def cartpole():
# Loading the double pendulum model
robot = example_robot_data.loadDoublePendulum()
robot_model = robot.model
state = crocoddyl.StateMultibody(robot_model)
actModel = ActuationModelDoublePendulum(state, actLink=1)
weights = np.array([1, 1, 1, 1] + [0.1] * 2)
runningCostModel = crocoddyl.CostModelSum(state, actModel.nu)
terminalCostModel = crocoddyl.CostModelSum(state, actModel.nu)
xRegCost = crocoddyl.CostModelState(
state, crocoddyl.ActivationModelQuad(state.ndx), state.zero(),
actModel.nu)
uRegCost = crocoddyl.CostModelControl(state,
crocoddyl.ActivationModelQuad(1),
actModel.nu)
xPendCost = CostModelDoublePendulum(
state, crocoddyl.ActivationModelWeightedQuad(np.matrix(weights).T),
actModel.nu)
dt = 1e-2
runningCostModel.addCost("uReg", uRegCost, 1e-4 / dt)
runningCostModel.addCost("xGoal", xPendCost, 1e-5 / dt)
terminalCostModel.addCost("xGoal", xPendCost, 1e4)
runningModel = crocoddyl.IntegratedActionModelEuler(
crocoddyl.DifferentialActionModelFreeFwdDynamics(
state, actModel, runningCostModel), dt)
terminalModel = crocoddyl.IntegratedActionModelEuler(
crocoddyl.DifferentialActionModelFreeFwdDynamics(
state, actModel, terminalCostModel), dt)
return runningModel, terminalModel
def runBenchmark(model):
robot_model = ROBOT.model
q0 = np.matrix([0.173046, 1., -0.52366, 0., 0., 0.1, -0.005]).T
x0 = np.vstack([q0, np.zeros((robot_model.nv, 1))])
# Note that we need to include a cost model (i.e. set of cost functions) in
# order to fully define the action model for our optimal control problem.
# For this particular example, we formulate three running-cost functions:
# goal-tracking cost, state and control regularization; and one terminal-cost:
# goal cost. First, let's create the common cost functions.
state = crocoddyl.StateMultibody(robot_model)
Mref = crocoddyl.FramePlacement(
robot_model.getFrameId("gripper_left_joint"),
pinocchio.SE3(np.eye(3), np.matrix([[.0], [.0], [.4]])))
goalTrackingCost = crocoddyl.CostModelFramePlacement(state, Mref)
xRegCost = crocoddyl.CostModelState(state)
uRegCost = crocoddyl.CostModelControl(state)
# Create a cost model per the running and terminal action model.
runningCostModel = crocoddyl.CostModelSum(state)
terminalCostModel = crocoddyl.CostModelSum(state)
# Then let's added the running and terminal cost functions
runningCostModel.addCost("gripperPose", goalTrackingCost, 1e-3)
runningCostModel.addCost("xReg", xRegCost, 1e-7)
runningCostModel.addCost("uReg", uRegCost, 1e-7)
terminalCostModel.addCost("gripperPose", goalTrackingCost, 1)
# Next, we need to create an action model for running and terminal knots. The
# forward dynamics (computed using ABA) are implemented
# inside DifferentialActionModelFullyActuated.
runningModel = crocoddyl.IntegratedActionModelEuler(
model(state, runningCostModel), 1e-3)
runningModel.differential.armature = np.matrix(
[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.]).T
terminalModel = crocoddyl.IntegratedActionModelEuler(
model(state, terminalCostModel), 1e-3)
terminalModel.differential.armature = np.matrix(
[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.]).T
# For this optimal control problem, we define 100 knots (or running action
# models) plus a terminal knot
problem = crocoddyl.ShootingProblem(x0, [runningModel] * N, terminalModel)
# Creating the DDP solver for this OC problem, defining a logger
ddp = crocoddyl.SolverDDP(problem)
duration = []
for i in range(T):
c_start = time.time()
ddp.solve([], [], MAXITER)
c_end = time.time()
duration.append(1e3 * (c_end - c_start))
avrg_duration = sum(duration) / len(duration)
min_duration = min(duration)
max_duration = max(duration)
return avrg_duration, min_duration, max_duration
def createProblem(model):
robot_model = ROBOT.model
q0 = np.matrix([0.173046, 1., -0.52366, 0., 0., 0.1, -0.005]).T
x0 = np.vstack([q0, np.zeros((robot_model.nv, 1))])
# Note that we need to include a cost model (i.e. set of cost functions) in
# order to fully define the action model for our optimal control problem.
# For this particular example, we formulate three running-cost functions:
# goal-tracking cost, state and control regularization; and one terminal-cost:
# goal cost. First, let's create the common cost functions.
state = crocoddyl.StateMultibody(robot_model)
Mref = crocoddyl.FramePlacement(
robot_model.getFrameId("gripper_left_joint"),
pinocchio.SE3(np.eye(3), np.matrix([[.0], [.0], [.4]])))
goalTrackingCost = crocoddyl.CostModelFramePlacement(state, Mref)
xRegCost = crocoddyl.CostModelState(state)
uRegCost = crocoddyl.CostModelControl(state)
# Create a cost model per the running and terminal action model.
runningCostModel = crocoddyl.CostModelSum(state)
terminalCostModel = crocoddyl.CostModelSum(state)
# Then let's added the running and terminal cost functions
runningCostModel.addCost("gripperPose", goalTrackingCost, 1)
runningCostModel.addCost("xReg", xRegCost, 1e-4)
runningCostModel.addCost("uReg", uRegCost, 1e-4)
terminalCostModel.addCost("gripperPose", goalTrackingCost, 1)
# Next, we need to create an action model for running and terminal knots. The
# forward dynamics (computed using ABA) are implemented
# inside DifferentialActionModelFullyActuated.
actuation = crocoddyl.ActuationModelFull(state)
runningModel = crocoddyl.IntegratedActionModelEuler(
model(state, actuation, runningCostModel), 1e-3)
runningModel.differential.armature = np.matrix(
[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.]).T
terminalModel = crocoddyl.IntegratedActionModelEuler(
model(state, actuation, terminalCostModel), 1e-3)
terminalModel.differential.armature = np.matrix(
[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.]).T
# For this optimal control problem, we define 100 knots (or running action
# models) plus a terminal knot
problem = crocoddyl.ShootingProblem(x0, [runningModel] * N, terminalModel)
xs = [x0] * (len(problem.runningModels) + 1)
us = [
m.quasiStatic(d, x0)
for m, d in list(zip(problem.runningModels, problem.runningDatas))
]
return xs, us, problem
class TalosArmIntegratedRK4Test(ActionModelAbstractTestCase):
ROBOT_MODEL = example_robot_data.load('talos_arm').model
STATE = crocoddyl.StateMultibody(ROBOT_MODEL)
ACTUATION = crocoddyl.ActuationModelFull(STATE)
COST_SUM = crocoddyl.CostModelSum(STATE)
COST_SUM.addCost(
'gripperPose',
crocoddyl.CostModelResidual(
STATE,
crocoddyl.ResidualModelFramePlacement(
STATE, ROBOT_MODEL.getFrameId("gripper_left_joint"),
pinocchio.SE3.Random())), 1e-3)
COST_SUM.addCost(
"xReg",
crocoddyl.CostModelResidual(STATE,
crocoddyl.ResidualModelState(STATE)), 1e-7)
COST_SUM.addCost(
"uReg",
crocoddyl.CostModelResidual(STATE,
crocoddyl.ResidualModelControl(STATE)),
1e-7)
DIFFERENTIAL = crocoddyl.DifferentialActionModelFreeFwdDynamics(
STATE, ACTUATION, COST_SUM)
MODEL = crocoddyl.IntegratedActionModelRK(DIFFERENTIAL,
crocoddyl.RKType.four, 1e-3)
MODEL_DER = IntegratedActionModelRK4Derived(DIFFERENTIAL, 1e-3)
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 swingFootTask: swinging foot task
:return pseudo-impulse differential action model
"""
# Creating a 6D multi-contact model, and then including the supporting
# foot
contactModel = crocoddyl.ContactModelMultiple(self.state,
self.actuation.nu)
for i in supportFootIds:
Mref = crocoddyl.FramePlacement(i, pinocchio.SE3.Identity())
supportContactModel = crocoddyl.ContactModel6D(
self.state, Mref, self.actuation.nu, np.array([0., 0.]))
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.WrenchCone(np.identity(3), self.mu,
np.array([0.1, 0.05]))
wrenchCone = crocoddyl.CostModelContactWrenchCone(
self.state,
crocoddyl.ActivationModelQuadraticBarrier(
crocoddyl.ActivationBounds(cone.lb, cone.ub)),
crocoddyl.FrameWrenchCone(i, cone), self.actuation.nu)
costModel.addCost(self.rmodel.frames[i].name + "_wrenchCone",
wrenchCone, 1e1)
if swingFootTask is not None:
for i in swingFootTask:
footTrack = crocoddyl.CostModelFramePlacement(
self.state, i, self.actuation.nu)
costModel.addCost(self.rmodel.frames[i.id].name + "_footTrack",
footTrack, 1e8)
footVel = crocoddyl.FrameMotion(i.id, pinocchio.Motion.Zero())
impulseFootVelCost = crocoddyl.CostModelFrameVelocity(
self.state, footVel, self.actuation.nu)
costModel.addCost(
self.rmodel.frames[i.id].name + "_impulseVel",
impulseFootVelCost, 1e6)
stateWeights = np.array([0] * 3 + [500.] * 3 + [0.01] *
(self.state.nv - 6) + [10] * self.state.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 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
class TalosArmShootingTest(ShootingProblemTestCase):
ROBOT_MODEL = example_robot_data.load('talos_arm').model
STATE = crocoddyl.StateMultibody(ROBOT_MODEL)
ACTUATION = crocoddyl.ActuationModelFull(STATE)
COST_SUM = crocoddyl.CostModelSum(STATE)
COST_SUM.addCost(
'gripperPose',
crocoddyl.CostModelResidual(
STATE,
crocoddyl.ResidualModelFramePlacement(
STATE, ROBOT_MODEL.getFrameId("gripper_left_joint"),
pinocchio.SE3.Random())), 1e-3)
COST_SUM.addCost(
"xReg",
crocoddyl.CostModelResidual(STATE,
crocoddyl.ResidualModelState(STATE)), 1e-7)
COST_SUM.addCost(
"uReg",
crocoddyl.CostModelResidual(STATE,
crocoddyl.ResidualModelControl(STATE)),
1e-7)
DIFF_MODEL = crocoddyl.DifferentialActionModelFreeFwdDynamics(
STATE, ACTUATION, COST_SUM)
DIFF_MODEL_DER = DifferentialFreeFwdDynamicsModelDerived(
STATE, ACTUATION, COST_SUM)
MODEL = crocoddyl.IntegratedActionModelEuler(DIFF_MODEL, 1e-3)
MODEL_DER = crocoddyl.IntegratedActionModelEuler(DIFF_MODEL_DER, 1e-3)
def createImpulseModel(self, supportFootIds, swingFootTask, JMinvJt_damping=1e-12, r_coeff=0.0):
""" Action model for impulse models.
An impulse model consists of describing the impulse dynamics against a set of contacts.
:param supportFootIds: Ids of the constrained feet
:param swingFootTask: swinging foot task
:return impulse action model
"""
# Creating a 3D multi-contact model, and then including the supporting foot
impulseModel = crocoddyl.ImpulseModelMultiple(self.state)
for i in supportFootIds:
supportContactModel = crocoddyl.ImpulseModel3D(self.state, i)
impulseModel.addImpulse(self.rmodel.frames[i].name + "_impulse", supportContactModel)
# Creating the cost model for a contact phase
costModel = crocoddyl.CostModelSum(self.state, 0)
if swingFootTask is not None:
for i in swingFootTask:
xref = crocoddyl.FrameTranslation(i.id, i.placement.translation)
footTrack = crocoddyl.CostModelFrameTranslation(self.state, xref, 0)
costModel.addCost(self.rmodel.frames[i.id].name + "_footTrack", footTrack, 1e7)
stateWeights = np.array([1.] * 6 + [10.] * (self.rmodel.nv - 6) + [10.] * self.rmodel.nv)
stateReg = crocoddyl.CostModelState(self.state, crocoddyl.ActivationModelWeightedQuad(stateWeights**2),
self.rmodel.defaultState, 0)
costModel.addCost("stateReg", stateReg, 1e1)
# Creating the action model for the KKT dynamics with simpletic Euler
# integration scheme
model = crocoddyl.ActionModelImpulseFwdDynamics(self.state, impulseModel, costModel)
model.JMinvJt_damping = JMinvJt_damping
model.r_coeff = r_coeff
return model
class TalosArmFreeFwdDynamicsWithArmatureTest(ActionModelAbstractTestCase):
ROBOT_MODEL = example_robot_data.load('talos_arm').model
STATE = crocoddyl.StateMultibody(ROBOT_MODEL)
ACTUATION = crocoddyl.ActuationModelFull(STATE)
COST_SUM = crocoddyl.CostModelSum(STATE)
COST_SUM.addCost(
'gripperPose',
crocoddyl.CostModelResidual(
STATE,
crocoddyl.ResidualModelFramePlacement(
STATE, ROBOT_MODEL.getFrameId("gripper_left_joint"),
pinocchio.SE3.Random())), 1e-3)
COST_SUM.addCost(
"xReg",
crocoddyl.CostModelResidual(STATE,
crocoddyl.ResidualModelState(STATE)), 1e-7)
COST_SUM.addCost(
"uReg",
crocoddyl.CostModelResidual(STATE,
crocoddyl.ResidualModelControl(STATE)),
1e-7)
MODEL = crocoddyl.DifferentialActionModelFreeFwdDynamics(
STATE, ACTUATION, COST_SUM)
MODEL_DER = DifferentialFreeFwdDynamicsModelDerived(
STATE, ACTUATION, COST_SUM)
MODEL.armature = 0.1 * np.ones(ROBOT_MODEL.nv)
MODEL_DER.set_armature(0.1 * np.ones(ROBOT_MODEL.nv))
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
class AnymalFreeFwdDynamicsTest(ActionModelAbstractTestCase):
ROBOT_MODEL = example_robot_data.loadANYmal().model
STATE = crocoddyl.StateMultibody(ROBOT_MODEL)
ACTUATION = crocoddyl.ActuationModelFloatingBase(STATE)
COST_SUM = crocoddyl.CostModelSum(STATE, ACTUATION.nu)
COST_SUM.addCost("xReg", crocoddyl.CostModelState(STATE, ACTUATION.nu), 1e-7)
COST_SUM.addCost("uReg", crocoddyl.CostModelControl(STATE, ACTUATION.nu), 1e-7)
MODEL = crocoddyl.DifferentialActionModelFreeFwdDynamics(STATE, ACTUATION, COST_SUM)
MODEL_DER = DifferentialFreeFwdDynamicsDerived(STATE, ACTUATION, COST_SUM)
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
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 6D multi-contact model, and then including the supporting
# foot
contactModel = crocoddyl.ContactModelMultiple(self.state,
self.actuation.nu)
for i in supportFootIds:
Mref = crocoddyl.FramePlacement(i, pinocchio.SE3.Identity())
supportContactModel = \
crocoddyl.ContactModel6D(self.state, Mref, self.actuation.nu, np.matrix([0., 0.]).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)
if swingFootTask is not None:
for i in swingFootTask:
footTrack = crocoddyl.CostModelFramePlacement(
self.state, i, self.actuation.nu)
costModel.addCost(
self.rmodel.frames[i.frame].name + "_footTrack", footTrack,
1e6)
stateWeights = np.array([0] * 3 + [500.] * 3 + [0.01] *
(self.state.nv - 6) + [10] * self.state.nv)
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)
# Creating the action model for the KKT dynamics with simpletic Euler
# integration scheme
dmodel = crocoddyl.DifferentialActionModelContactFwdDynamics(
self.state, self.actuation, contactModel, costModel)
model = crocoddyl.IntegratedActionModelEuler(dmodel, timeStep)
return model
def solver(starting_condition, T=30, precision=1e-9, maxiters=1000):
"""Solve one pendulum problem"""
robot = example_robot_data.loadDoublePendulum()
robot_model = robot.model
state = crocoddyl.StateMultibody(robot_model)
actModel = ActuationModelDoublePendulum(state, actLink=1)
weights = np.array([1.5, 1.5, 1, 1] + [0.1] * 2)
runningCostModel = crocoddyl.CostModelSum(state, actModel.nu)
dt = 1e-2
xRegCost = crocoddyl.CostModelState(
state, crocoddyl.ActivationModelQuad(state.ndx), state.zero(),
actModel.nu)
uRegCost = crocoddyl.CostModelControl(state,
crocoddyl.ActivationModelQuad(1),
actModel.nu)
xPendCost = CostModelDoublePendulum(
state, crocoddyl.ActivationModelWeightedQuad(weights), actModel.nu)
runningCostModel.addCost("uReg", uRegCost, 1e-4 / dt)
runningCostModel.addCost("xGoal", xPendCost, 1e-5 / dt)
runningModel = crocoddyl.IntegratedActionModelEuler(
crocoddyl.DifferentialActionModelFreeFwdDynamics(
state, actModel, runningCostModel), dt)
terminalCostModel = crocoddyl.CostModelSum(state, actModel.nu)
terminalCostModel.addCost("xGoal", xPendCost, 1e4)
terminal_model = crocoddyl.IntegratedActionModelEuler(
crocoddyl.DifferentialActionModelFreeFwdDynamics(
state, actModel, terminalCostModel), dt)
problem = crocoddyl.ShootingProblem(starting_condition, [runningModel] * T,
terminal_model)
fddp = crocoddyl.SolverFDDP(problem)
fddp.th_stop = precision
fddp.solve([], [], maxiters)
class AnymalIntegratedRK4Test(ActionModelAbstractTestCase):
ROBOT_MODEL = example_robot_data.load('anymal').model
STATE = crocoddyl.StateMultibody(ROBOT_MODEL)
ACTUATION = crocoddyl.ActuationModelFloatingBase(STATE)
COST_SUM = crocoddyl.CostModelSum(STATE, ACTUATION.nu)
COST_SUM.addCost("xReg", crocoddyl.CostModelResidual(STATE, crocoddyl.ResidualModelState(STATE, ACTUATION.nu)),
1e-7)
COST_SUM.addCost("uReg", crocoddyl.CostModelResidual(STATE, crocoddyl.ResidualModelControl(STATE, ACTUATION.nu)),
1e-7)
DIFFERENTIAL = crocoddyl.DifferentialActionModelFreeFwdDynamics(STATE, ACTUATION, COST_SUM)
MODEL = crocoddyl.IntegratedActionModelRK4(DIFFERENTIAL, 1e-3)
MODEL_DER = IntegratedActionModelRK4Derived(DIFFERENTIAL, 1e-3)
class FreeFwdDynamicsTest(ActionModelAbstractTestCase):
ROBOT_MODEL = pinocchio.buildSampleModelManipulator()
STATE = crocoddyl.StateMultibody(ROBOT_MODEL)
COST_SUM = crocoddyl.CostModelSum(STATE, ROBOT_MODEL.nv)
COST_SUM.addCost('xReg', crocoddyl.CostModelState(STATE), 1.)
COST_SUM.addCost(
'frTrack',
crocoddyl.CostModelFramePlacement(
STATE,
crocoddyl.FramePlacement(ROBOT_MODEL.getFrameId("effector_body"),
pinocchio.SE3.Random())), 1.)
MODEL = crocoddyl.DifferentialActionModelFreeFwdDynamics(STATE, COST_SUM)
MODEL_DER = DifferentialFreeFwdDynamicsDerived(STATE, COST_SUM)
def createFootSwitchModel(self, supportFootIds, swingFootTask):
""" Action model for a foot switch phase.
:param supportFootIds: Ids of the constrained feet
:param swingFootTask: swinging foot task
:return action model for a foot switch 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., 0.]).T)
contactModel.addContact('contact_' + str(i), supportContactModel)
# Creating the cost model for a contact phase
costModel = crocoddyl.CostModelSum(self.state, self.actuation.nu)
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("footTrack_" + str(i), footTrack, 1e7)
stateWeights = np.array([0] * 3 + [500.] * 3 + [0.01] *
(self.rmodel.nv - 6) + [10] * self.rmodel.nv)
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-3)
for i in swingFootTask:
vref = crocoddyl.FrameMotion(i.frame, pinocchio.Motion.Zero())
impactFootVelCost = crocoddyl.CostModelFrameVelocity(
self.state, vref, self.actuation.nu)
costModel.addCost('impactVel_' + str(i.frame), impactFootVelCost,
1e6)
# Creating the action model for the KKT dynamics with simpletic Euler
# integration scheme
dmodel = crocoddyl.DifferentialActionModelContactFwdDynamics(
self.state, self.actuation, contactModel, costModel)
model = crocoddyl.IntegratedActionModelEuler(dmodel, 0.)
return model
class TalosArmFreeFwdDynamicsTest(ActionModelAbstractTestCase):
ROBOT_MODEL = example_robot_data.loadTalosArm().model
STATE = crocoddyl.StateMultibody(ROBOT_MODEL)
ACTUATION = crocoddyl.ActuationModelFull(STATE)
COST_SUM = crocoddyl.CostModelSum(STATE)
COST_SUM.addCost(
'gripperPose',
crocoddyl.CostModelFramePlacement(
STATE, crocoddyl.FramePlacement(ROBOT_MODEL.getFrameId("gripper_left_joint"), pinocchio.SE3.Random())),
1e-3)
COST_SUM.addCost("xReg", crocoddyl.CostModelState(STATE), 1e-7)
COST_SUM.addCost("uReg", crocoddyl.CostModelControl(STATE), 1e-7)
MODEL = crocoddyl.DifferentialActionModelFreeFwdDynamics(STATE, ACTUATION, COST_SUM)
MODEL_DER = DifferentialFreeFwdDynamicsDerived(STATE, ACTUATION, COST_SUM)
class ManipulatorDDPTest(SolverAbstractTestCase):
ROBOT_MODEL = pinocchio.buildSampleModelManipulator()
STATE = crocoddyl.StateMultibody(ROBOT_MODEL)
COST_SUM = crocoddyl.CostModelSum(STATE, ROBOT_MODEL.nv)
COST_SUM.addCost('xReg', crocoddyl.CostModelState(STATE), 1e-7)
COST_SUM.addCost('uReg', crocoddyl.CostModelControl(STATE), 1e-7)
COST_SUM.addCost(
'frTrack',
crocoddyl.CostModelFramePlacement(
STATE, crocoddyl.FramePlacement(ROBOT_MODEL.getFrameId("effector_body"), pinocchio.SE3.Random())), 1.)
DIFF_MODEL = crocoddyl.DifferentialActionModelFreeFwdDynamics(STATE, COST_SUM)
MODEL = crocoddyl.IntegratedActionModelEuler(crocoddyl.DifferentialActionModelFreeFwdDynamics(STATE, COST_SUM),
1e-3)
SOLVER = crocoddyl.SolverDDP
SOLVER_DER = DDPDerived
def setUp(self):
self.robot_data = self.ROBOT_MODEL.createData()
self.x = self.ROBOT_STATE.rand()
self.u = pinocchio.utils.rand(self.ROBOT_MODEL.nv)
self.cost_sum = crocoddyl.CostModelSum(self.ROBOT_STATE)
self.cost_sum.addCost('myCost', self.COST, 1.)
self.multibody_data = crocoddyl.DataCollectorMultibody(self.robot_data)
self.data = self.COST.createData(self.multibody_data)
self.data_sum = self.cost_sum.createData(self.multibody_data)
nq, nv = self.ROBOT_MODEL.nq, self.ROBOT_MODEL.nv
pinocchio.forwardKinematics(self.ROBOT_MODEL, self.robot_data, self.x[:nq], self.x[nq:])
pinocchio.computeForwardKinematicsDerivatives(self.ROBOT_MODEL, self.robot_data, self.x[:nq], self.x[nq:],
pinocchio.utils.zero(nv))
pinocchio.computeJointJacobians(self.ROBOT_MODEL, self.robot_data, self.x[:nq])
pinocchio.updateFramePlacements(self.ROBOT_MODEL, self.robot_data)
pinocchio.jacobianCenterOfMass(self.ROBOT_MODEL, self.robot_data, self.x[:nq], False)
class TalosArmFDDPTest(SolverAbstractTestCase):
ROBOT_MODEL = example_robot_data.load('talos_arm').model
STATE = crocoddyl.StateMultibody(ROBOT_MODEL)
ACTUATION = crocoddyl.ActuationModelFull(STATE)
COST_SUM = crocoddyl.CostModelSum(STATE)
COST_SUM.addCost(
'gripperPose',
crocoddyl.CostModelFramePlacement(
STATE,
crocoddyl.FramePlacement(
ROBOT_MODEL.getFrameId("gripper_left_joint"),
pinocchio.SE3.Random())), 1e-3)
COST_SUM.addCost("xReg", crocoddyl.CostModelState(STATE), 1e-7)
COST_SUM.addCost("uReg", crocoddyl.CostModelControl(STATE), 1e-7)
DIFF_MODEL = crocoddyl.DifferentialActionModelFreeFwdDynamics(
STATE, ACTUATION, COST_SUM)
MODEL = crocoddyl.IntegratedActionModelEuler(DIFF_MODEL, 1e-3)
SOLVER = crocoddyl.SolverFDDP
SOLVER_DER = FDDPDerived
def createImpulseModel(self, supportFootIds, swingFootTask):
""" Action model for impulse models.
An impulse model consists of describing the impulse dynamics against a set of contacts.
:param supportFootIds: Ids of the constrained feet
:param swingFootTask: swinging foot task
:return impulse action model
"""
# Creating a 6D multi-contact model, and then including the supporting foot
impulseModel = crocoddyl.ImpulseModelMultiple(self.state)
for i in supportFootIds:
supportContactModel = crocoddyl.ImpulseModel6D(self.state, i)
impulseModel.addImpulse(self.rmodel.frames[i].name + "_impulse",
supportContactModel)
# Creating the cost model for a contact phase
costModel = crocoddyl.CostModelSum(self.state, 0)
if swingFootTask is not None:
for i in swingFootTask:
frameTranslationResidual = crocoddyl.ResidualModelFrameTranslation(
self.state, i[0], i[1].translation, 0)
footTrack = crocoddyl.CostModelResidual(
self.state, frameTranslationResidual)
costModel.addCost(self.rmodel.frames[i[0]].name + "_footTrack",
footTrack, 1e8)
stateWeights = np.array([1.] * 6 + [0.1] * (self.rmodel.nv - 6) +
[10] * self.rmodel.nv)
stateResidual = crocoddyl.ResidualModelState(self.state,
self.rmodel.defaultState,
0)
stateActivation = crocoddyl.ActivationModelWeightedQuad(
stateWeights**2)
stateReg = crocoddyl.CostModelResidual(self.state, stateActivation,
stateResidual)
costModel.addCost("stateReg", stateReg, 1e1)
# Creating the action model for the KKT dynamics with simpletic Euler
# integration scheme
model = crocoddyl.ActionModelImpulseFwdDynamics(
self.state, impulseModel, costModel)
return model
WITHPLOT = 'plot' in sys.argv or 'CROCODDYL_PLOT' in os.environ
crocoddyl.switchToNumpyMatrix()
# In this example test, we will solve the reaching-goal task with the Talos arm.
# For that, we use the forward dynamics (with its analytical derivatives)
# developed inside crocoddyl; it describes inside DifferentialActionModelFullyActuated class.
# Finally, we use an Euler sympletic integration scheme.
# First, let's load the Pinocchio model for the Talos arm.
talos_arm = example_robot_data.loadTalosArm()
robot_model = talos_arm.model
# Create a cost model per the running and terminal action model.
state = crocoddyl.StateMultibody(robot_model)
runningCostModel = crocoddyl.CostModelSum(state)
terminalCostModel = crocoddyl.CostModelSum(state)
# Note that we need to include a cost model (i.e. set of cost functions) in
# order to fully define the action model for our optimal control problem.
# For this particular example, we formulate three running-cost functions:
# goal-tracking cost, state and control regularization; and one terminal-cost:
# goal cost. First, let's create the common cost functions.
Mref = crocoddyl.FramePlacement(
robot_model.getFrameId("gripper_left_joint"),
pinocchio.SE3(np.eye(3), np.matrix([[.0], [.0], [.4]])))
goalTrackingCost = crocoddyl.CostModelFramePlacement(state, Mref)
xRegCost = crocoddyl.CostModelState(state)
uRegCost = crocoddyl.CostModelControl(state)
# Then let's added the running and terminal cost functions
def solve_problem(terminal_model=None,
initial_configuration=None,
horizon: int = 100,
precision: float = 1e-9,
maxiters: int = 1000):
"""
Solve the problem for a given initial_position.
@params:
1: terminal_model = Terminal model with neural network inside it, for the crocoddyl problem.
If none, then Crocoddyl Integrated Action Model will be used as terminal model.
2: initial_configuration = initial position for the unicycle,
either a list or a numpy array or a tensor.
3: horizon = Time horizon for the unicycle. Defaults to 100
4: stop = ddp.th_stop. Defaults to 1e-9
5: maxiters = maximum iterations allowed for crocoddyl.Defaults to 1000
@returns:
ddp
"""
if isinstance(initial_configuration, list):
initial_configuration = np.array(initial_configuration)
elif isinstance(initial_configuration, torch.Tensor):
initial_configuration = initial_configuration.numpy()
# Loading the double pendulum model
robot = example_robot_data.loadDoublePendulum()
robot_model = robot.model
state = crocoddyl.StateMultibody(robot_model)
actModel = ActuationModelDoublePendulum(state, actLink=1)
weights = np.array([1, 1, 1, 1] + [0.1] * 2)
runningCostModel = crocoddyl.CostModelSum(state, actModel.nu)
xRegCost = crocoddyl.CostModelState(
state, crocoddyl.ActivationModelQuad(state.ndx), state.zero(),
actModel.nu)
uRegCost = crocoddyl.CostModelControl(state,
crocoddyl.ActivationModelQuad(1),
actModel.nu)
xPendCost = CostModelDoublePendulum(
state, crocoddyl.ActivationModelWeightedQuad(np.matrix(weights).T),
actModel.nu)
dt = 1e-2
runningCostModel.addCost("uReg", uRegCost, 1e-4 / dt)
runningCostModel.addCost("xGoal", xPendCost, 1e-5 / dt)
runningModel = crocoddyl.IntegratedActionModelEuler(
crocoddyl.DifferentialActionModelFreeFwdDynamics(
state, actModel, runningCostModel), dt)
if terminal_model is None:
terminalCostModel = crocoddyl.CostModelSum(state, actModel.nu)
terminalCostModel.addCost("xGoal", xPendCost, 1e4)
terminal_model = crocoddyl.IntegratedActionModelEuler(
crocoddyl.DifferentialActionModelFreeFwdDynamics(
state, actModel, terminalCostModel), dt)
# Creating the shooting problem and the FDDP solver
problem = crocoddyl.ShootingProblem(initial_configuration.T,
[runningModel] * horizon,
terminal_model)
fddp = crocoddyl.SolverFDDP(problem)
fddp.th_stop = precision
fddp.solve([], [], maxiters)
return fddp
target_pos = np.array([1, 0, 1])
target_quat = pinocchio.Quaternion(1, 0, 0, 0)
state = crocoddyl.StateMultibody(robot_model)
d_cog = 0.1525
cf = 6.6e-5
cm = 1e-6
u_lim = 5
l_lim = 0.1
tau_f = np.array([[0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [1.0, 1.0, 1.0, 1.0], [0.0, d_cog, 0.0, -d_cog],
[-d_cog, 0.0, d_cog, 0.0], [-cm / cf, cm / cf, -cm / cf, cm / cf]])
actModel = crocoddyl.ActuationModelMultiCopterBase(state, 4, tau_f)
runningCostModel = crocoddyl.CostModelSum(state, actModel.nu)
terminalCostModel = crocoddyl.CostModelSum(state, actModel.nu)
# Needed objects to create the costs
Mref = crocoddyl.FramePlacement(robot_model.getFrameId("base_link"), pinocchio.SE3(target_quat.matrix(), target_pos))
wBasePos, wBaseOri, wBaseVel = 0.1, 1000, 1000
stateWeights = np.array([wBasePos] * 3 + [wBaseOri] * 3 + [wBaseVel] * robot_model.nv)
# Costs
goalTrackingCost = crocoddyl.CostModelFramePlacement(state, Mref, actModel.nu)
xRegCost = crocoddyl.CostModelState(state, crocoddyl.ActivationModelWeightedQuad(stateWeights), state.zero(),
actModel.nu)
uRegCost = crocoddyl.CostModelControl(state, actModel.nu)
runningCostModel.addCost("xReg", xRegCost, 1e-6)
runningCostModel.addCost("uReg", uRegCost, 1e-6)
runningCostModel.addCost("trackPose", goalTrackingCost, 1e-2)
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 6D 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.ContactModel6D(self.state, i,
pinocchio.SE3.Identity(),
nu, np.array([0., 0.]))
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.WrenchCone(self.Rsurf, self.mu,
np.array([0.1, 0.05]))
wrenchResidual = crocoddyl.ResidualModelContactWrenchCone(
self.state, i, cone, nu)
wrenchActivation = crocoddyl.ActivationModelQuadraticBarrier(
crocoddyl.ActivationBounds(cone.lb, cone.ub))
wrenchCone = crocoddyl.CostModelResidual(self.state,
wrenchActivation,
wrenchResidual)
costModel.addCost(self.rmodel.frames[i].name + "_wrenchCone",
wrenchCone, 1e1)
if swingFootTask is not None:
for i in swingFootTask:
framePlacementResidual = crocoddyl.ResidualModelFramePlacement(
self.state, i[0], i[1], nu)
footTrack = crocoddyl.CostModelResidual(
self.state, framePlacementResidual)
costModel.addCost(self.rmodel.frames[i[0]].name + "_footTrack",
footTrack, 1e6)
stateWeights = np.array([0] * 3 + [500.] * 3 + [0.01] *
(self.state.nv - 6) + [10] * self.state.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-1)
# 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
def optimalSolution(init_states: Union[list, np.ndarray, torch.Tensor],
terminal_model: crocoddyl.ActionModelAbstract = None,
horizon: int = 150,
precision: float = 1e-9,
maxiters: int = 1000,
use_fddp: bool = True):
"""Solve double pendulum problem with the given terminal model for the given position
Parameters
----------
init_states : list or array or tensor
These are the initial, starting configurations for the double pendulum
terminal_model: crocoddyl.ActionModelAbstract
The terminal model to be used to solve the problem
horizon : int
Time horizon for the running model
precision : float
precision for ddp.th_stop
maxiters : int
Maximum iterations allowed for the problem
use_fddp : boolean
Solve using ddp or fddp
Returns
--------
ddp : crocoddyl.Solverddp
the optimal ddp or fddp of the prblem
"""
if isinstance(init_states, torch.Tensor):
init_states = init_states.numpy()
init_states = np.atleast_2d(init_states)
solutions = []
for init_state in init_states:
robot = example_robot_data.loadDoublePendulum()
robot_model = robot.model
state = crocoddyl.StateMultibody(robot_model)
actModel = ActuationModelDoublePendulum(state, actLink=1)
weights = np.array([1.5, 1.5, 1, 1] + [0.1] * 2)
runningCostModel = crocoddyl.CostModelSum(state, actModel.nu)
dt = 1e-2
xRegCost = crocoddyl.CostModelState(
state, crocoddyl.ActivationModelQuad(state.ndx), state.zero(),
actModel.nu)
uRegCost = crocoddyl.CostModelControl(
state, crocoddyl.ActivationModelQuad(1), actModel.nu)
xPendCost = CostModelDoublePendulum(
state, crocoddyl.ActivationModelWeightedQuad(weights),
actModel.nu)
runningCostModel.addCost("uReg", uRegCost, 1e-4 / dt)
runningCostModel.addCost("xGoal", xPendCost, 1e-5 / dt)
runningModel = crocoddyl.IntegratedActionModelEuler(
crocoddyl.DifferentialActionModelFreeFwdDynamics(
state, actModel, runningCostModel), dt)
if terminal_model is None:
terminalCostModel = crocoddyl.CostModelSum(state, actModel.nu)
terminalCostModel.addCost("xGoal", xPendCost, 1e4)
terminal_model = crocoddyl.IntegratedActionModelEuler(
crocoddyl.DifferentialActionModelFreeFwdDynamics(
state, actModel, terminalCostModel), dt)
problem = crocoddyl.ShootingProblem(init_state,
[runningModel] * horizon,
terminal_model)
if use_fddp:
fddp = crocoddyl.SolverFDDP(problem)
else:
fddp = crocoddyl.SolverDDP(problem)
fddp.th_stop = precision
fddp.solve([], [], maxiters)
solutions.append(fddp)
return solutions
ROBOT_STATE = crocoddyl.StateMultibody(ROBOT_MODEL)
ACTUATION = crocoddyl.ActuationModelFloatingBase(ROBOT_STATE)
CONTACTS = crocoddyl.ContactModelMultiple(ROBOT_STATE, ACTUATION.nu)
CONTACT_6D_1 = crocoddyl.ContactModel6D(
ROBOT_STATE,
crocoddyl.FramePlacement(ROBOT_MODEL.getFrameId('r_sole'),
pinocchio.SE3.Random()), ACTUATION.nu,
pinocchio.utils.rand(2))
CONTACT_6D_2 = crocoddyl.ContactModel6D(
ROBOT_STATE,
crocoddyl.FramePlacement(ROBOT_MODEL.getFrameId('l_sole'),
pinocchio.SE3.Random()), ACTUATION.nu,
pinocchio.utils.rand(2))
CONTACTS.addContact("r_sole_contact", CONTACT_6D_1)
CONTACTS.addContact("l_sole_contact", CONTACT_6D_2)
COSTS = crocoddyl.CostModelSum(ROBOT_STATE, ACTUATION.nu, False)
COSTS.addCost(
"force",
crocoddyl.CostModelContactForce(
ROBOT_STATE,
crocoddyl.FrameForce(ROBOT_MODEL.getFrameId('r_sole'),
pinocchio.Force.Random()), ACTUATION.nu), 1.)
MODEL = crocoddyl.DifferentialActionModelContactFwdDynamics(
ROBOT_STATE, ACTUATION, CONTACTS, COSTS, 0., True)
DATA = MODEL.createData()
# Created DAM numdiff
MODEL_ND = crocoddyl.DifferentialActionModelNumDiff(MODEL)
dnum = MODEL_ND.createData()
x = ROBOT_STATE.rand()
# Create robot model and data
ROBOT_MODEL = example_robot_data.loadICub().model
ROBOT_DATA = ROBOT_MODEL.createData()
# Create differential action model and data; link the contact data
ROBOT_STATE = crocoddyl.StateMultibody(ROBOT_MODEL)
ACTUATION = crocoddyl.ActuationModelFloatingBase(ROBOT_STATE)
IMPULSES = crocoddyl.ImpulseModelMultiple(ROBOT_STATE)
IMPULSE_6D = crocoddyl.ImpulseModel6D(ROBOT_STATE,
ROBOT_MODEL.getFrameId('r_sole'))
IMPULSE_3D = crocoddyl.ImpulseModel3D(ROBOT_STATE,
ROBOT_MODEL.getFrameId('l_sole'))
IMPULSES.addImpulse("r_sole_impulse", IMPULSE_6D)
IMPULSES.addImpulse("l_sole_impulse", IMPULSE_3D)
COSTS = crocoddyl.CostModelSum(ROBOT_STATE, 0)
COSTS.addCost("impulse_com", crocoddyl.CostModelImpulseCoM(ROBOT_STATE), 1.)
MODEL = crocoddyl.ActionModelImpulseFwdDynamics(ROBOT_STATE, IMPULSES, COSTS,
0., 0., True)
DATA = MODEL.createData()
# Created DAM numdiff
MODEL_ND = crocoddyl.ActionModelNumDiff(MODEL)
MODEL_ND.disturbance *= 10
dnum = MODEL_ND.createData()
x = ROBOT_STATE.rand()
u = pinocchio.utils.rand(0) # (ACTUATION.nu)
MODEL.calc(DATA, x, u)
MODEL.calcDiff(DATA, x, u)
Pref = crocoddyl.FramePlacement(
leftFootId, pinocchio.SE3(np.eye(3), np.array([0., 0.4, 0.])))
footTrackingCost1 = crocoddyl.CostModelFramePlacement(
state, crocoddyl.ActivationModelWeightedQuad(footTrackingWeights**2), Pref,
actuation.nu)
Pref = crocoddyl.FramePlacement(
leftFootId, pinocchio.SE3(np.eye(3), np.array([0.3, 0.15, 0.35])))
footTrackingCost2 = crocoddyl.CostModelFramePlacement(
state, crocoddyl.ActivationModelWeightedQuad(footTrackingWeights**2), Pref,
actuation.nu)
# Cost for CoM reference
comTrack = crocoddyl.CostModelCoMPosition(state, comRef, actuation.nu)
# Create cost model per each action model. We divide the motion in 3 phases plus its terminal model
runningCostModel1 = crocoddyl.CostModelSum(state, actuation.nu)
runningCostModel2 = crocoddyl.CostModelSum(state, actuation.nu)
runningCostModel3 = crocoddyl.CostModelSum(state, actuation.nu)
terminalCostModel = crocoddyl.CostModelSum(state, actuation.nu)
# Then let's added the running and terminal cost functions
runningCostModel1.addCost("gripperPose", handTrackingCost, 1e2)
runningCostModel1.addCost("stateReg", xRegCost, 1e-3)
runningCostModel1.addCost("ctrlReg", uRegCost, 1e-4)
runningCostModel1.addCost("limitCost", limitCost, 1e3)
runningCostModel2.addCost("gripperPose", handTrackingCost, 1e2)
runningCostModel2.addCost("footPose", footTrackingCost1, 1e1)
runningCostModel2.addCost("stateReg", xRegCost, 1e-3)
runningCostModel2.addCost("ctrlReg", uRegCost, 1e-4)
runningCostModel2.addCost("limitCost", limitCost, 1e3)