Gait2dc Class Reference

The class describes the Gait2dc model. More...

Inheritance diagram for Gait2dc:

Public Member Functions
function	extractControl (in obj, in type, in controlname)
	Function to obtain index of contol with a specific type (and name)
function	extractState (in obj, in type, in statename)
	Function to obtain index of state with a specific type (and name)
function	Gait2dc (in varargin)
	Default constructor setting default Gait2dc object.
function	getCoP (in obj, in grf)
	Function to calculate the center of pressure.
function	getDynamics (in obj, in x, in xdot, in u)
	Function to compute implicit differential equation for 2D musculoskeletal model.
function	getErate_bhargava (in obj, in F_ce, in stim, in act, in l_ce, in v_ce, in t_stim)
	Model function to calculate the energy rate of a single time step using Bhargava et al.
function	getErate_Houdijk (in obj, in F_ce, in act, in l_ce, in v_ce)
	Model function to calculate the energy rate of a single time.
function	getErate_Lichtwark (in obj, in F_ce, in act, in l_ce, in v_ce, in t_stim)
	Model function to calculate the energy rate of a single time step using a continuous version of Lichtwark & Wilson's model.
function	getErate_margaria (in obj, in F_ce, in v_ce)
	Model function to calculate the energy rate of a single time step using Margaria's model.
function	getErate_Minetti (in obj, in act, in v_ce)
	Model function to calculate the energy rate of a single time.
function	getErate_uchida (in obj, in F_ce, in stim, in act, in l_ce, in v_ce)
	Model function to calculate the energy rate of a single time.
function	getErate_Umberger (in obj, in F_ce, in stim, in act, in l_ce, in v_ce)
	Model function to calculate the energy rate of a single time step with Umberger et al.
function	getEratec_bhargava (in obj, in F_ce, in stim, in act, in l_ce, in v_ce, in dFdx, in dFdxdot, in epsilon)
	Model function to calculate the energy rate of a single time step using a continuous version of Bhargava et al.
function	getEratec_Houdijk (in obj, in F_ce, in act, in l_ce, in v_ce, in dFdx, in dFdxdot, in epsilon)
	Model function to calculate the energy rate of a single time step using a continuous version of Houdijk et al.
function	getEratec_Lichtwark (in obj, in F_ce, in act, in l_ce, in v_ce, in dFdx, in dFdxdot, in epsilon)
	Model function to calculate the energy rate of a single time step using a continuous version of Lichtwark & Wilson's model.
function	getEratec_margaria (in obj, in F_ce, in v_ce, in dFdx, in dFdxdot, in epsilon)
	Model function to calculate the energy rate of a single time step using a continuous version of Margaria's model.
function	getEratec_Minetti (in obj, in act, in v_ce)
	Model function to calculate the energy rate of a single time step using Minetti's model.
function	getEratec_umberger (in obj, in F_ce, in stim, in act, in l_ce, in v_ce, in dFdx, in dFdxdot, in epsilon)
	Model function to calculate the energy rate of a single time step with the continuous version of Umberger et al.
function	getFkin (in obj, in x)
	Function returns position and orientation of all segments, for the system in position q.
function	getGRF (in obj, in x)
	Function returning the ground reaction forces for the system in state x.
function	getJointmoments (in obj, in x, in u)
	Function returns joint moments, for the system in state x.
function	getLCE (in obj, in x)
	Function returns length of contractile element, for the system in state x.
function	getLdotCE (in obj, in xdot)
	Function returns length change of contractile element, for the system in state x.
function	getLdotMTU (in obj, in x)
	Function returns length change of entire muscle-tendon-unit, for the system in state x.
function	getLdotSEE (in obj, in x, in xdot)
	Function returns length change of serial elastic element, for the system in state x.
function	getLMTU (in obj, in x)
	Function returns length of entire muscle-tendon-unit, for the system in state x.
function	getLSEE (in obj, in x)
	Function returns length of serial elastic element, for the system in state x.
function	getMetabolicRate_pernode (in obj, in x, in xdot, in u, in t_stim, in name, in getCont, in epsilon, in exponent)
	Model function to calculate metabolic cost of a movement.
function	getMomentArms (in obj)
	Function to extract moment arms matrix from muscle table.
function	getMuscleCEforces (in obj, in x, in xdot)
	Function returning muscle forces of CE for the system in state x.
function	getMuscleCEpower (in obj, in x, in xdot)
	Function returns power generated by muscle contractile elements, for the system in state x.
function	getMuscleforces (in obj, in x)
	Function returning muscle forces for the system in state x.
function	getMusclePower (in obj, in x)
	Function returns power generated by entire muscle-tendon-unit, for the system in state x.
function	getMuscleSEEpower (in obj, in x, in xdot)
	Function returns power generated by muscle serial elastic elements, for the system in state x.
function	setbodymass (in obj, in bodymass)
	Function to set body mass, does not influence the.
function	setMuscles (in obj, in muscles)
	Function to set the muscles table.
function	setSegmentMass (in obj, in segmentName, in segmentMass)
	Function to set segment mass.
function	setSegments (in obj, in segmentTable)
	Function to set segment Table.
function	setTreadmillSpeed (in obj, in speed)
	Function to set the speed of the ground, to model a treadmill.
function	showMarker (in obj, in x, in markerTable, in measuredMean)
	Function to plot marker positions.
virtual	showStick (in obj, in x)
	Abstract function to show model as stick figure.
function	showStick (in obj, in x, in range, in plotFeet, in plotGRF, in plotCPs, in plotJointCOSYs)
	Function to show model as stick figure.
function	showTreadmill (in obj, in x_points, in y_points, in xrange, in yrange, in durTrial, in nFrames)
	Function to visualize treadmill as moving scatter plot.
virtual	simuAccGyro (in obj, in data, in q, in qd, in qdd)
	Abstract function to simulate acceleration and gyroscope signals.
function	simuAccGyro (in obj, in variables, in q, in qd, in qdd, in idxSegment, in idxAcc, in idxGyro, in dlocalAll, in plocalAll)
	Function to simulate acceleration and gyroscope signals.
function	simuMarker (in obj, in variables, in q, in idxSegment, in plocalAll, in dlocalAll)
	Matlab function to simulates markers placed on 2D model.

Static Public Member Functions
function	getMexFiles ()
	Function to make MEX functions.

Public Attributes
Property	CPs
	Table: Contact points.
Property	dofs
	Table: Degrees of freedom (Range of Dofs should not be changed here.
Property	drag_coefficient
	Double: Air drag coefficient in N/(m/s)^2 (default: 0.2128)
Constant Property	FOOTSOLEOFFSET = 0.0702
	Double: Distance between foot sole and ankle joint in m.
Property	gravity
	Double array: Gravity vector in m/(s^2)
Constant Property	GRFNAMES = {'rightFx', 'rightFy', 'rightFz', 'rightMx', 'rightMy', 'rightMz', 'leftFx', 'leftFy', 'leftFz', 'leftMx', 'leftMy', 'leftMz' }
	Cell array with string: Gives the names for the GRF vector returned by getGRF()
Constant Property	HEELDEFAULTOFFSET = 0.06
	Double: Distance between heel and ankle joint for default body height in m.
Property	joints
	Table: Joints.
Property	lambda
	Double array: Lambda values (default: [0.01 0.1]) (1x2)
Property	mExtraScaleFactor
	Double: Scale factor for extra torques in Nm (default: 100 since we used this in previous simulations.
Property	muscles
	Table: Muscles.
Property	slope
	Double: Slope of ground in deg (positive is uphill)
Constant Property	TOEOFFSET = 0.05
	Double: Distance between toe and CP toe in m.
Property	torques
	Table: Torque actuators.
Property	wind_speed
	Double: Wind speed in direction of +X in m/s (default: 0)

Protected Member Functions
function	getCoM (in obj, in x)
	Function to calculate the center of mass.
function	getFootAngle (in obj, in x)
	Function to calculate the angle between foot and ground.
function	getRandomParticipant (in obj, in SDmusParam)
	Function to generate a participant with random muscle parameters.
function	getSameRandomParticipant (in obj, in SDmusParamVector)
	Function to generate a participant with random muscle parameters.
function	initMex (in obj)
	Initialize model mex file.
function	initModel (in obj, in varargin)
	Function to initialize model with default parameters.
function	readParameter (in obj)
	Function to read parameter matrix into tables.
function	scaleParameters (in obj)
	Function to scale the parameters defined in the excelfile.
function	update_constraints (in obj)
	Function defining the table Gait2dc.constraints.
function	update_controls (in obj)
	Function defining the table Gait2dc.controls.
function	update_idxControls (in obj)
	Function defining Model.hidxControls.
function	update_idxcxCP (in obj)
	Function defining Gait2dc.idxcxCPleft and Gait2dc.idxcxCPright.
function	update_idxForward (in obj)
	Function defining Model.idxForward.
function	update_idxForwardAll (in obj)
	Function defining Model.idxForwardAll.
function	update_idxParamSections (in obj, in src, in evnt)
	Function performed to update start indices of sections in Gait2dc.parameter.
function	update_idxSideward (in obj)
	Function defining Model.idxSideward.
function	update_idxSidewardAll (in obj)
	Function defining Model.idxSidewardAll.
function	update_idxStates (in obj)
	Function defining Model.hidxStates.
function	update_idxSymmetry (in obj)
	Function defining Gait2dc.idxSymmetry.
function	update_idxTorqueDof (in obj)
	Function defining Model.idxTorqueDof.
function	update_idxUpward (in obj)
	Function defining Model.idxUpward.
function	update_mexParameter (in obj, in src, in evnt)
	Function performed to update the Gait2dc.parameter, the mex and the tables.
function	update_states (in obj)
	Function defining the table Gait2dc.states.

Protected Attributes
Property	bodyheight
	Double: Bodyheight in m (default: 1.80)
Property	bodymass
	Double: Bodymass in kg (default: 75)
Property	constraints
	Table: Information on constraints implemented in the mex and here.
Property	controls
	Table: Information on controls of the model.
Property	excelfile
	String: Filename of parameter file including path and extension.
Property	foot
	Table: Defining size of feet for visualization.
Property	idxcxCPleft
	Double array: Indices for x position of left contact points.
Property	idxcxCPright
	Double array: Indices for x position of right contact points.
Property	idxForward
	Double array: Indices for forward translation.
Property	idxForwardAll
	Double array: Indices for forward translation, speed, position of contact points and force at contact points.
Property	idxParamSections
	Double array: Start indices of sections in Gait2dc.parameter.
Property	idxSideward
	Double array: Indices for sideward translation.
Property	idxSidewardAll
	Double array: Indices for sideward translation, speed, position of contact points and force at contact points.
Property	idxSymmetry
	Struct: Double arrays with indices for symmetry to map right to left.
Property	idxTorqueDof
	Double array: Indices of dofs of torque actuators.
Property	idxUpward
	Double array: Indices for upward translation.
Property	init
	Double: Showing if the mex model is initialized.
Property	nConstraints
	Double: Number of constraints (height of Model.constraints)
Property	nControls
	Double: Number of controls (height of Model.controls)
Property	nCPs
	Double: Number of contact points (height of Model.CPs)
Property	nDofs
	Double: Number of degree of freedoms (height of Model.dofs)
Property	nJoints
	Double: Number of joints (height of Model.joints)
Property	nMus
	Double: Number of muscles (height of Model.muscles)
Property	nSegments
	Double: Number of segments (height of Model.segments)
Property	nStates
	Double: Number of states (height of Model.states)
Property	nTor
	Double: Number of torque actuators (height of Model.torques)
Property	parameter
	Double matrix: Entries of parameter excel file.
Property	segments
	Table: Segments (Segment properties should not be changed)
Property	speed_left
	Double: Speed of simulated additional Treadmill.
Property	speed_right
Property	states
	Table: Information on states of the model.

Detailed Description

The class describes the Gait2dc model.

• The lower body is modeled in the sagittal plane.
• The model is configured using an excel file. This code relies on the structure of this file (hardcoded indices for each section in the file). Please don't change the structure. Thus, the order of the table entries should not be changed!!!
• In the list of the CPs (Gait2dc.CPs), additional CPs can be added.

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/+Treadmill/script2D.m.

Constructor & Destructor Documentation

Gait2dc()

function Gait2dc

(

in

varargin

)

Default constructor setting default Gait2dc object.

Initializes the model and builds and initializes the mex function.

The standard model can be called using:

Gait2dc('gait2dc_par.xls')

The excelfile must be in the matlab path.

Parameters

varargin

Variable length input with: excelfile String: Excel file with path, name and extension. If the excel is given, Gait2dc.scaleParameters will be called. OR parameter Matrix: Model parameters like they would be loaded from the excel (see Gait2dc.parameter). If the matrix is given and not an excel file, Gait2dc.scaleParameters will not be called. AND bodyheight (optional) Double: Bodyheight in m (If not given, default will be used and not the entry from excel or parameter matrix. Use empty to skip.) bodymass (optional) Double: Bodymass in kg (If not given, default will be used and not the entry from excel or parameter matrix. Use empty to skip.)

Return values

obj	Gait2dc class object

Member Function Documentation

extractControl()

function extractControl ( in  obj, in  type, in  controlname  )

inherited

Function to obtain index of contol with a specific type (and name)

Parameters

obj	Model class object
type	String: Type of the control
controlname	(optional) String or cell array of strings: Name of the control

Return values

iControl

Double array: Indices in Model.controls matching type (and name)

extractState()

function extractState ( in  obj, in  type, in  statename  )

inherited

Function to obtain index of state with a specific type (and name)

Parameters

obj	Model class object
type	String: Type of the state
statename	(optional) String or cell array of strings: Name of the state

Return values

iState

Double array: Indices in Model.states matching type (and name)

getCoM()

function getCoM ( in  obj, in  x  )

protected

Function to calculate the center of mass.

It solves the center of mass (CoM) coordinates from the locations of the individual centers of mass

Parameters

obj	Model class object
x	Double vector: joint angles (1xnStates or nStatesx1)

Return values

CoM	Double vector: x, y location of center of mass

getCoP()

function getCoP ( in  obj, in  grf  )

inherited

Function to calculate the center of pressure.

It solves the center of pressure (COP) coordinates from: COP x F + Ty = M, where COP is a point in the XZ plane and Ty is the "free moment" on the Y axis. expand the equation:

1. COPy * Fz - COPz * Fy + 0 = Mx
2. COPz * Fx - COPx * Fz + Ty = My
3. COPx * Fy - COPy * Fx + 0 = Mz

Use COPy = 0, to get COPx = Mz / Fy and COPz = -Mx / Fy

For 2D, COPz will be 0.

Parameters

obj	Model class object
grf	Double vector: Ground contact vector containing Fx, Fy, Fz, Mx, My, Mz (right), and Fx, Fy, Fz, Mx, My, Mz (left) (12)

Return values

CoP_r	Double vector: Center of pressure in x, y and z direction for right foot (3)
CoP_l	Double vector: Center of pressure in x, y and z direction for left foot (3)

getDynamics()

function getDynamics ( in  obj, in  x, in  xdot, in  u  )

virtual

Function to compute implicit differential equation for 2D musculoskeletal model.

This function calls the mex file of gait2dc.c: [f, dfdx, dfdxdot, dfdumus, dfdMextra] = gait2dc('Dynamics',x,xdot,umus,Mextra);

with the neural excitation umus and the extra torques Mextra.

The dynamic residuals will be between fmin and fmax when inputs satisfy system dynamics: fmin <= f(x,dx/dt,umus,Mextra) <= fmax

The last four outputs are optional and some computation time is saved if you do not request all of them.

Parameters

obj	Gait2dc class object
x	Double array: State of the model (Gait2dc.nStates x 1)
xdot	Double array: State derivatives (Gait2dc.nStates x 1)
u	Double array: Controls of the model (Gait2dc.nControls x 1)

Return values

f	Double array: Dynamic residuals (Gait2dc.nConstraints x 1)
dfdx	(optional) Double matrix: Transpose of Jacobian matrix df/dx (Gait2dc.nStates x Gait2dc.nConstraints)
dfdxdot	(optional) Double matrix: Transpose of Jacobian matrix df/dxdot (Gait2dc.nStates x Gait2dc.nConstraints)
dfdu	(optional) Double matrix: Transpose of Jacobian matrix df/du (Gait2dc.nControls x Gait3d.nConstraints)

Reimplemented from Model.

getErate_bhargava()

function getErate_bhargava ( in  obj, in  F_ce, in  stim, in  act, in  l_ce, in  v_ce, in  t_stim  )

inherited

Model function to calculate the energy rate of a single time step using Bhargava et al.

's model

Function to calculate the energy rate at a single time step using a continuous version of Bhargava et al.'s model. Model paper: Bhargava et al., J Biomech, 2004

Inputs are muscle states of the specific muscle that is considered.

Parameters

obj	Model object
F_ce	Force in the contractile element
stim	Stimulation of the muscle (between 0 and 1)
act	Activation level of the muscle (between 0 and 1)
l_ce	Normalized length of the contractile element
v_ce	Normalized velocity of the contractile element
t_stim	Duration of stimulation of muscle

The output of getEratec_bhargava.m is a double which is equal to the energy rate of the time step in W/kg

Return values

Edot	The energy expenditure during the current time step

getErate_Houdijk()

function getErate_Houdijk ( in  obj, in  F_ce, in  act, in  l_ce, in  v_ce  )

inherited

Model function to calculate the energy rate of a single time.

Function to calculate the energy rate at a single time step using Houdijk et al.'s model. Houdijk et al., J Biomech, 2006. The paper desription is not optimal, see comments

Inputs are muscle parameters of the specific muscle that is considered. Inputs are muscle states of the specific muscle that is considered.

Parameters

obj	Model object
F_ce	Force in the contractile element
act	Activation level of the muscle (between 0 and 1)
l_ce	Normalized length of the contractile element
v_ce	Normalized velocity of the contractile element

The output of getErate_Houdijk.m is a double which is equal to the energy rate of the time step in W/kg

Return values

Edot	The energy expenditure during the current time step
w	Muscle work during the current time step

getErate_Lichtwark()

function getErate_Lichtwark ( in  obj, in  F_ce, in  act, in  l_ce, in  v_ce, in  t_stim  )

inherited

Model function to calculate the energy rate of a single time step using a continuous version of Lichtwark & Wilson's model.

Function to calculate the energy rate at a single time step using Lichtwark & Wilson's model, described in the supplement of Lichtwark & Wilson, J Biomech, 2007. The exception in gamma (line 68), which is according to Lichtwark & Wilson, J Exp Biol, 2005, because results were better in the 2019 comparison paper

Inputs are muscle parameters of the specific muscle that is considered.

Parameters

obj	Model object
F_ce	Force in the contractile element
act	Activation level of the muscle (between 0 and 1)
l_ce	Normalized length of the contractile element
v_ce	Normalized velocity of the contractile element
t_stim	Duration of stimulation of muscle

The output of getErate_Lichtwark.m is a double which is equal to the energy rate of the time step in W/kg

Return values

Edot	The energy expenditure during the current time step

getErate_margaria()

function getErate_margaria ( in  obj, in  F_ce, in  v_ce  )

inherited

Model function to calculate the energy rate of a single time step using Margaria's model.

Function to calculate the energy rate at a single time step using Margaria's model: 25 % efficient during shortening, 120% during lengthening. Margaria, Int Z Angew Physiol Einschl Arbeitsphysiol, 1968

Inputs are muscle parameters of the specific muscle that is considered.

Parameters

obj	Model object
F_ce	Force in the contractile element
v_ce	Normalized velocity of the contractile element

The output of getErate_margaria.m is a double which is equal to the energy rate of the time step in W/kg

Return values

Edot	is the energy expenditure during the current time step

getErate_Minetti()

function getErate_Minetti ( in  obj, in  act, in  v_ce  )

inherited

Model function to calculate the energy rate of a single time.

Function to calculate the energy rate at a single time step using Minetti's model. Based on: Minetti & Alexander, J Theor Biol, 1997. Uses muscle-level work instead of torque-level

Inputs are muscle parameters of the specific muscle that is considered.

Parameters

obj	Model object
act	activation level of the muscle (between 0 and 1)
v_ce	current velocity of the contractile element

The output of getErate_Minetti is a double which is equal to the energy rate

Return values

Edot	is the energy expenditure during the current time step

getErate_uchida()

function getErate_uchida ( in  obj, in  F_ce, in  stim, in  act, in  l_ce, in  v_ce  )

inherited

Model function to calculate the energy rate of a single time.

Function to calculate the energy rate at a single time step using Uchida's model: Uchida et al., PLOS ONE, 2016

Inputs are muscle states of the specific muscle that is considered

Parameters

obj	Model class object
F_ce	Double vector: Muscle force of CE returned by obj.getMuscleCEforces(x) (Model.nMus x 1)
stim	Double vector: Stimulation of muscles = neural excitation u (Model.nMus x 1)
act	Double vector: Activation of muscles a (Model.nMus x 1)
l_ce	Double vector: Length of contractile element of muscles s (Model.nMus x 1)
v_ce	Double vector: Velocity of contractile element of muscles (Model.nMus x 1)

The output of getErate_uchida.m is a double which is equal to the energy rate of the time step in W/kg

Return values

Edot	Double vector: Energy expenditure during one time step (energy rate) in W (Model.nMus x 1)
w_ce	Double vector: Mechanical work rate of contractile element in W/kg (normalized to muscle mass) (Model.nMus x 1)
h_sl	Double vector: Heat rate due to shortening and lengthening of muscles in W/kg (normalized to muscle mass) (Model.nMus x 1)
h_am	Double vector: Heat rate from the activation of muscles and its maintenance in W/kg (normalized to muscle mass) (Model.nMus x 1)

getErate_Umberger()

function getErate_Umberger ( in  obj, in  F_ce, in  stim, in  act, in  l_ce, in  v_ce  )

inherited

Model function to calculate the energy rate of a single time step with Umberger et al.

's model. Ross Miller's code was also used as a reference.

Function to calculate the energy rate at a single time step using Umberger's model. It uses the 2010 version (no negative work): Umberger, J R Soc Interface, 2010 2003 (original) Version: Umberger et al., "A model of human muscle energy expenditure," Computer methods in biomechanics and biomedical engineering, vol. 6, no. 2, pp. 99–111, 2003.

Inputs are muscle states of the specific muscle that is considered

Parameters

obj	Gait2dc class object
F_ce	Double vector: Muscle force of CE returned by Model.getMuscleCEforces(x) (Model.nMus x 1)
stim	Double vector: Stimulation of muscles = neural excitation u (Model.nMus x 1)
act	Double vector: Activation of muscles a (Model.nMus x 1)
l_ce	Double vector: Length of contractile element of muscles s (Model.nMus x 1)
v_ce	Double vector: Velocity of contractile element of muscles (Model.nMus x 1)

The output of getErate_Umberger.m is a double which is equal to the energy rate of the time step in W/kg

Return values

Edot	Double vector: Energy expenditure during one time step (energy rate) in W (Model.nMus x 1)
w_ce	Double vector: Mechanical work rate of contractile element in W/kg (normalized to muscle mass) (Model.nMus x 1)
h_sl	Double vector: Heat rate due to shortening and lengthening of muscles in W/kg (normalized to muscle mass) (Model.nMus x 1)
h_am	Double vector: Heat rate from the activation of muscles and its maintenance in W/kg (normalized to muscle mass) (Model.nMus x 1)

getEratec_bhargava()

function getEratec_bhargava ( in  obj, in  F_ce, in  stim, in  act, in  l_ce, in  v_ce, in  dFdx, in  dFdxdot, in  epsilon  )

inherited

Model function to calculate the energy rate of a single time step using a continuous version of Bhargava et al.

's model

Function to calculate the energy rate at a single time step using a continuous version of Bhargava et al.'s model. Line 60, phi, was chosen based on graphs of phi as a function of t_stim, since t_stim cannot be differentiated. Model paper: bhargava et al., J Biomech, 2004

Inputs are muscle states of the specific muscle that is considered.

Parameters

obj	Model object
F_ce	Force in the contractile element
stim	Stimulation of the muscle (between 0 and 1)
act	Activation level of the muscle (between 0 and 1)
l_ce	Normalized length of the contractile element
v_ce	Normalized velocity of the contractile element
dFdx	Derivative of CE forces with respect to the state
dFdxdot	Derivative of CE forces with respect to the state derivative
epsilon	Measure of the nonlinearity of the continuous functions

The output of getEratec_bhargava.m is a double which is equal to the energy rate of the time step in W/kg

Return values

Edot	The energy expenditure during the current time step
dEdot	The gradient of Edot with respect to all states and inputs

getEratec_Houdijk()

function getEratec_Houdijk ( in  obj, in  F_ce, in  act, in  l_ce, in  v_ce, in  dFdx, in  dFdxdot, in  epsilon  )

inherited

Model function to calculate the energy rate of a single time step using a continuous version of Houdijk et al.

's model

Function to calculate the energy rate at a single time step using a continuous version of Houdijk et al.'s model. Houdijk et al., J Biomech, 2006.

Inputs are muscle parameters of the specific muscle that is considered. Inputs are muscle states of the specific muscle that is considered.

Parameters

obj	Model object
F_ce	Force in the contractile element
act	Activation level of the muscle (between 0 and 1)
l_ce	Normalized length of the contractile element
v_ce	Normalized velocity of the contractile element
dFdx	Derivative of CE forces with respect to the state
dFdxdot	Derivative of CE forces with respect to the state derivative
epsilon	Measure of the nonlinearity of the continuous functions

The output of getEratec_Houdijk.m is a double which is equal to the energy rate of the time step in W/kg

Return values

Edot	The energy expenditure during the current time step
dEdot	The gradient of Edot with respect to all states and inputs%

getEratec_Lichtwark()

function getEratec_Lichtwark ( in  obj, in  F_ce, in  act, in  l_ce, in  v_ce, in  dFdx, in  dFdxdot, in  epsilon  )

inherited

Model function to calculate the energy rate of a single time step using a continuous version of Lichtwark & Wilson's model.

Function to calculate the energy rate at a single time step using a continuous version of Lichtwark & Wilson's model, described in the supplement of Lichtwark & Wilson, J Biomech, 2007.

Inputs are muscle parameters of the specific muscle that is considered.

Parameters

obj	Model object
F_ce	Force in the contractile element
act	Activation level of the muscle (between 0 and 1)
l_ce	Normalized length of the contractile element
v_ce	Normalized velocity of the contractile element
dFdx	Derivative of CE forces with respect to the state
dFdxdot	Derivative of CE forces with respect to the state derivative
epsilon	Measure of the nonlinearity of the continuous functions

The output of getEratec_Lichtwark.m is a double which is equal to the energy rate of the time step in W/kg

Return values

Edot	The energy expenditure during the current time step
dEdot	The gradien

getEratec_margaria()

function getEratec_margaria ( in  obj, in  F_ce, in  v_ce, in  dFdx, in  dFdxdot, in  epsilon  )

inherited

Model function to calculate the energy rate of a single time step using a continuous version of Margaria's model.

Function to calculate the energy rate at a single time step using a continuous version of Margaria's model: 25 % efficient during shortening, 120% during lengthening. Margaria, Int Z Angew Physiol Einschl Arbeitsphysiol, 1968

Inputs are muscle parameters of the specific muscle that is considered.

Parameters

obj	Model object
F_ce	Force in the contractile element
v_ce	Normalized velocity of the contractile element
dFdx	Derivative of CE forces with respect to the state
dFdxdot	Derivative of CE forces with respect to the state derivative
epsilon	Measure of the nonlinearity of the continuous functions

The output of getEratec_margaria.m is a double which is equal to the energy rate of the time step in W/kg

Return values

Edot	is the energy expenditure during the current time step
dEdot	is the gradient of Edot with respect to all states and inputs

getEratec_Minetti()

function getEratec_Minetti ( in  obj, in  act, in  v_ce  )

inherited

Model function to calculate the energy rate of a single time step using Minetti's model.

No discsontinuities here, so it is the same as the original model.

Function to calculate the energy rate at a single time step using Minetti's model. Based on: Minetti & Alexander, J Theor Biol, 1997. Uses muscle-level work instead of torque-level

Inputs are muscle parameters of the specific muscle that is considered.

Parameters

obj	Model object
act	activation level of the muscle (between 0 and 1)
v_ce	current velocity of the contractile element

The output of getEratec_Minetti.m is a double which is equal to the energy rate of the time step in W/kg

Return values

Edot	is the energy expenditure during the current time step
dEdot	is the gradient of Edot with respect to all states and inputs

getEratec_umberger()

function getEratec_umberger ( in  obj, in  F_ce, in  stim, in  act, in  l_ce, in  v_ce, in  dFdx, in  dFdxdot, in  epsilon  )

inherited

Model function to calculate the energy rate of a single time step with the continuous version of Umberger et al.

's model

Function to calculate the energy rate at a single time step using a continuous version of Umberger's model. This one is published in Koelewijn, Dorscky et al., Comp Meth Biomed Biomech Eng, 2016, and uses the 2010 version (no negative work): Umberger, J R Soc Interface, 2010

Inputs are muscle states of the specific muscle that is considered.

Parameters

obj	Model object
F_ce	Force in the contractile element
stim	Stimulation of the muscle (between 0 and 1)
act	Activation level of the muscle (between 0 and 1)
l_ce	Normalized length of the contractile element
v_ce	Normalized velocity of the contractile element
dFdx	Derivative of CE forces with respect to the state
dFdxdot	Derivative of CE forces with respect to the state derivative
epsilon	Measure of the nonlinearity of the continuous functions

The output of getEratec_umberger.m is a double which is equal to the energy rate of the time step in W/kg

Return values

Edot	The energy expenditure during the current time step
dEdot	The gradient of Edot with respect to all states and inputs

getFkin()

function getFkin	(	in	obj,
		in	x
	)

Function returns position and orientation of all segments, for the system in position q.

This function can be used to plot the segments or for marker tracking. It calls the mex file of gait2d.c: FK = gait2dc('Fkin', x);

The order is the following for each segment:

px', 'py', 'R11', 'R12', 'R21', 'R22'

p can be obtained by:

idxSegment = 1; % see Gait2dc.segments for the order
p = FK((1:2) + (idxSegment-1)*6);

R can be obtained by:

R = reshape(FK((3:6) + (idxSegment-1)*6), 2, 2)';

Parameters

obj	Gait2dc class object
x	Double array: State of the model (Gait2dc.nStates x 1)

Return values

FK	Double array: position and orientation of all segments. Details see above. (Gait2dc.nSegments * 6)
dFKdq	(optional) Double matrix: Jacobian of FK with respect to q (Gait2dc.nSegments * 6 x Gait2dc.nDofs)
dFKdotdq	(optional) Double matrix: Jacobian of dFK/dt with respect to q (Gait2dc.nSegments * 6 x Gait2dc.nDofs)

getFootAngle()

function getFootAngle ( in  obj, in  x  )

protected

Function to calculate the angle between foot and ground.

Function uses gait2dc('Stick', x(:, iTime)) to get the position of the foot segment.

This implementation is only suited for our 2D model containing two contact points per foot (heel and toe)!

Parameters

obj	Gait2dc class object
x	Double matrice: State vector of model for n time points (Gait2dc.nStates x n)

Return values

angle_r	Double vector: Angle between right foot and ground in degree. Angles ranges from -180 to 180 deg. (n x 1)
angle_l	Double vector: Angle between left foot and ground in degree. Angles ranges from -180 to 180 deg. (n x 1)

getGRF()

function getGRF ( in  obj, in  x  )

virtual

Function returning the ground reaction forces for the system in state x.

This function calls the mex file of gait2dc.c: [grf, dgrfdx] = gait2dc('GRF', x);

Parameters

obj	Gait2dc class object
x	Double array: State of the model (Gait2dc.nStates x 1)

Return values

grf	Double array (12x1) containing: right Fx, Fy, Fz (in bodyweight) right Mx, My, Mz (in bodyweight*m) left Fx, Fy, Fz (in bodyweight) left Mx, My, Mz (in bodyweight*m)
dgrfdx	(optional) Double matrix: Transpose of Jacobian matrix dgrf/dx (Gait2dc.nStates x 12)

Reimplemented from Model.

getJointmoments()

function getJointmoments ( in  obj, in  x, in  u  )

virtual

Function returns joint moments, for the system in state x.

This includes passive joint moments and muscle moments and extra moments.

Parameters

obj	Gait2dc class object
x	Double array: State of the model (Gait2dc.nStates x 1)
u	(optional) Double array: Controls of the model which are only needed if you want to apply extra moments (i.e. arm torques) (Gait2dc.nControls x 1)

Return values

M	Double array: Moment for each DOF (Gait2dc.nDofs x 1)
dMdx	(optional) Double matrix: Transpose of Jacobian matrix dM/dx (Gait2dc.nStates x Gait2dc.nDofs)
dMdu	(optional) Double matrix: Transpose of Jacobian matrix dM/du (Gait2dc.nControls x Gait2dc.nDofs)

Reimplemented from Model.

getLCE()

function getLCE	(	in	obj,
		in	x
	)

Function returns length of contractile element, for the system in state x.

This function simply scales s using lceopt.

Parameters

obj	Gait2dc class object
x	Double array: State of the model (Gait2dc.nStates x 1)

Return values

L_CE	Double array: CE length (m) of each muscle (Gait2dc.nMus x 1)

getLdotCE()

function getLdotCE	(	in	obj,
		in	xdot
	)

Function returns length change of contractile element, for the system in state x.

This function simply scales sdot using lceopt.

Parameters

obj	Gait2dc class object
xdot	Double array: State derivatives (Gait2dc.nStates x 1)

Return values

Ldot_CE

Double array: CE length change (m/s) of each muscle (Gait2dc.nMus x 1)

getLdotMTU()

function getLdotMTU	(	in	obj,
		in	x
	)

Function returns length change of entire muscle-tendon-unit, for the system in state x.

This function does not ensure that the order of muscle moment arms fit to the order of DoFs in qdot in the states. This must be ensured by the user. The order of muscle moment arms is defined in the excel file defining the model.

The same length is also computed in MusclePath() in gait2dc.c.

Parameters

obj	Gait2dc class object
x	Double array: State of the model (Gait2dc.nStates x 1)

Return values

Ldot_MTU

Double array: MTU length change (m/s) of each muscle (Gait2dc.nMus x 1)

getLdotSEE()

function getLdotSEE	(	in	obj,
		in	x,
		in	xdot
	)

Function returns length change of serial elastic element, for the system in state x.

This function computes the length change of the SEE as Ldot_MTU-Ldot_CE.

Parameters

obj	Gait2dc class object
x	Double array: State of the model (Gait2dc.nStates x 1)
xdot	Double array: State derivatives (Gait2dc.nStates x 1)

Return values

Ldot_SEE

Double array: SEE length change (m/s) of each muscle (Gait2dc.nMus x 1)

getLMTU()

function getLMTU	(	in	obj,
		in	x
	)

Function returns length of entire muscle-tendon-unit, for the system in state x.

This function replicated the computation done in gait2dc.c.

Parameters

obj	Gait2dc class object
x	Double array: State of the model (Gait2dc.nStates x 1)

Return values

L_MTU

Double array: MTU length (m) of each muscle (Gait2dc.nMus x 1)

getLSEE()

function getLSEE	(	in	obj,
		in	x
	)

Function returns length of serial elastic element, for the system in state x.

This function uses the difference of the length of the entire muscle-tendon-unit and of the contracile element.

Parameters

obj	Gait2dc class object
x	Double array: State of the model (Gait2dc.nStates x 1)

Return values

L_SEE

Double array: SEE length (m) of each muscle (Gait2dc.nMus x 1)

getMetabolicRate_pernode()

function getMetabolicRate_pernode ( in  obj, in  x, in  xdot, in  u, in  t_stim, in  name, in  getCont, in  epsilon, in  exponent  )

inherited

Model function to calculate metabolic cost of a movement.

Function to calculate the metabolic cost of a movement. Seven different models are currently implemented

Parameters

obj	Model object
x	Double vector: States of the current node
xdot	Double vector: Derivatives of states
u	Double vector: Controls of the current node
t_stim	Double vector: how long each muscle was already stimulated
name	(optional) String: name of the model that is being used. Options are umberger, lichtwark, bhargava, margaria, minetti, houdijk, and uchida
getCont	(optional) Boolean: If true, get the continuous version which is needed if we use the output for simulation. (default: 0)
epsilon	(optional) double parameter: Measure of nonlinearity of model, which is only used in the continuous model version. Default 0.
exponent	(optional) integer: if metabolic cost is the objective, this number allows to minimize the square, cube, or nth-power of metabolic cost. Default is 1

Return values

Edot	Double vector: Energy expenditure during one time step (energy rate) in W (Model.nMus x 1)
dEdotdx	Double vector: Derivative of Edot w.r.t to x (Model.nStates x 1)
dEdotdu	Double vector: Derivative of Edot w.r.t to u (Model.nControls x 1)
dEdotdT	Double: Derivative of Edot w.r.t to T

getMexFiles()

function getMexFiles ( )

static

Function to make MEX functions.

Builds the MEX function from Autolev source code, and from gait2dc.c MEX wrapper.

getMomentArms()

function getMomentArms

(

in

obj

)

Function to extract moment arms matrix from muscle table.

It extract the moment arm matrix which is defined by the model file (excel file) and saved in model.muscles. It is equal to the variable "MA" in gait2dc.c.

It is not ensured whether the order in obj.muscles fit to to the order of the joints.

Parameters

obj	Gait2dc class object

Return values

momentarms

Double matrix: Muscle moment arms in m (Gait2dc.nMus x Gait2dc.nJoints)

getMuscleCEforces()

function getMuscleCEforces ( in  obj, in  x, in  xdot  )

virtual

Function returning muscle forces of CE for the system in state x.

This function calls the mex file of gait2dc.c: [forces] = gait2dc('MuscleCEforces', x);

Parameters

obj	Gait2dc class object
x	Double array: State of the model (Gait2dc.nStates x 1)
xdot	Double array: State derivatives (Gait2dc.nStates x 1)

Return values

forcesCE	Double array: Muscle forces of CE (in N) (Gait2dc.nMus x 1)
dforcesCEdx	Double array: Transpose of Jacobian matrix d force / d x (Gait2dc.nStates x Gait2dc.nMus)
dforcesCEdxdot	Double array: Transpose of Jacobian matrix d force / d xdot (Gait2dc.nStates x Gait2dc.nMus)

Reimplemented from Model.

getMuscleCEpower()

function getMuscleCEpower ( in  obj, in  x, in  xdot  )

virtual

Function returns power generated by muscle contractile elements, for the system in state x.

xdot must be the state derivatives, such that the muscle balance equations are satisfied. It is up to the user to ensure that the muscle contraction balance f(x,xdot)=0 when this function is used.

Parameters

obj	Gait2dc class object
x	Double array: State of the model (Gait2dc.nStates x 1)
xdot	Double array: State derivatives (Gait2dc.nStates x 1)

Return values

powers	Double array: CE power output (W) of each muscle (Gait2dc.nMus x 1)
conDynRes	Double array: Contraction dynamics residuals (Gait2dc.nMus x 1)

Reimplemented from Model.

getMuscleforces()

function getMuscleforces ( in  obj, in  x  )

virtual

Function returning muscle forces for the system in state x.

This function calls the mex file of gait2dc.c: [forces] = gait2dc('Muscleforces', x);

Parameters

obj	Gait2dc class object
x	Double array: State of the model (Gait2dc.nStates x 1)

Return values

forces	Double array: Muscle forces (in N) (Gait2dc.nMus x 1)
dforcesdx	Double array: Transpose of Jacobian matrix d force / d x (Gait2dc.nStates x Gait2dc.nMus)

Reimplemented from Model.

getMusclePower()

function getMusclePower	(	in	obj,
		in	x
	)

Function returns power generated by entire muscle-tendon-unit, for the system in state x.

This function calls Gait2dc:getLdotMTU() which does not ensure that the order of muscle moment arms fit to the order of DoFs in qdot in the states. This must be ensured by the user. The order of muscle moment arms is defined in the excel file defining the model.

Parameters

obj	Gait2dc class object
x	Double array: State of the model (Gait2dc.nStates x 1)

Return values

powers

Double array: MTU power output (W) of each muscle (Gait2dc.nMus x 1)

getMuscleSEEpower()

function getMuscleSEEpower	(	in	obj,
		in	x,
		in	xdot
	)

Function returns power generated by muscle serial elastic elements, for the system in state x.

xdot must be the state derivatives, such that the muscle balance equations are satisfied. It is up to the user to ensure that the muscle contraction balance f(x,xdot)=0 when this function is used.

Parameters

obj	Gait2dc class object
x	Double array: State of the model (Gait2dc.nStates x 1)
xdot	Double array: State derivatives (Gait2dc.nStates x 1)

Return values

powersSEE

Double array: SEE power output (W) of each muscle (Gait2dc.nMus x 1)

getRandomParticipant()

function getRandomParticipant ( in  obj, in  SDmusParam  )

protected

Function to generate a participant with random muscle parameters.

This function generates a new model object where muscle parameters were independenlty normally distributed around the muscle parameters of obj using the standard deviation SDmusParam. In Dorschky et al., "Optimal control simulation predicts effects of midsole materials on energy cost of running" (2019), we change fmax, lceopt, width, L0, kPEE, umax, vmax, tact, tdeact, gmax, arel, and the moment arms at each joint.

We use the same muscle parameters for right and left muscles (symmetric model). Otherwise it does not make sense to use the symmetry option in the simulation.

To generate this new model, we use the excelfile, bodyheight, and bodymass of obj. Other parameters which were changed in obj will not be copied since we have to create a new model object. If we would not create a new model object, but make a deep copy by inheriting from matlab.mixin.Copyable, this would cause problems with the listener callbacks (They would not be called after changes of the muscle parameters.). => If you find a better solution, please adapt this function.

This function does not shuffle or reset the random number generator (see https://de.mathworks.com/help/matlab/ref/rng.html).

Parameters

obj	Gait2dc model object
SDmusParam	Double: Standard deviation (SD) for distribution around default value in % of the default value.

Return values

randModel

Gait2dc model object: New model generated using excelfile, bodyheight and bodymass of obj. Afterwards muscle parameters were changed randomly following a normal distribution.

getSameRandomParticipant()

function getSameRandomParticipant ( in  obj, in  SDmusParamVector  )

protected

Function to generate a participant with random muscle parameters.

This function generates a new model object where muscle parameters were independenlty normally distributed around the muscle parameters of obj using the standard deviation SDmusParam. In Dorschky et al., "Optimal control simulation predicts effects of midsole materials on energy cost of running" (2019), we change fmax, lceopt, width, L0, kPEE, umax, vmax, tact, tdeact, gmax, arel, and the moment arms at each joint.

We use the same muscle parameters for right and left muscles (symmetric model). Otherwise it does not make sense to use the symmetry option in the simulation.

To generate this new model, we use the excelfile, bodyheight, and bodymass of obj. Other parameters which were changed in obj will not be copied since we have to create a new model object. If we would not create a new model object, but make a deep copy by inheriting from matlab.mixin.Copyable, this would cause problems with the listener callbacks (They would not be called after changes of the muscle parameters.). => If you find a better solution, please adapt this function.

This function does not shuffle or reset the random number generator (see https://de.mathworks.com/help/matlab/ref/rng.html).

Parameters

obj	Gait2dc model object
SDmusParamVector	Double vector: nParams (or larger) xnMus vector of normalized deviations from the mean.
randModel	Gait2dc model object: New model generated using excelfile, bodyheight and bodymass of obj. Afterwards muscle parameters were changed randomly following a normal distribution.

initMex()

function initMex ( in  obj )

protectedvirtual

Initialize model mex file.

This function calls the mex file of gait2dc.c [info] = gait2dc('Initialize', model)

This initializes the model. This is required before anything is done with the model.

Input: param Matric containing model parameters loaded from the excel file after scaling.

Output: xneutral Model state vector (Gait2dc.nStates x 1) for a neutral state where the model is in free fall with feet not quite touching the ground, but otherwise close to static equilibrium.

Parameters

obj	Gait2dc class object

Reimplemented from Model.

initModel()

function initModel ( in  obj, in  varargin  )

protectedvirtual

Function to initialize model with default parameters.

Sets bodyheight and mass and creates default foot table.

Parameters

obj	Gait2dc class object
varargin	Cell: Can contain bodyheight Double: Bodyheight in m bodymass Double: Bodymass in kg

Reimplemented from Model.

readParameter()

function readParameter ( in  obj )

protected

Function to read parameter matrix into tables.

Function reads the parameters from the matrix Gait2dc.parameter and sets Gait2dc.segments, Gait2dc.joints, Gait2dc.dofs, Gait2dc.muscles and Gait2dc.CPs. If you change sth here, scaleParameters() should be also checked!!! Sets also the default range of Gait2dc.CPs. Gait2dc.bodymass and Gait2dc.bodyheight are set according to the input of the constructor (value in excelfile is ignored).

Parameters

obj	Gait2dc class object

scaleParameters()

function scaleParameters ( in  obj )

protected

Function to scale the parameters defined in the excelfile.

Uses bodymass and height according to Winter 2005. Bodymass and heigt have to be set during object initialization. Changes later changes are not possible. Please create a new object in this case.

Parameters

obj	Gait2dc class object

setbodymass()

function setbodymass ( in  obj, in  bodymass  )

inherited

Function to set body mass, does not influence the.

Parameters

obj	Model class object
segmentTable	Double: bodymass

setMuscles()

function setMuscles ( in  obj, in  muscles  )

inherited

Function to set the muscles table.

Parameters

obj	Model class object
segmentTable	Table: muscles

setSegmentMass()

function setSegmentMass ( in  obj, in  segmentName, in  segmentMass  )

inherited

Function to set segment mass.

Parameters

obj	Model class object
segmentName	String: Name of the segment
segmentMass	Double: Mass of the segment in kg

setSegments()

function setSegments ( in  obj, in  segmentTable  )

inherited

Function to set segment Table.

Parameters

obj	Model class object
segmentTable	Table: segmentTable

setTreadmillSpeed()

function setTreadmillSpeed	(	in	obj,
		in	speed
	)

Function to set the speed of the ground, to model a treadmill.

This function allows you to model a treadmill. It can handle two types of inputs. If it is a double, the value will be set as the treadmill speed. If it is a struct, a split-belt treadmill can be modelled

Parameters

obj	Gait2d_osim class object
speed	Double or Struct: Treadmill speed in m/s. If it is a double, the value is used for the left and right belt. If is is a struct, speed.left and speed.right are used for the left and right belt, respectively.

showMarker()

function showMarker	(	in	obj,
		in	x,
		in	markerTable,
		in	measuredMean
	)

Function to plot marker positions.

The motion in x and the matrix measured have to fit to each other. If you want to plot for example only a single node, markerTable.mean must be only the data of this single node.

You can use the function like this:

figure();
x = result.X(result.problem.idx.states(:, 1:result.problem.nNodes)); % get states
result.problem.model.showStick(x, [], 1, 0, 1); % plot stick figure
markerTable = result.problem.objectiveTerms(1).varargin{1}.variables; % assuming trackMarker is your first objective
markerMean = cell2mat(markerTable.mean')/1000; % extract and convert from mm to meter
result.problem.model.showMarker(x, markerTable, markerMean); % plot marker data

Todo:

The function is not yet supporting Gait2dc.slope ~= 0.

Parameters

obj	Gait2dc class object
x	Double matrix: State vector of model for n time points (Gait2dc.nStates x n)
markerTable	Table: Variables table specifying markers with at least the columns: type, name, segment, position, direction to call Gait2dc.simuMarker.
measuredMean	(optional) Double matrix: Measured marker data in meter(!) which will be plotted as reference. The matrix must have the same number of time points as the state vector x. Further, the matrix columns must correspond to the rows of the markerTable in the same order to be able to match coordinates of the markers. (n x height(markerTable)) (default: empty)

showStick() [1/2]

virtual showStick ( in  obj, in  x  )

virtualinherited

Abstract function to show model as stick figure.

showStick() [2/2]

function showStick	(	in	obj,
		in	x,
		in	range,
		in	plotFeet,
		in	plotGRF,
		in	plotCPs,
		in	plotJointCOSYs
	)

Function to show model as stick figure.

Todo:

If the slope ~= 0, the ranges are not perfect yet. If ranges are given, they will not be kept constant. If no ranges are given, the stick figures are not perfectly centered.

Parameters

obj	Gait2dc class object
x	Double matrice: State vector of model for n time points (Gait2dc.nStates x n)
range	(optional) Double matrice: Defining the range of the figure with [xmin, xmax; ymin, ymax]. (2 x 2) (default: [pelvisX-1, pelvisX+1; -0.2, 2])
plotFeet	(optional) Bool: If true, the undeformed feet are plotted independently from the CPs (default: 0)
plotGRF	(optional) Bool: If true, it plots arrows for the GRFs (default: 0)
plotCPs	(optional) Bool: If true, it plots spheres for the CPs (default: 0)
plotJointCOSYs	(optional) Bool: If true, it plots the coordinate systems of the joints (default: 0)

showTreadmill()

function showTreadmill	(	in	obj,
		in	x_points,
		in	y_points,
		in	xrange,
		in	yrange,
		in	durTrial,
		in	nFrames
	)

Function to visualize treadmill as moving scatter plot.

Parameters

obj	Gait2dc class object
xpoints	Double matrix: Defining the x - positions of scatter plot in current frame representing the treadmill
ypoints	Double matrix: Defining the y - positions of scatter plot in current frame representing the treadmill
xrange	Double matrix: Defining the range of the figure with [xmin, xmax]. (2 x 1)
yrange	Double matrix: Defining the range of the figure with [ymin, ymax]. (2 x 1)
durTrial	Double: duration of gait cycle
nFrames	Integer: number of Nodes

Return values

x_points	Double matrix: Updated x_points accrording to treadmill speed
y_points	Double matrix: Updated y_points accrording to treadmill speed

simuAccGyro() [1/2]

virtual simuAccGyro ( in  obj, in  data, in  q, in  qd, in  qdd  )

virtualinherited

Abstract function to simulate acceleration and gyroscope signals.

simuAccGyro() [2/2]

function simuAccGyro	(	in	obj,
		in	variables,
		in	q,
		in	qd,
		in	qdd,
		in	idxSegment,
		in	idxAcc,
		in	idxGyro,
		in	dlocalAll,
		in	plocalAll
	)

Function to simulate acceleration and gyroscope signals.

Do not change "obj" or "variables" in this function! This will allow Matlab to "pass by reference" and avoid function call overhead.

Position has to given as X and Y position of sensor in segment coordinate system in m.

Direction has to be given in axis definition, e.g [1, 0, 0].

Parameters

obj	Gait2dc class object
variables	Table: Variable table containing the accelerometer and gyroscope data with at least the columns: type, name, segment, position, direction
q	Generalized coordinates (Gait2dc.nDofs x 1)
qd	First derivatives of generalized coordinates (Gait2dc.nDofs x 1)
qdd	Second derivatives of generalized coordinates (Gait2dc.nDofs x 1) (use NaN to skip)
idxSegment	(optional) Double array: Indices of segments fitting to respective IMU (variables.nVars.all x 1) => It is faster to pass them than to recalculate each time.
idxAcc	(optional) Double array: Indices in variables that have type 'acc' (nAcc x 1) => It is faster to pass them than to recalculate each time.
idxGyro	(optional) Double array: Indices in variables that have type 'gyro' (nGyro x 1) => It is faster to pass them than to recalculate each time.
dlocalAll	(optional) Double matrix: Local direction of the IMU saved in variables (variables.nVars.all x 3) => It is faster to pass them than to extract them each time.
plocalAll	(optional) Double matrix: Local position of the IMU saved in variables (variables.nVars.all x 3) => It is faster to pass them than to extract them each time.

Return values

s	Simulated sensor signals (data.nVars.all x 1)
ds_dq	Sparse Jacobian ds/dq (data.nVars.all x Gait2dc.nDofs)
ds_dqd	Sparse Jacobian ds/dqd (data.nVars.all x Gait2dc.nDofs)
ds_dqdd	Sparse Jacobian ds/dqdd (data.nVars.all x Gait2dc.nDofs)

simuMarker()

function simuMarker	(	in	obj,
		in	variables,
		in	q,
		in	idxSegment,
		in	plocalAll,
		in	dlocalAll
	)

Matlab function to simulates markers placed on 2D model.

Do not change "obj" or "variables" in this function! This will allow Matlab to "pass by reference" and avoid function call overhead.

Position has to given as X, Y (and Z) position of marker in segment coordinate system in m. Direction has to be given in axis definition, e.g [1, 0, 0]. For position and direction, we will use only the first two entries for the 2D model.

Parameters

obj	Gait2dc class object
variables	Table: Variable table containing the marker data with at least the columns: type, name, segment, position, direction
q	Double array: Generalized coordinates (Gait2dc.nDofs x 1)
idxSegment	(optional) Double array: Indices of segments fitting to respective markers (variables.nVars.all x 1) => It is faster to pass them than to recalculate each time.
plocalAll	(optional) Double matrix: Local position of the markers saved in variables (variables.nVars.all x 2(or3)) => It is faster to pass them than to extract them each time.
dlocalAll	(optional) Double matrix: Local direction of the markers saved in variables (variables.nVars.all x 2(or3)) => It is faster to pass them than to extract them each time.

Return values

m	Simulated marker signals in meter (variables.nVars.all x 1)
dm_dq	Sparse Jacobian dm/dq (variables.nVars.all x Gait2dc.nDofs)

update_constraints()

function update_constraints ( in  obj )

protectedvirtual

Function defining the table Gait2dc.constraints.

Table lists type, name, equation (string), fmin and fmax

The constraints are composed of Gait2dc.nConstraints = 2* Gait2dc.nDofs + 2* Gait2dc.nMus + 4* Gait2dc.nCPs

• implicite differential equations: qdot-dq/dt = 0 (Gait2dc.nDofs x 1)
• equations of motion from Autolev (Gait2dc.nDofs x 1)
• muscle contraction dynamics (Gait2dc.nMus x 1)
• muscle activation dynamics: da/dt - (u-a)(c1*u + c2) = 0 (Gait2dc.nMus x 1)
• four equations for each contact point (4* Gait2dc.nCPs x 1)

Parameters

obj	Gait2dc class object

Reimplemented from Model.

update_controls()

function update_controls ( in  obj )

protectedvirtual

Function defining the table Gait2dc.controls.

Table lists type, name, xmin, xmax and xneutral

Parameters

obj	Gait2dc class object

Reimplemented from Model.

update_idxControls()

function update_idxControls ( in  obj )

protectedinherited

Function defining Model.hidxControls.

Parameters

obj	Model class object

update_idxcxCP()

function update_idxcxCP ( in  obj )

protected

Function defining Gait2dc.idxcxCPleft and Gait2dc.idxcxCPright.

Parameters

obj	Gait2dc class object

update_idxForward()

function update_idxForward ( in  obj )

protectedinherited

Function defining Model.idxForward.

Provides the indices of state variables that have forward translation. States have to be updated before!

Parameters

obj	Model class object

update_idxForwardAll()

function update_idxForwardAll ( in  obj )

protectedinherited

Function defining Model.idxForwardAll.

Provides the indices of state variables that have forward translation, speed, position of contact points and force at contact points. States and idxForward have to be updated before!

Parameters

obj	Model class object

update_idxParamSections()

function update_idxParamSections ( in  obj, in  src, in  evnt  )

protected

Function performed to update start indices of sections in Gait2dc.parameter.

• Updates Gait2dc.idxParamSections
• Called with a PostSet event after set parameter
• Done in a similar way as in gait2dc.c

Parameters

obj	Gait2dc class object
src	(optional) meta.property: Object describing the source of the event
evnt	(optional) event.Propertyevent: Object describing the event

update_idxSideward()

function update_idxSideward ( in  obj )

protectedinherited

Function defining Model.idxSideward.

Provides the indices of state variables that have sideward translation. States have to be updated before!

Parameters

obj	Model class object

update_idxSidewardAll()

function update_idxSidewardAll ( in  obj )

protectedinherited

Function defining Model.idxSidewardAll.

Provides the indices of state variables that have sideward translation, speed, position of contact points and force at contact points. States and idxSideward have to be updated before!

Parameters

obj	Model class object

update_idxStates()

function update_idxStates ( in  obj )

protectedinherited

Function defining Model.hidxStates.

Parameters

obj	Model class object

update_idxSymmetry()

function update_idxSymmetry ( in  obj )

protectedvirtual

Function defining Gait2dc.idxSymmetry.

Parameters

obj	Gait2dc class object

Reimplemented from Model.

update_idxTorqueDof()

function update_idxTorqueDof ( in  obj )

protectedinherited

Function defining Model.idxTorqueDof.

Searches for indices of dof which have torque actuators in Model.torques.

Parameters

obj	Model class object

update_idxUpward()

function update_idxUpward ( in  obj )

protectedinherited

Function defining Model.idxUpward.

Provides the indices of state variables that have upward translation. States have to be updated before!

Parameters

obj	Model class object

update_mexParameter()

function update_mexParameter ( in  obj, in  src, in  evnt  )

protectedvirtual

Function performed to update the Gait2dc.parameter, the mex and the tables.

• Called with a PostSet event after set lambda, bodyheight, bodymass, gravity, drag_coefficient, wind_speed, slope, joints, muscles, CPs, dofs, segments.
• Reinitializes mex with new parameter matrixs.
• This function calls all the other update functions. If we would also add a listener for them, we could not ensure that they are called in the correct order!

Parameters

obj	Gait2dc class object
src	meta.property: Object describing the source of the event
evnt	(optional) event.Propertyevent: Object describing the event

Reimplemented from Model.

update_states()

function update_states ( in  obj )

protectedvirtual

Function defining the table Gait2dc.states.

Table lists type, name, xmin, xmax and xneutral

Todo:

Variables of contact points of neutral position shouldn't be zero.

Parameters

obj	Gait2dc class object

Reimplemented from Model.

Member Data Documentation

bodyheight

Property bodyheight

protected

Double: Bodyheight in m (default: 1.80)

bodymass

Property bodymass

protected

Double: Bodymass in kg (default: 75)

constraints

Property constraints

protectedinherited

Table: Information on constraints implemented in the mex and here.

controls

Property controls

protectedinherited

Table: Information on controls of the model.

CPs

Property CPs

inherited

Table: Contact points.

dofs

Property dofs

inherited

Table: Degrees of freedom (Range of Dofs should not be changed here.

Set the bounds of the Problem instead.)

drag_coefficient

Property drag_coefficient

inherited

Double: Air drag coefficient in N/(m/s)^2 (default: 0.2128)

excelfile

Property excelfile

protected

String: Filename of parameter file including path and extension.

foot

Property foot

protected

Table: Defining size of feet for visualization.

The x and y coordinates are defined relative to the ankle joint in m. The length of the foot is equal to the length of the foot segment defined in the table Gait2dc.segments. The size of the foot does not influence the ground contact.

FOOTSOLEOFFSET

Constant Property FOOTSOLEOFFSET = 0.0702

Double: Distance between foot sole and ankle joint in m.

gravity

Property gravity

inherited

Double array: Gravity vector in m/(s^2)

GRFNAMES

Constant Property GRFNAMES = {'rightFx', 'rightFy', 'rightFz', 'rightMx', 'rightMy', 'rightMz', 'leftFx', 'leftFy', 'leftFz', 'leftMx', 'leftMy', 'leftMz' }

inherited

Cell array with string: Gives the names for the GRF vector returned by getGRF()

HEELDEFAULTOFFSET

Constant Property HEELDEFAULTOFFSET = 0.06

Double: Distance between heel and ankle joint for default body height in m.

idxcxCPleft

Property idxcxCPleft

protected

Double array: Indices for x position of left contact points.

idxcxCPright

Property idxcxCPright

protected

Double array: Indices for x position of right contact points.

idxForward

Property idxForward

protectedinherited

Double array: Indices for forward translation.

idxForwardAll

Property idxForwardAll

protectedinherited

Double array: Indices for forward translation, speed, position of contact points and force at contact points.

idxParamSections

Property idxParamSections

protected

Double array: Start indices of sections in Gait2dc.parameter.

idxSideward

Property idxSideward

protectedinherited

Double array: Indices for sideward translation.

idxSidewardAll

Property idxSidewardAll

protectedinherited

Double array: Indices for sideward translation, speed, position of contact points and force at contact points.

idxSymmetry

Property idxSymmetry

protectedinherited

Struct: Double arrays with indices for symmetry to map right to left.

idxTorqueDof

Property idxTorqueDof

protectedinherited

Double array: Indices of dofs of torque actuators.

idxUpward

Property idxUpward

protectedinherited

Double array: Indices for upward translation.

init

Property init

protectedinherited

Double: Showing if the mex model is initialized.

joints

Property joints

inherited

Table: Joints.

lambda

Property lambda

Double array: Lambda values (default: [0.01 0.1]) (1x2)

mExtraScaleFactor

Property mExtraScaleFactor

inherited

Double: Scale factor for extra torques in Nm (default: 100 since we used this in previous simulations.

However, it's probably overwritten in the construction (see Gait3d.m)!)

muscles

Property muscles

inherited

Table: Muscles.

nConstraints

Property nConstraints

protectedinherited

Double: Number of constraints (height of Model.constraints)

nControls

Property nControls

protectedinherited

Double: Number of controls (height of Model.controls)

nCPs

Property nCPs

protectedinherited

Double: Number of contact points (height of Model.CPs)

nDofs

Property nDofs

protectedinherited

Double: Number of degree of freedoms (height of Model.dofs)

nJoints

Property nJoints

protectedinherited

Double: Number of joints (height of Model.joints)

nMus

Property nMus

protectedinherited

Double: Number of muscles (height of Model.muscles)

nSegments

Property nSegments

protectedinherited

Double: Number of segments (height of Model.segments)

nStates

Property nStates

protectedinherited

Double: Number of states (height of Model.states)

nTor

Property nTor

protectedinherited

Double: Number of torque actuators (height of Model.torques)

parameter

Property parameter

protected

Double matrix: Entries of parameter excel file.

It is linked to Gait2dc.bodyheight, Gait2dc.bodymass, Gait2dc.gravity, Gait2dc.drag_coefficient, Gait2dc.wind_speed, Gait2dc.slope, Gait2dc.dofs, Gait2dc.segments, Gait2dc.joints, Gait2dc.muscles and Gait2dc.CPs.

segments

Property segments

protectedinherited

Table: Segments (Segment properties should not be changed)

slope

Property slope

Double: Slope of ground in deg (positive is uphill)

speed_left

Property speed_left

protected

Double: Speed of simulated additional Treadmill.

speed_right

Property speed_right

protected

states

Property states

protectedinherited

Table: Information on states of the model.

TOEOFFSET

Constant Property TOEOFFSET = 0.05

Double: Distance between toe and CP toe in m.

torques

Property torques

inherited

Table: Torque actuators.

wind_speed

Property wind_speed

inherited

Double: Wind speed in direction of +X in m/s (default: 0)

---

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

• BioMAC-Sim-Toolbox/src/model/gait2dc/@Gait2dc/Gait2dc.m