- Generated on Wed Jul 20 2022 12:57:44 for Rigid Body Dynamics Library by
1.9.3
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Rigid Body Dynamics Library
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#include <BalanceToolkit.h>
Public Member Functions | |
| FootPlacementEstimatorInfo () | |
Data Fields | |
| double | f |
| unsigned int | iterations |
| double | phi |
| Math::Vector3d | r0F0 |
| double | projectionError |
| Math::Vector3d | n |
| Math::Vector3d | u |
| Math::Vector3d | k |
| Math::Vector3d | r0C0 |
| Math::Vector3d | v0C0 |
| Math::Vector3d | r0P0 |
| Math::Vector3d | HC0 |
| Math::Matrix3d | JC0 |
| Math::Vector3d | w0C0 |
| Math::Vector3d | HP0 |
| Math::Matrix3d | JP0 |
| Math::Vector3d | w0P0 |
| double | h |
| double | nJC0n |
| double | v0C0u |
| double | v0C0k |
| double | w0C0n |
| double | w0F0nPlus |
| double | l |
| double | E |
| double | Df_Dphi |
| double | Df_Dw0C0n |
| double | Df_Dh |
| double | Df_Dv0C0u |
| double | Df_Dv0C0k |
| double | Df_DnJC0n |
| double | Df_Dm |
| double | Df_Dg |
| double | Ds_Dl |
| double | Ds_DnJC0n |
| double | Ds_DE |
| double | Ds_Dv0C0u |
| double | Ds_Dv0C0k |
| double | Ds_Dw0C0n |
| double | Dphi_Dl |
| double | Dphi_DnJC0n |
| double | Dphi_DE |
| double | Dphi_Dv0C0u |
| double | Dphi_Dv0C0k |
| double | Dphi_Dw0C0n |
This struct contains the location of the balance restoring step location evaluated by the 3DFPE algorithm described by Millard et al. and all of the additional information needed to judge if the assumptions of the FPE3D are being met, and if not, how much error is introduced. All quantities are expressed in MKS units. If you cannot get access to Millard et al., note that a similar derivation appears in Sloot et al. but that some variable names have changed (the u & v-directions in Millard et al. are the s & t directions in Sloot et al.).
Millard, M., McPhee, J., & Kubica, E. (2012). Foot placement and balance in 3D. Journal of Computational and Nonlinear Dynamics, 7(2), 021015.
Sloot LH, Millard M, Werner C, Mombaur K. Slow but Steady: Similar Sit-to-Stand Balance at Seat-Off in Older vs. Younger Adults. Frontiers in sports and active living. 2020;2.
A small apology for the terse variable names. These terse names are needed to do write these functions without making obvious errors. Nice human-readable variable names could have been used, however, time and memory would have to have been spent to copy these over. In case you need to modify the guts of this code a description of the variable convention appears below.
The variables follow a notation convention that is similar to that used in multibody-dynamics.
Global quantities : [ Descriptor ] [Resolved in frame] e.g. g0 : gravity vector in K0, the inertial frame
Single-point/body quantites : [ Descriptor ] [About Point ] [Resolved in frame] [optional operator] Two-point quantites : [ Descriptor ] [From Point ] [To Point ] [Resolved in frame] [optional operator]
Global descriptors g : gravity
Single Point/Body Descriptors
e : unit vector E : rotation matrix K : a frame: consists of a point in space and a rotation matrix J : inertia H : angular momentum
Direction Vectors (lower case) u : vector in the direction of a balancing step (See Fig. 6 of Millard et al.) v : vertical vector k : vector normal to the the plane
Two-Point Descriptors: r: position v: velocity w: angular velocity
Point C: the whole-body-center of mass (COM) P: the projection plane origin: the ground projection of the COM
0: the origin of the lab/inertial frame S: the contact surface frame origin
Frames 0: the lab/inertial frame S: the contact surface frame origin i: Body fixed frame
Operations: x : Cross-product matrix. For example r0C0 is the vector, r0C0x is the cross-product matrix of r0C0. u/v/x: Dot product. For example w0C0n is an angular velocity from the base frame (0) to the point (C) in coordinates of the base frame (0) in the (n) direction.
N.B. The ascii name convention should have something extra to distinguish operators, maybe an underscore: w0C0_n instead of w0C0n
Examples: r0F0 : (r) position vector (0) from the base frame origin (F) to the foot placement estimator location (0) resolved in the coordinates of the base frame
r0P0 : (r) position vector (0) from the base frame origin (P) to the foot placement estimator location (0) resolved in the coordinates of the base frame
JC0 : (J) inertia matrix (C) about the center-of-mass (CoM) (0) resolved in the coordinates of the lab frame
Definition at line 112 of file BalanceToolkit.h.
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inline |
Definition at line 248 of file BalanceToolkit.h.
| double Df_Dg |
Partial derivative of the FPE constraint equation
(Eqn. 45 of Millard et al.) f w.r.t. to the force of gravity
Definition at line 209 of file BalanceToolkit.h.
| double Df_Dh |
Partial derivative of the FPE constraint equation
(Eqn. 45 of Millard et al.) f w.r.t. COM height
Definition at line 191 of file BalanceToolkit.h.
| double Df_Dm |
Partial derivative of the FPE constraint equation
(Eqn. 45 of Millard et al.) f w.r.t. the total system mass
Definition at line 206 of file BalanceToolkit.h.
| double Df_DnJC0n |
Partial derivative of the FPE constraint equation
(Eqn. 45 of Millard et al.) f w.r.t. the whole body moment of inertia about the center of mass in the n direction
Definition at line 203 of file BalanceToolkit.h.
| double Df_Dphi |
Partial derivative of the FPE constraint equation
(Eqn. 45 of Millard et al.) f w.r.t. phi
Definition at line 184 of file BalanceToolkit.h.
| double Df_Dv0C0k |
Partial derivative of the FPE constraint equation
(Eqn. 45 of Millard et al.) f w.r.t. the pre-contact COM velocity in the k direction
Definition at line 199 of file BalanceToolkit.h.
| double Df_Dv0C0u |
Partial derivative of the FPE constraint equation
(Eqn. 45 of Millard et al.) f w.r.t. the pre-contact COM velocity in the u direction
Definition at line 195 of file BalanceToolkit.h.
| double Df_Dw0C0n |
Partial derivative of the FPE constraint equation
(Eqn. 45 of Millard et al.) f w.r.t. the pre-contact whole body angular velocity about the center of mass in the n direction
Definition at line 188 of file BalanceToolkit.h.
| double Dphi_DE |
The sensitivity of the FPE angle phi w.r.t. small changes in E, the post-contact sytem energy
Definition at line 236 of file BalanceToolkit.h.
| double Dphi_Dl |
The sensitivity of the FPE angle phi w.r.t. small changes in l, the distance between the COM and the FPE location
Definition at line 230 of file BalanceToolkit.h.
| double Dphi_DnJC0n |
The sensitivity of the FPE angle phi w.r.t. small changes in J, the moment of inertia of the body about the COM in the n direction
Definition at line 233 of file BalanceToolkit.h.
| double Dphi_Dv0C0k |
The sensitivity of the FPE angle phi w.r.t. small changes in v0C0 the velocity of the center of mass in k, the vertical direction
Definition at line 242 of file BalanceToolkit.h.
| double Dphi_Dv0C0u |
The sensitivity of the FPE angle phi w.r.t. small changes in v0C0 the velocity of the center of mass in the u-direction
Definition at line 239 of file BalanceToolkit.h.
| double Dphi_Dw0C0n |
The sensitivity of the FPE angle phi w.r.t. small changes in the whole body angular velocity about the center of mass in the n direction.
Definition at line 245 of file BalanceToolkit.h.
| double Ds_DE |
The sensitivity of the FPE step length w.r.t. small changes in E, the peak potential energy obtained by the system as it comes to balance over its foot after contact.
Definition at line 218 of file BalanceToolkit.h.
| double Ds_Dl |
The sensitivity of the FPE step length w.r.t. small changes in the distance l between the COM and the FPE.
Definition at line 212 of file BalanceToolkit.h.
| double Ds_DnJC0n |
The sensitivity of the FPE step length w.r.t. small changes in J.
Definition at line 214 of file BalanceToolkit.h.
| double Ds_Dv0C0k |
The sensitivity of the FPE step length w.r.t. small changes in v0C0 the velocity of the center of mass in k, the vertical direction
Definition at line 224 of file BalanceToolkit.h.
| double Ds_Dv0C0u |
The sensitivity of the FPE step length w.r.t. small changes in v0C0 the velocity of the center of mass in the u direction
Definition at line 221 of file BalanceToolkit.h.
| double Ds_Dw0C0n |
The sensitivity of the FPE step length w.r.t. small changes in the whole body angular velocity about the center of mass in the n direction.
Definition at line 227 of file BalanceToolkit.h.
| double E |
The post-contact system energy of the FPE model
Definition at line 181 of file BalanceToolkit.h.
| double f |
Numerical 3DFPE constraint error (Eqn. 45 of Millard et al.)
Definition at line 115 of file BalanceToolkit.h.
| double h |
Height of the center-of-mass
Definition at line 164 of file BalanceToolkit.h.
| Math::Vector3d HC0 |
Whole body angular momentum about the center of mass
Definition at line 151 of file BalanceToolkit.h.
| Math::Vector3d HP0 |
Whole body angular momentum about the center of mass
Definition at line 157 of file BalanceToolkit.h.
| unsigned int iterations |
Number of iterations used by the root solving method to numerically solve Eqn. 45 of Millard et al.
Definition at line 119 of file BalanceToolkit.h.
| Math::Matrix3d JC0 |
Whole body moment of inertia the center of mass
Definition at line 153 of file BalanceToolkit.h.
| Math::Matrix3d JP0 |
Whole body moment of inertia about the center of mass ground projection
Definition at line 160 of file BalanceToolkit.h.
Vertical direction vector
Definition at line 143 of file BalanceToolkit.h.
| double l |
The leg length of the FPE model: the distance from the COM to the FPE
Definition at line 179 of file BalanceToolkit.h.
Direction vector that is normal to the projection plane (Eqn. 43), and is parallel to the horizontal component of HP0.
Definition at line 138 of file BalanceToolkit.h.
| double nJC0n |
Whole body moment of inertia about the center of mass in the n direction
Definition at line 167 of file BalanceToolkit.h.
| double phi |
The foot contact angle: the angle between the gravity vector and the vector between the CoM and the contact location (See Fig. 6)
Definition at line 123 of file BalanceToolkit.h.
| double projectionError |
The percentage of HP0 (the angular momentum of the whole body when evaluated by the center-of-mass ground projection point) that is in the vertical direction. Momentum in this direction is assumed to be zero by the FPE.
Definition at line 133 of file BalanceToolkit.h.
| Math::Vector3d r0C0 |
Vector to the COM
Definition at line 145 of file BalanceToolkit.h.
| Math::Vector3d r0F0 |
The location of the foot-placement-estimator in the base frame.
Definition at line 126 of file BalanceToolkit.h.
| Math::Vector3d r0P0 |
Vector to the COM ground projection
Definition at line 149 of file BalanceToolkit.h.
Direction vector defined by n cross k, where k is the vertical direction vector.
Definition at line 141 of file BalanceToolkit.h.
| Math::Vector3d v0C0 |
Vector to the COM ground projection
Definition at line 147 of file BalanceToolkit.h.
| double v0C0k |
Velocity of the COM in the k direction
Definition at line 171 of file BalanceToolkit.h.
| double v0C0u |
Velocity of the COM in the u direction
Definition at line 169 of file BalanceToolkit.h.
| Math::Vector3d w0C0 |
Average angular velocity of the center of mass in the n direction
Definition at line 155 of file BalanceToolkit.h.
| double w0C0n |
Whole body angular velocity in the n direction
Definition at line 173 of file BalanceToolkit.h.
| double w0F0nPlus |
Post-contact whole body angular velocity in the n direction about the foot placement estimator location
Definition at line 176 of file BalanceToolkit.h.
| Math::Vector3d w0P0 |
Average angular velocity about the center-of-mass ground projection
Definition at line 162 of file BalanceToolkit.h.
1.9.3