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Add demo for quadrotor taylor dynamics. (#77)
This has input limit. The V-rep formulation can work but H-rep will use up the memory. Also supports homogeneous_y tag in the Lagrangian.
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| Original file line number | Diff line number | Diff line change |
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| """ | ||
| Certify the compatible CLF/CBF using taylor expansion of the 12-state quadrotor | ||
| dynamics. | ||
| """ | ||
|
|
||
| import itertools | ||
| import os | ||
|
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||
| import numpy as np | ||
| import pydrake.solvers as solvers | ||
| import pydrake.symbolic as sym | ||
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| import compatible_clf_cbf.clf_cbf as clf_cbf | ||
| import compatible_clf_cbf.clf as clf | ||
| from compatible_clf_cbf.utils import BackoffScale | ||
| from examples.quadrotor.plant import QuadrotorPlant | ||
|
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| def search(use_y_squared: bool, with_u_bound: bool, use_v_rep: bool): | ||
| x = sym.MakeVectorContinuousVariable(12, "x") | ||
| quadrotor = QuadrotorPlant() | ||
| f, g = quadrotor.affine_dynamics_taylor(x, np.zeros((12,)), f_degree=3, g_degree=2) | ||
|
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||
| if with_u_bound: | ||
| u_bound = quadrotor.m * quadrotor.g | ||
| if use_v_rep: | ||
| u_vertices = np.array(list(itertools.product([0, u_bound], repeat=4))) | ||
| u_extreme_rays = None | ||
| Au = None | ||
| bu = None | ||
| else: | ||
| Au = np.concatenate((np.eye(4), -np.eye(4)), axis=0) | ||
| bu = np.concatenate((np.full((4,), u_bound), np.zeros((4,)))) | ||
| u_vertices = None | ||
| u_extreme_rays = None | ||
| else: | ||
| u_vertices = None | ||
| u_extreme_rays = None | ||
| Au, bu = None, None | ||
|
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||
| exclude_sets = [clf_cbf.ExcludeSet(np.array([sym.Polynomial(x[2] + 2.5)]))] | ||
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| compatible = clf_cbf.CompatibleClfCbf( | ||
| f=f, | ||
| g=g, | ||
| x=x, | ||
| exclude_sets=exclude_sets, | ||
| within_set=None, | ||
| Au=Au, | ||
| bu=bu, | ||
| u_vertices=u_vertices, | ||
| u_extreme_rays=u_extreme_rays, | ||
| num_cbf=1, | ||
| with_clf=True, | ||
| use_y_squared=use_y_squared, | ||
| state_eq_constraints=None, | ||
| ) | ||
|
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||
| x_set = sym.Variables(x) | ||
| V_init = clf.load_clf( | ||
| os.path.join( | ||
| os.path.dirname(os.path.abspath(__file__)), | ||
| "../../data/quadrotor_taylor_clf.pkl", | ||
| ), | ||
| x_set, | ||
| )["V"] | ||
|
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||
| h_init = np.array([1 - V_init]) | ||
|
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| if with_u_bound and use_v_rep: | ||
| compatible_lagrangian_degrees = clf_cbf.CompatibleWVrepLagrangianDegrees( | ||
| u_vertices=[clf_cbf.XYDegree(x=2, y=0) for _ in range(u_vertices.shape[0])], | ||
| u_extreme_rays=None, | ||
| xi_y=None, | ||
| y=( | ||
| None | ||
| if use_y_squared | ||
| else [clf_cbf.XYDegree(x=6, y=0) for _ in range(compatible.y.size)] | ||
| ), | ||
| y_cross=( | ||
| None | ||
| if use_y_squared | ||
| else [ | ||
| clf_cbf.XYDegree(x=4, y=0) | ||
| for _ in range(compatible.y_cross_poly.size) | ||
| ] | ||
| ), | ||
| rho_minus_V=clf_cbf.XYDegree(x=4, y=2, homogeneous_y=True), | ||
| h_plus_eps=[clf_cbf.XYDegree(x=4, y=2, homogeneous_y=True)], | ||
| state_eq_constraints=None, | ||
| ) | ||
| else: | ||
| compatible_lagrangian_degrees = clf_cbf.CompatibleLagrangianDegrees( | ||
| lambda_y=[clf_cbf.XYDegree(x=2, y=0) for _ in range(4)], | ||
| xi_y=clf_cbf.XYDegree(x=1, y=0), | ||
| y=( | ||
| None | ||
| if use_y_squared | ||
| else [clf_cbf.XYDegree(x=4, y=0) for _ in range(compatible.y.size)] | ||
| ), | ||
| y_cross=( | ||
| None | ||
| if use_y_squared | ||
| else [ | ||
| clf_cbf.XYDegree(x=4, y=0) | ||
| for _ in range(compatible.y_cross_poly.size) | ||
| ] | ||
| ), | ||
| rho_minus_V=clf_cbf.XYDegree(x=2, y=2, homogeneous_y=True), | ||
| h_plus_eps=[clf_cbf.XYDegree(x=2, y=2, homogeneous_y=True)], | ||
| state_eq_constraints=None, | ||
| ) | ||
| safety_sets_lagrangian_degrees = clf_cbf.SafetySetLagrangianDegrees( | ||
| exclude=[ | ||
| clf_cbf.ExcludeRegionLagrangianDegrees( | ||
| cbf=[0], unsafe_region=[0], state_eq_constraints=[0] | ||
| ) | ||
| ], | ||
| within=[], | ||
| ) | ||
| barrier_eps = np.array([0.000]) | ||
| x_equilibrium = np.zeros((12,)) | ||
|
|
||
| candidate_compatible_states = np.zeros((4, 12)) | ||
| candidate_compatible_states[0, :3] = np.array([-1.5, 0, 0]) | ||
| candidate_compatible_states[1, :3] = np.array([1.5, 0, 0]) | ||
| candidate_compatible_states[2, :3] = np.array([0, 1.5, 0]) | ||
| candidate_compatible_states[3, :3] = np.array([0, -1.5, 0]) | ||
|
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| compatible_states_options = clf_cbf.CompatibleStatesOptions( | ||
| candidate_compatible_states=candidate_compatible_states, | ||
| anchor_states=np.zeros((1, 12)), | ||
| h_anchor_bounds=[(np.array([0.5]), np.array([1.0]))], | ||
| weight_V=1, | ||
| weight_h=np.array([1]), | ||
| V_margin=None, | ||
| h_margins=None, | ||
| ) | ||
|
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| solver_options = solvers.SolverOptions() | ||
| solver_options.SetOption(solvers.CommonSolverOption.kPrintToConsole, True) | ||
|
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| kappa_V = 0.1 | ||
| kappa_h = np.array([0.1]) | ||
| V_degree = 2 | ||
| h_degrees = [2] | ||
| backoff_scale = BackoffScale(rel=None, abs=0.001) | ||
| V, h = compatible.bilinear_alternation( | ||
| V_init, | ||
| h_init, | ||
| compatible_lagrangian_degrees, | ||
| safety_sets_lagrangian_degrees, | ||
| kappa_V, | ||
| kappa_h, | ||
| barrier_eps, | ||
| x_equilibrium, | ||
| V_degree, | ||
| h_degrees, | ||
| max_iter=5, | ||
| solver_options=solver_options, | ||
| lagrangian_coefficient_tol=None, | ||
| compatible_states_options=compatible_states_options, | ||
| backoff_scale=backoff_scale, | ||
| lagrangian_sos_type=solvers.MathematicalProgram.NonnegativePolynomial.kSos, | ||
| ) | ||
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| def main(): | ||
| # search(use_y_squared=True, with_u_bound=False, use_v_rep=False) | ||
| # Using H-rep will cause out-of-memory issue. | ||
| # search(use_y_squared=True, with_u_bound=True, use_v_rep=False) | ||
| search(use_y_squared=True, with_u_bound=True, use_v_rep=True) | ||
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|
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| if __name__ == "__main__": | ||
| main() |
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