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#ifndef MILLARD2016TORQUEMUSCLE_H_
#define MILLARD2016TORQUEMUSCLE_H_
/*
* RBDL - Rigid Body Dynamics Library: Addon : muscle
* Copyright (c) 2016 Matthew Millard <matthew.millard@iwr.uni-heidelberg.de>
*
* Licensed under the zlib license. See LICENSE for more details.
*/
#include <vector>
#include <rbdl/rbdl_math.h>
#include "../geometry/SmoothSegmentedFunction.h"
namespace RigidBodyDynamics {
namespace Addons {
namespace Muscle{
#ifdef RBDL_BUILD_ADDON_MUSCLE_FITTING
class TorqueMuscleFittingToolkit;
class FitTorqueMuscleParameters;
#endif
/**
This struct contains an enumerated list of the data sets which
constain torque muscles. Thus far this list includes
-Anderson2007: Table 3 from Anderson et al.
-Gymnast: A set of torque muscles for the whole body (in progress)
For details of these data sets please refer to the main description
of this class.
*/
const static struct DataSet{
enum item{
Anderson2007 = 0,
Gymnast,
Last
};
const static char* names[];
DataSet(){}
} DataSet;
/**
This struct contains an enumerated list of the genders for which
data torque data has been reported.
*/
const static struct GenderSet{
enum item {
Male = 0,
Female,
Last
};
const static char* names[];
GenderSet(){}
} GenderSet;
/**
This struct contains an enumerated list of the age groups for which
data torque data has been reported.
*/
const static struct AgeGroupSet{
enum item {
Young18To25 = 0,
Middle55To65,
SeniorOver65,
Last
};
const static char* names[];
AgeGroupSet(){}
} AgeGroupSet;
/**
This struct contains an enumerated list of the joint-torque-directions
for which data torque data has been reported.
*/
const static struct JointTorqueSet{
enum item{
HipExtension = 0,
HipFlexion = 1,
KneeExtension = 2,
KneeFlexion = 3,
AnkleExtension = 4,
AnkleFlexion = 5,
ElbowExtension = 6,
ElbowFlexion = 7,
ShoulderExtension = 8,
ShoulderFlexion = 9,
WristExtension = 10,
WristFlexion = 11,
ShoulderHorizontalAdduction = 12,
ShoulderHorizontalAbduction = 13,
ShoulderInternalRotation = 14,
ShoulderExternalRotation = 15,
WristUlnarDeviation = 16,
WristRadialDeviation = 17,
WristPronation = 18,
WristSupination = 19,
LumbarExtension = 20,
LumbarFlexion = 21,
Last = 22
};
const static char* names[];
JointTorqueSet(){}
} JointTorqueSet;
/**
This struct contains 3 enumerated lists (Gender, AgeGroup,
JointTorque) that lists the genders, age groups, and
joint-torque-directions for which the Anderson2007 data set contains
data. Please refer to the class description for more details about
this data set and how to use it.
*/
const static struct Anderson2007{
enum Gender {
Male = GenderSet::Male,
Female = GenderSet::Female,
LastGender
};
enum AgeGroup {
Young18To25 = AgeGroupSet::Young18To25,
Middle55To65 = AgeGroupSet::Middle55To65,
SeniorOver65 = AgeGroupSet::SeniorOver65,
LastAgeGroup
};
enum JointTorque{
HipExtension = JointTorqueSet::HipExtension ,
HipFlexion = JointTorqueSet::HipFlexion ,
KneeExtension = JointTorqueSet::KneeExtension ,
KneeFlexion = JointTorqueSet::KneeFlexion ,
AnkleExtension = JointTorqueSet::AnkleExtension,
AnkleFlexion = JointTorqueSet::AnkleFlexion,
LastJointTorque
};
const static char* GenderNames[];
const static char* AgeGroupNames[];
const static char* JointTorqueNames[];
Anderson2007(){}
} Anderson2007;
/**
This struct contains 3 enumerated lists (Gender, AgeGroup,
JointTorque) that lists the genders, age groups, and
joint-torque-directions for which the Gymnast data set contains
data. At the present time Gymnast data set only contains data
appropriate for a young (18-25) elite male gymnast. Please refer
to the main class description for details on this data set and how
to use it.
*/
const static struct Gymnast{
enum Gender {
Male = GenderSet::Male,
LastGender
};
enum AgeGroup {
Young18To25 = AgeGroupSet::Young18To25,
LastAgeGroup
};
enum TableIndex {
TauMax = 0,
OmegaMax,
ActiveAngleAtOneNormTorque,
ActiveAngularStandardDeviation,
TvAtMaxEccentricVelocity,
TvAtHalfMaxConcentricVelocity,
PassiveAngleAtZeroTorque,
PassiveAngleAtOneNormTorque,
LastTableIndex
};
enum JointTorque {
HipExtension = JointTorqueSet::HipExtension ,
HipFlexion = JointTorqueSet::HipFlexion ,
KneeExtension = JointTorqueSet::KneeExtension ,
KneeFlexion = JointTorqueSet::KneeFlexion ,
AnkleExtension = JointTorqueSet::AnkleExtension ,
AnkleFlexion = JointTorqueSet::AnkleFlexion ,
ElbowExtension = JointTorqueSet::ElbowExtension ,
ElbowFlexion = JointTorqueSet::ElbowFlexion ,
ShoulderExtension = JointTorqueSet::ShoulderExtension ,
ShoulderFlexion = JointTorqueSet::ShoulderFlexion ,
WristExtension = JointTorqueSet::WristExtension ,
WristFlexion = JointTorqueSet::WristFlexion ,
ShoulderHorizontalAdduction =
JointTorqueSet::ShoulderHorizontalAdduction,
ShoulderHorizontalAbduction =
JointTorqueSet::ShoulderHorizontalAbduction,
ShoulderInternalRotation =
JointTorqueSet::ShoulderInternalRotation ,
ShoulderExternalRotation =
JointTorqueSet::ShoulderExternalRotation ,
WristUlnarDeviation = JointTorqueSet::WristUlnarDeviation ,
WristRadialDeviation = JointTorqueSet::WristRadialDeviation,
WristPronation = JointTorqueSet::WristPronation ,
WristSupination = JointTorqueSet::WristSupination ,
LumbarExtension = JointTorqueSet::LumbarExtension,
LumbarFlexion = JointTorqueSet::LumbarFlexion,
LastJointTorque
};
const static char* GenderNames[];
const static char* AgeGroupNames[];
const static char* JointTorqueNames[];
Gymnast(){}
} Gymnast;
/**
This is a struct that contains subject-specific information that
does not change for a given subject.
@param gender
Male/Female. Selecting a gender that
is not present in a data set will result in
the program aborting and an error message
being printed to the terminal.
@param ageGroup:
Presently the age group options include Young (18-25),
middle aged (55-65), and senior (>65). Selecting an
age group that is not present in a data set will result
in the program aborting and an error message
being printed to the terminal.
@param mSubjectHeightInMeters
This parameter is used to scale from the normalized
curves reported by Anderson et al.
See the class description for details.
@param mSubjectMassInKg
This parameter is used to scale from the normalized
curves reported by Anderson et al.
See the class description for details.
*/
struct SubjectInformation{
GenderSet::item gender;
AgeGroupSet::item ageGroup;
double heightInMeters;
double massInKg;
};
struct TorqueMuscleSummary{
/**The angle of the fiber (rad)*/
double fiberAngle;
/**The angular velocity of the fiber (rad/s)*/
double fiberAngularVelocity;
/**The activation of the muscle*/
double activation;
/** The normalized value of the passive-torque-angle curve.
Here a value of 1 means 1 maximum-isometric-torque. (Nm/Nm)*/
double fiberPassiveTorqueAngleMultiplier;
/**The normalized value of the active-torque-angle curve.
Here a value of 1 means 1 maximum-isometric-torque. (Nm/Nm)*/
double fiberActiveTorqueAngleMultiplier;
/**The normalized value of the torque-angular-velocity curve.
Here a value of 1 means 1 maximum-isometric-torque. (Nm/Nm)*/
double fiberTorqueAngularVelocityMultiplier;
/**The torque generated by the damping element (Nm/Nm)*/
double fiberNormalizedDampingTorque;
/**The torque generated by the entire fiber (Nm)*/
double fiberTorque;
/**The joint torque developed by the muscle. This is signed so
that it is consistent with the sign convention of the joint
chosen by the user. (Nm)*/
double jointTorque;
TorqueMuscleSummary():
fiberAngle(nan("1")),
fiberAngularVelocity(nan("1")),
activation(nan("1")),
fiberPassiveTorqueAngleMultiplier(nan("1")),
fiberActiveTorqueAngleMultiplier(nan("1")),
fiberTorqueAngularVelocityMultiplier(nan("1")),
fiberNormalizedDampingTorque(nan("1")),
fiberTorque(nan("1")),
jointTorque(nan("1")){}
};
struct TorqueMuscleInfo{
/**The angle of the joint (radians)*/
double jointAngle;
/**The angular velocity of the joint, where the sign convention
is chosen by the user at the time the torque muscle is created
(radians/sec)*/
double jointAngularVelocity;
/**The angle that the muscle fiber spans (radians)*/
double fiberAngle;
//The angle that the tendon spans (radians)
//double tendonAngle;
/**The rate-of-angular-lengthening of the fiber.
A positive sign is for a concentric contraction,
that is where the fibers are shortening. (radians/sec)*/
double fiberAngularVelocity;
/*The rate-of-angular-lengthening of the tendon.
A positive sign is for a concentric contraction,
that is where the tendon is shortening. (radians/sec)*/
//double tendonAngularVelocity;
/** The normalized value of the passive-torque-angle curve.
Here a value of 1 means 1 maximum-isometric-torque. (Nm/Nm)*/
double fiberPassiveTorqueAngleMultiplier;
double DfiberPassiveTorqueAngleMultiplier_DblendingVariable;
double DfiberPassiveTorqueAngleMultiplier_DangleOffset;
/**The normalized value of the active-torque-angle curve.
Here a value of 1 means 1 maximum-isometric-torque. (Nm/Nm)*/
double fiberActiveTorqueAngleMultiplier;
double DfiberActiveTorqueAngleMultiplier_DblendingVariable;
/**The normalized value of the torque-angular-velocity curve.
Here a value of 1 means 1 maximum-isometric-torque. (Nm/Nm)*/
double fiberTorqueAngularVelocityMultiplier;
double DfiberTorqueAngularVelocityMultiplier_DblendingVariable;
/*The normalized value of the tendon-torque-angle curve.
Here a value of 1 means 1 maximum-isometric-torque. (Nm/Nm)*/
//double tendonTorqueAngleMultiplier;
/**The activation of the muscle*/
double activation;
/**The torque generated by the active element of the muscle
fiber (Nm)*/
double fiberActiveTorque;
/**The total torque generated by the passive elements of the muscle
fiber (Nm)*/
double fiberPassiveTorque;
/**The torque generated by the passive elastic element of the
muscle fiber (Nm)
*/
double fiberPassiveElasticTorque;
/**The torque generated by the damping element (Nm)*/
double fiberDampingTorque;
/**The torque generated by the damping element (Nm)*/
double fiberNormDampingTorque;
/**The torque generated by the entire fiber (Nm)*/
double fiberTorque;
/*The torque transmitted through the tendon across the joint (Nm)*/
//double tendonTorque;
/**The joint torque developed by the muscle. This is signed so
that it is consistent with the sign convention of the joint
chosen by the user. (Nm)*/
double jointTorque;
/**The stiffness of the fiber (Nm/rad)*/
double fiberStiffness;
/*The stiffness of the tendon (Nm/rad)*/
//double tendonStiffness;
/** The stiffness of the joint. This is signed so
that it is consistent with the sign convention of the joint
chosen by the user. (Nm/rad)*/
double jointStiffness;
/**The power output of the active fiber element. A positive
power means that the fiber is contracting concentrically.
(Watts - Nm/s)*/
double fiberActivePower;
/**The power output of the passive fiber element. A positive
power means that the passive element is recoiling concentrically
(Watts - Nm/s)*/
double fiberPassivePower;
/**The total power output of the fiber element.(Watts - Nm/s)*/
double fiberPower;
/** The power output by this muscle at the joint. This is
signed so that it is consistent with the sign convention of the
joint chosen by the user. (Nm/rad)*/
double jointPower;
/**The partial derivative of joint torque w.r.t activation*/
double DjointTorque_Dactivation;
/**The partial derivative of joint torque w.r.t the joint angle*/
double DjointTorque_DjointAngle;
/**The partial derivative of joint torque w.r.t the joint
angular velocity*/
double DjointTorque_DjointAngularVelocity;
///First derivatives for the fitting algorithm
double DjointTorque_DactiveTorqueAngleBlendingVariable;
double DjointTorque_DpassiveTorqueAngleBlendingVariable;
double DjointTorque_DtorqueAngularVelocityBlendingVariable;
double DjointTorque_DmaximumIsometricTorque;
double DjointTorque_DpassiveTorqueAngleCurveAngleOffset;
double DjointTorque_DactiveTorqueAngleAngleScaling;
double DjointTorque_DmaximumAngularVelocity;
///This vector contains additional quantities that are needed by
/// the fitting functions, and is not for external use. Use this
/// vector at your own risk, as its definition/sizing etc may
/// change.
RigidBodyDynamics::Math::VectorNd fittingInfo;
TorqueMuscleInfo():
jointAngle(nan("1")),
jointAngularVelocity(nan("1")),
fiberAngle(nan("1")),
fiberAngularVelocity(nan("1")),
fiberPassiveTorqueAngleMultiplier(nan("1")),
DfiberPassiveTorqueAngleMultiplier_DblendingVariable(nan("1")),
DfiberPassiveTorqueAngleMultiplier_DangleOffset(nan("1")),
fiberActiveTorqueAngleMultiplier(nan("1")),
DfiberActiveTorqueAngleMultiplier_DblendingVariable(nan("1")),
fiberTorqueAngularVelocityMultiplier(nan("1")),
DfiberTorqueAngularVelocityMultiplier_DblendingVariable(nan("1")),
activation(nan("1")),
fiberActiveTorque(nan("1")),
fiberPassiveTorque(nan("1")),
fiberPassiveElasticTorque(nan("1")),
fiberDampingTorque(nan("1")),
fiberNormDampingTorque(nan("1")),
fiberTorque(nan("1")),
jointTorque(nan("1")),
fiberStiffness(nan("1")),
jointStiffness(nan("1")),
fiberActivePower(nan("1")),
fiberPassivePower(nan("1")),
fiberPower(nan("1")),
jointPower(nan("1")),
DjointTorque_Dactivation(nan("1")),
DjointTorque_DjointAngle(nan("1")),
DjointTorque_DjointAngularVelocity(nan("1")),
DjointTorque_DactiveTorqueAngleBlendingVariable(nan("1")),
DjointTorque_DpassiveTorqueAngleBlendingVariable(nan("1")),
DjointTorque_DtorqueAngularVelocityBlendingVariable(nan("1")),
DjointTorque_DmaximumIsometricTorque(nan("1")),
DjointTorque_DpassiveTorqueAngleCurveAngleOffset(nan("1")),
DjointTorque_DactiveTorqueAngleAngleScaling(nan("1")),
DjointTorque_DmaximumAngularVelocity(nan("1"))
{}
};
struct TorqueMuscleParameterFittingData {
unsigned int indexAtMaximumActivation;
unsigned int indexAtMinimumActivation;
unsigned int indexAtMaxPassiveTorqueAngleMultiplier;
bool isTorqueMuscleActive;
double activeTorqueAngleBlendingVariable;
double passiveTorqueAngleBlendingVariable;
double torqueVelocityBlendingVariable;
double passiveTorqueAngleCurveOffset;
double maximumActiveIsometricTorque;
double activeTorqueAngleAngleScaling;
double maximumAngularVelocity;
//double objectiveValue;
//double constraintError;
bool fittingConverged;
TorqueMuscleSummary summaryDataAtMinimumActivation;
TorqueMuscleSummary summaryDataAtMaximumActivation;
TorqueMuscleSummary summaryDataAtMaximumPassiveTorqueAngleMultiplier;
TorqueMuscleParameterFittingData():
indexAtMaximumActivation(std::numeric_limits<unsigned int>::infinity()),
indexAtMinimumActivation(std::numeric_limits<unsigned int>::infinity()),
indexAtMaxPassiveTorqueAngleMultiplier(std::numeric_limits<unsigned int>::infinity()),
isTorqueMuscleActive(true),
activeTorqueAngleBlendingVariable(nan("1")),
passiveTorqueAngleBlendingVariable(nan("1")),
torqueVelocityBlendingVariable(nan("1")),
passiveTorqueAngleCurveOffset(nan("1")),
maximumActiveIsometricTorque(nan("1")),
activeTorqueAngleAngleScaling(nan("1")),
maximumAngularVelocity(nan("1")),
fittingConverged(false),
summaryDataAtMinimumActivation(),
summaryDataAtMaximumActivation(),
summaryDataAtMaximumPassiveTorqueAngleMultiplier(){}
};
struct TorqueMuscleDataFeatures{
unsigned int indexOfMaxActivation;
unsigned int indexOfMinActivation;
unsigned int indexOfMaxPassiveTorqueAngleMultiplier;
bool isInactive;
TorqueMuscleSummary summaryAtMaxActivation;
TorqueMuscleSummary summaryAtMinActivation;
TorqueMuscleSummary summaryAtMaxPassiveTorqueAngleMultiplier;
};
/**
\brief This class implements a rigid-tendon muscle-torque-generator
(MTG) for a growing list of joints and torque-directions. For a
detailed description of the MTGs available and the automatic
fitting routine (implemented in TorqueMuscleFittingToolkit) please
see the publication: M.Millard, A.L.Kleesattel, M.Harant, &
K.Mombaur. A reduced muscle model and planar musculoskeletal model
fit for the synthesis of whole body movements. Journal of
Biomechanics. (under review as of August 2018)
This rigid-tendon torque muscle model provides modeling support
for 3 phenomena
- torque-angle curve (\f$\mathbf{t}_A(\theta)\f$): the variation of active isometric torque in one direction as a function of joint angle
- torque-velocity curve (\f$\mathbf{t}_V(\dot{\theta})\f$): the variation of torque as a function of angular velocity
- passive-torque-angle curve (\f$\mathbf{t}_P(\theta-\theta_S)\f$): the variation of passive torque as a function of joint angle. Here \f$s_P\f$ and \f$\theta_S\f$ are user-defined scaling and shift parameters.
each of which are represented as smooth normalized curves that
vary between 0 and 1. A series of scaling
(\f$s^A, s^V, s^\tau\f$), shifting (\f$\Delta^P\f$), and blending
(\f$\lambda^A,\lambda^V,\lambda^P\f$) variables have been introduced
to these curves to make it possible to easily fit these curves to
a specific subject. These fitting variables can be set/fitted by
making use of the functions in this class. Alternatively these
fitting variables can be automatically adjusted (using IPOPT) by
making use of the TorqueMuscleFittingToolkit.
\image html fig_MuscleAddon_BlendableTorqueMuscle.png "Examples of the adjustable characteristic curves"
These three curves are used to compute the
torque developed \f$\tau\f$ given the angle of the joint
\f$\theta\f$, the angular-velocity of the joint \f$\dot{\theta}\f$,
and the activation of the muscle \f$\mathbf{a}\f$ (a 0-1 quantity
that defines how much the muscle is turned-on, or activated), and
the maximum-isometric torque \f$\tau_{ISO}\f$
\f[
\tau (\mathbf{a}, \theta,\dot{\theta}) =
\tau_{ISO} ( \mathbf{a} \, \mathbf{t}_A(\theta) \mathbf{t}_V(\dot{\theta}/\dot{\theta}_{MAX})
+\mathbf{t}_P(1- \beta (\dot{\theta}/\dot{\theta}_{MAX})) \, )
\f]
The damping term \f$\beta\f$ is necessary to supress vibration
that will occur as the passive element \f$\mathbf{t}_P\f$ is streched,
its stiffness increases, and the natural frequency of the overall
system rises. By default \f$\beta\f$ is set to 0.1 which has proven
effective for supressing vibration in the trunk segments during a
stoop lift in which the stiffness of the lumbar back muscles grows
appreciably. This model does not yet provide support for the
following phenomena but will in the future.
- activation dynamics: currently is left to the user
- tendon-elasticity
- muscle short-range-stiffness
All of these characteristic curves are represented using \f$C_2\f$
continuous \f$5^{th}\f$ order Bezier curves that have been fitted to
the data from data in the literature. In many cases these
curves have been carefully edited so that they fit the curves of
the original papers, but have more desireable numerical properties
for optimal control work. The characterisic curves provided by this
class have been fitted to a growing list of data sets:
-Anderson Data Set: from Anderson et al. 2007
-Whole-body Gymnast Data Set: from Jackson, Kentel et al., Anderson et al., Dolan et al. and Raschke et al.
<b>Data Set: Anderson2007</b>
This data set uses the mean value of the coefficients published
in Anderson et al. The standard deviation table has also been
entered. However, since it is unclear how to use the standard
deviation in a consistent way across all joints/parameters this
table is not yet accessible through the constructor. This data
set includes coefficients for the following
- Number of subjects: 34
- Gender: male and female
- Age: young (18-25, 14 subjects), middle-aged (55-65, 14 subjects), senior (> 65, 6 subjects)
- Joint: hip/knee/ankle
- Direction: extension/flexion
<b>Notes</b>
-# Angles are plotted using units of degrees for readability. The
actual curves are described in units of radians
-# See Anderson et al. for further details.
\image html fig_MuscleAddon_Anderson2007AllPositiveSigns.png "Characteristic from Anderson et al. 2007 [1]"
<b>Data Set: Gymnast</b>
This data set is an attempt at making enough torque muscles for a
whole body. Since no single source in the literature comes close to
measuring the characteristics of all of the joints, data from
Jackson et al., Kentel et al., Anderson et al., Dolan et al, and
Raschke et al.
have been combined. Since the subjects used in these various studies
are wildly different (Jackson et al. measured an elite male gymnast;
Kentel et al. measured an elite tennis player; Anderson et al. measured,
in the category of young male, a selection of active undergraduate
students, Dolan et al from 126 women and 23 men, and Raschke from 5
male subjects) scaling has been used to make the strength of the subject
consistent. Scaling coefficients for the lower body, shoulders and
elbow, and forearm/wrist have been calculated using measurements
that overlapped between datasets. Presently this data set includes
curves for 22 torque muscles.
- Number of subjects: 1 elite gymnast (69.6 kg, 1.732 m)
- Gender: male
- Age: 21 years old
- Joint and Directions available
-# Ankle: flexion/extension (scaled from Anderson)
-# Knee: flexion/extension (from Jackson)
-# Hip: flexion/extension (from Jackson)
-# Lumbar: active extension curves (\f$\mathbf{t}_A\f$ and \f$\mathbf{t}_P\f$) from Raschke et al. passive extension from Dolan et al. The torque velocity curve has since been updated using an estimate from the archiecture of the lumbar extensors
-# Lumbar: active flexion \f$\tau_{ISO}\f$ from Beimborn et al.
-# Shoulder: flexion/extension (from Jackson)
-# Shoulder: horizontal adduction/abduction (from Kentel, scaled to Jackson's subject)
-# Shoulder: internal rotation/external rotation (from Kentel, scaled to Jackson's subject)
-# Elbow: flexion/extension (from Kentel, scaled to Jackson's subject)
-# Wrist: pronation/supination (from Kentel, scaled to Jackson's subject)
-# Wrist: extension/flextion (from Jackson)
-# Wrist: ulnar/radial deviation (from Kentel, scaled to Jackson's subject)
- Missing Joint and directions
-# Ankle inversion/eversion
-# Hip adduction/abduction
-# Hip internal rotation/external rotation
-# Lumbar extension/flexion
-# Lumbar bending
-# Lumbar twisting
-# Shoulder Adduction
-# Shoulder Abduction
-# Scapular elevation/depression
-# Scapular adduction/abduction
-# Scapular upward/downward rotation
In all cases the curves have been fitted to Bezier curves that
are constructed using functions in TorqueMuscleFunctionFactory.
<b>Notes</b>
-# Angles are plotted using units of degrees for readability. The actual curves are described in units of radians
-# Hip and Knee characteristics taken from Jackson. Ankle extension is from Anderson et al., scaled using Jackson-to-Anderson hip/knee strength ratios from Jackson ratios
-# Shoulder horizontal adduction/abduction and internal/external rotation is a scaled version of the Kentel. Strength was scaled using the Jackson-to-Kentel shoulder flex/ext ratios.
-# Elbow extension/flexion and forearm pronation/supination. Elbow strength scaled from Kentel using the ratio of maximum isometric shoulder ext/flextion between Kentel and Jackson. Forearm pronation/supination scaled using the maximum torque strength ratio of wrist extension/flextion between Kentel and Jackson
-# Wrist ext/flexion directly from Jackson, while the curves for ulnar and radial deviation have been scaled (using the maximum isometric torque ratios of wrist extension and flexion from both models) from Kentel et al.
-# Lumbar-extension active-torque-angle-curve in extension comes from Raschke et al.
-# Lumbar-extension passive-torque-angle-curve comes from Dolan et al.
-# Lumbar-flexion \f$\tau_{ISO}\f$ comes from Beimborn et al.'s observation that the strength ratio of back extensors to flextors at a flextion angle of zero is most often repored as 1.3:1.
-# Lumbar-extension and flexion torque-velocity-curves have been estumated using the architecture of these two muscles. This update has been made because the force-velocity curve proposed by Raschke and Chaffin in Fig. 4 has such a low maximum angular velocity (60 dec/sec) that none of our optimal control simulations predicted lumbar flexion during movement. Using muscle archectural information for the erector spinae (ES) and rectus abdominus (RA), assuming both are made of slow twitch fibers the maximum angular velocites are 433 deg/sec and 1102 deg/sec about the constant assumed moment arms for the lumbar extensors and flexors respectively. The following architectural information was used:
-# 7.1 cm :ES moment arm from Németh & Ohlsén
-# 8.08 cm :ES optimal fiber length taken from a weighted PSCA average of the ES muscles from Christophy et al. Table 1
-# 7.02 \f$\ell/s\f$ :ES maximum angular velocity for slow twitch muscle from Ranatunga
-# 0.151 :ES tv at half max. angular velocity
-# 10.9 cm :RA moment arm from Németh & Ohlsén
-# 29.9 cm :RA optimal fiber length from Christophy et al. Table 1
-# 7.02 \f$\ell/s\f$ :RA maximum angular velocity for slow twitch muscle from Ranatunga
-# 0.151 :RA tv at half max. angular velocity for slow twitch muscle from Ranatunga
-# Any passive curve that is not accompanied by a curve from the literature (see the plots for details) is an educated guess.
\image html fig_MuscleAddon_Gymnast_HipKneeAnkle.png " Hip/Knee/Ankle: from Jackson and Anderson et al. "
\image html fig_MuscleAddon_Gymnast_Lumbar.png " Lumbar Extension/Flexion: from Dolan et al.,Raschke et al., and Beimborn et al."
\image html fig_MuscleAddon_Gymnast_Shoulder3Dof.png " Shoulder 3 DoF torques: from Jackson and Kentel et al. "
\image html fig_MuscleAddon_Gymnast_ElbowForearm.png " Elbow flexion/extension: from Kentel et al."
\image html fig_MuscleAddon_Gymnast_Wrist3Dof.png " Wrist 3 DoF torques: from Jackson and Kentel et al."
<b>Parameterized Curves used here vs. Literature</b>
The curves used in this implementation are 2nd order 2-dimensional
Bezier curves. The curves described in Anderson et al., Jackson,
Kentel were not directly used because they are not continuous to the
second derivative (a requirement for most gradient based optimization
routines). There are some other detailed differences that might be
of interest:
-# Anderson et al.'s torque-velocity curve tends to large
negative values for fast eccentric contractions. This is
in contrast to the literature which says that at large
eccentric contractions the torque-velocity curve (or the
force-velocity-curve) tends to a value between 1.0 and 1.4.
-# Anderson et al.'s torque-velcity curve for ankle extension
did not cross the x-axis on the concentric side of the curve.
This would endow the plantar flexors with super-human abilities.
This error has been corrected by fitting a Bezier curve to a
Hill-type curve that passes through the point where
\f$\dot{\theta}= \frac{1}{2} \dot{\theta}_{MAX}\f$
-# Anderson et al.'s, Jackson, and Kentel et al. had discontinuities
in the first derivative of the force velocity curve at
\f$\dot{\theta}=0\f$. While this follows Huxley's famous observations
that the slope does discontinuously change at at \f$\dot{\theta}=0\f$,
this is not a phenomena that is not compatible with most optimal
control formulations and thus this discontinuity is not present in
the force velocity curves used in this model.
-# Anderson et al. and Kentel et al.'s active-torque-angle curves
can achieve negative values - this is obviously undesirable as it
will allow a muscle to push.
-# Kentel et al.'s activation inhibition function does not always
cross 1.0 for \f$\dot{\theta}=0\f$, which means that \f$\tau_{ISO}\f$
is not reached. This makes for a confusing model to use.
<b>Coordinate Mapping</b>
Every author chose a particular convention for measuring
the angles of the hip, knee, ankle joint, shoulder, elbow, wrist and
lumbar --- see the figure for details. These conventions have all
been mapped to the one used in the illustrations. You will need to
use the figure, your model, and the constructors appropriately
so that
-# the joint angle of your model is correctly mapped to the
fiber angle of the Millard2016TorqueMuscle;
-# the sign of the muscle's output torque matches the
sign associated with your model.
To map from your model's joint coordinates to the joint coordines
used in this model (see the figure in the description)
the followinq equation is used at the torque level
\f$ jointTorque = signOfJointTorque*fiberTorque \f$
where fiberTorque is the torque produced by Anderson et al.'s curves,
which is always positive. At the position level, the angles from your
models joint angle to Anderson et al.'s joint angle (called fiberAngle)
are mapped using
\f$ fiberAngle = signOfJointAngleRelativeToAnderson2007*(jointAngle-jointAngleOffsetRelativeToAnderson2007). \f$
Internally the sign of the fiber velocity follows signOfJointTorque so
that the signs of joint power and muscle power are consistent.
<b>Strength Scaling: Anderson2007 Data Set</b>
The leg strength (here we mean \f$\tau_{ISO}\f$)
predicted by Anderson et al.'s curves should be taken
as a good first approximation. While Anderson et al.'s data set is
the most comprehensive in the literature, they only measured torques
from active people: they did not include people at the extremes
(both very weak, and very strong), nor did they include children.
Finally, the torques produced by each subject were normalized by
mSubjectMassInKg*subjectHeightInM*accelerationDueToGravity. Strength
is a strange phenomena which is not nicely normalized by just these
quantites, and so the strength predicted by Anderson et al.'s curves
might not fit your subject even if they are represented in Anderson
et al.'s data set.
<b>Strength Scaling: Gymnast Data Set</b>
The strength used in the Gymnast data set is fitted to an elite
male gymnast. It goes without saying that an elite gymnast has
strength proportions, and an absolute strength that are not typical.
In the future it would be nice to have a function that could provide
an educated guess about how to map Gymnast's strengths to that of
another subject. For the moment I have no idea how to do this, nor
am I aware of any works in the literature that can provide insight
of how to do this. For now the whole-body Gymnast model should be
viewed as being a representation of what is possible for a human,
but not a typical human. At the present time the default strength
settings of the Gymnast are not scaled by subject height, nor
weight.
If you happen to know the maximum-isometric-active-torque (note this
does not include the passive component) that your subject can
produce, you can update the strength of the torque-muscle using the
functions getMaximumActiveIsometricTorque(), and
setMaximumActiveIsometricTorque().
<b>Fitting to a Specific Subject</b>
If you have recorded the motions and external forces acting on a
subject during a movement of interest, you can make use of the
TorqueMuscleFittingToolkit to adjust the MTG so that it is strong
enough and flexible enough to allow a model of the subject to
reproduce the experimental data. Please see the
TorqueMuscleFittingToolkit class for details.
<b>Limitations</b>
This rigid-tendon torque muscle has some limitations that you should
be aware of:
-# There are no elastic tendons. That means that the mapping between
the mechanical work done by this torque actuator will greatly differ
from the positive mechanical work done by a torque actuator that
includes an elastic tendon. This difference is greatest for those
muscles with long tendons - namely the Achilles tendon in humans.
If you are
interested in fiber kinematics, fiber work, or metabolic energy
consumption you cannot use this model especially for muscles that
have long tendons.
-# This model formulation predicts torque well, but does a poor job
of predicting joint stiffness. In this model stiffness is given
by the partial derivative of torque w.r.t. joint angle. Since the
active-torque-angle curve fits a bell-shaped curve, it is possible
to construct a torque muscle that has a region of physically
impossible negative stiffness. Real muscle, in constrast, always
has a positive stiffness even on the descending limb of the
active-torque-angle curve (see Rassier et al. for details).
-# Muscles that cross 2 joints (e.g. the hamstrings) produce coupled
torques at both of those joints. In this model there is no coupling
between joints. Furthermore, because of the lack of coupling the
curves used here are only valid for the posture that Anderson et al.,
Jackson, and Kentel et al.
used when they made their data collection. If you are interested
in simulating postures that are very different from those described
in by these authors then the results produced by this model should
be treated as very rough.
-# Because this is a joint-torque muscle, none of the joint contact
forces predicted will come close to matching what is produced by
line-type muscles. If you are interested in joint-contact forces you
cannot use this model.
This simple model is a fast approximate means to constrain the joint
torque developed in the body to something that is physiologically
possible. That is it.
<b>Units</b>
Although the figure in this description has angles in units
of degrees, this is only to help intuitition: when using
the model, use radians. This model uses MKS:
-Distance: m
-Angles: radians
-Angular velocity: radians/s
-Mass: kg
-Torque: Nm
-Time: second
-Power: Nm/second
<b> Developer Notes </b>
All of the numerical evaluations of this model take place
in a few private stateless functions:
-updateTorqueMuscleSummary
-updTorqueMuscleSummaryCurveValues
-updTorqueMuscleInfo
-updInvertTorqueMuscleSummary
If you want to change something fundamental about the
mathematics of the model, then you have to update these functions.
<b>References</b>
-# Anderson, D. E., Madigan, M. L., & Nussbaum, M. A. (2007).
Maximum voluntary joint torque as a function of joint angle
and angular velocity: model development and application to
the lower limb. Journal of biomechanics, 40(14), 3105-3113.
-# Beimborn, D. S., & Morrissey, M. C. (1988). A review of the
literature related to trunk muscle performance. Spine, 13(6), 655-660.
-# Christophy, M., Senan, N. A. F., Lotz, J. C., & O’Reilly, O. M.
(2012). A musculoskeletal model for the lumbar spine.
Biomechanics and Modeling in Mechanobiology, 11(1-2), 19-34.
-# Dolan, P., A. F. Mannion, and M. A. Adams. Passive tissues help
the back muscles to generate extensor moments during lifting.
Journal of Biomechanics 27, no. 8 (1994): 1077-1085.
-# Jackson, M.I. (2010). The mechanics of the Table Contact
Phase of Gymnastics Vaulting. Doctoral Thesis, Loughborough
University.
-# Kentel, B.B., King, M.A., & Mitchell, S.R. (2011).
Evaluation of a subject-specific torque-driven computer simulation
model of one-handed tennis backhand ground strokes. Journal of
Applied Biomechanics, 27(4),345-354.
-# Millard, M., Uchida, T., Seth, A., & Delp, S. L. (2013).
Flexing computational muscle: modeling and simulation of
musculotendon dynamics. Journal of biomechanical engineering,
135(2), 021005.
-# Németh, G., & Ohlsén, H. (1986). Moment arm lengths of trunk
muscles to the lumbosacral joint obtained in vivo with computed
tomography. Spine, 11(2), 158-160.
-# Ranatunga, K. W. (1984). The force-velocity relation of rat
fast-and slow-twitch muscles examined at different temperatures.
The Journal of Physiology, 351, 517.
-# Raschke, U., & Chaffin, D. B. (1996). Support for a linear
length-tension relation of the torso extensor muscles: an
investigation of the length and velocity EMG-force relationships.
Journal of biomechanics, 29(12), 1597-1604.
-# Rassier, D. E., Herzog, W., Wakeling, J., & Syme, D. A. (2003).
Stretch-induced, steady-state force enhancement in single
skeletal muscle fibers exceeds the isometric force at optimum
fiber length. Journal of biomechanics, 36(9), 1309-1316.
*/
class Millard2016TorqueMuscle {
#ifdef RBDL_BUILD_ADDON_MUSCLE_FITTING
friend class TorqueMuscleFittingToolkit;
friend class FitTorqueMuscleParameters;
#endif
public:
/**
Default constructor, which for the moment does nothing.
Calling any of the models functions after the default
construction will result in a runtime error.
*/
Millard2016TorqueMuscle();
/**
This constructor allows you to easily access the large
table of built-in torque muscle coefficients to create
a torque muscle that best represents the joint of interest.
<b> Note: directions </b>
This constructs a single joint-torque muscle:
it can only generate torque in one direction. If you want
to generate a torque in two directions, you need 2 torque
muscles.
<b> Note: signs and offsets </b>
All of the angles in these models are defined anatomically.
You will need to set a series of variables to correctly
map from your model's joint coordinates and sign conventions
to that of the models:
jointAngleOffsetRelativeToDoxygenFigures,
signOfJointAngleRelativeToDoxygenFigures,
signOfJointTorqueToDoxygenFigures. Also note that due to
the anatomical angle definitions some left and right handed
joints will require different signs. This will be true
for internal/external rotation at the shoulder,
horizontal adduction/abduction at the shoulder, ulnar/radial
deviation at the wrist, pronation/supination of the wrist,
and others as the list of directions grows.
<b> Note: blending variables </b>
When this constructor is called the blending variables for the
active-torque-angle-curve, torque-angular-velocity-curve, and
passive-torque-angle-curve are set to 0.
@param dataSet
The desired source of joint torque
coefficients. Use the DataSet structure to choose
the desired data set (e.g. DataSet::Anderson2007,
or DataSet::Gymnast)
@param subjectInfo
A struct that contains metadata about the subject
which is used to scale the maximum torque of the
torque muscle.
@param jointTorque
Select the joint and torque direction of interest.
Use the struct for each data set to choose a
joint-torque-direction that is in the set (e.g.
Anderson2007::HipExtension, or
Gymnast::ShoulderHorizontalAdduction)
@param jointAngleOffsetRelativeToDoxygenFigures
Offset angle between your model's joints and the
reference figures in class description.
@param signOfJointAngleRelativeToDoxygenFigures
The sign convention that converts your model's joint
angles to the angles used in the reference figures.
@param signOfJointTorqueToDoxygenFigures
The sign that maps fiberTorque from Anderson's model
(which is always positive) to the correctly signed
joint torque for your model.
@param name
The name of the muscle. This is needed to do useful
things like provide error messages that are human
readable.
@throws abort() when
-# The combination of dataSet, gender, joint, and jointDirection does not correspond to a valid entry
-# mSubjectHeightInMeters <= 0
-# mSubjectMassInKg <= 0
-# abs(signOfJointTorque)-1 > epsilon
*/
Millard2016TorqueMuscle(
DataSet::item dataSet,
const SubjectInformation &subjectInfo,
int jointTorque,
double jointAngleOffsetRelativeToDoxygenFigures,
double signOfJointAngleRelativeToDoxygenFigures,
double signOfJointTorqueToDoxygenFigures,
const std::string& name
);
/**
Calculates the signed joint torque developed by the
muscle. Note that the signs that are needed to map from the
native curves to those of your specific model are set when the
muscle is constructed.
\f[
\tau_{M} = \pm \tau_{ISO}( \mathbf{a} \, \mathbf{t}_A(\theta) \mathbf{t}_V(\dot{\theta}/\dot{\theta}_{MAX})
+\mathbf{t}_P(1- \beta (\dot{\theta}/\dot{\theta}_{MAX})) \, )
\f]
@param jointAngle (radians)
@param jointAngularVelocity (radians/sec)
@param activation: the percentage of the muscle that is
turned on [0-1]. This function allows activations to be
outside [0,1], because this is useful during the
intermediate solutions of an optimization run. However,
you must ensure after the fact that your activations
fall within a bound of [0,1].
@returns torque developed by the muscle in (Nm).
*/
double calcJointTorque(
double jointAngle,
double jointAngularVelocity,
double activation) const;
/**
This function will calculate the muscle activation needed to
generate the joint torque. This function is useful in the
process of fitting the strength of a model to inverse-dynamics
data. The value for activation is arrived at by evaluating this
equation
\f[
\mathbf{a} = \dfrac{ \dfrac{\tau (\mathbf{a}, \theta,\dot{\theta})}{ \tau_{ISO}}
- \mathbf{t}_P(1- \beta (\dot{\theta}/\dot{\theta}_{MAX}))}{
\mathbf{t}_A(\theta) \mathbf{t}_V(\dot{\theta}/\dot{\theta}_{MAX})}.
\f]
If the passive forces at the desired angle actually exceed the
desired torque, a negative value for activation will be returned.
If you see this it just means the passive-torque-angle curve of
this muscle needs to be adjusted.
<b>Note </b>
An activation value of 0 is passed out if the sign of the
desired jointTorque differs from the sign of the joint torque
that this muscle can produce.
@param jointAngle (radians)
@param jointAngularVelocity (radians/sec)
@param jointTorque (Nm).
@param updTorqueMuscleSummaryStruct
TorqueMuscleSummary struct which contains the
calculated activation along with all of the
internal parameters of the muscle so that you can
understand why the activation value takes the
value that it does. See the TorqueMuscleSummary
(in this file) for details.
*/
void calcActivation(double jointAngle,
double jointAngularVelocity,
double jointTorque,
TorqueMuscleSummary
&updTorqueMuscleSummaryStruct) const;
/**
This function will compute the scaling factor \f$A\f$ that would
be needed in order for this muscle to generate a specific
joint torque \f$\tau^*\f$ at a specific activation level.
\f[
A = \dfrac{\tau^*}{
\tau_{ISO}( \mathbf{a} \, \mathbf{t}_A(\theta) \mathbf{t}_V(\dot{\theta}/\dot{\theta}_{MAX})
+\mathbf{t}_P(1- \beta (\dot{\theta}/\dot{\theta}_{MAX})) \, )}
\f]
This function
is useful in the process of determining how to much to
scale the strength of a default model to match
inverse-dynamics data of a subject. In contrast to calcActivation,
if the passive forces of the muscle exceed the desired joint
torque the resulting scale factor will drop.
@param jointAngle (radians)
@param jointAngularVelocity (radians/sec)
@param jointTorque (Nm)
@param activation
@returns scaleFactor: The scale that would make the current
muscle produce exactly the desired torque at the
specfied angle and angular velocity. Note: a value
of 0 is passed out if the sign of the desired
jointTorque differs from the sign of the
joint torque that this muscle can produce.
*/
double calcMaximumActiveIsometricTorqueScalingFactor(
double jointAngle,
double jointAngularVelocity,
double activation,
double jointTorque) const;
/**
Calculates a large number of internal quantities of the
torque muscle ranging from the values of the muscle's
components, the stiffness of the muscle, and its power output.
See the struct TorqueMuscleInfo (in this file) for details.
@param jointAngle (radians)
@param jointAngularVelocity (radians/sec)
@param activation: the percentage of the muscle that is
turned on [0-1]. This function allows activations to be
outside [0,1], because this is useful during the
intermediate solutions of an optimization run. However,
you must ensure after the fact that your activations
fall within a bound of [0,1].
@param updTorqueMuscleInfoStruct: A torque muscle struct
*/
void calcTorqueMuscleInfo(
double jointAngle,
double jointAngularVelocity,
double activation,
TorqueMuscleInfo& updTorqueMuscleInfoStruct) const;
/**
@return the sign of the joint torque (+/- 1)
*/
double getJointTorqueSign() const;
/**
@return the sign of the angle sign relative to the
figures in the class description (+/- 1)
*/
double getJointAngleSign() const;
/**
@return the offset angle between the model's joint
and the figures in the class description (rad)
*/
double getJointAngleOffset() const;
/**
@return the maximum-active-isometric torque that this muscle
can produce in Nm.
*/
double getMaximumActiveIsometricTorque() const;
/**
@return the joint angle at which the normalized
active-torque-angle curve peaks at its
maximum value of 1.0. Angle is in radians
*/
double getJointAngleAtMaximumActiveIsometricTorque() const;
/**
@return the width of the active torque angle curve.
Note that this will return the angular width of
the non-blended curve.
Angle is in radians.
*/
double getActiveTorqueAngleCurveWidth() const;
/**
@return the joint angle at which the normalized
passive-torque-angle curve reaches a value
of 1.0. If this curve never reaches a value
of 1.0 (because it is flat, or the
mPassiveTorqueScale has been set to 0) a value
of std::numeric_limits<double>::signaling_NaN()
is returned. Use the std function isfinite to
test if a signaling_NaN has been returned.
Angle is in radians
*/
double getJointAngleAtOneNormalizedPassiveIsometricTorque() const;
/**
@return the joint angle at which the normalized
passive-torque-angle curve reaches its
minimum value
Angle is in radians
*/
double getJointAngleAtSmallestNormalizedPassiveIsometricTorque() const;
/**
@return the maximum concentric angular velocity
in radians/sec. This scalar positive quantity
corresponds to the angular speed at which
the torque-velocity curve crosses zero.
*/
double getMaximumConcentricJointAngularVelocity() const;
/**
@return the passive-torque-scale \f$s_P\f$ that is applied
to the passive-torque-curve.
*/
double getPassiveTorqueScale() const;
/**
@return the angle \f$\theta_S\f$ that the passive curve has
been shifted. Note that the sign convention is in the sense
of the fiber angle, not in the sense of the joint angle.
(radians).
*/
double getPassiveCurveAngleOffset() const;
/**
@return The maximum normalized damping term \f$\beta_{MAX}\f$ term
in the torque muscle model. See class description
for details.
*/
double getNormalizedDampingCoefficient() const;
/**
@param beta -t normalized damping term \f$\beta\f$ term
in the torque muscle model. See class description
for details.
@throw abort() if beta < 0
*/
void setNormalizedDampingCoefficient(double beta);
/**
Sets the scaling of the passive-joint-torques. By default
this scale
is one.
@param passiveTorqueScale
The scale \f$s_P\f$ applied to the
passive-joint-torque curve (unitless)
*/
void setPassiveTorqueScale(double passiveTorqueScale);
/**
@param passiveCurveAngleOffsetVal the angle \f$\Delta_p\f$
that the passive curve should be shifted. Note that the
sign convention is in the sense of the fiber angle, not
in the sense of the joint angle. Angles in radians
*/
void setPassiveCurveAngleOffset(
double passiveCurveAngleOffsetVal);
double getTorqueVelocityMultiplierAtHalfOmegaMax() const;
void setTorqueVelocityMultiplierAtHalfOmegaMax(double tvAtHalfOmegaMax);
/**
This function iteratively solves for the scaling
so that at the specified jointAngle the passive curve
develops the specified passiveTorque
@param jointAngle the target joint angle in radians
@param passiveFiberTorque the target passive joint torque in Nm.
@throws abort if jointAngle is not in the domain of the curve
@throws abort if passiveFiberTorque < sqrt(eps)
*/
void fitPassiveTorqueScale(double jointAngle,
double passiveFiberTorque);
/**
This function solves for the passive curve angle offset
so that at the specified jointAngle the passive curve
develops the specified passiveTorque
@param jointAngle the target joint angle in radians
@param passiveFiberTorque the target passive joint torque in Nm.
@throws abort if passiveTorque < sqrt(eps)
*/
void fitPassiveCurveAngleOffset(double jointAngle,
double passiveFiberTorque);
/**
Sets the strength of the muscle to match a desired value.
@param maxIsometricTorque
The desired maximum-active-isometric torque of the
muscle (Nm)
*/
void setMaximumActiveIsometricTorque(
double maxIsometricTorque);
/**
@param maxAngularVelocity the maximum concentric joint
angular velocity magnitude in radians/sec. This scalar
quantity is not signed and must be greater than 0.
*/
void setMaximumConcentricJointAngularVelocity(
double maxAngularVelocity);
/**
@return the SmoothSegmentedFunction represents the
active-torque-angle curve profile.
*/
const RigidBodyDynamics::Addons::Geometry::
SmoothSegmentedFunction& getActiveTorqueAngleCurve() const;
/**
@return the SmoothSegmentedFunction that represents the
passive-torque-angle curve.
*/
const RigidBodyDynamics::Addons::Geometry::
SmoothSegmentedFunction& getPassiveTorqueAngleCurve() const;
/**
@return the SmoothSegmentedFunction the represents the
torque-angular-velocity curve.
*/
const RigidBodyDynamics::Addons::Geometry::
SmoothSegmentedFunction& getTorqueAngularVelocityCurve() const;
/**
@returns Value of \f$\lambda^A\f$ that is currently in use.
*/
double getActiveTorqueAngleCurveBlendingVariable() const;
/**
@returns Value of \f$\lambda^P\f$ that is currently in use.
*/
double getPassiveTorqueAngleCurveBlendingVariable() const;
/**
@returns Value of \f$\lambda^V\f$ that is currently in use.
*/
double getTorqueAngularVelocityCurveBlendingVariable() const;
/**
@param blendingVariable [0-1]
The desired value of \f$\lambda^A\f$. Note at
\f$\lambda^A=1\f$ the curve is a horizontal line
with a value of 1.
*/
void setActiveTorqueAngleCurveBlendingVariable(
double blendingVariable);
/**
@param blendingVariable [0-1]
The desired value of \f$\lambda^P\f$. Note at
\f$\lambda^P=1\f$ the curve is a horizontal line
with a value of 0.
*/
void setPassiveTorqueAngleCurveBlendingVariable(
double blendingVariable);
/**
@param blendingVariable [0-1]
The desired value of \f$\lambda^V\f$. Note at
\f$\lambda^V=1\f$ the curve is a horizontal line
with a value of 1.
*/
void setTorqueAngularVelocityCurveBlendingVariable(
double blendingVariable);
/**
@returns the scaling parameter that is applied to the
domain of the active-torque-angle curve. Note that
a value greater than 1 means that the curve has
been stretched.
*/
double getActiveTorqueAngleCurveAngleScaling() const;
/**
@param angleScaling
Scale the domain of the active torque angle curve.
This scaling is applied so that the angle at which
the curve peaks remains unchanged. Note that an
angleScaling > 1 means that the typically bell-shaped
curve will be wider.
*/
void setActiveTorqueAngleCurveAngleScaling(double angleScaling);
/**
@param fittedParameters: the structure returned after
one of the optimization-based fitting functions from
TorqueMuscleFittingToolkit has been called. If the
fitting was successful, calling this function will
update all of the adjusted parameters.
*/
void setFittedParameters (
const TorqueMuscleParameterFittingData &fittedParameters);
/**
Prints 2 csv files:
-# 'fileName' + '_variableLengthfixedVelocity': All of the
fields in TorqueMuscleInfo are recorded to file as the
jointAngle varies but the jointAngularVelocity is zero.
-#'fileName' + '_fixedLengthVariableVelocity': All of the fields
in TorqueMuscleInfo are recorded to file as the jointAngle is
fixed but the jointAngularVelocity varies.
Each column has a header, so that you can tell what each
piece of data means.
@param path: the path to the destination folder. Don't put
an '\' on the end.
@param fileNameWithoutExtension: the name of the file, but
without an extension.
@param numberOfSamplePoints: the number of sample points to
use in the files.
*/
void printJointTorqueProfileToFile(
const std::string& path,
const std::string& fileNameWithoutExtension,
int numberOfSamplePoints);
std::string getName();
void setName(std::string& name);
private:
bool mMuscleCurvesAreDirty;
void updateTorqueMuscleCurves();
TorqueMuscleInfo mTmInfo;
TorqueMuscleSummary mTmSummary;
RigidBodyDynamics::Addons::Geometry::
SmoothSegmentedFunction mTaCurve;
double mTaLambda;
static const double mTaLambdaMax;// = 1.0 -> defined in the cc file
RigidBodyDynamics::Addons::Geometry::
SmoothSegmentedFunction mTpCurve;
double mTpLambda;
static const double mTpLambdaMax;// = 0.0 -> defined in the cc file
RigidBodyDynamics::Addons::Geometry::
SmoothSegmentedFunction mTvCurve;
double mTvLambda;
///This is set to the maximum eccentric value of the
/// torque-velocity curve so that the optimization problem
/// of solving for mTaLambda, mTvLambda &
/// mMaxActiveIsometricTorque is convex. This parameter is
/// updated in updateTorqueMuscleCurves
double mTvLambdaMax;
RigidBodyDynamics::Math::VectorNd mAnderson2007c1c2c3c4c5c6;
RigidBodyDynamics::Math::VectorNd mAnderson2007b1k1b2k2;
RigidBodyDynamics::Math::VectorNd mGymnastParams;
DataSet::item mDataSet;
bool mUseTabularOmegaMax;
bool mUseTabularMaxActiveIsometricTorque;
bool mUseTabularTorqueVelocityMultiplierAtHalfOmegaMax;
double mTorqueVelocityMultiplierAtHalfOmegaMax;
double mMaxActiveIsometricTorque;
double mAngleAtOneNormActiveTorque;
double mTaAngleScaling;
double mOmegaMax;
double mAngleAtOneNormPassiveTorque;
double mAngleAtSmallestNormPassiveTorque;
double mPassiveTorqueScale;
double mPassiveCurveAngleOffset;
double mBetaMax; //passive damping coefficient
double mSubjectHeightInMeters;
double mSubjectMassInKg;
double mScaleFactorAnderson2007;
double mSignOfJointAngle;
double mSignOfConcentricAnglularVelocity;
double mSignOfJointTorque;
double mAngleOffset;
std::string mMuscleName;
double calcJointAngle(double fiberAngle) const;
double calcFiberAngle(double jointAngle) const;
double calcFiberAngularVelocity(
double jointAngularVelocity) const;
double calcJointAngularVelocity(
double fiberAngularVelocity) const;
//const static RigidBodyDynamics::Math::MatrixNd&
//getAnderson2007ParameterMatrix();
static double const Anderson2007Table3Mean[36][14];
static double const Anderson2007Table3Std[36][14];
static double const GymnastWholeBody[22][12];
void calcTorqueMuscleDataFeatures(
RigidBodyDynamics::Math::VectorNd const &jointTorque,
RigidBodyDynamics::Math::VectorNd const &jointAngle,
RigidBodyDynamics::Math::VectorNd const &jointAangularVelocity,
double activeTorqueAngleBlendingVariable,
double passiveTorqueAngleBlendingVariable,
double torqueVelocityBlendingVariable,
double activeTorqueAngleAngleScaling,
double activeTorqueAngleAtOneNormTorque,
double passiveTorqueAngleCurveOffset,
double maxAngularVelocity,
double maxActiveIsometricTorque,
TorqueMuscleDataFeatures &tmf) const;
/**
This function will calculate the angle at which the blendable
passive torque angle curve develops a desired torque. Note
that if the blendingVariable is set to 1.0 then the curve is
y = 0, and a NaN will be returned.
@param normPassiveFiberTorque: the normalized passive fiber torque
@param blendingVariable: A variable between [0,1] where 0
is equivalent to using the default passive-torque-angle
curve and 1 will set this curve to 0. Any value between
0-1 will smoothly interpolate between these extremes.
@param passiveTorqueAngleCurveOffset: the angular shift of the
passive-torque-angle curve.
@returns fiber angle in radians at which the
blendable passive curve developes the desired curve.
*/
double calcFiberAngleGivenNormalizedPassiveTorque(
double normPassiveFiberTorque,
double blendingVariable,
double passiveTorqueAngleCurveOffset) const;
/**
This function will calculate the value of a blended smooth
segmented curve \f$\mathbf{f}(\mathbf{c}, a,\lambda,\lambda^{max})\f$,
where \f$\mathbf{c}\f$ is a smooth-segmented-curve
\f[
\mathbf{f}(a,\lambda,\lambda^{max},\mathbf{c}()) = \mathbf{c}(a)
(1-\lambda) + \lambda\lambda^{max}
\f]
<b>Note </b>
At the moment this function only returns first derivatives.
@param curveArgument: [\f$-\infty,infty\f$]
the argument \f$a\f$ to the smooth-segmented-curve
\f$\mathbf{c}()\f$. Units: depend on the curve.
@param blendingVariable: [0-1].
the value of \f$\lambda\f$ the blending variable.
Unitless
@param maximumBlendingValue: the scalar value the blended function
tends to with a blending variable \f$\lambda=1\f$.
@param derivativeOrderArgument: [0,1].
The order of the derivative of the
SmoothSegmentedFunction w.r.t.
its scalar input argument.
@param derivativeOrderBlendingVariable: [0,1].
This parameter is set to choose the derivative order
with respect to the blending variable.
@param curve: the SmoothSegmentedCurve to evaluate.
@returns the value of the blended curve or its derivative
*/
double calcBlendedCurveDerivative(
double curveArgument,
double blendingVariable,
double maximumBlendingValue,
unsigned int derivativeOrderArgument,
unsigned int derivativeOrderBlendingVariable,
RigidBodyDynamics::Addons::Geometry::SmoothSegmentedFunction
const &curve) const;
/**
This function will calculate the inverse value of a blended smooth
segmented curve, that is \f$a\f$, in the function
\f$\mathbf{f}(\mathbf{c}, a,\lambda,\lambda^{max})\f$,
where \f$\mathbf{c}\f$ is a smooth-segmented-curve
\f[
\mathbf{f}(a,\lambda,\lambda^{max},\mathbf{c}()) = \mathbf{c}(a)
(1-\lambda) + \lambda\lambda^{max}
\f]
<b>Note </b>
At the moment this function only returns first derivatives.
@param blendedCurveValue:
the value of \f$\mathbf{f}(a,\lambda,\lambda^{max},\mathbf{c}())\f$
@param argGuess:
an initial guess for the value of \f$a\f$, which is necessary
as not all blended functions are monotonic.
@param blendingVariable: [0-1].
the value of \f$\lambda\f$ the blending variable.
Unitless
@param maximumBlendingValue: the scalar value the blended function
tends to with a blending variable \f$\lambda=1\f$.
@param curve: the SmoothSegmentedCurve to evaluate.
@returns the value of the argument \f$a\f$ which will evaluate
to the given value of \f$\mathbf{f}(a,\lambda,\lambda^{max},\mathbf{c}())\f$
*/
double calcInverseBlendedCurveValue(
double blendedCurveValue,
double argGuess,
double blendingVariable,
double maximumBlendingValue,
RigidBodyDynamics::Addons::Geometry::SmoothSegmentedFunction
const &curve) const;
/**
This function evaluates all of the quantities needed to
compute the torque the muscle is generating but nothing extra.
@param activation: the activation of the muscle which can
range from 0-1.
@param jointAngle: the angle of the joint(radians)
@param jointAngularVelocity: the angular velocity of the joint
((rad/s))
@param activeTorqueAngleBlendingVariable: the blending variable
associated with the active-torque-angle curve
@param passiveTorqueAngleBlendingVariable: the blending variable
associated with the passive-torque-angle curve
@param activeTorqueAngularVelocityBlendingVariable: the blending
variable associated with the torque-angular velocity
curve.
@param activeTorqueAngleAngleScaling:
the scaling of the angle. By default this is set to 1.0,
but if desired, the active torque angle curve can be
re-scaled to make it wider or narrower. This scaling is
done such that the angular location of peak
active-torque-angle multiplier does not change.
@param activeTorqueAngleAtOneNormTorque:
the angle at which the torque-angle curve hits a
normalized value of 1.0.
@param passiveTorqueAngleCurveOffset: the angular shift of the
passive-torque-angle curve.
@param maxAngularVelocity:
the maximum angular velocity of the muscle - used
to normalize the angular velocity prior to evaluating
the force-velocity curve.
@param maxActiveIsometricTorque: the maximum isometric torque
@param updTms: the torque-muscle-summary structure to be
updated.
*/
void updTorqueMuscleSummary(
double activation,
double jointAngle,
double jointAngularVelocity,
double activeTorqueAngleBlendingVariable,
double passiveTorqueAngleBlendingVariable,
double activeTorqueAngularVelocityBlendingVariable,
double activeTorqueAngleAngleScaling,
double activeTorqueAngleAtOneNormTorque,
double passiveTorqueAngleCurveOffset,
double maxAngularVelocity,
double maxActiveIsometricTorque,
TorqueMuscleSummary &updTms) const;
/**
This function evaluates the curves values that are a part of the
torque-muscle-summary structure.
@param fiberAngle: the angle of the muscle fiber (radians)
@param normFiberAngularVelocity: the normalized angular
velocity of the fiber ((rad/s)/(rad/s))
@param activeTorqueAngleBlendingVariable: the blending variable
associated with the active-torque-angle curve
@param passiveTorqueAngleBlendingVariable: the blending variable
associated with the passive-torque-angle curve
@param activeTorqueAngularVelocityBlendingVariable: the blending
variable associated with the torque-angular velocity
curve.
@param activeTorqueAngleAngleScaling:
the scaling of the angle. By default this is set to 1.0,
but if desired, the active torque angle curve can be
re-scaled to make it wider or narrower. This scaling is
done such that the angular location of peak
active-torque-angle multiplier does not change.
@param activeTorqueAngleAtOneNormTorque:
the angle at which the torque-angle curve hits a
normalized value of 1.0.
@param passiveTorqueAngleCurveOffset: the angular shift of the
passive-torque-angle curve.
@param updTms: the torque-muscle-summary structure to be
updated.
*/
void updTorqueMuscleSummaryCurveValues(
double fiberAngle,
double normFiberAngularVelocity,
double activeTorqueAngleBlendingVariable,
double passiveTorqueAngleBlendingVariable,
double activeTorqueAngularVelocityBlendingVariable,
double activeTorqueAngleAngleScaling,
double activeTorqueAngleAtOneNormTorque,
double passiveTorqueAngleCurveOffset,
TorqueMuscleSummary &updTms) const;
/**
This function evaluates the curves values and derivatives in
the TorqueMuscleInfo structue that are functions of fiberAngle
and the normalized fiber angular velocity.
@param activation: the activation of the muscle [0-1]
@param jointAngle: the angle of the joint(radians)
@param jointAngularVelocity: the angular velocity of the joint
((rad/s))
@param activeTorqueAngleBlendingVariable: the blending variable
associated with the active-torque-angle curve
@param passiveTorqueAngleBlendingVariable: the blending variable
associated with the passive-torque-angle curve
@param activeTorqueAngularVelocityBlendingVariable: the blending
variable associated with the torque-angular velocity
curve.
@param activeTorqueAngleAngleScaling:
the scaling of the angle. By default this is set to 1.0,
but if desired, the active torque angle curve can be
re-scaled to make it wider or narrower. This scaling is
done such that the angular location of peak
active-torque-angle multiplier does not change.
@param activeTorqueAngleAtOneNormTorque:
the angle at which the torque-angle curve hits a
normalized value of 1.0.
@param passiveTorqueAngleCurveOffset: the angular shift of the
passive-torque-angle curve.
@param maxAngularVelocity:
the maximum angular velocity of the muscle - used
to normalize the angular velocity prior to evaluating
the force-velocity curve.
@param maxActiveIsometricTorque:
the maximum active isometric torque the muscle can
generate
@param updTmi: the torque-muscle-info structure to be
updated.
*/
void updTorqueMuscleInfo(
double activation,
double jointAngle,
double jointAngularVelocity,
double activeTorqueAngleBlendingVariable,
double passiveTorqueAngleBlendingVariable,
double activeTorqueAngularVelocityBlendingVariable,
double activeTorqueAngleAngleScaling,
double activeTorqueAngleAtOneNormTorque,
double passiveTorqueAngleCurveOffset,
double maxAngularVelocity,
double maxActiveIsometricTorque,
TorqueMuscleInfo &updTmi) const;
/**
This function evaluates all of the quantities needed to
compute the activation of the muscle given its torque. In this
case the activation assigned to the TorqueMuscleSummary
structure is allowed to go outside of the bounds [0,1].
@param jointTorque: the torque generated by the muscle at the
joint (Nm)
@param jointAngle: the angle of the joint(radians)
@param jointAngularVelocity: the angular velocity of the joint
((rad/s))
@param activeTorqueAngleBlendingVariable: the blending variable
associated with the active-torque-angle curve
@param passiveTorqueAngleBlendingVariable: the blending variable
associated with the passive-torque-angle curve
@param activeTorqueAngularVelocityBlendingVariable: the blending
variable associated with the torque-angular velocity
curve.
@param activeTorqueAngleAngleScaling:
the scaling of the angle. By default this is set to 1.0,
but if desired, the active torque angle curve can be
re-scaled to make it wider or narrower. This scaling is
done such that the angular location of peak
active-torque-angle multiplier does not change.
@param activeTorqueAngleAtOneNormTorque:
the angle at which the torque-angle curve hits a
normalized value of 1.0.
@param passiveTorqueAngleCurveOffset: the angular shift of the
passive-torque-angle curve.
@param maxAngularVelocity:
the maximum angular velocity of the muscle - used
to normalize the angular velocity prior to evaluating
the force-velocity curve.
@param maxActiveIsometricTorque: the maximum isometric torque
@param updTms: the torque-muscle-summary structure to be
updated.
*/
void updInvertTorqueMuscleSummary(
double jointTorque,
double jointAngle,
double jointAngularVelocity,
double activeTorqueAngleBlendingVariable,
double passiveTorqueAngleBlendingVariable,
double activeTorqueAngularVelocityBlendingVariable,
double activeTorqueAngleAngleScaling,
double activeTorqueAngleAtOneNormTorque,
double passiveTorqueAngleCurveOffset,
double maxAngularVelocity,
double maxActiveIsometricTorque,
TorqueMuscleSummary &updTms) const;
};
}
}
}
#endif
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