# walking_toy.mbd
#-----------------------------------------------------------------------------
# [Data Block]
begin: data;
problem: initial value;
end: data;
#-----------------------------------------------------------------------------
# [<Problem> Block]
begin: initial value;
initial time: 0.;
final time: 7.;
time step: 1.e-4;
max iterations: 500;
tolerance: 1.e-7;
end: initial value;
#-----------------------------------------------------------------------------
# [Control Data Block]
begin: control data;
output frequency: 50;
structural nodes: 9;
abstract nodes: 4;
rigid bodies: 2;
joints: 4;
forces: 11;
genels: 4;
gravity;
end: control data;
#-----------------------------------------------------------------------------
# Design Variables
set: real m_Body = 0.2; #[kg] Mass of the body
set: real I_Body = 0.001; #[kg-m^2] Moment of inertia of the body
set: real h_BodyCG = 0.07; #[m] Height of the body CG
set: real d_BodyCG = -0.01; #[m] Longitudinal offset of the body CG
set: real m_Leg = 0.05; #[kg] Mass of the leg
set: real I_Leg = 0.0001; #[kg-m^2] Moment of inertia of the leg
set: real h_LegCG = 0.05; #[m] Height of the leg CG
set: real d_LegCG = -0.01; #[m] Longitudinal offset of the leg CG
set: real R = 0.2; #[m] Radius of the foot curvature
set: real L = 0.05; #[m] Foot length (not used here)
set: real h_Rev = 0.1; #[m] Height of the revolute hinge
set: real d_Rev = 0.; #[m] Longitudinal offset of the revolute hinge
set: real RZ_RevMax = 15.*pi/180.; #[rad] Maximum angle of the revolute hinge
set: real theta = 10.*pi/180.; #[rad] Surface angle
set: real v0_head = -0.2; #[m/s] Initial head velocity
set: real Kc = 100000.; #[N/m] Contact stiffness
set: real Ec = 1.4; #[-] Contact stiffness exponent
set: real Cc = 100.; #[Ns/m] Contact damping
set: real Dc = 0.001; #[m] Contact damping activation depth
set: real Ks_a = 1000.; #[Nm/rad] Revolute hinge stopper stiffness
set: real Es_a = 1.4; #[-] Revolute hinge stopper stiffness exponent
set: real Cs_a = 10.; #[Nms/rad] Revolute hinge stopper damping
set: real Ds_a = 0.01; #[rad] Revolute hinge stopper damping activation depth
set: real mu = 0.3; #[-] Friction coefficient
set: real Vt = 0.005; #[m/s] Friction threshold velocity
#-----------------------------------------------------------------------------
# Reference Labels
set: integer Ref_Surface = 1;
set: integer Ref_FootCurvCenter = 2;
set: integer Ref_BodyCG = 3;
set: integer Ref_LegCG = 4;
set: integer Ref_JoRevh_Body_Leg = 5;
set: integer Ref_FrontFootEdge = 6;
set: integer Ref_RearFootEdge = 7;
# Structural Node Labels
set: integer NoSta_Surface = 1;
set: integer NoDyn_Body = 2;
set: integer NoDyn_Leg = 3;
set: integer NoDum_Body_RelTo_Surface = 4;
set: integer NoDum_Leg_RelTo_Surface = 5;
set: integer NoDum_FrontFootEdge = 6;
set: integer NoDum_RearFootEdge = 7;
set: integer NoDum_FrontFootEdge_RelTo_Surface = 8;
set: integer NoDum_RearFootEdge_RelTo_Surface = 9;
# Abstract Node Labels
set: integer NoAbs_FN_Body = 1;
set: integer NoAbs_FN_Leg = 2;
set: integer NoAbs_FN_FrontFootEdge = 3;
set: integer NoAbs_FN_RearFootEdge = 4;
# Body Labels
set: integer Body_Body = 1;
set: integer Body_Leg = 2;
# Joint Labels
set: integer JoClamp_Surface = 1;
set: integer JoInp_Surface_Body = 2;
set: integer JoRevrot_Surface_Body = 3;
set: integer JoRevh_Body_Leg = 4;
# Force Labels
set: integer FoStrin_Normal_Body_Surface = 1;
set: integer FoStrin_Friction_Body_Surface = 2;
set: integer CoStrin_Friction_Body_Surface = 3;
set: integer FoStrin_Normal_Leg_Surface = 4;
set: integer FoStrin_Friction_Leg_Surface = 5;
set: integer CoStrin_Friction_Leg_Surface = 6;
set: integer FoStrin_Normal_FrontFootEdge_Surface = 7;
set: integer FoStrin_Normal_RearFootEdge_Surface = 8;
set: integer FoStrin_Friction_FrontFootEdge_Surface = 9;
set: integer FoStrin_Friction_RearFootEdge_Surface = 10;
set: integer CoStrin_Stopper_Leg_Body = 11;
# Genel Labels
set: integer GeClamp_FN_Body = 1;
set: integer GeClamp_FN_Leg = 2;
set: integer GeClamp_FN_FrontFootEdge = 3;
set: integer GeClamp_FN_RearFootEdge = 4;
#-----------------------------------------------------------------------------
# Scalar Functions
scalar function: "cubstep",
cubicspline, do not extrapolate,
-0.03, 0.00,
-0.02, 0.00,
-0.01, 0.00,
0.00, 0.00,
1.00, 1.00,
1.01, 1.00,
1.02, 1.00,
1.03, 1.00;
scalar function: "cubsign",
cubicspline, do not extrapolate,
-1.03, -1.00,
-1.02, -1.00,
-1.01, -1.00,
-1.00, -1.00,
1.00, 1.00,
1.01, 1.00,
1.02, 1.00,
1.03, 1.00;
#-----------------------------------------------------------------------------
# References
reference: Ref_Surface,
null, # absolute position
euler, theta, 0., 0., # absolute orientation
null, # absolute velocity
null; # absolute angular velocity
reference: Ref_FootCurvCenter,
reference, Ref_Surface, 0., 0., R, # absolute position
reference, Ref_Surface, eye, # absolute orientation
reference, Ref_Surface, 0., -v0_head, 0., # absolute velocity
reference, Ref_Surface, null; # absolute angular velocity
reference: Ref_BodyCG,
reference, Ref_Surface, 0., -d_BodyCG, h_BodyCG, # absolute position
reference, Ref_Surface, eye, # absolute orientation
reference, Ref_Surface, null, # absolute velocity
reference, Ref_Surface, null; # absolute angular velocity
reference: Ref_LegCG,
reference, Ref_Surface, 0., -d_LegCG, h_LegCG, # absolute position
reference, Ref_Surface, eye, # absolute orientation
reference, Ref_Surface, null, # absolute velocity
reference, Ref_Surface, null; # absolute angular velocity
reference: Ref_JoRevh_Body_Leg,
reference, Ref_Surface, 0., -d_Rev, h_Rev, # absolute position
reference, Ref_Surface, euler, 0., pi/2., 0., # absolute orientation
reference, Ref_Surface, null, # absolute velocity
reference, Ref_Surface, null; # absolute angular velocity
reference: Ref_FrontFootEdge,
reference, Ref_Surface, null, # absolute position
reference, Ref_Surface, eye, # absolute orientation
reference, Ref_Surface, null, # absolute velocity
reference, Ref_Surface, null; # absolute angular velocity
reference: Ref_RearFootEdge,
reference, Ref_Surface, null, # absolute position
reference, Ref_Surface, eye, # absolute orientation
reference, Ref_Surface, null, # absolute velocity
reference, Ref_Surface, null; # absolute angular velocity
#-----------------------------------------------------------------------------
# [Nodes Block]
begin: nodes;
#-----------------------------------------------------------------------------
# Nodes
structural: NoSta_Surface, static,
reference, Ref_Surface, null, # absolute position
reference, Ref_Surface, eye, # absolute orientation
reference, Ref_Surface, null, # absolute velocity
reference, Ref_Surface, null; # absolute angular velocity
structural: NoDyn_Body, dynamic,
reference, Ref_FootCurvCenter, null, # absolute position
reference, Ref_FootCurvCenter, eye, # absolute orientation
reference, Ref_FootCurvCenter, null, # absolute velocity
reference, Ref_FootCurvCenter, null, # absolute angular velocity
accelerations, yes;
structural: NoDyn_Leg, dynamic,
reference, Ref_FootCurvCenter, null, # absolute position
reference, Ref_FootCurvCenter, eye, # absolute orientation
reference, Ref_FootCurvCenter, null, # absolute velocity
reference, Ref_FootCurvCenter, null, # absolute angular velocity
accelerations, yes;
structural: NoDum_Body_RelTo_Surface, dummy, NoDyn_Body,
relative frame, NoSta_Surface;
structural: NoDum_Leg_RelTo_Surface, dummy, NoDyn_Leg,
relative frame, NoSta_Surface;
structural: NoDum_FrontFootEdge, dummy, NoDyn_Body,
offset,
reference, Ref_FrontFootEdge, null, # relative offset
reference, Ref_FrontFootEdge, eye; # relative orientation
structural: NoDum_RearFootEdge, dummy, NoDyn_Leg,
offset,
reference, Ref_RearFootEdge, null, # relative offset
reference, Ref_RearFootEdge, eye; # relative orientation
structural: NoDum_FrontFootEdge_RelTo_Surface, dummy, NoDum_FrontFootEdge,
relative frame, NoSta_Surface;
structural: NoDum_RearFootEdge_RelTo_Surface, dummy, NoDum_RearFootEdge,
relative frame, NoSta_Surface;
abstract: NoAbs_FN_Body, algebraic;
abstract: NoAbs_FN_Leg, algebraic;
abstract: NoAbs_FN_FrontFootEdge, algebraic;
abstract: NoAbs_FN_RearFootEdge, algebraic;
end: nodes;
#-----------------------------------------------------------------------------
# Plugin Variables
set: [node, DZ_Body, NoDum_Body_RelTo_Surface, structural, string="X[3]"];
set: [node, VY_Body, NoDum_Body_RelTo_Surface, structural, string="XP[2]"];
set: [node, VZ_Body, NoDum_Body_RelTo_Surface, structural, string="XP[3]"];
set: [node, WX_Body, NoDum_Body_RelTo_Surface, structural, string="omega[1]"];
set: [node, RX_Body, NoDum_Body_RelTo_Surface, structural, string="E[1]"];
set: [node, DZ_Leg, NoDum_Leg_RelTo_Surface, structural, string="X[3]"];
set: [node, VY_Leg, NoDum_Leg_RelTo_Surface, structural, string="XP[2]"];
set: [node, VZ_Leg, NoDum_Leg_RelTo_Surface, structural, string="XP[3]"];
set: [node, WX_Leg, NoDum_Leg_RelTo_Surface, structural, string="omega[1]"];
set: [node, RX_Leg, NoDum_Leg_RelTo_Surface, structural, string="E[1]"];
set: [node, DZ_F, NoDum_FrontFootEdge_RelTo_Surface, structural, string="X[3]"];
set: [node, VY_F, NoDum_FrontFootEdge_RelTo_Surface, structural, string="XP[2]"];
set: [node, VZ_F, NoDum_FrontFootEdge_RelTo_Surface, structural, string="XP[3]"];
set: [node, DZ_R, NoDum_RearFootEdge_RelTo_Surface, structural, string="X[3]"];
set: [node, VY_R, NoDum_RearFootEdge_RelTo_Surface, structural, string="XP[2]"];
set: [node, VZ_R, NoDum_RearFootEdge_RelTo_Surface, structural, string="XP[3]"];
#-----------------------------------------------------------------------------
# [Elements Block]
begin: elements;
#-----------------------------------------------------------------------------
# Bodies
body: Body_Body, NoDyn_Body,
m_Body, # mass
reference, Ref_BodyCG, null, # relative center of mass
diag, I_Body, 1., 1.; # inertia matrix
body: Body_Leg, NoDyn_Leg,
m_Leg, # mass
reference, Ref_LegCG, null, # relative center of mass
diag, I_Leg, 1., 1.; # inertia matrix
#-----------------------------------------------------------------------------
# Joints
joint: JoClamp_Surface,
clamp,
NoSta_Surface,
position, node,
orientation, node;
joint: JoInp_Surface_Body,
in plane,
NoSta_Surface,
null, # relative plane position
1., 0., 0., # relative normal direction
NoDyn_Body;
joint: JoRevrot_Surface_Body,
revolute rotation,
NoSta_Surface,
hinge,
euler, 0., pi/2., 0., # relative orientation
NoDyn_Body,
hinge,
euler, 0., pi/2., 0.; # relative orientation
joint: JoRevh_Body_Leg,
revolute hinge,
NoDyn_Body,
reference, Ref_JoRevh_Body_Leg, null, # relative offset
hinge, reference, Ref_JoRevh_Body_Leg, eye, # relative orientation
NoDyn_Leg,
reference, Ref_JoRevh_Body_Leg, null, # relative offset
hinge, reference, Ref_JoRevh_Body_Leg, eye; # relative orientation
#-----------------------------------------------------------------------------
# Genels
genel: GeClamp_FN_Body,
clamp,
NoAbs_FN_Body, abstract,
string, "max(0,Kc*sign(R-DZ_Body)*abs(R-DZ_Body)^Ec\
+Cc*(0-VZ_Body)*model::sf::cubstep((R-DZ_Body)/Dc))\
*step(RX_Body)";
genel: GeClamp_FN_Leg,
clamp,
NoAbs_FN_Leg, abstract,
string, "max(0,Kc*sign(R-DZ_Leg)*abs(R-DZ_Leg)^Ec\
+Cc*(0-VZ_Leg)*model::sf::cubstep((R-DZ_Leg)/Dc))\
*step(-RX_Leg)";
genel: GeClamp_FN_FrontFootEdge,
clamp,
NoAbs_FN_FrontFootEdge, abstract,
string, "max(0,Kc*sign(0-DZ_F)*abs(0-DZ_F)^Ec\
+Cc*(0-VZ_F)*model::sf::cubstep((0-DZ_F)/Dc))\
*(1-step(RX_Body))";
genel: GeClamp_FN_RearFootEdge,
clamp,
NoAbs_FN_RearFootEdge, abstract,
string, "max(0,Kc*sign(0-DZ_R)*abs(0-DZ_R)^Ec\
+Cc*(0-VZ_R)*model::sf::cubstep((0-DZ_R)/Dc))\
*(1-step(-RX_Leg))";
#-----------------------------------------------------------------------------
# Plugin Variables
set: [element, RZ_Rev, JoRevh_Body_Leg, joint, string="rz"];
set: [element, WZ_Rev, JoRevh_Body_Leg, joint, string="wz"];
set: [dof, FN_Body, NoAbs_FN_Body, abstract, algebraic];
set: [dof, FN_Leg, NoAbs_FN_Leg, abstract, algebraic];
set: [dof, FN_F, NoAbs_FN_FrontFootEdge, abstract, algebraic];
set: [dof, FN_R, NoAbs_FN_RearFootEdge, abstract, algebraic];
#-----------------------------------------------------------------------------
# Forces
force: FoStrin_Normal_Body_Surface,
absolute internal,
NoDyn_Body,
position, null, # relative arm
NoSta_Surface,
position, null, # relative arm
single, reference, Ref_Surface, 0., 0., 1., string, "FN_Body"; # force value
force: FoStrin_Friction_Body_Surface,
absolute internal,
NoDyn_Body,
position, null, # relative arm
NoSta_Surface,
position, null, # relative arm
single, reference, Ref_Surface, 0., 1., 0.,
string, "-model::sf::cubsign((VY_Body+R*WX_Body)/Vt)*mu*FN_Body"; # force value
couple: CoStrin_Friction_Body_Surface,
absolute internal,
NoDyn_Body,
NoSta_Surface,
single, reference, Ref_Surface, 1., 0., 0.,
string, "-R*model::sf::cubsign((VY_Body+R*WX_Body)/Vt)*mu*FN_Body"; # couple value
force: FoStrin_Normal_Leg_Surface,
absolute internal,
NoDyn_Leg,
position, null, # relative arm
NoSta_Surface,
position, null, # relative arm
single, reference, Ref_Surface, 0., 0., 1., string, "FN_Leg"; # force value
force: FoStrin_Friction_Leg_Surface,
absolute internal,
NoDyn_Leg,
position, null, # relative arm
NoSta_Surface,
position, null, # relative arm
single, reference, Ref_Surface, 0., 1., 0.,
string, "-model::sf::cubsign((VY_Leg+R*WX_Leg)/Vt)*mu*FN_Leg"; # force value
couple: CoStrin_Friction_Leg_Surface,
absolute internal,
NoDyn_Leg,
NoSta_Surface,
single, reference, Ref_Surface, 1., 0., 0.,
string, "-R*model::sf::cubsign((VY_Leg+R*WX_Leg)/Vt)*mu*FN_Leg"; # couple value
force: FoStrin_Normal_FrontFootEdge_Surface,
absolute internal,
NoDyn_Body,
position, reference, Ref_FrontFootEdge, null, # relative arm
NoSta_Surface,
position, null, # relative arm
single, reference, Ref_Surface, 0., 0., 1., string, "FN_F"; # force value
force: FoStrin_Normal_RearFootEdge_Surface,
absolute internal,
NoDyn_Leg,
position, reference, Ref_RearFootEdge, null, # relative arm
NoSta_Surface,
position, null, # relative arm
single, reference, Ref_Surface, 0., 0., 1., string, "FN_R"; # force value
force: FoStrin_Friction_FrontFootEdge_Surface,
absolute internal,
NoDyn_Body,
position, reference, Ref_FrontFootEdge, null, # relative arm
NoSta_Surface,
position, null, # relative arm
single, reference, Ref_Surface, 0., 1., 0.,
string, "-model::sf::cubsign(VY_F/Vt)*mu*FN_F"; # force value
force: FoStrin_Friction_RearFootEdge_Surface,
absolute internal,
NoDyn_Leg,
position, reference, Ref_RearFootEdge, null, # relative arm
NoSta_Surface,
position, null, # relative arm
single, reference, Ref_Surface, 0., 1., 0.,
string, "-model::sf::cubsign(VY_R/Vt)*mu*FN_R"; # force value
couple: CoStrin_Stopper_Leg_Body,
follower internal,
NoDyn_Leg,
position, reference, Ref_JoRevh_Body_Leg, null, # relative arm
NoDyn_Body,
position, reference, Ref_JoRevh_Body_Leg, null, # relative arm
single, reference, Ref_JoRevh_Body_Leg, 0., 0., 1.,
string, "max(0,Ks_a*sign(0-RZ_Rev)*abs(0-RZ_Rev)^Es_a\
+Cs_a*(0-WZ_Rev)*model::sf::cubstep((0-RZ_Rev)/Ds_a))\
-max(0,Ks_a*sign(RZ_Rev-RZ_RevMax)*abs(RZ_Rev-RZ_RevMax)^Es_a\
+Cs_a*(WZ_Rev-0)*model::sf::cubstep((RZ_Rev-RZ_RevMax)/Ds_a))"; # couple value
#-----------------------------------------------------------------------------
# Gravity
gravity: 0., 0., -1., const, 9.81;
end: elements;
