Collocation Class Reference

The class for defining an optimal control of musculoskeletal. More...

Inheritance diagram for Collocation:

Public Member Functions
function	addConstraint (in obj, in fh, in cmin, in cmax, in varargin)
	Function adding constraint to the optimization problem.
function	addObjective (in obj, in fh, in weight, in varargin)
	Function adding objective term to the optimization problem.
function	addOptimVar (in obj, in name, in xmin, in xmax, in xinit)
	Function adding optimization variables to the state vector.
function	checkXScaling (in obj, in X)
	Matlab function to check the scaling withing X.
function	Collocation (in model, in nNodes, in Euler, in logfile, in plotLog)
	Constructor setting default Collocation options.
function	comFixConstraint (in obj, in option, in X, in targetMotion)
	Function to compute constraint violation of center of mass motion.
function	computeJpattern (in obj)
	Function computing the jacobian pattern.
function	confun (in obj, in X)
	Function to compute constraint violations at state vector X.
function	cotTerm (in obj, in option, in X, in name, in epsilon, in exponent)
	Collocation function to compute cost of transport of the muscles from states vector.
function	curveConstraint_pelvis213 (in obj, in option, in X, in radius)
	Function to compute the periodicity constraint for curved running.
function	derivativetest (in obj, in xr)
	Function to test the whole problem which was defined.
function	durationConstraint (in obj, in option, in X, in targetDuration)
	Computes constraint violation demanding periodic movement.
function	dynamicConstraints (in obj, in option, in X)
	Computes constaint violation demanding dynamic equilibrium.
function	dynamicsFirstNodeConstraint (in obj, in option, in X)
	Matlab function to constrain the first node.
function	effortTermMuscles (in obj, in option, in X, in weigthsType, in exponent, in speedWeighting)
	Matlab function to compute effort of the muscles from states vector.
function	effortTermMusclesAct (in obj, in option, in X, in weigthsType, in exponent, in speedWeighting)
	Matlab function to compute effort of the muscles from states vector.
function	effortTermTorques (in obj, in option, in X, in exponent, in speedWeighting)
	Matlab function to compute effort of the torques from states vector.
function	equilibriumConstraints (in obj, in option, in X)
	Matlab function to compute dynamic constraint for standing.
function	equilibriumConstraintsCPOffset (in obj, in option, in X)
	Matlab function to compute dynamic constraint for standing with a vertical offset of the contact points.
function	extractData (in obj, in X, in settings, in variableTable, in getFullCycle)
	Function to extract simulated and tracked data of the problem.
function	fromStandingConstraint (in obj, in option, in X)
	Matlab function to find walking/running from standing.
function	getCEPower (in obj, in X)
	Function to compute the CE Power over the whole movemenent.
function	getComMotion (in obj, in X)
	Computes center of mass motion.
function	getComMotionDeriv (in obj, in X)
	Function to compute center of mass motion.
function	getMetabolicCost (in obj, in X, in name, in getCont, in epsilon, in exponent)
	Function to calculate metabolic cost of a movement.
function	getSimData (in obj, in X, in simVar, in modelName)
	Matlab function to extract simulated variables.
function	getStepLength (in obj, in X, in name)
	Computes step length.
function	getStimTime (in obj, in X)
	Collocation function to calculate the stimulation time for one gait cycle.
function	gradient (in obj, in X)
	Function computing gradient at state vector X.
function	headStabTerm (in obj, in option, in X)
	Matlab function to compute Veerkamp's HeadStab.
function	impactTerm (in obj, in option, in X)
	Matlab function to compute Veerkamp's FGImpact.
function	initObjectives (in obj)
	Function initializing the objective functions.
function get	isPeriodic (in obj)
	Function returning isPeriodic parameter.
function get	isSymmetric (in obj)
	Function returning isSymmetric parameter.
function	jacobian (in obj, in X)
	Function to compute jacobian at state vector X.
function	jacstructure (in obj)
	Function providing the jacobian pattern.
function	jointAccelerationTerm (in obj, in option, in X)
	Matlab function to compute effort of the muscles from states vector.
function	kneeExtTerm (in obj, in option, in X)
	Matlab function to compute Veerkamp's KneeExt.
function	makeinitialguess (in obj, in init)
	Function to define an initial guess.
function get	nNodesDur (in obj)
	Function returning nNodesDur parameter.
function	objfun (in obj, in X)
	Function computing objective value at state vector X.
function	passiveMomentTerm (in obj, in option, in X, in exponent)
	Collocation function to compute effort of the torques from states vector.
function	periodicityConstraint (in obj, in option, in X, in sym)
	Computes constaint violation demanding periodic movement.
function	plotlog (in obj, in X)
	Function plotting stick figure, objective values and constraint violations.
function	plotStickSlider (in obj, in X, in subTrans, in showStickOpt, in markerTable)
	Matlab function to create plot stick figure with slider.
function	printlog (in obj)
	Function logging objective value and constraint violations.
function	regTerm (in obj, in option, in X)
	Computes differences between collocation nodes to ensure smoothness.
function	report (in obj, in X, in settings, in style, in resultFilename)
	Computes function to report a current state vector of the problem.
function	resampleInitialContact (in obj, in X, in foot, in contact_names)
	Resamples X so that the Heelstrike is at the first node.
function	setPlotLim (in values)
	Helperfunction setting the limits for objective and constraints plot.
function	shift_index (in X_tmp, in amount)
function	showSingleStick (in es, in ignoredArg)
function	speedConstraint (in obj, in option, in X, in targetSpeed)
	Computes constraint violation demanding periodic movement.
function	trackAcc (in obj, in option, in X, in data, in weight)
	Matlab function to track accelerometer data.
function	trackAngles (in obj, in option, in X, in data)
	Computes difference between simulated and measured angles.
function	trackDuration (in obj, in option, in X, in data)
	Matlab function to track duration of the gait cycle.
function	trackGRF (in obj, in option, in X, in data)
	Matlab function to track ground reaction forces.
function	trackGyro (in obj, in option, in X, in data, in weight)
	Matlab function to track gyroscope data.
function	trackMarker (in obj, in option, in X, in data)
	Computes difference between simulated and measured marker data.
function	trackSpeed (in obj, in option, in X, in data)
	Matlab function to track speed of the gait cycle.
function	trackTranslations (in obj, in option, in X, in data)
	Computes difference between simulated and measured translations.
function	trackTranslationsAndAngles (in obj, in option, in X, in data)
	Computes difference between simulated and measured translations and angles in one term.
function	translationSpeedConstraint (in obj, in option, in X)
	Computes constraint based on speed and translation.
function	writeMotionToOsim (in obj, in X, in filename, in variableTable, in rangeNodes, in t0)
	Function to write motion from a solution X to OpenSim files.
function	writeMovie (in obj, in X, in filename, in fps, in subTrans, in showStickOpt, in makeGIF, in playSpeed, in markerTable, in rangeNodes)
	Matlab function to create a movie of a simulation result.
function	writeMovieCurvedRunning (in obj, in X, in filename, in radius, in fps, in showStickOpt, in makeGIF)
	Matlab function to create a movie of a simulation result for curved running.

Static Public Member Functions
static function	matcompare (in a, in b)
	Helperfunction to compare matrices and mind maximum abs error.
function	plotMeanSimVarTable (in tables, in style)
	Computes function to plot the mean and SD of multiple simulation variable tables.
function	plotMultSimVarTables (in tables, in style, in plotStance)
	Function to plot the content of multiple simulation variable tables.
static function	resampleX (in x, in N)
	Function for resampling state vector for makeinitialguess.

Public Attributes
Property	c_lb
	Double array: Lower bound of constaints.
Property	c_ub
	Double array: Upper bound of constraints.
Property	initialguess
	Struct: Intial guess for x.
Property	model
	Model: Object of class Model.m.
Property	name
	String: Name of result file.
Property	X_lb
	Double array: Lower bound of state vector.
Property	X_ub
	Double array: Upper bound of state vector.

Private Attributes
Property	constraintTerms
	Struct array: Constraints.
Property	Euler
	String: Midpoint euler 'ME' or backward euler 'BE' or semi-implicit euler 'SIE'.
Property	idx
	Struct: Indices for position of variables in state vector X.
Property	isPeriodic
	Bool: True if the periodicityConstraint() was used.
Property	isSymmetric
	Bool: True if the periodicityConstraint() was used and there sym is true.
Property	Jnnz
	Double: Number of non-zero entries in jacobian pattern.
Property	Jpattern
	Double matrix: Jacobian pattern.
Property	log
	Struct: Information for logging objectives and constrained violations.
Property	nConstraints
	Double: Total number of constraints.
Property	nNodes
	Double: Number of collocation nodes.
Property	nNodesDur
	Double: Number of collocation nodes which define the duration of the simulation.
Property	nVars
	Double: Number of variables that are optimized.
Property	objectiveInit
	Struct: Contains values extracted during initialization of objective functions.
Property	objectiveTerms
	Struct array: Ojective terms.
Property	plotLog
	Bool: If true, plot log in call of Collocation.objfun() (stick figure, objective, constrains) (default: 0)

Detailed Description

The class for defining an optimal control of musculoskeletal.

Author

Eva Dorschky, Marlies Nitschke

Date

November, 2017

Examples

/home/runner/work/BioMAC-Sim-Toolbox/BioMAC-Sim-Toolbox/ExampleScripts/+IntroductionExamples/script2D.m, and /home/runner/work/BioMAC-Sim-Toolbox/BioMAC-Sim-Toolbox/ExampleScripts/+IntroductionExamples/scriptPlotting.m.

Constructor & Destructor Documentation

Collocation()

function Collocation	(	in	model,
		in	nNodes,
		in	Euler,
		in	logfile,
		in	plotLog
	)

Constructor setting default Collocation options.

Parameters

model	Model class object
nNodes	(optional) Double: Number of collocation nodes
Euler	(optional) String: Discretization method: backward euler 'BE' or midpoint euler 'ME' or semi-implicit euler 'SIE
logfile	(optional) String: Logfile including the path. The input can be skipped with an empty string.
plotLog	(optional) Bool: If true, plot log in call of Collocation.objfun() (stick figure, objective, constrains) (default: 0)

Return values

obj	Collocation class object

Member Function Documentation

addConstraint()

function addConstraint	(	in	obj,
		in	fh,
		in	cmin,
		in	cmax,
		in	varargin
	)

Function adding constraint to the optimization problem.

The constraints are called by the name of the function handle. The upper and lower bounds of the constraints can be set to zero for equalitiy constraints. The constraints can be a vector or a matrix to define constraints at a single or mulitple collocation nodes. (nconstraintspernode x 1|.nNodes).

problem.addConstraint(@dynamicConstraints,repmat(model.init.fmin,1,N),repmat(model.init.fmax,1,N))
problem.addConstraint(@periodicityConstraint,zeros(model.nStates+model.nControls,1),zeros(model.nStates+model.nControls,1),sym)

Parameters

obj	Collocation class object
fh	Function handle: Method defined in Collocation
cmin	Double array: Lower bound on constraint
cmax	Double array: Upper bound on constraint
varargin	(optional) Input parameter for function handle

addObjective()

function addObjective	(	in	obj,
		in	fh,
		in	weight,
		in	varargin
	)

Function adding objective term to the optimization problem.

Todo:

check if xmin, xmax, xinit have the correct size

The objective terms are summed up in objective function using the function and weights which are defined as input.

problem.addObjective(@regTerm,W.reg)
problem.addObjective(@effortTerm,W.effort,'volumeweighted',2)
problem.addObjective(@trackGRF,W.track,trackingData)
problem.addObjective(@trackAngles,W.track,trackingData)

Parameters

obj	Collocation class object
fh	Function handle: Method defined in the Collocation class folder
weight	Double: Weight of the objective term in the objective function
varargin	(optional) Input parameter for function handle

addOptimVar()

function addOptimVar	(	in	obj,
		in	name,
		in	xmin,
		in	xmax,
		in	xinit
	)

Function adding optimization variables to the state vector.

Variables that should be optimized can be added to the collocation problem. The 'name' how the variables are called in the objective functions/ constraints need to be defined as first input, e.g. X(obj.idx.(name)). The lower and upper bounds xmin < x < xmax need to be defined as second and third input. Moreover, an initial guess for x can be defined. If no initial guess is provided, the mid point between the lower and upper bound is used.

The variables can be a vector or a matrix defining the variables at multiple collocation nodes (nvarspernode x 1|Collocation.nNodes|Collocation.nNodes+1).

problem.addOptimVar('states',repmat(model.states.xmin,1,N+1),repmat(model.states.xmax,1,N+1));
problem.addOptimVar('controls',repmat(model.controls.xmin,1,N+1),repmat(model.controls.xmax,1,N+1));
problem.addOptimVar('dur',0.1,1);
problem.addOptimVar('speed',targetspeed,targetspeed);

Parameters

obj	Collocation class object
name	String: Name of variable
xmin	Double, vector or matrix: Lower bounds
xmax	Double, vector or matrix: Upper bounds
xinit	(optional) Vector or matrix: Initial guess

checkXScaling()

function checkXScaling	(	in	obj,
		in	X
	)

Matlab function to check the scaling withing X.

It plots the ranges (min and max) of the absolute values in X for each type of states and controls. This function can be used to check whether the scaling of the states and controls

The function can be called using:

result.problem.checkXScaling(result.X);

Parameters

obj	Collocation class object
X	Double matrix: State vector (i.e. result) of the problem

comFixConstraint()

function comFixConstraint	(	in	obj,
		in	option,
		in	X,
		in	targetMotion
	)

Function to compute constraint violation of center of mass motion.

This function was never actually used. If you would like to, make sure that it is tested before.

Parameters

obj	Collocation class object
option	String parsing the demanded output
X	Double array: State vector containing at least speed of the movement
targetMotion	Double: target motion of the center of mass

computeJpattern()

function computeJpattern

(

in

obj

)

Function computing the jacobian pattern.

Parameters

obj	Collocation class object

confun()

function confun ( in  obj, in  X  )

virtual

Function to compute constraint violations at state vector X.

Parameters

obj	Collocation class object
X	Double array: State vector with variables that are optimized

Return values

c	Double array: Constraint violations at state vector X

Reimplemented from Problem.

cotTerm()

function cotTerm	(	in	obj,
		in	option,
		in	X,
		in	name,
		in	epsilon,
		in	exponent
	)

Collocation function to compute cost of transport of the muscles from states vector.

Parameters

obj	Collocation class object
option	String parsing the demanded output: 'objval' or 'gradient' (or 'init' for initialization)
X	Double array: State vector containing at least 'states', 'controls', 'dur', and 'speed' of the model
name	(optional) name of the model to be used, defaults to lichtwark
epsilon	(optional) level of nonlinearity, defaults to 10^-3
exponent	(optional) Positive integer: Exponent of energy rate in optimization

curveConstraint_pelvis213()

function curveConstraint_pelvis213	(	in	obj,
		in	option,
		in	X,
		in	radius
	)

Function to compute the periodicity constraint for curved running.

It ensures a perdiodic movement on a circle with a specifc radius. It was defined for our 3D model with the pelvis rotation sequence 213.

It uses the following equations:

• \( c = \vert\vert v \vert\vert \cdot T \)
• \( \theta = 2 \arcsin \left( \frac{c}{2r} \right) \)

Parameters

obj	Collocation class object
option	String: Parsing the demanded output
X	Double array: State vector containing at least 'states' and 'controls' of the model and speed and duration of the periodic movement
radius	Double: Radius of the circle

derivativetest()

function derivativetest ( in  obj, in  xr  )

inherited

Function to test the whole problem which was defined.

durationConstraint()

function durationConstraint	(	in	obj,
		in	option,
		in	X,
		in	targetDuration
	)

Computes constraint violation demanding periodic movement.

Parameters

obj	Collocation class object
option	String parsing the demanded output
X	Double array: State vector containing at least speed of the movement
targetDuration	Double: target duration to reach

dynamicConstraints()

function dynamicConstraints	(	in	obj,
		in	option,
		in	X
	)

Computes constaint violation demanding dynamic equilibrium.

Parameters

obj	Collocation class object
option	String parsing the demanded output
X	Double array: State vector containing at least 'states' and 'controls' of the model and speed and duration of the periodic movement

dynamicsFirstNodeConstraint()

function dynamicsFirstNodeConstraint	(	in	obj,
		in	option,
		in	X
	)

Matlab function to constrain the first node.

It ensures the dynamics at the first node: f(x[1], (x[2]-x[1])/h, u[1]) = 0 without the constraints for qdot for the pelvis

This constraint can be used when no periodicity constraint is used.

Parameters

obj	Collocation class object
option	String parsing the demanded output
X	Double array: State vector containing at least 'states' and 'controls' of the model and 'duration' of movement

effortTermMuscles()

function effortTermMuscles	(	in	obj,
		in	option,
		in	X,
		in	weigthsType,
		in	exponent,
		in	speedWeighting
	)

Matlab function to compute effort of the muscles from states vector.

Parameters

obj	Collocation class object
option	String parsing the demanded output: 'objval' or 'gradient' (or 'init' for initialization)
X	Double array: State vector containing at least 'controls' of the model
weigthsType	(optional) String parsing weights
exponent	(optional) Positive integer: Exponent of muscle controls (default: 3)
speedWeighting	(optional) Boolean: If true, the objective will be divided by norm(speed)^exponent. (default: false)

effortTermMusclesAct()

function effortTermMusclesAct	(	in	obj,
		in	option,
		in	X,
		in	weigthsType,
		in	exponent,
		in	speedWeighting
	)

Matlab function to compute effort of the muscles from states vector.

This function is using the muscle activation whereas Collocation.effortTermMusclesAct() is using the neural excitation.

Parameters

obj	Collocation class object
option	String parsing the demanded output: 'objval' or 'gradient' (or 'init' for initialization)
X	Double array: State vector containing at least 'states' of the model
weigthsType	(optional) String parsing weights
exponent	(optional) Positive integer: Exponent of muscle activation (default: 3)
speedWeighting	(optional) Boolean: If true, the objective will be divided by norm(speed)^exponent. (default: false)

effortTermTorques()

function effortTermTorques	(	in	obj,
		in	option,
		in	X,
		in	exponent,
		in	speedWeighting
	)

Matlab function to compute effort of the torques from states vector.

Parameters

obj	Collocation class object
option	String parsing the demanded output: 'objval' or 'gradient' (or 'init' for initialization)
X	Double array: State vector containing at least 'controls' of the model
exponent	(optional) Positive integer: Exponent of torque controls (default: 2)
speedWeighting	(optional) Boolean: If true, the objective will be divided by norm(speed)^exponent. (default: false)

equilibriumConstraints()

function equilibriumConstraints	(	in	obj,
		in	option,
		in	X
	)

Matlab function to compute dynamic constraint for standing.

It ensures equilibrium at node 1.

Parameters

obj	Collocation class object
option	String parsing the demanded output
X	Double array: State vector containing at least 'states' and 'controls' of the model and speed and duration of the periodic movement

equilibriumConstraintsCPOffset()

function equilibriumConstraintsCPOffset	(	in	obj,
		in	option,
		in	X
	)

Matlab function to compute dynamic constraint for standing with a vertical offset of the contact points.

Parameters

obj	Collocation class object
option	String parsing the demanded output
X	Double array: State vector containing at least 'states' and 'controls' of the model and speed and duration of the periodic movement

extractData()

function extractData	(	in	obj,
		in	X,
		in	settings,
		in	variableTable,
		in	getFullCycle
	)

Function to extract simulated and tracked data of the problem.

Using the fields of settings, you can specify which simulated data will be extracted. For each type, you define the names. The fieldname corresponds to the type of the variable. You do not have to use all of the fields! Just use the ones you need.

Example entries for all possible fields of settings:

settings.translation   = {'pelvis_tx', 'pelvis_ty'};
settings.angle         = {'hip_flexion_r','knee_angle_r', 'ankle_angle_r'};
settings.qdot          = {'hip_flexion_r','knee_angle_r', 'ankle_angle_r'};
settings.moment        = {'hip_flexion_r','knee_angle_r', 'ankle_angle_r'};
settings.torque        = {'arm_flex_r', 'arm_add_r', 'arm_rot_r', 'elbow_flex_r', 'pro_sup_r'};
settings.GRF           = {'GRF_x_r', 'GRF_y_r'};
settings.CoP           = {'CoP_x_r'};
settings.acc           = accTable; % variables table specifying acc with at least the columns: type, name, unit, segment, position, direction
settings.gyro          = gyroTable; % variables table specifying gyro with at least the columns: type, name, unit, segment, position, direction
settings.marker        = markerTable; % variables table specifying markers with at least the columns: type, name, unit, segment, position, direction
settings.u             = {'Iliopsoas_r', 'Glutei_r', 'Hamstrings_r', 'Rectus_r', 'Vasti_r', 'Gastroc_r', 'Soleus_r', 'TibialisAnt_r'};
settings.a             = settings.u;
settings.s             = settings.u;
settings.sdot          = settings.u;
settings.LMTU          = settings.u;
settings.LCE           = settings.u;
settings.LSEE          = settings.u;
settings.LdotMTU       = settings.u;
settings.LdotCE        = settings.u;
settings.LdotSEEE      = settings.u;
settings.muscleForce   = settings.u;
settings.CEForce       = settings.u;
settings.musclePower   = settings.u;
settings.CEPower       = settings.u;
settings.SEEPower      = settings.u;
settings.muscleMetRate = settings.u;
settings.jointPower    = {'hip_flexion_r','knee_angle_r', 'ankle_angle_r'};
settings.CoM           = {'CoM_x', 'CoM_y'};
settings.footAngle     = {'angle_r', 'angle_l' };
settings.standing      = {'standing_r', 'standing_l'};
settings.duration      = 1;

By default, the following variables will automatically be extracted if you do not overwrite the respective fields in settings:

• translation: all
• angle: all joint angles of both sides (no global orientation)
• moment: all joint moments of both sides
• GRF: all of both sides
• a and u:
  • 2D: all of both sides
  • 3D: in totla 16 largest muscles of both sides

The function will further extract all tracked variables which are defined in settings.

Additionally, you can use the input variableTable to specify a variable table with additional (reference) data which was not tracked. You can for example use the variables table in a TrackingData object:

variableTable = trackingdata.variables;

Parameters

obj	Collocation class object
X	Double matrix: State vector (i.e. result) of the problem
settings	(optional) Struct: Describing which data should be extracted (see details above; use empty to skip)
variableTable	(optional) Table: Additional reference data with the data beeing in the columns 'mean' and 'var'. (default: empty)
getFullCycle	(optional) Boolean: Defines if a full gait cycle should be constructed for symmetric simulations: 0: requested variable names for the half cycle 1: requested variable names for the entire cycle by using symmetry

Return values

simVarTable

Table: Summarizing all simulated, tracked and optionally additional data which was requested. The three different data kinds are saved in the following columns: simulated data: 'sim' tracked data: 'mean' and 'var' additional data: 'mean_extra' and 'var_extra'

fromStandingConstraint()

function fromStandingConstraint	(	in	obj,
		in	option,
		in	X
	)

Matlab function to find walking/running from standing.

Todo:

Generalize this function and remove hard coded indices. E.g. we do not assume fixed indices for the states. The function should also work for 2D.

Parameters

obj	Collocation class object
option	String parsing the demanded output
X	Double array: State vector containing at least 'states' and 'controls' of the model and speed and duration of the periodic movement

getCEPower()

function getCEPower	(	in	obj,
		in	X
	)

Function to compute the CE Power over the whole movemenent.

Computes the CE power according to Ton's paper:

A. J. van den Bogert, M. Hupperets, H. Schlarb, and B. Krabbe. Predictive musculoskeletal simulation using optimal control: effects of added limb mass on energy cost and kinematics of walking and running. Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology, 226(2):123{133, 2012.

His old implementation was used as basis for this implementation.

We do only take the simulated motion into account, i.e. we do not multiply the output times two for symmetric simulations.

Todo:

Implement powerd. There were multiple implementations of it. See comments. Add a description for the outcome powerd and rename it!

Parameters

obj	Collocation object
X	Double matrix: State vector (i.e. result) of the problem

Return values

totalCEPower	Double: Total mechanical work of the muscle fibres in W
powers	Double array: CE power output in W of each muscle and time point (Model.nMus x Collocation.nNodes)

getComMotion()

function getComMotion	(	in	obj,
		in	X
	)

Computes center of mass motion.

Parameters

obj	Collocation class object
X	Double array: State vector containing at least speed of the movement

getComMotionDeriv()

function getComMotionDeriv	(	in	obj,
		in	X
	)

Function to compute center of mass motion.

Parameters

obj	Collocation class object
X	Double array: State vector containing at least speed of the movement

getMetabolicCost()

function getMetabolicCost	(	in	obj,
		in	X,
		in	name,
		in	getCont,
		in	epsilon,
		in	exponent
	)

Function to calculate metabolic cost of a movement.

Function to calculate the metabolic cost of a movement using Umberger's model. Ross Miller's code was also used as a reference.

See also the metabolic cost paper: A Koelewijn, E Dorschky, A van den Bogert; A metabolic energy expenditure model with a continuous first derivative and its application to predictive simulations of gait. Computer Methods in Biomechanics and Biomedical Engineering 21(4):1-11, 2018.

This function does only return the energy of the present movement. => We did not multiplied by two for symmetric movements here. Since metCost is computed from mean energy expenditure, it would be false to multiply the metCost by 2 for symmetric movements!!!

To get the cost of a result, you can call:

[metCost, ~, metCostPerMus, metRate, CoT] = result.problem.getMetabolicCost(result.X);

Todo:

Agree for one method to define (compute or extract) speed!

Parameters

obj	Collocation object
X	Double matrix: State vector (i.e. result) of the problem
name	(optional) String: name of the model to be used default is umberger, other options are minetti, margaria, houdijk, bhargava, uchida, lichtwark, kim
getCont	(optional) Boolean: If true, get the continuous version which is needed if we use the output for simulation. (default: 0)
epsilon	(optional) Double: Amount of nonlinearity in continuous model it should be specified if a continuous model is used
exponent	(optional) integer: could be used to calculate square, cube or nth power of metabolic cost. Only used for derivatives. (default: 1)

Return values

metCost	Double: Metabolic Cost of movement in J/m/kg
metRate	Double: Metabolic Rate of movement in W/kg
CoT	Double: Cost of transport of movement in 1
metCostPerMus	Double vector: Metabolic Cost of movement in J/m/kg (obj.model.nMus x 1)
dmetCostdX	Double vector: Derivative of metCost w.r.t to X (size of X)
dmetRatedX	Double vector: Derivative of metRate w.r.t to X (size of X)
dCoTdX	Double vector: Derivative of metRate w.r.t to X (size of X)

getSimData()

function getSimData	(	in	obj,
		in	X,
		in	simVar,
		in	modelName
	)

Matlab function to extract simulated variables.

Warning: This function was not tested completely!

Currently, this function can return simulated data for the following data types:

• translation
• angle
• qdot
• moment
• GRF
• CoP
• marker
• acc
• gyro
• a
• s
• LMTU
• LCE
• LSEE
• LdotMTU
• LdotCE
• LdotSEE
• muscleForce
• CEForce
• u
• speed
• duration
• footAngle
• musclePower
• CEPower
• SEEPower
• torque
• sdot
• muscleMetRate
• CoM
• jointPower

Todo:

Check which unit is requested and convert the data if needed. However this is currently only done for angles which are automatically converted into degrees if the unit is 'deg'.

Todo:

Use model.GRFNAMES instead of hard coded indices. Eventally change the names in GRFNAMES

Todo:

Check again if we use always the correct discretization method. If we use BE, shouldn't we use states(idxSimVar, 2:nNodes+1) and controls(idxSimVar, 2:nNodes+1)?

Parameters

obj	Collocation class object
X	Double matrix: State vector (i.e. result) of the problem
simVar	Table: Information on variables from which we want to get the simulated data. This table has to contain the columns: type, name, and for IMU also position and direction.
modelName	For metabolic rate: name of the model that should be used

Return values

simVar

Table: Input table with an additional column "sim" containing the simulated data for this X.

getStepLength()

function getStepLength	(	in	obj,
		in	X,
		in	name
	)

Computes step length.

Parameters

obj	Collocation class object
X	Double array: State vector containing at least speed of the movement
name	Optional: left or right

getStimTime()

function getStimTime	(	in	obj,
		in	X
	)

Collocation function to calculate the stimulation time for one gait cycle.

The stimulation time is a variable that is necessary for some of the metabolic models, because the energy expenditure is dependent on the stimulation time. This function calculates the stimulation time at the beginning of the gait cycle by looping to the gait cycle once.

To get the cost of a result, you can call:

t_stim = problem.getStimTime(X);

Parameters

obj	Collocation object
X	Double matrix: State vector (i.e. result) of the problem

Return values

t_stim

Double matrix: Activation Time (nMus x nNodesDur)

gradient()

function gradient ( in  obj, in  X  )

virtual

Function computing gradient at state vector X.

Parameters

obj	Collocation class object
X	Double array: State vector with variables that are optimized

Return values

g	Double array: Gradient vector at state vector X

Reimplemented from Problem.

headStabTerm()

function headStabTerm	(	in	obj,
		in	option,
		in	X
	)

Matlab function to compute Veerkamp's HeadStab.

Parameters

obj	Collocation class object
option	String parsing the demanded output: 'objval' or 'gradient' (or 'init' for initialization)
X	Double array: State vector containing at least 'states' and 'dur' of the model

impactTerm()

function impactTerm	(	in	obj,
		in	option,
		in	X
	)

Matlab function to compute Veerkamp's FGImpact.

Parameters

obj	Collocation class object
option	String parsing the demanded output: 'objval' or 'gradient' (or 'init' for initialization)
X	Double array: State vector containing at least 'states' and 'dur' of the model

initObjectives()

function initObjectives

(

in

obj

)

Function initializing the objective functions.

Parameters

obj	Collocation class object

isPeriodic()

function get isPeriodic

(

in

obj

)

Function returning isPeriodic parameter.

Todo:

What if symmetric and not symmetric movement is loaded?

Todo:

: current hack without changing Model Class, is there a better way to make sure that always the right model is initialized?

Todo:

What if symmetric and not symmetric movement is loaded?

Todo:

: current hack without changing Model Class, is there a better way to make sure that always the right model is initialized?

Parameters

obj	Collocation class object

Return values

isPer

Bool: see Collocation.isPeriodic

isSymmetric()

function get isSymmetric

(

in

obj

)

Function returning isSymmetric parameter.

Parameters

obj	Collocation class object

Return values

isSym

Bool: see Collocation.isSymmetric

jacobian()

function jacobian ( in  obj, in  X  )

virtual

Function to compute jacobian at state vector X.

Parameters

obj	Collocation class object
X	Double array: State vector with variables that are optimized

Return values

J	Sparse matrix: Jacobian at state vector X

Reimplemented from Problem.

jacstructure()

function jacstructure ( in  obj )

virtual

Function providing the jacobian pattern.

Parameters

obj	Collocation class object

Return values

J	Double matrix: Pattern of jacobian matrix

Reimplemented from Problem.

jointAccelerationTerm()

function jointAccelerationTerm	(	in	obj,
		in	option,
		in	X
	)

Matlab function to compute effort of the muscles from states vector.

Parameters

obj	Collocation class object
option	String parsing the demanded output: 'objval' or 'gradient' (or 'init' for initialization)
X	Double array: State vector containing at least 'states' of the model

kneeExtTerm()

function kneeExtTerm	(	in	obj,
		in	option,
		in	X
	)

Matlab function to compute Veerkamp's KneeExt.

Parameters

obj	Collocation class object
option	String parsing the demanded output: 'objval' or 'gradient' (or 'init' for initialization)
X	Double array: State vector containing at least 'states' of the model

makeinitialguess()

function makeinitialguess	(	in	obj,
		in	init
	)

Function to define an initial guess.

Todo:

check if cmin and cmax have the correct size

The initial guess is initialized by adding the state variables. This function can be used to overwrite the initial guess, e.g. by loading an initial guess of a previous result. The input parameter 'init' can be used to define how the initial guess should be computed. If init = 'mid', the midpoint between the lower and upper bounds of the state vector X are used. If init = 'random', X is intialized by drawing random values from a uniform distribution between the lower and upper bound. If init contains the path to a result file, the result file is loaded. If neccessary, the result is resampled to the size of the current collocation problem.

problem.makeinitialguess('mid');

Parameters

obj	Collocation class object
init	String: Parsing the demanded initialguess OR Double vector: X which fits exactly the size of the current problem (no tests and no resampling)

matcompare()

static function matcompare ( in  a, in  b  )

staticinherited

Helperfunction to compare matrices and mind maximum abs error.

Used for derivativetest()

nNodesDur()

function get nNodesDur

(

in

obj

)

Function returning nNodesDur parameter.

Parameters

obj	Collocation class object

Return values

isPer

Bool: see Collocation.isPeriodic

objfun()

function objfun ( in  obj, in  X  )

virtual

Function computing objective value at state vector X.

Parameters

obj	Collocation class object
X	Double array: State vector with variables that are optimized

Return values

f	Double array: Objective value at state vector X

Reimplemented from Problem.

passiveMomentTerm()

function passiveMomentTerm	(	in	obj,
		in	option,
		in	X,
		in	exponent
	)

Collocation function to compute effort of the torques from states vector.

Parameters

obj	Collocation class object
option	String parsing the demanded output: 'objval' or 'gradient' (or 'init' for initialization)
X	Double array: State vector containing at least 'states' of the model
exponent	(optional) Positive integer: Exponent of passive moments (default: 2)

periodicityConstraint()

function periodicityConstraint	(	in	obj,
		in	option,
		in	X,
		in	sym
	)

Computes constaint violation demanding periodic movement.

Parameters

obj	Collocation class object
option	String parsing the demanded output
X	Double array: State vector containing at least 'states' and 'controls' of the model and speed and duration of the periodic movement
sym	Boolean if movement is symmetric (half period is optimized) or not

plotlog()

function plotlog	(	in	obj,
		in	X
	)

Function plotting stick figure, objective values and constraint violations.

Parameters

obj	Collocation class object
X	Double array: State vector with variables that are optimized

plotMeanSimVarTable()

function plotMeanSimVarTable ( in  tables, in  style  )

static

Computes function to plot the mean and SD of multiple simulation variable tables.

The function computes and plots the mean and variance for each column of tables.

When plotting IMU and marker data separate subplots are created for different directions and positions.

The function is not yet able to plot stance phases.

Collocation.plotMeanSimVarTable({simVarTable1, simVarTable2; simVarTable3, simVarTable4}, style);

Note

The function is currently assuming that tracking and reference data is identical over all tables within each column and is therefore only plotting the tracking and reference data of the first row.

Parameters

tables	Cell matrix: Each entry is a simVarTable containing a full gait cycle returned from Collocation.report or Collocation.extractData. The results in dimension 1 can for example be from another subject and in dimension 2 from another condition, e.g., walking with an exoskeleton.
style	(optional) Struct: Style of the figure containing the fields: figureSize xLabelFontSize yLabelFontSize xTickFontSize yTickFontSize legendFontSize lineWidth trackColor extraColor trackFaceAlpha extraFaceAlpha subFigSettings If a field is not defined, default values specified in the description of plotVarType() will be used. Use empty to skip the input.

Return values

meanTablesOut

Cell vector: SimVarTables reflecting the mean of each column in tables. The simulated means and variances are saved in the table columns 'sim' and 'simVar', respectively. The columns 'mean', 'var', 'mean_extra', and 'var_extra' reflect the tracking and reference data which is currently assumed to be equal for all tables within one column.

plotMultSimVarTables()

function plotMultSimVarTables ( in  tables, in  style, in  plotStance  )

static

Function to plot the content of multiple simulation variable tables.

Usage:

Collocation.plotMultSimVarTables({simVarTable1, simVarTable2; simVarTable3, simVarTable4}, style);

It is also possible to plot simVarTables with different content.

When plotting IMU and marker data separate subplots are created for different directions and positions.

Parameters

tables	Cell matrix: Each entry is a simVarTable containing a full gait cycle returned from Collocation.report or Collocation.extractData. The results in dimension 1 can for example be from another subject and in dimension 2 from another condition, e.g., walking with an exoskeleton.
style	(optional) Struct: Style of the figure containing the fields: figureSize xLabelFontSize yLabelFontSize xTickFontSize yTickFontSize legendFontSize lineWidth trackColor extraColor trackFaceAlpha extraFaceAlpha standingRightColor standingLeftColor standingFaceAlpha subFigSettings If a field is not defined, default values specified in the description of plotVarType() will be used. Use empty to skip the input.
plotStance	(optional) Boolean: If true and if the tables contain rows of type "standing", the stance phase(s) will be plotted. (default: false)

plotStickSlider()

function plotStickSlider	(	in	obj,
		in	X,
		in	subTrans,
		in	showStickOpt,
		in	markerTable
	)

Matlab function to create plot stick figure with slider.

Uses Model::showStick() to plot the result.

If you are adding more content to the plot, it will take noticable more time to initialize the figure. Be patient!

Example usage:

markerTable = result.problem.objectiveTerms(1).varargin{1}.variables; % assuming trackMarker is your first objective
result.problem.plotStickSlider(result.X, 0, {1, 0, 1, 0}, markerTable);

Parameters

obj	Collocation class object
X	Double matrix: State vector (i.e. result or initial guess) of the problem
subTrans	(optional) Bool: Subtract the horizontal translation of the pelvis from the movement. (default: false)
showStickOpt	(optional) Cell: Cell with optional input for model.showStick. Cell can contain all possible input options after ''range''. (default: empty cell)
markerTable	(optional) Table: Variables table specifying markers with at least the columns: type, name, segment, position, direction to call Model.showMarker. If the column "mean" is also give, it will be plotted as reference. (default: empty table)

printlog()

function printlog

(

in

obj

)

Function logging objective value and constraint violations.

Parameters

obj	Collocation class object

regTerm()

function regTerm	(	in	obj,
		in	option,
		in	X
	)

Computes differences between collocation nodes to ensure smoothness.

Parameters

obj	Collocation class object
option	String parsing the demanded output: 'objval' or 'gradient' (or 'init' for initialization)
X	Double array: State vector containing at least 'states' and 'controls' of the model

report()

function report ( in  obj, in  X, in  settings, in  style, in  resultFilename  )

virtual

Computes function to report a current state vector of the problem.

It calls extractData() (see for details) to obtain the simulated data.

If you want to plot a static solution with one node (e.g. standing), you can still compare this to extra data using settings.variableTable. However, the variables table has to be resampled to 100 nodes before calling report().

Parameters

obj	Collocation class object
X	Double matrix: State vector (i.e. result) of the problem
settings	(optional) Struct: Settings defining what to report. Additionally to the fields specified in extractData(), it supports the following fields: variableTable (see extractData()) plotObjectives (boolean, default: 1) plotConstraints (boolean, default: 1) plotStick (boolean, default: 1) plotInitialGuess (boolean, default: 0) plotStance (boolean, default: 0) (use empty to skip)
style	(optional) Struct: Settings defining the style for reporting. See plotVarType() for details. (use empty to skip)
resultFilename	(optional) String: Filename (without extension) to save Matlab figures and to save figures as tikz standalone.

Return values

conString	String: Formated text to be printed in the console containing problem informations
texString	String: Formated LaTeX text containing problem informations and tikz code for the figures.
simVarTable	Table: Summarizing all data which was reported (see Collocation.extractData() for details)

Reimplemented from Problem.

resampleInitialContact()

function resampleInitialContact	(	in	obj,
		in	X,
		in	foot,
		in	contact_names
	)

Resamples X so that the Heelstrike is at the first node.

Naive implementation that only considers one Heelstrike per foot

Todo:

Implement symmetric case, 3d-Curved running (?)

Parameters

obj	Collocation class object
X	Double array: State vector containing at least 'speed'
foot	left ('l') or right (default, 'r')
contact_names	[2 x n] cell containing all the contact names in the

resampleX()

static function resampleX ( in  x, in  N  )

static

Function for resampling state vector for makeinitialguess.

Parameters

x	Matrix with initial guess
N	Number of collocation nodes

Return values

xrep	Matrix with resampled initial guess

setPlotLim()

function setPlotLim

(

in

values

)

Helperfunction setting the limits for objective and constraints plot.

Parameters

values

Double matrix: Values plotted (sum is first term) (nEvaluations x nTerms)

shift_index()

function shift_index	(	in	X_tmp,
		in	amount
	)

showSingleStick()

function showSingleStick	(	in	es,
		in	ignoredArg
	)

speedConstraint()

function speedConstraint	(	in	obj,
		in	option,
		in	X,
		in	targetSpeed
	)

Computes constraint violation demanding periodic movement.

Parameters

obj	Collocation class object
option	String parsing the demanded output
X	Double array: State vector containing at least speed of the movement
targetSpeed	Double: target speed to reach

trackAcc()

function trackAcc	(	in	obj,
		in	option,
		in	X,
		in	data,
		in	weight
	)

Matlab function to track accelerometer data.

Supports data in millimeter per second squared ('mm/s^2') and meter per second squared ('m/s^2').

Parameters

obj	Collocation class object
option	String parsing the demanded output: 'objval' or 'gradient' (or 'init' for initialization)
X	Double array: State vector containing at least 'states' and 'dur' of the model
data	TrackingData: All rows with type 'acc' will be tracked
weight	(optional) String: Defines the weighting of the squared difference. The following options exist: 'varOverTrials' (default) for nTrials > 1: \( \frac{\left(y_{i}[k]- \hat{y}_{i}[k] \right)^2}{\sigma^2_{y,i}[k]} \), where \( \sigma^2_{y,i}[k] \) is the variance over all trials of signal i for the time point k (given in the data table). 'varOverTrials' (default) for nTrials = 1: \( \frac{\left(y_{i}[k]- \hat{y}_{i}[k] \right)^2}{1} \) , where no weighting is performed as the variance over one trial would be zero. 'varOverTime': \( \frac{\left(y_{i}[k]- \hat{y}_{i}[k] \right)^2}{\sigma^2_{y,i}} \) , where \( \sigma^2_{y,i} \) is the variance over all time points of signal i. 'minMaxSquared': \( \frac{\left(y_{i}[k]- \hat{y}_{i}[k] \right)^2}{\left(max(y_i)-min(y_i) \right)^2 } \) , where the range of signal i over all time points is computed.

Return values

output

Objective values for input option 'objval' or vector with gradient for input option 'gradient'

trackAngles()

function trackAngles	(	in	obj,
		in	option,
		in	X,
		in	data
	)

Computes difference between simulated and measured angles.

Supports data in radian ('rad') and degree ('deg').

Parameters

obj	Collocation class object
option	String parsing the demanded output: 'objval' or 'gradient' (or 'init' for initialization)
X	Double array: State vector containing at least 'states' of the model
data	TrackingData: All rows with type 'angle' will be tracked

Return values

output

Objective values for input option 'objval' or vector with gradient

trackDuration()

function trackDuration	(	in	obj,
		in	option,
		in	X,
		in	data
	)

Matlab function to track duration of the gait cycle.

Computes difference between simulated and measured duration

Parameters

obj	Collocation class object
option	String parsing the demanded output: 'objval' or 'gradient' (or 'init' for initialization)
X	Double array: State vector containing at least 'duration' of the model
data	TrackingData: The row with type 'duration' will be tracked. It assumes that there is only one row.

Return values

output

Objective values for input option 'objval' or vector with gradient for input option 'gradient'

trackGRF()

function trackGRF	(	in	obj,
		in	option,
		in	X,
		in	data
	)

Matlab function to track ground reaction forces.

Computes difference between simulated and measured ground reaction forces. Supports data in bodyweight ('BW'), bodyweight percentage ('BW'), and newton ('N').

Parameters

obj	Collocation class object
option	String parsing the demanded output: 'objval' or 'gradient' (or 'init' for initialization)
X	Double array: State vector containing at least 'states' of the model
data	TrackingData: All rows with type 'GRF' will be tracked

Return values

output

Objective values for input option 'objval' or vector with gradient for input option 'gradient'

trackGyro()

function trackGyro	(	in	obj,
		in	option,
		in	X,
		in	data,
		in	weight
	)

Matlab function to track gyroscope data.

Supports data in rad per second ('rad/s') and degree per second ('deg/s').

Parameters

obj	Collocation class object
option	String parsing the demanded output: 'objval' or 'gradient' (or 'init' for initialization)
X	Double array: State vector containing at least 'states' of the model
data	TrackingData: All rows with type 'gyro' will be tracked
weight	(optional) String: Defines the weighting of the squared difference. The following options exist: 'varOverTrials' (default) for nTrials > 1: \( \frac{\left(y_{i}[k]- \hat{y}_{i}[k] \right)^2}{\sigma^2_{y,i}[k]} \), where \( \sigma^2_{y,i}[k] \) is the variance over all trials of signal i for the time point k (given in the data table). 'varOverTrials' (default) for nTrials = 1: \( \frac{\left(y_{i}[k]- \hat{y}_{i}[k] \right)^2}{1} \) , where no weighting is performed as the variance over one trial would be zero. 'varOverTime': \( \frac{\left(y_{i}[k]- \hat{y}_{i}[k] \right)^2}{\sigma^2_{y,i}} \) , where \( \sigma^2_{y,i} \) is the variance over all time points of signal i. 'minMaxSquared': \( \frac{\left(y_{i}[k]- \hat{y}_{i}[k] \right)^2}{\left(max(y_i)-min(y_i) \right)^2 } \) , where the range of signal i over all time points is computed.

Return values

output

Objective values for input option 'objval' or vector with gradient for input option 'gradient'

trackMarker()

function trackMarker	(	in	obj,
		in	option,
		in	X,
		in	data
	)

Computes difference between simulated and measured marker data.

Supports data in millimeter ('mm') and meter ('m').

Parameters

obj	Collocation class object
option	String parsing the demanded output: 'objval' or 'gradient' (or 'init' for initialization)
X	Double array: State vector containing at least 'states' of the model
data	TrackingData: All rows with type 'marker' will be tracked

Return values

output

Objective values for input option 'objval' or vector with gradient

trackSpeed()

function trackSpeed	(	in	obj,
		in	option,
		in	X,
		in	data
	)

Matlab function to track speed of the gait cycle.

Computes difference between simulated and measured duration

Parameters

obj	Collocation class object
option	String parsing the demanded output: 'objval' or 'gradient' (or 'init' for initialization)
X	Double array: State vector containing at least 'speed' of the model
data	TrackingData: All rows with type 'speed' will be tracked

Return values

output

Objective values for input option 'objval' or vector with gradient for input option 'gradient'

trackTranslations()

function trackTranslations	(	in	obj,
		in	option,
		in	X,
		in	data
	)

Computes difference between simulated and measured translations.

Supports data in meter ('m') and millimeter ('mm').

Parameters

obj	Collocation class object
option	String parsing the demanded output: 'objval' or 'gradient' (or 'init' for initialization)
X	Double array: State vector containing at least 'states' of the model
data	TrackingData: All rows with type 'translation' will be tracked

Return values

output

Objective values for input option 'objval' or vector with gradient for input option 'gradient'

trackTranslationsAndAngles()

function trackTranslationsAndAngles	(	in	obj,
		in	option,
		in	X,
		in	data
	)

Computes difference between simulated and measured translations and angles in one term.

Parameters

obj	Collocation class object
option	String parsing the demanded output: 'objval' or 'gradient' (or 'init' for initialization)
X	Double array: State vector containing at least 'states' of the model
data	TrackingData: All rows with type 'angle' or 'translation' will be tracked

Return values

output

Objective values for input option 'objval' or vector with gradient for input option 'gradient'

translationSpeedConstraint()

function translationSpeedConstraint	(	in	obj,
		in	option,
		in	X
	)

Computes constraint based on speed and translation.

Constraint: deltaTranslation/duration - speed = 0

If two entries of type speed are contained in X, it assumes the first one to be forward (x-direction) and the second one to be sideward (z-direction).

Parameters

obj	Collocation class object
option	String parsing the demanded output
X	Double array: State vector containing at least states, speed and duration of the movement

writeMotionToOsim()

function writeMotionToOsim	(	in	obj,
		in	X,
		in	filename,
		in	variableTable,
		in	rangeNodes,
		in	t0
	)

Function to write motion from a solution X to OpenSim files.

Saves the motion to the following files:

1. <filename>_kinematics.mot containing the joint angles
2. <filename>_kinematics_subTrans.mot containing the joint angles while subtracting x and z translation
3. <filename>_kinetics_GRFs.mot containing GRFs
4. <filename>_kinetics_activation.sto containing muscle activation
5. <filename>_kinetics_moments.sto containing moments
6. <filename>_kinetics_force.sto containing muscle forces
7. <filename>_kinetics_controls.xml containing controls
8. Optional: <filename>_markers.trc containing marker positions of markerTable specified
9. Optional: <filename>_IMUs.csv containing IMU data of varTable (format definition of APDM)

No resampling is applied.

Parameters

obj	Collocation class object
X	Double matrix: State vector (i.e. result) of the problem
filename	String: Filename which is used to save the OpenSim files
variableTable	(optional) Table: Variables table specifying markers or IMUs with at least the columns: type, name, segment, position, direction to call Model.simuMarker or Model.simuAccGyro. Can be skipped when empty.
rangeNodes	(optional) Array: Specifying first and last node which should be exported. This might not work well for symmetric motions which are automatically mirrored.
t0	(optional) Double: Time at first time point which should be used to start the time vector. If this value is not given, the time vector will start at 0.

writeMovie()

function writeMovie	(	in	obj,
		in	X,
		in	filename,
		in	fps,
		in	subTrans,
		in	showStickOpt,
		in	makeGIF,
		in	playSpeed,
		in	markerTable,
		in	rangeNodes
	)

Matlab function to create a movie of a simulation result.

Uses Model::showStick() to plot the result.

Whether the optimal solution is converged is not checked.

Example usage:

markerTable = result.problem.objectiveTerms(1).varargin{1}.variables; % assuming trackMarker is your first objective
result.problem.writeMovie(result.X, result.filename, [], 0, {1, 0, 1, 0}, 1, 0, markerTable)

Parameters

obj	Collocation class object
X	Double matrix: State vector (i.e. result) of the problem
filename	(optional) String: Filename which is used to save the OpenSim files. Use an empty char array '' to not save a file.
fps	(optional) Double: Desired frame rate (frames per second) To skip the input, you can use []. (default: 5)
subTrans	(optional) Bool: Subtract the horizontal translation of the pelvis from the movement. To skip the input, you can use []. (default: false)
showStickOpt	(optional) Cell: Cell with optional input for model.showStick. Cell can contain all possible input options after ''range''. (default: empty cell)
makeGIF	(optional) Bool: If true, a gif will be saved. Otherwise an avi will be saved. (default: 0=avi)
playSpeed	(Optional) Double: If specified, the real duration of the simulated motion will be taken into account with playSpeed == 1: duration of movie reflects the duration of motion playSpeed < 1: slow motion (e.g. 0.5 => half the playback speed and double the duration) playSpeed > 1: fast motion (e.g. 2 => double the playback speed and half the duration) (default: 0: fps nodes are displayed per second and duration is not taken into account) Attention: The duration of the movie will not be equal to the duration of the motion since the function is plotting the motion till node nNodes and not till nNodes+1.
markerTable	(optional) Table: Variables table specifying markers with at least the columns: type, name, segment, position, direction to call Model.showMarker. If the column "mean" is also give, it will be plotted as reference. (default: empty table)
rangeNodes	(optional) Array: Specifying first and last node which should be used for the movie. This might not work well for symmetric motions which are automatically mirrored.

writeMovieCurvedRunning()

function writeMovieCurvedRunning	(	in	obj,
		in	X,
		in	filename,
		in	radius,
		in	fps,
		in	showStickOpt,
		in	makeGIF
	)

Matlab function to create a movie of a simulation result for curved running.

This function writes movies for simulations which used Collocation::curveConstraint_pelvis213() instead of Collocation::periodicityConstraint().

Whether the optimal solution is converged is not checked.

Parameters

obj	Collocation class object
X	Double matrix: State vector (i.e. result) of the problem
filename	String: Filename which is used to save the OpenSim files
radius	Double: Radius in m
fps	(optional) Double: Desired frame rate (frames per second) To skip the input, you can use []. (default: 5)
showStickOpt	(optional) Cell: Cell with optional input for model.showStick. Cell can contain all possible input options after ''range''. (default: empty cell)
makeGIF	(optional) Bool: If true, a gif will be saved. Otherwise an avi will be saved. (default: 0=avi)

Member Data Documentation

c_lb

Property c_lb

inherited

Double array: Lower bound of constaints.

c_ub

Property c_ub

inherited

Double array: Upper bound of constraints.

constraintTerms

Property constraintTerms

private

Struct array: Constraints.

Euler

Property Euler

private

String: Midpoint euler 'ME' or backward euler 'BE' or semi-implicit euler 'SIE'.

idx

Property idx

private

Struct: Indices for position of variables in state vector X.

initialguess

Property initialguess

inherited

Struct: Intial guess for x.

isPeriodic

Property isPeriodic

private

Bool: True if the periodicityConstraint() was used.

isSymmetric

Property isSymmetric

private

Bool: True if the periodicityConstraint() was used and there sym is true.

Jnnz

Property Jnnz

private

Double: Number of non-zero entries in jacobian pattern.

Jpattern

Property Jpattern

private

Double matrix: Jacobian pattern.

log

Property log

private

Struct: Information for logging objectives and constrained violations.

model

Property model

Model: Object of class Model.m.

name

Property name

inherited

String: Name of result file.

nConstraints

Property nConstraints

private

Double: Total number of constraints.

nNodes

Property nNodes

private

Double: Number of collocation nodes.

nNodesDur

Property nNodesDur

private

Double: Number of collocation nodes which define the duration of the simulation.

If Collocation.isPeriodic is true, it is Collocation.nNodes+1 since we are simulating an additional node. If Collocation.isPeriodic is false, it is Collocation.nNodes since we do not simulate an additional node. This has to be taken into account when specifying the duration of the simulation as h=T/(nNodesDur-1).

nVars

Property nVars

private

Double: Number of variables that are optimized.

objectiveInit

Property objectiveInit

private

Struct: Contains values extracted during initialization of objective functions.

This is used to avoid the extraction in every call of the objective in each iteration thus to improve performance. Since it is a transient property it will not be saved when saving the object.

objectiveTerms

Property objectiveTerms

private

Struct array: Ojective terms.

plotLog

Property plotLog

private

Bool: If true, plot log in call of Collocation.objfun() (stick figure, objective, constrains) (default: 0)

X_lb

Property X_lb

inherited

Double array: Lower bound of state vector.

X_ub

Property X_ub

inherited

Double array: Upper bound of state vector.

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

• BioMAC-Sim-Toolbox/src/problem/@Collocation/Collocation.m