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Add collocation method for optimal control problems #799

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Merged
merged 6 commits into from
Dec 2, 2022
Merged

Add collocation method for optimal control problems #799

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d9ec3ec
add trajectory_method='shooting'
murrayrm Nov 24, 2022
ce5e67a
add trajectory_method='collocation'
murrayrm Nov 24, 2022
8256fa0
set default trajectory_methood for ctime systems to collocation
murrayrm Nov 25, 2022
d121102
updated examples + code cleanup
murrayrm Nov 25, 2022
e0f71f4
update documentation + allow constraints in scipy.optimize form
murrayrm Nov 26, 2022
dd5e42d
add benchmarks for shooting vs collocation
murrayrm Nov 27, 2022
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38 changes: 21 additions & 17 deletions benchmarks/optimal_bench.py
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Original file line number Diff line number Diff line change
Expand Up @@ -35,6 +35,7 @@
'COBYLA': ('COBYLA', {}),
}


# Utility function to create a basis of a given size
def get_basis(name, size, Tf):
if name == 'poly':
Expand All @@ -43,14 +44,13 @@ def get_basis(name, size, Tf):
basis = fs.BezierFamily(size, T=Tf)
elif name == 'bspline':
basis = fs.BSplineFamily([0, Tf/2, Tf], size)
else:
basis = None
return basis


#
# Optimal trajectory generation with linear quadratic cost
#

def time_optimal_lq_basis(basis_name, basis_size, npoints):
# Assess performance as a function of basis type and size
def time_optimal_lq_basis(basis_name, basis_size, npoints, method):
# Create a sufficiently controllable random system to control
ntrys = 20
while ntrys > 0:
Expand Down Expand Up @@ -90,18 +90,20 @@ def time_optimal_lq_basis(basis_name, basis_size, npoints):

res = opt.solve_ocp(
sys, timepts, x0, traj_cost, constraints, terminal_cost=term_cost,
basis=basis,
basis=basis, trajectory_method=method,
)
# Only count this as a benchmark if we converged
assert res.success

# Parameterize the test against different choices of integrator and minimizer
time_optimal_lq_basis.param_names = ['basis', 'size', 'npoints']
time_optimal_lq_basis.param_names = ['basis', 'size', 'npoints', 'method']
time_optimal_lq_basis.params = (
['poly', 'bezier', 'bspline'], [8, 10, 12], [5, 10, 20])
[None, 'poly', 'bezier', 'bspline'],
[4, 8], [5, 10], ['shooting', 'collocation'])


def time_optimal_lq_methods(integrator_name, minimizer_name):
# Assess performance as a function of optimization and integration methods
def time_optimal_lq_methods(integrator_name, minimizer_name, method):
# Get the integrator and minimizer parameters to use
integrator = integrator_table[integrator_name]
minimizer = minimizer_table[minimizer_name]
Expand Down Expand Up @@ -134,17 +136,20 @@ def time_optimal_lq_methods(integrator_name, minimizer_name):
sys, timepts, x0, traj_cost, constraints, terminal_cost=term_cost,
solve_ivp_method=integrator[0], solve_ivp_kwargs=integrator[1],
minimize_method=minimizer[0], minimize_options=minimizer[1],
trajectory_method=method,
)
# Only count this as a benchmark if we converged
assert res.success

# Parameterize the test against different choices of integrator and minimizer
time_optimal_lq_methods.param_names = ['integrator', 'minimizer']
time_optimal_lq_methods.param_names = ['integrator', 'minimizer', 'method']
time_optimal_lq_methods.params = (
['RK23', 'RK45', 'LSODA'], ['trust', 'SLSQP', 'COBYLA'])
['RK23', 'RK45', 'LSODA'], ['trust', 'SLSQP', 'COBYLA'],
['shooting', 'collocation'])


def time_optimal_lq_size(nstates, ninputs, npoints):
# Assess performance as a function system size
def time_optimal_lq_size(nstates, ninputs, npoints, method):
# Create a sufficiently controllable random system to control
ntrys = 20
while ntrys > 0:
Expand Down Expand Up @@ -181,19 +186,18 @@ def time_optimal_lq_size(nstates, ninputs, npoints):

res = opt.solve_ocp(
sys, timepts, x0, traj_cost, constraints, terminal_cost=term_cost,
trajectory_method=method,
)
# Only count this as a benchmark if we converged
assert res.success

# Parameterize the test against different choices of integrator and minimizer
time_optimal_lq_size.param_names = ['nstates', 'ninputs', 'npoints']
time_optimal_lq_size.params = ([1, 2, 4], [1, 2, 4], [5, 10, 20])
time_optimal_lq_size.param_names = ['nstates', 'ninputs', 'npoints', 'method']
time_optimal_lq_size.params = (
[2, 4], [2, 4], [10, 20], ['shooting', 'collocation'])


#
# Aircraft MPC example (from multi-parametric toolbox)
#

def time_discrete_aircraft_mpc(minimizer_name):
# model of an aircraft discretized with 0.2s sampling time
# Source: https://www.mpt3.org/UI/RegulationProblem
Expand Down
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