3535'COBYLA' : ('COBYLA' , {}),
3636}
3737
38+
3839# Utility function to create a basis of a given size
3940def get_basis (name ,size ,Tf ):
4041if name == 'poly' :
@@ -43,14 +44,13 @@ def get_basis(name, size, Tf):
4344basis = fs .BezierFamily (size ,T = Tf )
4445elif name == 'bspline' :
4546basis = fs .BSplineFamily ([0 ,Tf / 2 ,Tf ],size )
47+ else :
48+ basis = None
4649return basis
4750
4851
49- #
50- # Optimal trajectory generation with linear quadratic cost
51- #
52-
53- def time_optimal_lq_basis (basis_name ,basis_size ,npoints ):
52+ # Assess performance as a function of basis type and size
53+ def time_optimal_lq_basis (basis_name ,basis_size ,npoints ,method ):
5454# Create a sufficiently controllable random system to control
5555ntrys = 20
5656while ntrys > 0 :
@@ -90,18 +90,20 @@ def time_optimal_lq_basis(basis_name, basis_size, npoints):
9090
9191res = opt .solve_ocp (
9292sys ,timepts ,x0 ,traj_cost ,constraints ,terminal_cost = term_cost ,
93- basis = basis ,
93+ basis = basis ,trajectory_method = method ,
9494 )
9595# Only count this as a benchmark if we converged
9696assert res .success
9797
9898# Parameterize the test against different choices of integrator and minimizer
99- time_optimal_lq_basis .param_names = ['basis' ,'size' ,'npoints' ]
99+ time_optimal_lq_basis .param_names = ['basis' ,'size' ,'npoints' , 'method' ]
100100time_optimal_lq_basis .params = (
101- ['poly' ,'bezier' ,'bspline' ], [8 ,10 ,12 ], [5 ,10 ,20 ])
101+ [None ,'poly' ,'bezier' ,'bspline' ],
102+ [4 ,8 ], [5 ,10 ], ['shooting' ,'collocation' ])
102103
103104
104- def time_optimal_lq_methods (integrator_name ,minimizer_name ):
105+ # Assess performance as a function of optimization and integration methods
106+ def time_optimal_lq_methods (integrator_name ,minimizer_name ,method ):
105107# Get the integrator and minimizer parameters to use
106108integrator = integrator_table [integrator_name ]
107109minimizer = minimizer_table [minimizer_name ]
@@ -134,17 +136,20 @@ def time_optimal_lq_methods(integrator_name, minimizer_name):
134136sys ,timepts ,x0 ,traj_cost ,constraints ,terminal_cost = term_cost ,
135137solve_ivp_method = integrator [0 ],solve_ivp_kwargs = integrator [1 ],
136138minimize_method = minimizer [0 ],minimize_options = minimizer [1 ],
139+ trajectory_method = method ,
137140 )
138141# Only count this as a benchmark if we converged
139142assert res .success
140143
141144# Parameterize the test against different choices of integrator and minimizer
142- time_optimal_lq_methods .param_names = ['integrator' ,'minimizer' ]
145+ time_optimal_lq_methods .param_names = ['integrator' ,'minimizer' , 'method' ]
143146time_optimal_lq_methods .params = (
144- ['RK23' ,'RK45' ,'LSODA' ], ['trust' ,'SLSQP' ,'COBYLA' ])
147+ ['RK23' ,'RK45' ,'LSODA' ], ['trust' ,'SLSQP' ,'COBYLA' ],
148+ ['shooting' ,'collocation' ])
145149
146150
147- def time_optimal_lq_size (nstates ,ninputs ,npoints ):
151+ # Assess performance as a function system size
152+ def time_optimal_lq_size (nstates ,ninputs ,npoints ,method ):
148153# Create a sufficiently controllable random system to control
149154ntrys = 20
150155while ntrys > 0 :
@@ -181,19 +186,18 @@ def time_optimal_lq_size(nstates, ninputs, npoints):
181186
182187res = opt .solve_ocp (
183188sys ,timepts ,x0 ,traj_cost ,constraints ,terminal_cost = term_cost ,
189+ trajectory_method = method ,
184190 )
185191# Only count this as a benchmark if we converged
186192assert res .success
187193
188194# Parameterize the test against different choices of integrator and minimizer
189- time_optimal_lq_size .param_names = ['nstates' ,'ninputs' ,'npoints' ]
190- time_optimal_lq_size .params = ([1 ,2 ,4 ], [1 ,2 ,4 ], [5 ,10 ,20 ])
195+ time_optimal_lq_size .param_names = ['nstates' ,'ninputs' ,'npoints' ,'method' ]
196+ time_optimal_lq_size .params = (
197+ [2 ,4 ], [2 ,4 ], [10 ,20 ], ['shooting' ,'collocation' ])
191198
192199
193- #
194200# Aircraft MPC example (from multi-parametric toolbox)
195- #
196-
197201def time_discrete_aircraft_mpc (minimizer_name ):
198202# model of an aircraft discretized with 0.2s sampling time
199203# Source: https://www.mpt3.org/UI/RegulationProblem