings (obj, t, x, u)
 
function resolveConstraints (obj, x, v)
 
function transitionUpdate (obj, t, x, u)
 
function setOutputFrame (obj, frame)
 
function setInputFrame (obj, frame)
 
function feedback (sys1, sys2)
 
function cascade (sys1, sys2)
 
function transverseLQR (p, w, xtraj, utraj, Qtraj, Rtraj, Qfinal, Qjump, periodic, TransSurf)
 Generates a hybrid solution of transverse TVLQR. More...
 
- Public Member Functions inherited from DrakeSystem
function DrakeSystem (num_xc, num_xd, num_u, num_y, direct_feedthrough_flag, time_invariant_flag)
 Construct a DrakeSystem. More...
 
function zeroCrossings (obj, t, x, u)
 Placeholder for the zeroCrossings method: a method phi = zeroCrossings(t,x,u) which triggers a zero crossing event when phi transitions from positive to negative. More...
 
function getNumContStates (obj)
 Returns the number of continuous states. More...
 
function getNumDiscStates (obj)
 Returns the number of discrete states. More...
 
function getNumInputs (obj)
 Returns the number of inputs to the system. More...
 
function getNumOutputs (obj)
 Returns the number of outputs from the system. More...
 
function getInitialStateWInput (obj, t, x, u)
 Hook in case a system needs to initial state based on current time and/or input. More...
 
function getInputSampleTimes (obj)
 Returns getSampleTime - a DrakeSystem can only have a single same time associated with it. More...
 
function getOutputSampleTimes (obj)
 Returns getSampleTime - a DrakeSystem can only have a single same time associated with it. More...
 
function setSampleTime (obj, ts)
 robust method for setting default sample time More...
 
function isDirectFeedthrough (obj)
 Check if the system is direct feedthrough (e.g., if the output depends on the immediate input) More...
 
function setDirectFeedthrough (obj, tf)
 Set the direct feedthrough flag. More...
 
function getModel (obj)
 Constructs a simulink system block for this system to be used by the simulink engine. More...
 
function findFixedPoint (obj, x0, u0)
 attempts to find a fixed point (xstar,ustar) which also satisfies the constraints, using (x0,u0) as the initial guess. More...
 
function getDefaultInput (obj)
 Define the default initial input so that behavior is well-defined if no controller is specified or if no control messages have been received yet. More...
 
function setNumContStates (obj, num_xc)
 Guards the num_states variable. More...
 
function setNumDiscStates (obj, num_xd)
 Guards the num_states variable. More...
 
function setNumInputs (obj, num_u)
 Guards the num_u variable. More...
 
function setInputLimits (obj, umin, umax)
 Guards the input limits to make sure it stay consistent. More...
 
function setNumOutputs (obj, num_y)
 Guards the number of outputs to make sure it's consistent. More...
 
function getNumZeroCrossings (obj)
 Returns the number of zero crossings. More...
 
function setNumZeroCrossings (obj, num_zcs)
 Guards the number of zero crossings to make sure it's valid. More...
 
function getNumStateConstraints (obj)
 
function getNumUnilateralConstraints (obj)
 
function addStateConstraint (obj, con, xind)
 
function updateStateConstraint (obj, id, con, xind)
 
function displayStateConstraints (obj)
 
function removeAllStateConstraints (obj)
 
function addStateConstraintsToProgram (obj, prog, indices)
 adds state constraints and unilateral constraints to the program on the specified indices. More...
 
function addInputConstraintsToProgram (obj, prog, indices)
 add bounding box constraint todo: consider whether it makes sense to a list of constraints objects instead of just input limits. More...
 
function stateConstraints (obj, x)
 Provides the old interface of a single constraint function which evaluates all of the equality constraints on the state (which should be == 0) More...
 
function linearize (obj, t0, x0, u0)
 Uses the geval engine to linearize the model around the nominal point, at least for the simple case. More...
 
function simulate (obj, varargin)
 
function simulateODE (obj, tspan, x0, options)
 Simulates the system using the ODE45 suite of solvers instead of the simulink solvers. More...
 
function feedback (sys1, sys2)
 Constructs a feedback combination of sys1 and sys2. More...
 
function cascade (sys1, sys2)
 Constructs a cascade combination of sys1 and sys2. More...
 
function extractPolynomialSystem (obj)
 Attempts to symbolically extract the extra structure of a polynomial system from the Drake system Will throw an error if the system is not truly polynomial. More...
 
function extractAffineSystem (obj)
 Attempts to symbolically extract the extra structure of an affine system from the Drake system Will throw an error if the system is not truly affine. More...
 
function extractLinearSystem (obj)
 Attempts to symbolically extract the extra structure of a linear system from the Drake system Will throw an error if the system is not truly linear. More...
 
function makeTrigPolySystem (obj, options)
 deprecated method (due to refactoring): please use extractTrigPolySystem instead More...
 
function systemGradTest (obj, t, x, u, options)
 Compare numerical and analytical derivatives of dynamics,update,and output. More...
 
function extractAffineSystem (obj)
 
function extractTrigPolySystem (sys, options)
 tries to convert the current system into a trig-poly system More...
 
function taylorApprox (sys, varargin)
 performs a taylorApproximation around a point or trajectory usage: taylorApprox(sys,t0,x0,u0,order[,ignores]) or taylorApprox(sys,x0traj,u0traj,order[,ignores]) it returns a polynomial system (or polynomial trajectory system) More...
 
function transverseLQR (obj, xtraj, utraj, Q, R, Qf, transSurf)
 Compute LQR control for transversal system. More...
 
function transverseLQRClosedLoop (obj, xtraj, utraj, Q, R, Vf, transSurf)
 
function tvlqr (obj, xtraj, utraj, Q, R, Qf, options)
 implements the time-varying linear (or affine) quadratic regulator More...
 
- Public Member Functions inherited from DynamicalSystem
function DynamicalSystem ()
 
function inInputFrame (sys, frame)
 Ensures that sys has the specified input frame, by searching for and cascading a coordinate transformation to the existing input if necessary. More...
 
function inStateFrame (sys, frame)
 Ensures that sys has the specified state frame. More...
 
function inOutputFrame (sys, frame)
 Ensures that sys has the specified output frame, by searching for and cascading a coordinate transformation to the existing output if necessary. More...
 
function cascade (sys1, sys2)
 Creates a new system with the output of system 1 connected to the input of system 2. More...
 
function feedback (sys1, sys2)
 Creates a new systems with sys1 and sys2 in a feedback interconnect (with sys1 on the forward path, and sys2 on the return path). More...
 
function parallel (sys1, sys2)
 Creates a new system that takes the inputs to both sys1 and sys2 as a single input (which is "demux"ed and passed independently to the two systems), and outputs the "mux"ed output of the two systems. More...
 
function sampledData (sys, tsin, tsout)
 Creates a new system which is a sampled data (e.g. More...
 
function resolveConstraints (obj, x0, v, constraints)
 attempts to find a x which satisfies the constraints, using x0 as the initial guess. More...
 
function addStateConstraintsToProgram (obj, prog, indices)
 adds state constraints and unilateral constriants to the program on the specified indices. More...
 
function getNumStates (obj)
 Returns the total number of states (discrete + continuous) in the system. More...
 
function getInputSampleTimes (obj)
 Returns the sample time of the input See getSampleTime for more details about sample times. More...
 
function getOutputSampleTimes (obj)
 Returns the sample time of the output See getSampleTime for more details about sample times. More...
 
function isDT (obj)
 Returns true if the system has no states, or has states and only one sample time [a b], with a>0. More...
 
function isCT (obj)
 Returns true if the system has only one sample time [a b], with a==0. More...
 
function isInheritedTime (obj)
 Returns true if the system has only one sample time [a b], with b==-1. More...
 
function isTI (obj)
 Returns true if the system is time-invariant. More...
 
function setTIFlag (obj, bval)
 Sets the time invariant flag. More...
 
function getInputFrame (obj)
 Access the CoordinateFrame object that defines the input to this system. More...
 
function setInputFrame (obj, fr)
 Set the CoordinateFrame object that defines the input of this system. More...
 
function getStateFrame (obj)
 Access the CoordinateFrame object that defines the state of this system. More...
 
function setStateFrame (obj, fr)
 Set the CoordinateFrame object that defines the state of this system. More...
 
function getOutputFrame (obj)
 Access the CoordinateFrame object that defines the output to this system. More...
 
function setOutputFrame (obj, fr)
 Set the CoordinateFrame object that defines the output of this system. More...
 
function getNumStateConstraints (obj)
 Returns the scalar number of state constraints (of the form phi(x)=0) More...
 
function stateConstraints (obj, x)
 defines state equality constraints in the form phi(x)=0 More...
 
function unilateralConstraints (obj, x)
 defines state unilateral constraints in the form phi(x)>=0 More...
 
function getNumUnilateralConstraints (obj)
 Returns the scalar number of state constraints (of the form phi(x)>=0) More...
 
function setSimulinkParam (obj, varargin)
 Sets parameters of the simulink model Syntax setSimulinkParam(obj,param_name,param_value[,param_name,param_value,]) % Se. More...
 
function linearize (obj, t0, x0, u0)
 Linearize the system about an operating point (continuous time) More...
 
function dlinearize (obj, ts, t0, x0, u0)
 Linearize the system about an operating point (discrete time) More...
 
function setParams (obj, p)
 This default setParams method attempts to set class properties of the system according to the coordinate names in the parameter frame. More...
 
function getParams (obj)
 This default getParams method attempts to get class properties of the system according to the coordinate names in the parameter frame. More...
 
function getNumParams (obj)
 
function setParamFrame (obj, fr)
 Set the CoordinateFrame object which describes any system parameters. More...
 
function getParamFrame (obj)
 Returns the CoordinateFrame object which describes any system parameters. More...
 
function setParamLimits (obj, pmin, pmax)
 Set lower and upper bounds on the system parameters. More...
 
function getParamLimits (obj)
 Returns the current lower and upper bounds on the system parameters. More...
 
function parameterEstimation (obj, data, options)
 Estimate parameter values from input-output data. More...
 
function runLCM (obj, x0, options)
 Runs the system as an lcm node. More...
 
function simulate (obj, tspan, x0, options)
 Simulates the dynamical system (using the simulink solvers) More...
 
function tiHinf (obj, x0, u0, Q, R, Bw, gamma)
 Suboptimal state-feedback H-infinity controller for LTI system with bound gamma. More...
 
function tilqr (obj, x0, u0, Q, R, options)
 Computes an LQR controller to stabilize the system around (x0,u0) More...
 
function tilyap (obj, x0, Q)
 Linearizes the system about the state x0 and returns a candidate LyapunovFunction generated by solving the quadratic Lyapunov equation. More...
 
function tvlyap (obj, xtraj, Q, Qf)
 Linearizes the system about the state trajectory xtraj and returns a candidate LyapunovFunction generated by integrating backwards the quadratic differential Lyapunov equation. More...
 

Static Public Member Functions

static function buildLQRTree (p, xG, uG, xSampleDistFun, Q, R, options)
 Runs the LQR tree algorithm using polynomial tools for verification. More...
 
static function doubleSafe (x)
 
static function trajCost (t, x, u, R)
 
static function trajFinalCost (t, x)
 
static function plotDircolTraj (t, x, u, plotdims)
 

Public Attributes

Property zero_mode_num
 
Property tilqr_mode_num
 
Property num_tvlqr_modes
 
Property xG
 
Property uG
 
Property Vf
 
Property xtraj
 
Property utraj
 
Property Vtv
 
Property S1
 precompute some values to optimize speed of guards and transitions More...
 
Property s2
 
Property s3
 
Property x0
 
Property t0
 
Property m
 
- Public Attributes inherited from DynamicalSystem
Property warning_manager
 

Additional Inherited Members

- Protected Member Functions inherited from DynamicalSystem
function stateIndicesForCombination (sys1, sys2)
 Helper method to figure out the indices of the discrete and continuous states after sys1 and sys2 have been combined into a single system. More...
 
function stateVectorToStructure (obj, xv, mdl)
 Converts the vector state xv to the structure xs for simulink state. More...
 
function stateStructureToVector (obj, xs)
 Converts the simulink state structure representation back to the vector state. More...
 

Constructor & Destructor Documentation

function LQRTree ( xG  ,
uG  ,
tilqr  ,
 
)
Return values
obj

Member Function Documentation

function addTrajectory ( obj  ,
xtraj  ,
utraj  ,
tvlqr  ,
Vtv  ,
parentID  ,
parentT   
)
Return values
obj
ind
static function buildLQRTree ( ,
xG  ,
uG  ,
xSampleDistFun  ,
,
,
options   
)
static

Runs the LQR tree algorithm using polynomial tools for verification.

Usage: controller = buildLQRTree(sys,xG,uG,xSampleDistFun,Q,R,options)

Inputs: sys - DynamicalSystem object xG,uG - describes the goal. sys.dynamics(0,xG,uG) must equal 0. xSampleDistFun - function handle to draw a random sample Q,R - default values used for both LTI and LTV stabilization

Outputs: controller - a hybrid LQR Tree controller object

Options: num_samples_before_done - number of consecutive successes for estimated probabilistic completeness (default 1000). num_branches - number of trajectories to add (default inf) t_max - longest trajectory (default 10s) plot_trajectories - default true plot_basins - default false plot_dims - default [1,2]. (but can be multiple rows for multiple subplots) plant_order - default is 3 degL1 - default is sampledFiniteTimeInvariance default

con - trajectory optimization constraints

xs,Tslb,Tsub - use these as initial samples first stabilize_goal - default is true Vf - default final condition verify - default is true (occasionally useful for faster debugging)

Return values
c
function checkFunnels ( obj  ,
 
)

find lowest V for this x, by searching over ti and tv funnels.

Return values
Vmin
mode
tmin
static function doubleSafe ( )
static
Return values
y
function getSampleTime ( obj  )
virtual
Return values
ts

Reimplemented from DrakeSystem.

function inAnyFunnelGuard ( obj  ,
,
ignoredArg  ,
 
)
Return values
phi
function onTreeConstraint ( obj  ,
 
)

note: the input x is in the plant state frame (everything else inside this class is stored in the input frame of the controller)

Return values
g
dg
m
tmin
static function plotDircolTraj ( ,
,
,
plotdims   
)
static
Return values
J
dJ
static function trajCost ( ,
,
,
 
)
static
Return values
g
dg
static function trajFinalCost ( ,
 
)
static
Return values
h
dh
function transitionIntoAnyFunnel ( obj  ,
m  ,
,
ignoredArg  ,
 
)
Return values
t0
to_mode_num
status

Member Data Documentation

Property m
Property num_tvlqr_modes
Property S1

precompute some values to optimize speed of guards and transitions

Property s2
Property s3
Property t0
Property tilqr_mode_num
Property uG
Property utraj
Property Vf
Property Vtv
Property x0
Property xG
Property xtraj
Property zero_mode_num

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