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Huawei wang homotopy direct collocation #40

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Huawei wang homotopy direct collocation #40

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Update direct collocation
HuaweiWang May 19, 2016
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Update direct collocation
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Update direct collocation
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Update direct collocation
HuaweiWang May 19, 2016
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Make the homotopy method more general
HuaweiWang May 20, 2016
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Update homotopy codes and unit test codes
HuaweiWang May 23, 2016
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Update homotopy codes and unit test codes
HuaweiWang May 23, 2016
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Update homotopy codes and unit test codes
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Update unit test codes
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Wrong update before
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Wrong update before
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Update Direct Collocation Unit Testing Codes
HuaweiWang May 24, 2016
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Homotopy file
HuaweiWang Aug 18, 2016
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36 changes: 34 additions & 2 deletions opty/direct_collocation.py
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Original file line number Diff line number Diff line change
Expand Up @@ -137,6 +137,7 @@ class ConstraintCollocator(object):
def __init__(self, equations_of_motion, state_symbols,
num_collocation_nodes, node_time_interval,
known_parameter_map={}, known_trajectory_map={},
homotopy_control, tracing_dynamic_control,
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Please make these as keyword arguments with defaults settings: homotopy=0, tracing=1.

instance_constraints=None, time_symbol=None, tmp_dir=None,
integration_method='backward euler'):
"""
Expand Down Expand Up @@ -166,6 +167,12 @@ def __init__(self, equations_of_motion, state_symbols,
ndarrays of floats of shape(N,). Any time varying parameters in
the equations of motion not provided in this dictionary will
become free trajectories optimization variables.
homotopy_control: float, optional
A parameter in homotopy method that controls the change of
motion equations.
tracing_dynamic_control: float, optional
A parameter in homotopy method that adjust the dynamics of extra
'data tracing' term.
integration_method : string, optional
The integration method to use, either `backward euler` or
`midpoint`.
Expand All @@ -188,7 +195,13 @@ def __init__(self, equations_of_motion, state_symbols,
to a directory here.

"""
self.eom = equations_of_motion
Lamda_matrix = sym.zeros(num_states)
Lamda_matrix[num_states/2:, num_states/2:] = homotopy_control * sym.eye(num_states/2)

k_matrix = sym.zeros(num_states)
k_matrix[num_states/2:, num_states/2:] = tracing_dynamic_control * sym.eye(num_states/2)

# self.eom = equations_of_motion
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delete this line


if time_symbol is not None:
self.time_symbol = time_symbol
Expand All @@ -205,13 +218,32 @@ def __init__(self, equations_of_motion, state_symbols,

self.known_parameter_map = known_parameter_map
self.known_trajectory_map = known_trajectory_map

self.num_know_trajectory_map = len(self.known_trajectory_map)

self.instance_constraints = instance_constraints

self.num_constraints = self.num_states * (num_collocation_nodes - 1)

self.tmp_dir = tmp_dir

self.eom = (1-Lamda_matrix)*equations_of_motion + Lamda_matrix
*(self.state_derivative_symbols - K_matrix*
(known_trajectory_map[self.num_know_trajectory_map
- self.num_states:]-self.state_symbols))
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I think this should be:

self.eom = (1-Lamda_matrix)*equations_of_motion + Lamda_matrix *(self.state_derivative_symbols - K_matrix*
          (sympy.Matrix([predefined symbols]) - self.num_states:]-self.state_symbols))

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If a given state is named x1, then we should create new symbols that mirror the states with a name x_1_m.

"""
add extra term in equations of motion, the goal is to have the following formula:
homotopy motion equations = [1 0 0 0 ] [f1(x, xd, p, r) ]
0 1 0 0 * f2(x, xd, p, r)
0 0 1-la 0 f3(x, xd, p, r)
[0 0 0 1-la] [f4(x, xd, p, r) ]

[0 0 0 0 ] [x1_dot] [e1] [x1]
+ 0 0 0 0 * ( x2_dot - K*( e2 - x2 ) )
0 0 la 0 x3_dot e3 x3
[0 0 0 la] [x4_dot] [e4] [x4]
"""

self._sort_parameters()
self._check_known_trajectories()
self._sort_trajectories()
Expand Down Expand Up @@ -409,7 +441,6 @@ def _discrete_symbols(self):
tuple([sym.Symbol(f.__class__.__name__ + 'n', real=True)
for f in self.known_input_trajectories])


# The current and next unknown input trajectories.
self.current_unknown_discrete_specified_symbols = \
tuple([sym.Symbol(f.__class__.__name__ + 'i', real=True)
Expand Down Expand Up @@ -460,6 +491,7 @@ def _discretize_eom(self):
xdot_sub = {d: (n - i) / h for d, i, n in zip(xd, xi, xn)}
x_sub = {d: (i + n) / 2 for d, i, n in zip(x, xi, xn)}
u_sub = {d: (i + n) / 2 for d, i, n in zip(u, ui, un)}

self.discrete_eom = me.msubs(self.eom, xdot_sub, x_sub, u_sub)

def _identify_functions_in_instance_constraints(self):
Expand Down