From 750f932a8d3e8bcaed86ff0d74d854489ee24d40 Mon Sep 17 00:00:00 2001 From: Maxim Vochten Date: Tue, 29 Oct 2024 13:34:17 +0100 Subject: [PATCH] enable option to calculate geometric invariants using rockit interface --- ...calculate_invariants_position_longtrial.py | 104 + ...it_calculate_vector_invariants_position.py | 12 +- ...calculate_vector_invariants_position_mf.py | 10 +- ...calculate_vector_invariants_position_mj.py | 12 +- invariants_py/data/trajectory_long.csv | 4542 +++++++++++++++++ pyproject.toml | 2 +- 6 files changed, 4671 insertions(+), 11 deletions(-) create mode 100644 examples/calculate_invariants_position_longtrial.py create mode 100644 invariants_py/data/trajectory_long.csv diff --git a/examples/calculate_invariants_position_longtrial.py b/examples/calculate_invariants_position_longtrial.py new file mode 100644 index 0000000..55ef813 --- /dev/null +++ b/examples/calculate_invariants_position_longtrial.py @@ -0,0 +1,104 @@ +# Example for calculating invariants from a long trial of position data. + +import pandas as pd +from mpl_toolkits.mplot3d import Axes3D +from invariants_py.calculate_invariants.rockit_calculate_vector_invariants_position import OCP_calc_pos +import numpy as np +import matplotlib.pyplot as plt +from invariants_py.reparameterization import reparameterize_positiontrajectory_arclength +from invariants_py.data_handler import find_data_path + +# Load the CSV file +df = pd.read_csv(find_data_path('trajectory_long.csv')) + +# Plot xyz coordinates with respect to timestamp +plt.figure() +plt.plot(df['timestamp'], df['x'], label='x') +plt.plot(df['timestamp'], df['y'], label='y') +plt.plot(df['timestamp'], df['z'], label='z') +plt.xlabel('Timestamp') +plt.ylabel('Coordinates') +plt.legend() +plt.title('XYZ Coordinates with respect to Timestamp') +plt.show() + +# Plot the trajectory in 3D +fig = plt.figure() +ax = fig.add_subplot(111, projection='3d') +ax.plot(df['x'], df['y'], df['z']) +ax.set_aspect('equal') +ax.set_xlabel('X') +ax.set_ylabel('Y') +ax.set_zlabel('Z') +ax.set_title('3D Trajectory') +plt.show() + +# Prepare the trajectory data +trajectory = np.column_stack((df['x'], df['y'], df['z'])) +timestamps = df['timestamp'].values +stepsize = np.mean(np.diff(timestamps)) + +# Downsample the trajectory to 100 samples +downsampled_indices = np.linspace(0, len(trajectory) - 1, 200, dtype=int) +trajectory = trajectory[downsampled_indices]/1000 # Convert to meters +timestamps = timestamps[downsampled_indices] +stepsize = np.mean(np.diff(timestamps)) + +# Reparameterize the trajectory based on arclength +# Note: The reparameterization is not necessary if the data size is within the limit +trajectory, arclength, arclength_n, nb_samples, stepsize = reparameterize_positiontrajectory_arclength(trajectory) + +# Use the standard approach if the data size is within the limit +ocp = OCP_calc_pos(window_len=len(trajectory),fatrop_solver=True,geometric=True) +invariants, reconstructed_trajectory, moving_frames = ocp.calculate_invariants(trajectory, stepsize) + +# Plot the calculated invariants as subplots +fig, axs = plt.subplots(3, 1, figsize=(10, 8)) + +axs[0].plot(timestamps, invariants[:, 0], label='Invariant 1') +axs[0].plot(0, 0, label='Invariant 1') +axs[0].set_xlabel('Timestamp') +axs[0].set_ylabel('Invariant 1') +axs[0].legend() +axs[0].set_title('Calculated Geometric Invariant 1') + +axs[1].plot(timestamps, invariants[:, 1], label='Invariant 2') +axs[1].set_xlabel('Timestamp') +axs[1].set_ylabel('Invariant 2') +axs[1].legend() +axs[1].set_title('Calculated Geometric Invariant 2') + +axs[2].plot(timestamps, invariants[:, 2], label='Invariant 3') +axs[2].set_xlabel('Timestamp') +axs[2].set_ylabel('Invariant 3') +axs[2].legend() +axs[2].set_title('Calculated Geometric Invariant 3') + +plt.tight_layout() +plt.show() + +# Plot reconstructed trajectory versus original trajectory +plt.figure() +plt.plot(timestamps, trajectory[:, 0], label='Original x') +plt.plot(timestamps, trajectory[:, 1], label='Original y') +plt.plot(timestamps, trajectory[:, 2], label='Original z') +plt.plot(timestamps, reconstructed_trajectory[:, 0], label='Reconstructed x') +plt.plot(timestamps, reconstructed_trajectory[:, 1], label='Reconstructed y') +plt.plot(timestamps, reconstructed_trajectory[:, 2], label='Reconstructed z') +plt.xlabel('Timestamp') +plt.ylabel('Coordinates') +plt.legend() +plt.title('Original and Reconstructed Trajectory') +plt.show() + +# Plot the reconstructed trajectory in 3D +fig = plt.figure() +ax = fig.add_subplot(111, projection='3d') +ax.plot(trajectory[:, 0], trajectory[:, 1], trajectory[:, 2]) +ax.plot(reconstructed_trajectory[:, 0], reconstructed_trajectory[:, 1], reconstructed_trajectory[:, 2]) +ax.set_aspect('equal') +ax.set_xlabel('X') +ax.set_ylabel('Y') +ax.set_zlabel('Z') +ax.set_title('Reconstructed 3D Trajectory') +plt.show() diff --git a/invariants_py/calculate_invariants/rockit_calculate_vector_invariants_position.py b/invariants_py/calculate_invariants/rockit_calculate_vector_invariants_position.py index cb4fa7a..f19eb08 100644 --- a/invariants_py/calculate_invariants/rockit_calculate_vector_invariants_position.py +++ b/invariants_py/calculate_invariants/rockit_calculate_vector_invariants_position.py @@ -26,7 +26,7 @@ class OCP_calc_pos: - def __init__(self, window_len=100, rms_error_traj=10**-3, fatrop_solver=False, bool_unsigned_invariants=False, planar_task=False, solver_options = {}): + def __init__(self, window_len=100, rms_error_traj=10**-3, fatrop_solver=False, bool_unsigned_invariants=False, planar_task=False, solver_options = {}, geometric=False): """ Initializes an instance of the RockitCalculateVectorInvariantsPosition class. It specifies the optimal control problem (OCP) for calculating the invariants of a trajectory in a symbolic way. @@ -113,8 +113,12 @@ def __init__(self, window_len=100, rms_error_traj=10**-3, fatrop_solver=False, b # TODO make normal to plane a parameter instead of hardcoding the Z-axis ocp.subject_to( cas.dot(R_t[:,2],np.array([0,0,1])) > 0) - # TODO can we implement geometric constraint (constant i1) by making i1 a state? - + # Geometric invariants (optional), i.e. enforce constant speed + if geometric: + L = ocp.state() # introduce extra state L for the speed + ocp.set_next(L, L) # enforce constant speed + ocp.subject_to(invars[0] - L == 0, include_last=False) # relate to first invariant + """ Objective function """ # Minimize moving frame invariants to deal with singularities and noise @@ -142,7 +146,7 @@ def __init__(self, window_len=100, rms_error_traj=10**-3, fatrop_solver=False, b ocp._method.set_option("linsol_lu_fact_tol",1e-12) else: ocp.method(rockit.MultipleShooting(N=N-1)) - ocp.solver('ipopt', {'expand':True, 'print_time':False, 'ipopt.tol':tolerance,'ipopt.print_info_string':'yes', 'ipopt.max_iter':max_iter,'ipopt.print_level':print_level, 'ipopt.ma57_automatic_scaling':'no', 'ipopt.linear_solver':'mumps'}) + ocp.solver('ipopt', {'expand':True, 'print_time':False, 'ipopt.tol':tolerance, 'ipopt.print_info_string':'yes', 'ipopt.max_iter':max_iter, 'ipopt.print_level':print_level, 'ipopt.ma57_automatic_scaling':'no', 'ipopt.linear_solver':'mumps'}) """ Encapsulate solver in a casadi function so that it can be easily reused """ ocp.solve() # code generation diff --git a/invariants_py/calculate_invariants/rockit_calculate_vector_invariants_position_mf.py b/invariants_py/calculate_invariants/rockit_calculate_vector_invariants_position_mf.py index 2218202..5226ab3 100644 --- a/invariants_py/calculate_invariants/rockit_calculate_vector_invariants_position_mf.py +++ b/invariants_py/calculate_invariants/rockit_calculate_vector_invariants_position_mf.py @@ -26,7 +26,7 @@ class OCP_calc_pos: - def __init__(self, window_len=100, rms_error_traj=10**-2, fatrop_solver=False, bool_unsigned_invariants=False, planar_task=False, solver_options = {}): + def __init__(self, window_len=100, rms_error_traj=10**-2, fatrop_solver=False, bool_unsigned_invariants=False, planar_task=False, geometric = False, solver_options = {}): """ Initializes an instance of the RockitCalculateVectorInvariantsPosition class. It specifies the optimal control problem (OCP) for calculating the invariants of a trajectory in a symbolic way. @@ -117,8 +117,12 @@ def __init__(self, window_len=100, rms_error_traj=10**-2, fatrop_solver=False, b # TODO make normal to plane a parameter instead of hardcoding the Z-axis ocp.subject_to( cas.dot(R_t[:,2],np.array([0,0,1])) > 0) - # TODO can we implement geometric constraint (constant i1) by making i1 a state? - + # Geometric invariants (optional), i.e. enforce constant speed + if geometric: + L = ocp.state() # introduce extra state L for the speed + ocp.set_next(L, L) # enforce constant speed + ocp.subject_to(invars[0] - L == 0, include_last=False) # relate to first invariant + """ Objective function """ # Minimize moving frame invariants to deal with singularities and noise diff --git a/invariants_py/calculate_invariants/rockit_calculate_vector_invariants_position_mj.py b/invariants_py/calculate_invariants/rockit_calculate_vector_invariants_position_mj.py index 115ecac..df073f8 100644 --- a/invariants_py/calculate_invariants/rockit_calculate_vector_invariants_position_mj.py +++ b/invariants_py/calculate_invariants/rockit_calculate_vector_invariants_position_mj.py @@ -8,7 +8,7 @@ class OCP_calc_pos: - def __init__(self, window_len = 100, w_pos = 1, w_regul_jerk = 10**-5 , bool_unsigned_invariants = False, w_regul_invars = 0, fatrop_solver = False, planar_task = False, solver_options = {}): + def __init__(self, window_len = 100, w_pos = 1, w_regul_jerk = 10**-5 , bool_unsigned_invariants = False, w_regul_invars = 0, fatrop_solver = False, planar_task = False, geometric = False, solver_options = {}): fatrop_solver = check_solver(fatrop_solver) # Set solver options @@ -42,8 +42,8 @@ def __init__(self, window_len = 100, w_pos = 1, w_regul_jerk = 10**-5 , bool_uns ''' Constraints ''' # test initial constraint on position - self.ocp.subject_to(self.ocp.at_tf(self.p_obj == self.p_obj_m)) - self.ocp.subject_to(self.ocp.at_t0(self.p_obj == self.p_obj_m)) + #self.ocp.subject_to(self.ocp.at_tf(self.p_obj == self.p_obj_m)) + #self.ocp.subject_to(self.ocp.at_t0(self.p_obj == self.p_obj_m)) # Orthonormality of rotation matrix (only needed for one timestep, property is propagated by integrator) self.ocp.subject_to(self.ocp.at_t0(ocp_helper.tril_vec(R_t.T @ R_t - np.eye(3))==0.)) @@ -71,6 +71,12 @@ def __init__(self, window_len = 100, w_pos = 1, w_regul_jerk = 10**-5 , bool_uns self.ocp.subject_to(self.i1 >= 0) # velocity always positive #ocp.subject_to(invars[1,:]>=0) # curvature rate always positive + # Geometric invariants (optional), i.e. enforce constant speed + if geometric: + L = self.ocp.state() # introduce extra state L for the speed + self.ocp.set_next(L, L) # enforce constant speed + self.ocp.subject_to(self.i1 - L == 0) # relate to first invariant + ''' Objective function ''' self.N_controls = window_len-1 diff --git a/invariants_py/data/trajectory_long.csv b/invariants_py/data/trajectory_long.csv new file mode 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