def createPseudoImpulseModel(self, supportFootIds, swingFootTask):
""" Action model for pseudo-impulse models.
A pseudo-impulse model consists of adding high-penalty cost for the contact velocities.
:param supportFootIds: Ids of the constrained feet
:param swingFootTask: swinging foot task
:return pseudo-impulse differential action model
"""
# Creating a 3D multi-contact model, and then including the supporting
# foot
nu = self.actuation.nu
contactModel = crocoddyl.ContactModelMultiple(self.state, nu)
for i in supportFootIds:
supportContactModel = crocoddyl.ContactModel3D(self.state, i, np.array([0., 0., 0.]), nu,
np.array([0., 50.]))
contactModel.addContact(self.rmodel.frames[i].name + "_contact", supportContactModel)
# Creating the cost model for a contact phase
costModel = crocoddyl.CostModelSum(self.state, nu)
for i in supportFootIds:
cone = crocoddyl.FrictionCone(self.Rsurf, self.mu, 4, False)
coneResidual = crocoddyl.ResidualModelContactFrictionCone(self.state, i, cone, nu)
coneActivation = crocoddyl.ActivationModelQuadraticBarrier(crocoddyl.ActivationBounds(cone.lb, cone.ub))
frictionCone = crocoddyl.CostModelResidual(self.state, coneActivation, coneResidual)
costModel.addCost(self.rmodel.frames[i].name + "_frictionCone", frictionCone, 1e1)
if swingFootTask is not None:
for i in swingFootTask:
frameTranslationResidual = crocoddyl.ResidualModelFrameTranslation(self.state, i[0], i[1].translation,
nu)
frameVelocityResidual = crocoddyl.ResidualModelFrameVelocity(self.state, i[0], pinocchio.Motion.Zero(),
pinocchio.LOCAL, nu)
footTrack = crocoddyl.CostModelResidual(self.state, frameTranslationResidual)
impulseFootVelCost = crocoddyl.CostModelResidual(self.state, frameVelocityResidual)
costModel.addCost(self.rmodel.frames[i[0]].name + "_footTrack", footTrack, 1e7)
costModel.addCost(self.rmodel.frames[i[0]].name + "_impulseVel", impulseFootVelCost, 1e6)
stateWeights = np.array([0.] * 3 + [500.] * 3 + [0.01] * (self.rmodel.nv - 6) + [10.] * self.rmodel.nv)
stateResidual = crocoddyl.ResidualModelState(self.state, self.rmodel.defaultState, nu)
stateActivation = crocoddyl.ActivationModelWeightedQuad(stateWeights**2)
ctrlResidual = crocoddyl.ResidualModelControl(self.state, nu)
stateReg = crocoddyl.CostModelResidual(self.state, stateActivation, stateResidual)
ctrlReg = crocoddyl.CostModelResidual(self.state, ctrlResidual)
costModel.addCost("stateReg", stateReg, 1e1)
costModel.addCost("ctrlReg", ctrlReg, 1e-3)
# Creating the action model for the KKT dynamics with simpletic Euler
# integration scheme
dmodel = crocoddyl.DifferentialActionModelContactFwdDynamics(self.state, self.actuation, contactModel,
costModel, 0., True)
if self.integrator == 'euler':
model = crocoddyl.IntegratedActionModelEuler(dmodel, 0.)
elif self.integrator == 'rk4':
model = crocoddyl.IntegratedActionModelRK(dmodel, crocoddyl.RKType.four, 0.)
elif self.integrator == 'rk3':
model = crocoddyl.IntegratedActionModelRK(dmodel, crocoddyl.RKType.three, 0.)
elif self.integrator == 'rk2':
model = crocoddyl.IntegratedActionModelRK(dmodel, crocoddyl.RKType.two, 0.)
else:
model = crocoddyl.IntegratedActionModelEuler(dmodel, 0.)
return model
def createPseudoImpulseModel(self, supportFootIds, swingFootTask):
""" Action model for pseudo-impulse models.
A pseudo-impulse model consists of adding high-penalty cost for the contact velocities.
:param supportFootIds: Ids of the constrained feet
:param swingFootTask: swinging foot task
:return pseudo-impulse differential action model
"""
# Creating a 3D multi-contact model, and then including the supporting
# foot
contactModel = crocoddyl.ContactModelMultiple(self.state,
self.actuation.nu)
for i in supportFootIds:
xref = crocoddyl.FrameTranslation(i, np.array([0., 0., 0.]))
supportContactModel = crocoddyl.ContactModel3D(
self.state, xref, self.actuation.nu, np.array([0., 50.]))
contactModel.addContact(self.rmodel.frames[i].name + "_contact",
supportContactModel)
# Creating the cost model for a contact phase
costModel = crocoddyl.CostModelSum(self.state, self.actuation.nu)
for i in supportFootIds:
cone = crocoddyl.FrictionCone(self.nsurf, self.mu, 4, False)
frictionCone = crocoddyl.CostModelContactFrictionCone(
self.state,
crocoddyl.ActivationModelQuadraticBarrier(
crocoddyl.ActivationBounds(cone.lb, cone.ub)),
crocoddyl.FrameFrictionCone(i, cone), self.actuation.nu)
costModel.addCost(self.rmodel.frames[i].name + "_frictionCone",
frictionCone, 1e1)
if swingFootTask is not None:
for i in swingFootTask:
xref = crocoddyl.FrameTranslation(i.frame, i.oMf.translation)
vref = crocoddyl.FrameMotion(i.frame, pinocchio.Motion.Zero())
footTrack = crocoddyl.CostModelFrameTranslation(
self.state, xref, self.actuation.nu)
impulseFootVelCost = crocoddyl.CostModelFrameVelocity(
self.state, vref, self.actuation.nu)
costModel.addCost(
self.rmodel.frames[i.frame].name + "_footTrack", footTrack,
1e7)
costModel.addCost(
self.rmodel.frames[i.frame].name + "_impulseVel",
impulseFootVelCost, 1e6)
stateWeights = np.array([0.] * 3 + [500.] * 3 + [0.01] *
(self.rmodel.nv - 6) + [10.] * self.rmodel.nv)
stateReg = crocoddyl.CostModelState(
self.state, crocoddyl.ActivationModelWeightedQuad(stateWeights**2),
self.rmodel.defaultState, self.actuation.nu)
ctrlReg = crocoddyl.CostModelControl(self.state, self.actuation.nu)
costModel.addCost("stateReg", stateReg, 1e1)
costModel.addCost("ctrlReg", ctrlReg, 1e-3)
# Creating the action model for the KKT dynamics with simpletic Euler
# integration scheme
dmodel = crocoddyl.DifferentialActionModelContactFwdDynamics(
self.state, self.actuation, contactModel, costModel, 0., True)
model = crocoddyl.IntegratedActionModelEuler(dmodel, 0.)
return model
def createSwingFootModel(self, timeStep, supportFootIds, comTask=None, swingFootTask=None):
""" Action model for a swing foot phase.
:param timeStep: step duration of the action model
:param supportFootIds: Ids of the constrained feet
:param comTask: CoM task
:param swingFootTask: swinging foot task
:return action model for a swing foot phase
"""
# Creating a 3D multi-contact model, and then including the supporting
# foot
contactModel = crocoddyl.ContactModelMultiple(self.state, self.actuation.nu)
for i in supportFootIds:
xref = crocoddyl.FrameTranslation(i, np.matrix([0., 0., 0.]).T)
supportContactModel = crocoddyl.ContactModel3D(self.state, xref, self.actuation.nu, np.matrix([0., 50.]).T)
contactModel.addContact(self.rmodel.frames[i].name + "_contact", supportContactModel)
# Creating the cost model for a contact phase
costModel = crocoddyl.CostModelSum(self.state, self.actuation.nu)
if isinstance(comTask, np.ndarray):
comTrack = crocoddyl.CostModelCoMPosition(self.state, comTask, self.actuation.nu)
costModel.addCost("comTrack", comTrack, 1e6)
for i in supportFootIds:
cone = crocoddyl.FrictionCone(self.nsurf, self.mu, 4, False)
frictionCone = crocoddyl.CostModelContactFrictionCone(
self.state, crocoddyl.ActivationModelQuadraticBarrier(crocoddyl.ActivationBounds(cone.lb, cone.ub)),
cone, i, self.actuation.nu)
costModel.addCost(self.rmodel.frames[i].name + "_frictionCone", frictionCone, 1e1)
if swingFootTask is not None:
for i in swingFootTask:
xref = crocoddyl.FrameTranslation(i.frame, i.oMf.translation)
footTrack = crocoddyl.CostModelFrameTranslation(self.state, xref, self.actuation.nu)
costModel.addCost(self.rmodel.frames[i.frame].name + "_footTrack", footTrack, 1e6)
stateWeights = np.array([0.] * 3 + [500.] * 3 + [0.01] * (self.rmodel.nv - 6) + [10.] * 6 + [1.] *
(self.rmodel.nv - 6))
stateReg = crocoddyl.CostModelState(self.state,
crocoddyl.ActivationModelWeightedQuad(np.matrix(stateWeights**2).T),
self.rmodel.defaultState, self.actuation.nu)
ctrlReg = crocoddyl.CostModelControl(self.state, self.actuation.nu)
costModel.addCost("stateReg", stateReg, 1e1)
costModel.addCost("ctrlReg", ctrlReg, 1e-1)
lb = self.state.diff(0 * self.state.lb, self.state.lb)
ub = self.state.diff(0 * self.state.ub, self.state.ub)
stateBounds = crocoddyl.CostModelState(
self.state, crocoddyl.ActivationModelQuadraticBarrier(crocoddyl.ActivationBounds(lb, ub)),
0 * self.rmodel.defaultState, self.actuation.nu)
costModel.addCost("stateBounds", stateBounds, 1e3)
# Creating the action model for the KKT dynamics with simpletic Euler
# integration scheme
dmodel = crocoddyl.DifferentialActionModelContactFwdDynamics(self.state, self.actuation, contactModel,
costModel, 0., True)
model = crocoddyl.IntegratedActionModelEuler(dmodel, timeStep)
return model
CONTACTS = crocoddyl.ContactModelMultiple(ROBOT_STATE, ACTUATION.nu)
CONTACT_6D = crocoddyl.ContactModel6D(
ROBOT_STATE,
crocoddyl.FramePlacement(ROBOT_MODEL.getFrameId('r_sole'),
pinocchio.SE3.Random()), ACTUATION.nu,
pinocchio.utils.rand(2))
CONTACT_3D = crocoddyl.ContactModel3D(
ROBOT_STATE,
crocoddyl.FrameTranslation(ROBOT_MODEL.getFrameId('l_sole'),
pinocchio.SE3.Random().translation),
ACTUATION.nu, pinocchio.utils.rand(2))
CONTACTS.addContact("r_sole_contact", CONTACT_6D)
CONTACTS.addContact("l_sole_contact", CONTACT_3D)
COSTS = crocoddyl.CostModelSum(ROBOT_STATE, ACTUATION.nu, True)
frictionCone = crocoddyl.FrictionCone(np.matrix([0., 0., 1.]).T, 0.7, 4, False)
activation = crocoddyl.ActivationModelQuadraticBarrier(
crocoddyl.ActivationBounds(frictionCone.lb, frictionCone.ub))
COSTS.addCost(
"r_sole_friction_cone",
crocoddyl.CostModelContactFrictionCone(ROBOT_STATE, activation,
frictionCone,
ROBOT_MODEL.getFrameId('r_sole'),
ACTUATION.nu), 1.)
COSTS.addCost(
"l_sole_friction_cone",
crocoddyl.CostModelContactFrictionCone(ROBOT_STATE, activation,
frictionCone,
ROBOT_MODEL.getFrameId('l_sole'),
ACTUATION.nu), 1.)
MODEL = crocoddyl.DifferentialActionModelContactFwdDynamics(
def __init__(self, nx=12, nu=12, mu=0.8, log=True):
crocoddyl.ActionModelAbstract.__init__(self, crocoddyl.StateVector(nx),
nu, 1)
#:param state: state description,
#:param nu: dimension of control vector,
#:param nr: dimension of the cost-residual vector (default 1)
# Time step of the solver
self.dt = 0.02
# Mass of the robot
self.mass = 2.97784899
# Inertia matrix of the robot in body frame (found in urdf)
self.gI = np.diag([0.00578574, 0.01938108, 0.02476124])
# Friction coefficient
self.mu = mu
# Matrix A -- X_k+1 = AX + BU --
self.A = np.zeros((12, 12))
# Matrix B
self.B = np.zeros((12, 12))
# Vector xref
self.xref = np.zeros(12)
# Vector g
self.g = np.zeros((12, ))
# Weight vector for the state
self.stateWeight = np.full(12, 2)
# Weight on the friction cost
self.frictionWeight = 0.1
# Weight on the command forces
self.weightForces = np.full(12, 0.1)
# Levers Arms used in B
self.lever_arms = np.zeros((3, 4))
# Initial position of footholds in the "straight standing" default configuration
# footholds = [[ px_foot1 , px_foot2 ... ] ,
# [ py_foot1 , py_foot2 ... ] ,
# [ pz_foot1 , pz_foot2 ... ] ] 2D -- pz = 0
self.footholds = np.array([[0.19, 0.19, -0.19, -0.19],
[0.15005, -0.15005, 0.15005, -0.15005],
[0.0, 0.0, 0.0, 0.0]])
# S matrix
# Represents the feet that are in contact with the ground such as :
# S = [1 0 0 1] --> FL(Front Left) in contact, FR not , HL not , HR in contact
self.S = np.ones(4)
# List of the feet in contact with the ground used to compute B
# if S = [1 0 0 1] ; L_feet = [1 1 1 0 0 0 0 0 0 1 1 1]
self.L_feet = np.zeros(12)
# Cone crocoddyl class
R = np.identity(3) # Rotation matrix wrt inertial frame
number_facets = 4 # Number of facets for cone approximation
self.cone = crocoddyl.FrictionCone(R, self.mu, number_facets, False)
self.lb = np.tile(self.cone.lb, 4)
self.ub = np.tile(self.cone.ub, 4)
# Matrice Fa of the cone class, repeated 4 times (4 feet)
self.Fa = np.zeros((20, 12))
# Inequality activation model.
# The activation is zero when r is between the lower (lb) and upper (ub) bounds, beta
# determines how much of the total range is not activated. This is the activation
# equations:
# a(r) = 0.5 * ||r||^2 for lb < r < ub
# a(r) = 0. for lb >= r >= ub.
self.activation = crocoddyl.ActivationModelQuadraticBarrier(
(crocoddyl.ActivationBounds(self.lb, self.ub)))
self.dataCost = self.activation.createData()
self.Lu_f = np.zeros(12)
self.Luu_f = np.zeros((12, 12))
# Log parameters
self.log = log
self.log_cost_friction = []
self.log_cost_state = []
self.log_state = []
self.log_u = []
# Other dynamic models
self.I_inv = np.zeros((3, 3))
self.derivative_B = np.zeros(
(12, 12)) # Here lever arm is constant, not used
def createSwingFootModel(self, timeStep, supportFootIds, comTask=None, swingFootTask=None):
""" Action model for a swing foot phase.
:param timeStep: step duration of the action model
:param supportFootIds: Ids of the constrained feet
:param comTask: CoM task
:param swingFootTask: swinging foot task
:return action model for a swing foot phase
"""
# Creating a 3D multi-contact model, and then including the supporting
# foot
nu = self.actuation.nu
contactModel = crocoddyl.ContactModelMultiple(self.state, nu)
for i in supportFootIds:
supportContactModel = crocoddyl.ContactModel3D(self.state, i, np.array([0., 0., 0.]), nu,
np.array([0., 50.]))
contactModel.addContact(self.rmodel.frames[i].name + "_contact", supportContactModel)
# Creating the cost model for a contact phase
costModel = crocoddyl.CostModelSum(self.state, nu)
if isinstance(comTask, np.ndarray):
comResidual = crocoddyl.ResidualModelCoMPosition(self.state, comTask, nu)
comTrack = crocoddyl.CostModelResidual(self.state, comResidual)
costModel.addCost("comTrack", comTrack, 1e6)
for i in supportFootIds:
cone = crocoddyl.FrictionCone(self.Rsurf, self.mu, 4, False)
coneResidual = crocoddyl.ResidualModelContactFrictionCone(self.state, i, cone, nu)
coneActivation = crocoddyl.ActivationModelQuadraticBarrier(crocoddyl.ActivationBounds(cone.lb, cone.ub))
frictionCone = crocoddyl.CostModelResidual(self.state, coneActivation, coneResidual)
costModel.addCost(self.rmodel.frames[i].name + "_frictionCone", frictionCone, 1e1)
if swingFootTask is not None:
for i in swingFootTask:
frameTranslationResidual = crocoddyl.ResidualModelFrameTranslation(self.state, i[0], i[1].translation,
nu)
footTrack = crocoddyl.CostModelResidual(self.state, frameTranslationResidual)
costModel.addCost(self.rmodel.frames[i[0]].name + "_footTrack", footTrack, 1e6)
stateWeights = np.array([0.] * 3 + [500.] * 3 + [0.01] * (self.rmodel.nv - 6) + [10.] * 6 + [1.] *
(self.rmodel.nv - 6))
stateResidual = crocoddyl.ResidualModelState(self.state, self.rmodel.defaultState, nu)
stateActivation = crocoddyl.ActivationModelWeightedQuad(stateWeights**2)
ctrlResidual = crocoddyl.ResidualModelControl(self.state, nu)
stateReg = crocoddyl.CostModelResidual(self.state, stateActivation, stateResidual)
ctrlReg = crocoddyl.CostModelResidual(self.state, ctrlResidual)
costModel.addCost("stateReg", stateReg, 1e1)
costModel.addCost("ctrlReg", ctrlReg, 1e-1)
lb = np.concatenate([self.state.lb[1:self.state.nv + 1], self.state.lb[-self.state.nv:]])
ub = np.concatenate([self.state.ub[1:self.state.nv + 1], self.state.ub[-self.state.nv:]])
stateBoundsResidual = crocoddyl.ResidualModelState(self.state, nu)
stateBoundsActivation = crocoddyl.ActivationModelQuadraticBarrier(crocoddyl.ActivationBounds(lb, ub))
stateBounds = crocoddyl.CostModelResidual(self.state, stateBoundsActivation, stateBoundsResidual)
costModel.addCost("stateBounds", stateBounds, 1e3)
# Creating the action model for the KKT dynamics with simpletic Euler
# integration scheme
dmodel = crocoddyl.DifferentialActionModelContactFwdDynamics(self.state, self.actuation, contactModel,
costModel, 0., True)
if self.integrator == 'euler':
model = crocoddyl.IntegratedActionModelEuler(dmodel, self.control, timeStep)
elif self.integrator == 'rk4':
model = crocoddyl.IntegratedActionModelRK(dmodel, self.control, crocoddyl.RKType.four, timeStep)
elif self.integrator == 'rk3':
model = crocoddyl.IntegratedActionModelRK(dmodel, self.control, crocoddyl.RKType.three, timeStep)
elif self.integrator == 'rk2':
model = crocoddyl.IntegratedActionModelRK(dmodel, self.control, crocoddyl.RKType.two, timeStep)
else:
model = crocoddyl.IntegratedActionModelEuler(dmodel, self.control, timeStep)
return model
contact_location = crocoddyl.FrameTranslation(footFrameID,
np.array([0., 0., 0.]))
supportContactModel = crocoddyl.ContactModel2D(
state, contact_location, actuation.nu,
np.array([0.,
1 / dt])) # makes the velocity drift disappear in one timestep
contactModel.addContact("foot_contact", supportContactModel)
# FRICTION CONE
# the friction cone can also have the [min, maximum] force parameters
# 4 is the number of faces for the approximation
mu = 0.7
normalDirection = np.array([0, 0, 1])
minForce = 0
maxForce = 200
cone = crocoddyl.FrictionCone(normalDirection, mu, 4, True, minForce, maxForce)
coneBounds = crocoddyl.ActivationBounds(cone.lb, cone.ub)
coneActivation = crocoddyl.ActivationModelWeightedQuadraticBarrier(
coneBounds, np.array([1, 1, 0, 0]))
frameFriction = crocoddyl.FrameFrictionCone(footFrameID, cone)
frictionCone = crocoddyl.CostModelContactFrictionCone(state, coneActivation,
frameFriction,
actuation.nu)
# Creating the action model for the KKT dynamics with simpletic Euler integration scheme
contactCostModel = crocoddyl.CostModelSum(state, actuation.nu)
# contactCostModel.addCost('frictionCone', frictionCone, 1e-6)
contactCostModel.addCost('joule_dissipation', joule_dissipation, 5e-3)
contactCostModel.addCost('joint_friction', joint_friction, 5e-3)
contactCostModel.addCost('velocityRegularization', v2, 1e-1)
contactCostModel.addCost('nonPenetration', nonPenetration, 1e5)
