From 9fa8fc4c15c4561e7d5ac67d0917159b7f87bbf4 Mon Sep 17 00:00:00 2001 From: Michelle Ho Date: Wed, 15 May 2024 16:56:41 -0700 Subject: [PATCH] running rpo custom environment --- .gitignore | 3 + cleanrl/ppo.py | 15 +- cleanrl/ppo_continuous_action.py | 13 +- cleanrl/sac_continuous_action.py | 13 +- env_original/__init__.py | 0 env_original/rpo_detubmling/__init__.py | 0 .../rpo_detubmling/dynamics/dyn_misc.py | 67 -- .../rpo_detubmling/dynamics/dynamics_6dof.py | 136 ---- .../rpo_detubmling/dynamics/dynamics_rot.py | 323 ---------- .../rpo_detubmling/dynamics/dynamics_trans.py | 610 ------------------ .../rpo_detubmling/dynamics/oe_conversion.py | 143 ---- .../rpo_detubmling/dynamics/plot_misc.py | 100 --- env_original/rpo_detubmling/dynamics/test.gif | Bin 1648836 -> 0 bytes .../rpo_detubmling/dynamics/test_rot_anime.py | 25 - .../rpo_detubmling/rpo_detumbling_2D.py | 79 --- .../rpo_detubmling/rpo_detumbling_3D.py | 67 -- env_original/rpo_detubmling/rpo_funcs.py | 32 - testenv.py | 4 + 18 files changed, 36 insertions(+), 1594 deletions(-) delete mode 100644 env_original/__init__.py delete mode 100644 env_original/rpo_detubmling/__init__.py delete mode 100644 env_original/rpo_detubmling/dynamics/dyn_misc.py delete mode 100644 env_original/rpo_detubmling/dynamics/dynamics_6dof.py delete mode 100644 env_original/rpo_detubmling/dynamics/dynamics_rot.py delete mode 100644 env_original/rpo_detubmling/dynamics/dynamics_trans.py delete mode 100644 env_original/rpo_detubmling/dynamics/oe_conversion.py delete mode 100644 env_original/rpo_detubmling/dynamics/plot_misc.py delete mode 100644 env_original/rpo_detubmling/dynamics/test.gif delete mode 100644 env_original/rpo_detubmling/dynamics/test_rot_anime.py delete mode 100644 env_original/rpo_detubmling/rpo_detumbling_2D.py delete mode 100644 env_original/rpo_detubmling/rpo_detumbling_3D.py delete mode 100644 env_original/rpo_detubmling/rpo_funcs.py create mode 100644 testenv.py diff --git a/.gitignore b/.gitignore index 1d4cfa0e4..7bbc84573 100644 --- a/.gitignore +++ b/.gitignore @@ -129,3 +129,6 @@ venv.bak/ # mypy .mypy_cache/ + +# Your virtual environment +cleanrl_venv/ diff --git a/cleanrl/ppo.py b/cleanrl/ppo.py index edde76bae..954042739 100644 --- a/cleanrl/ppo.py +++ b/cleanrl/ppo.py @@ -4,7 +4,9 @@ import time from dataclasses import dataclass -import gymnasium as gym +import gym_examples +import gym +# import gymnasium as gym import numpy as np import torch import torch.nn as nn @@ -12,6 +14,7 @@ import tyro from torch.distributions.categorical import Categorical from torch.utils.tensorboard import SummaryWriter +import gym_examples @dataclass @@ -34,7 +37,9 @@ class Args: """whether to capture videos of the agent performances (check out `videos` folder)""" # Algorithm specific arguments - env_id: str = "CartPole-v1" + ##TODO: change + # env_id: str = "CartPole-v1" + env_id: str = "RPO_DeTumbling2D-v0" """the id of the environment""" total_timesteps: int = 500000 """total timesteps of the experiments""" @@ -81,10 +86,12 @@ class Args: def make_env(env_id, idx, capture_video, run_name): def thunk(): if capture_video and idx == 0: - env = gym.make(env_id, render_mode="rgb_array") + # env = gym.make(env_id, render_mode="rgb_array") + env = gym.make('gym_examples/RPO_Detumble2DEnv-v0', render_mode="rgb_array") env = gym.wrappers.RecordVideo(env, f"videos/{run_name}") else: - env = gym.make(env_id) + # env = gym.make(env_id) + env = gym.make('gym_examples/RPO_Detumble2DEnv-v0') env = gym.wrappers.RecordEpisodeStatistics(env) return env diff --git a/cleanrl/ppo_continuous_action.py b/cleanrl/ppo_continuous_action.py index b454521b6..e9e468f76 100644 --- a/cleanrl/ppo_continuous_action.py +++ b/cleanrl/ppo_continuous_action.py @@ -4,7 +4,9 @@ import time from dataclasses import dataclass -import gymnasium as gym +# import gymnasium as gym +import gym +import gym_examples import numpy as np import torch import torch.nn as nn @@ -40,7 +42,8 @@ class Args: """the user or org name of the model repository from the Hugging Face Hub""" # Algorithm specific arguments - env_id: str = "HalfCheetah-v4" + # env_id: str = "HalfCheetah-v4" + env_id: str = "gym_examples/RPO_Detumble2DEnv-v0" """the id of the environment""" total_timesteps: int = 1000000 """total timesteps of the experiments""" @@ -87,10 +90,12 @@ class Args: def make_env(env_id, idx, capture_video, run_name, gamma): def thunk(): if capture_video and idx == 0: - env = gym.make(env_id, render_mode="rgb_array") + # env = gym.make(env_id, render_mode="rgb_array") + env = gym.make('gym_examples/RPO_Detumble2DEnv-v0', render_mode="rgb_array") env = gym.wrappers.RecordVideo(env, f"videos/{run_name}") else: - env = gym.make(env_id) + # env = gym.make(env_id) + env = gym.make('gym_examples/RPO_Detumble2DEnv-v0') env = gym.wrappers.FlattenObservation(env) # deal with dm_control's Dict observation space env = gym.wrappers.RecordEpisodeStatistics(env) env = gym.wrappers.ClipAction(env) diff --git a/cleanrl/sac_continuous_action.py b/cleanrl/sac_continuous_action.py index 019608442..7ec93ced7 100644 --- a/cleanrl/sac_continuous_action.py +++ b/cleanrl/sac_continuous_action.py @@ -4,7 +4,9 @@ import time from dataclasses import dataclass -import gymnasium as gym +# import gymnasium as gym +import gym +import gym_examples import numpy as np import torch import torch.nn as nn @@ -35,7 +37,8 @@ class Args: """whether to capture videos of the agent performances (check out `videos` folder)""" # Algorithm specific arguments - env_id: str = "Hopper-v4" + # env_id: str = "Hopper-v4" + env_id: str = "gym_examples/RPO_Detumble2DEnv-v0" """the environment id of the task""" total_timesteps: int = 1000000 """total timesteps of the experiments""" @@ -68,10 +71,12 @@ class Args: def make_env(env_id, seed, idx, capture_video, run_name): def thunk(): if capture_video and idx == 0: - env = gym.make(env_id, render_mode="rgb_array") + # env = gym.make(env_id, render_mode="rgb_array") + env = gym.make('gym_examples/RPO_Detumble2DEnv-v0', render_mode="rgb_array") env = gym.wrappers.RecordVideo(env, f"videos/{run_name}") else: - env = gym.make(env_id) + # env = gym.make(env_id) + env = gym.make('gym_examples/RPO_Detumble2DEnv-v0') env = gym.wrappers.RecordEpisodeStatistics(env) env.action_space.seed(seed) return env diff --git a/env_original/__init__.py b/env_original/__init__.py deleted file mode 100644 index e69de29bb..000000000 diff --git a/env_original/rpo_detubmling/__init__.py b/env_original/rpo_detubmling/__init__.py deleted file mode 100644 index e69de29bb..000000000 diff --git a/env_original/rpo_detubmling/dynamics/dyn_misc.py b/env_original/rpo_detubmling/dynamics/dyn_misc.py deleted file mode 100644 index 30549a880..000000000 --- a/env_original/rpo_detubmling/dynamics/dyn_misc.py +++ /dev/null @@ -1,67 +0,0 @@ -### miscellaneous functions for dynamics ### - -import numpy as np -import numpy.linalg as la - - -# skew matrix -def skw(a): - return np.array([[0, -a[2], a[1]], - [a[2], 0, -a[0]], - [-a[1], a[0], 0]]) - - -def unit_rtn(r,v): - # radial vector - ur = r/la.norm(r) - un = np.cross(r,v)/la.norm(np.cross(r,v)) - ut = np.cross(un,ur) - - return np.vstack((ur, ut, un)) - -# Rotation matrix -def Rx(x): - mat = np.array([[1, 0, 0], - [0, np.cos(x), np.sin(x)], - [0, -np.sin(x), np.cos(x)]]) - return mat - -def Ry(x): - mat = np.array([[np.cos(x), 0, -np.sin(x)], - [0, 1, 0], - [np.sin(x), 0, np.cos(x)]]) - return mat - -def Rz(x): - mat = np.array([[np.cos(x), np.sin(x), 0], - [-np.sin(x), np.cos(x), 0], - [0, 0, 1]]) - return mat - - -def transform_coordinates(u_vectors, v_vectors, point_u): - """ - Transform coordinates from one system to another. - inputs: - u_vectors: A 3x3 numpy array representing the unit vectors of the original coordinate system - v_vectors: A 3x3 numpy array representing the unit vectors of the new coordinate system - point_u: The coordinates of the point in the original system - return: - The coordinates of the point in the new system - """ - # Construct the transformation matrix - T = np.array([[np.dot(v, u) for u in u_vectors] for v in v_vectors]) - - return np.dot(T, point_u) - - -# Kepler equation solver -def solve_kepler(M, e): - E = np.pi - for _ in range(100): - E_next = E - (E - e*np.sin(E) - M)/(1 - e*np.cos(E)) - - if abs(E_next - E) < 1e-5: - break - - return E_next \ No newline at end of file diff --git a/env_original/rpo_detubmling/dynamics/dynamics_6dof.py b/env_original/rpo_detubmling/dynamics/dynamics_6dof.py deleted file mode 100644 index 32ae9b790..000000000 --- a/env_original/rpo_detubmling/dynamics/dynamics_6dof.py +++ /dev/null @@ -1,136 +0,0 @@ -# Orbit dynamics -import numpy as np -import numpy.linalg as la -from scipy.integrate import odeint - -from .dyn_misc import * -from .dynamics_trans import * -from .dynamics_rot import * -from .oe_conversion import * - - -### linear dynamics - -def linearize_6dof(oe, qw, time, J): - """ - linearize the nonlinear dynamics of 6DoF relative motion - input: - oe: OE (chief); 6 x (n_time) - qw: attitude (deputy); 7 x (n_time) - time: time; 1 x (n_time) - J: inertia matrix - return: - mats: dictionary containing the linearized matrices - stm: state transition matrix; 6 x 6 x n_time - stm_qw: state transition matrix for attitude; 7 x 7 x n_time - cim: control input matrix; 6 x 3 x n_time - cim_qw: control input matrix for attitude; 7 x 3 x n_time - psi: ROE -> RTN map; 6 x 6 x n_time - rs: residual for translational motion; 6 x n_time - rqw: residual for rotational motion; 7 x n_time - """ - - n_time = len(time) - dt = time[1]-time[0] - - psi = np.empty(shape=(6, 6, n_time), dtype=float) # ROE -> RTN map - stm = np.empty(shape=(6, 6, n_time), dtype=float) - stm_qw = np.empty(shape=(7, 7, n_time), dtype=float) - cim = np.empty(shape=(6, 3, n_time), dtype=float) - cim_qw = np.empty(shape=(7, 3, n_time), dtype=float) - rs = np.empty(shape=(6, n_time), dtype=float) - rqw = np.empty(shape=(7, n_time), dtype=float) - - # Time Loop - for i in range(n_time): - - # ROE to RTN map (TODO: check only translational motion matters (i think so?)) - psi[:,:,i] = map_mtx_roe_to_rtn(oe[:,i]) # N.B.: has dimension [-,-,-,1/s,1/s,1/s] - - if i < n_time: - stm[:,:,i] = state_transition_roe(oe[:,i],dt) # N.B.: is a-dimentional - cim[:,:,i] = control_input_matrix_roe(oe[:,i]) # N.B.: has dimension [s] - stm_qw[:,:,i] = get_stm_qw(qw[:,i],dt,J) - cim_qw[:,:,i] = get_cim_qw(qw[:,i],J) - - # update residuals - # TODO: currently trapezoidal approximation. We can do better (Malyuta's rendezvous paper has 3rd order approx.) - if i > 0: - Aqq_i, Aqw_i, Aww_i = dyn_qw_lin(qw[:,i-1], J) - Aqq_ip1, Aqw_ip1, Aww_ip1 = dyn_qw_lin(qw[:,i], J) - - dq_i = q_kin(qw[0:4, i-1], qw[4:7, i-1]) # _{i} - dq_ip1 = q_kin(qw[0:4, i], qw[4:7, i] ) # _{i+1} - dw_i = euler_dyn(qw[4:7, i-1], J, np.array([0,0,0])) - dw_ip1 = euler_dyn(qw[4:7, i], J, np.array([0,0,0])) - - dqw_i = np.concatenate((dq_i, dw_i)) - dqw_ip1 = np.concatenate((dq_ip1, dw_ip1)) - - A_i = np.block([[Aqq_i, Aqw_i ],[np.zeros((3,4)), Aww_i ]]) - # A_ip1 = np.block([[Aqq_ip1, Aqw_ip1],[np.zeros((3,4)), Aww_ip1]]) - - rs[:,i-1] = np.zeros((6,1)).reshape((6,)) - # rqw[:,i-1] = (stm_qw[:,:,i-1] @ (dqw_i - A_i @ qw[:,i-1]) + \ - # dqw_ip1 - A_ip1 @ qw[:,i]) * dt/2 - rqw[:,i-1] = stm_qw[:,:,i-1] @ (dqw_i - A_i @ qw[:,i-1]) * dt - - mats = {"stm_r": stm, "stm_qw": stm_qw, "cim_r": cim, "cim_qw": cim_qw, "psi": psi, "rs": rs, "rqw": rqw} - - return mats - - -### nonlinear dynamics - -def get_6dof_discrete_control(x_ref, action, koe_c, mu_E, t, J, j2=True, drag=False): - - x_0 = x_ref[:,0] - - if koe_c.shape[1] != len(t): - raise ValueError("koe_c and t must have the same length of timestep. Re-check your input...") - - roe_0 = x_0[0:6] / koe_c[0,0] # non-dimensionalize - qw_0 = x_0[6:13] - - koe_c_0 = koe_c[:,0] - rc, vc = koe_to_rv(koe_c_0, mu_E) - koe_d_0 = qnsroe_to_koe(roe_0, koe_c_0) - - koe_c_list = np.empty(shape=(6,len(t)), dtype=float) - koe_d_list = np.empty(shape=(6,len(t)), dtype=float) - qw_list = np.empty(shape=(7,len(t)), dtype=float) - roe_list = np.empty(shape=(6,len(t)), dtype=float) - - # oe_list[:,0] = koe_d.reshape((6,)) - koe_c_list[:,0] = koe_c_0.reshape((6,)) - koe_d_list[:,0] = koe_d_0.reshape((6,)) - qw_list[:,0] = qw_0.reshape((7,)) - roe_list[:,0] = roe_0.reshape((6,)) # non-dimensionalized - - for i in range(len(t)-1): - dv = action[0:3,i] # in the chief's RTN frame - dm = action[3:6,i] # in the deputy's body frame - rc, vc = koe_to_rv(koe_c_list[:,i], mu_E) - rd, vd = koe_to_rv(koe_d_list[:,i], mu_E) - urtn_c = unit_rtn(rc, vc) - urtn_d = unit_rtn(rd, vd) - dv = transform_coordinates(urtn_c,urtn_d,dv) # chief's RTN -> deputy's RTN - - F = dv / (t[i+1] - t[i]) # in deputy's RTN frame - T = dm / (t[i+1] - t[i]) # in deputy's body frame - - time = np.array([0, t[i+1]-t[i]]) - x0 = np.concatenate((roe_list[:,i], koe_c[:,i])) - roe_ = odeint(gve_qnsroe_full, x0, time, args=(mu_E, F, j2, drag)) - qw_ = odeint(ode_qw, qw_list[:,i].flatten(), time, args=(J, T)) - - roe_list[:,i+1] = roe_[-1,0:6].reshape((6,)) - qw_list[:,i+1] = qw_[-1,:].reshape((7,)) - koe_c_list[:,i+1] = roe_[-1, 6:12].reshape((6,)) # chief - koe_d_list[:,i+1] = qnsroe_to_koe(roe_list[:, i+1], koe_c_list[:,i+1]).reshape((6,)) # deputy - - # post-processing: dimensionalize - for i in range(len(t)): - roe_list[:,i] = roe_list[:,i] * koe_c_list[0,i] - - return koe_c_list, qw_list, roe_list, \ No newline at end of file diff --git a/env_original/rpo_detubmling/dynamics/dynamics_rot.py b/env_original/rpo_detubmling/dynamics/dynamics_rot.py deleted file mode 100644 index 5bbf7a8ef..000000000 --- a/env_original/rpo_detubmling/dynamics/dynamics_rot.py +++ /dev/null @@ -1,323 +0,0 @@ -#### rotational dynamics library #### - -# Orbit dynamics -import numpy as np -import numpy.linalg as la -from dyn_misc import * -from dynamics_trans import * -import scipy as sp -from scipy.linalg import expm -from scipy.integrate import solve_ivp -from scipy.integrate import odeint - - -### Quaternion setup -# q = [q0, q1, q2, q3] = [scalar, vector] - -def q_mul(q0, q1): - return np.array([ - q0[0]*q1[0] - q0[1]*q1[1] - q0[2]*q1[2] - q0[3]*q1[3], - q0[0]*q1[1] + q0[1]*q1[0] + q0[2]*q1[3] - q0[3]*q1[2], - q0[0]*q1[2] - q0[1]*q1[3] + q0[2]*q1[0] + q0[3]*q1[1], - q0[0]*q1[3] + q0[1]*q1[2] - q0[2]*q1[1] + q0[3]*q1[0] - ]) - -def q_cross(q0, q1): - return np.array([ - q0[0]*q1[1] - q0[1]*q1[0] - q0[2]*q1[3] + q0[3]*q1[2], - q0[0]*q1[2] + q0[1]*q1[3] - q0[2]*q1[0] - q0[3]*q1[1], - q0[0]*q1[3] - q0[1]*q1[2] + q0[2]*q1[1] - q0[3]*q1[0] - ]) - -def q_conj(q): - return np.array([q[0], -q[1], -q[2], -q[3]]) - -def q_inv(q): - return q_conj(q) / la.norm(q) - -def q_rot(q, v): - # Rotate vector v by quaternion q - qv = np.array([0, v[0], v[1], v[2]]) - qv = q_mul(q_mul(q_inv(q), qv), q) - return qv[1:] - -def q2rotmat(q): - # Convert quaternion to rotation matrix - q0, q1, q2, q3 = q - return np.array([ - [1 - 2*q2**2 - 2*q3**2, 2*q1*q2 - 2*q0*q3, 2*q1*q3 + 2*q0*q2], - [2*q1*q2 + 2*q0*q3, 1 - 2*q1**2 - 2*q3**2, 2*q2*q3 - 2*q0*q1], - [2*q1*q3 - 2*q0*q2, 2*q2*q3 + 2*q0*q1, 1 - 2*q1**2 - 2*q2**2] - ]) - - -### EoM ### -def q_kin(q, omega): - # qdot = 0.5 * q * omega - return 0.5 * q_mul(q, np.array([0, omega[0], omega[1], omega[2]])) - -def euler_dyn(w, I, tau): - return la.inv(I).dot(tau - np.cross(w, I.dot(w))) - -def euler_dyn_rel(w_dc_d, q_dc, w_cI_c, wdot_cI_c, I, tau): - """ - Assuming the angular velocity and acceleration of the cheif (no torque applied), - compute the relative angular acceleration of the deputy. - See "6-DOF robust adaptive terminal sliding mode control for spacecraft formation flying" (Wang et al., 2012, Acta) Eq. 22-d - inpus: - - w_cI_c : absolute ang. vel. of the chief (c) in the chief body frame - - w_dc_d : relative ang. vel. of deputy (d) w.r.t. c in d body frame - - q_dc : quaternion of d w.r.t. c - - w_cI_c : absolute ang. vel. of c in c body frame - - wdot_cI_c: absolute ang. acc. of c in c body frame - - I : inertia matrix of d - - tau : torque applied to d - return: - - wdot_dc_d : relative ang. acc. of d w.r.t. c in d body frame - """ - w_cI_d = q_conj(q_dc) @ w_cI_c @ q_dc - wdot_cI_d = q_conj(q_dc) @ wdot_cI_c @ q_dc - - return la.inv(I) @ (tau - np.cross(w_dc_d + w_cI_d, (I @ (w_dc_d + w_cI_d)))) - wdot_cI_d + np.sross(w_dc_d, w_cI_d) - - -def ode_qw(qw,t,J,T): - q = qw[0:4] - w = qw[4:7] - return np.concatenate((q_kin(q, w), euler_dyn(w, J, T))) - - -#### Linearized dynamics #### -def dyn_qw_lin(qw, I): - """ - Obtain the linearized dynamics of the quaternion and angular velocity (continuous time) - """ - q = qw[:4] - w = qw[4:7] - Aqq = 0.5 * np.array([[0, -w[0], -w[1], -w[2]], - [w[0], 0, w[2], -w[1]], - [w[1], -w[2], 0, w[0]], - [w[2], w[1], -w[0], 0]]) - Aqw = 0.5 * np.array([[-q[1], -q[2], -q[3]], - [q[0], -q[3], q[2]], - [q[3], q[0], -q[1]], - [-q[2], q[1], q[0]]]) - Aww = -np.linalg.inv(I) @ (skw(w) @ I - skw(I @ w)) - return Aqq, Aqw, Aww - - -def get_phi(t, A, p=5): - """ - numerically computing the matrix exp(A*t) - p: order of the approximation - """ - phi = np.eye(7) - for i in range(1, p): - phi += np.linalg.matrix_power(A*t, i) / np.math.factorial(i) - return phi - - -def get_stm_qw(qw, dt, J): - """ - Retrieve the STM of the [q,w] dynamics - """ - Aqq, Aqw, Aww = dyn_qw_lin(qw, J) - - A = np.zeros((7, 7)) - A[0:4, 0:4] = Aqq - A[0:4, 4:7] = Aqw - A[4:7, 4:7] = Aww - - cim_qw = np.zeros((7, 3)) - cim_qw[4:7, 0:3] = np.eye(3) # if the input is angular velocity - - return get_phi(dt, A, 5) - - -def dyn_qw_lin_discrete(qw, dt, J): - Aqq, Aqw, Aww = dyn_qw_lin(qw, J) - - A = np.zeros((7, 7)) - A[0:4, 0:4] = Aqq - A[0:4, 4:7] = Aqw - A[4:7, 4:7] = Aww - - cim_qw = np.zeros((7, 3)) - cim_qw[4:7, 0:3] = np.eye(3) # if the input is angular velocity - - phi0 = np.eye(7) - A_ = get_phi(dt, A, 5) - - # Define the function to be integrated - fun = lambda t, y: get_phi(t, A, 5).reshape(49, 1).flatten() - - # Solve the differential equation - sol = solve_ivp(fun, [0, dt], phi0.flatten(), method='RK45') - - D_ = sol.y[:, -1].reshape(7, 7) - B_ = D_ @ cim_qw - - return A_, B_, D_ - - -def get_cim_qw(qw, J): - """ - Assumption: control input is the angular velocity (delta_w), not the torque - """ - cim_qw = np.zeros(shape=(7,3), dtype=float) - cim_qw[4:7, 0:3] = np.eye(3) - return cim_qw - - - -### make a reference trajectory (analytical) - -def sph_interp_angle(qw0, qwf, n_time, dt): - - qhat = q_mul(q_conj(qw0[:4]), qwf[:4]) - sin_theta0f = np.linalg.norm(qhat[1:4]) - u0f = qhat[1:4] / sin_theta0f - theta0f = np.arctan2(sin_theta0f, qhat[0]) * 2 - theta0f = np.mod(theta0f + np.pi, 2 * np.pi) - np.pi # wrap to -pi ~ pi - - qw = np.zeros((7, n_time)) - dw = np.zeros((3, n_time)) - for k in range(n_time ): - ang = k * theta0f / (2 * n_time) - q_k = np.hstack(([np.cos(ang)], u0f * np.sin(ang))) - qw[:4, k] = q_mul(qw0[:4], q_k) - qw[4:7, k] = theta0f / (n_time * dt) * u0f - dw[:,k] = theta0f / n_time * u0f - - return qw, dw - - - -def track_target(r_rtn, t, r_target=np.zeros((3,1))): - """ - Analytical formulation of quaternion to track the target (default: origin) - """ - - if len(t) != r_rtn.shape[1]: - raise ValueError("dimension of t and r_rtn is different. check the variable sizes.") - - n_time = len(t) - 1 - qw = np.zeros((7, n_time + 1)) - dM = np.zeros((3, n_time)) - dt = t[1] - t[0] - - x_d = np.array([1, 0, 0]) # Body frame +x is the line of sight - - for i in range(n_time + 1): - r = r_target - r_rtn[:3, i].reshape((3,1)) # Adjust target location if necessary - x_rho = r / np.linalg.norm(r) - q_v = skw(x_d) @ x_rho / np.sqrt(2 * (1 + x_d @ x_rho)) - q_0 = np.sqrt(2 * (1 + x_d @ x_rho)) / 2 - qw[0:4, i] = np.concatenate((np.array([q_0]), q_v)).flatten() - - # Check for singularity - if np.any(np.isnan(q_v)): - print(f'warning; singularity at timestep {i+1}/{n_time+1}') - if i > 0: - qw[0:4, i] = qw[0:4, i-1] - - if i > 0: - # Compute the angular velocity - q1 = qw[0:4, i-1] - q2 = qw[0:4, i] - w = 2/dt * np.array([ - q1[0]*q2[1] - q1[1]*q2[0] - q1[2]*q2[3] + q1[3]*q2[2], - q1[0]*q2[2] + q1[1]*q2[3] - q1[2]*q2[0] - q1[3]*q2[1], - q1[0]*q2[3] - q1[1]*q2[2] + q1[2]*q2[1] - q1[3]*q2[0] - ]) - qw[4:7, i-1] = w - - if i > 1: - dM[:, i-2] = qw[4:7, i-1] - qw[4:7, i-2] - - # Set the angular velocity at the end to the previous value - qw[4:7, -1] = qw[4:7, -2] - dM[:, -1] = np.zeros(3) - - return qw, dM - - -def get_rot_discrete_control(qw_0, action, t, J): - """ - Nonlinear propagation of rotational motion (3dof) with time-variant control input - inputs: - - x_ref: initial state of the deputy [q_0, w_0] (7x1) - - action: control input (3xN) - - t: time vector (N,) - - J: inertia matrix of the deputy (3x3) - returns: - - qw_list: list of quaternion and angular velocity (7xN) - """ - - qw_list = np.empty(shape=(7,len(t)), dtype=float) - - # oe_list[:,0] = koe_d.reshape((6,)) - qw_list[:,0] = qw_0.reshape((7,)) - - for i in range(len(t)-1): - dm = action[:,i] # in the deputy's body frame - T = dm / (t[i+1] - t[i]) # in deputy's body frame - time = np.array([0, t[i+1]-t[i]]) - qw_ = odeint(ode_qw, qw_list[:,i].flatten(), time, args=(J, T)) - qw_list[:,i+1] = qw_[-1,:].reshape((7,)) - - return qw_list - - - -## analytical solution of torque-free motion -# assumimg I1 >= I2 >= I3 -def qw_fwd(q,w,t0,tf,J): - I1, I2, I3 = J[0,0], J[1,1], J[2,2] - H = J @ w - T = 1/2 * w.T @ H - - ω1m = ((H**2 - 2*I3*T) / (I1*(I2-I3)))**0.5 - if H**2 >= 2*I2*T: - ω2m = ((2*I2*T - H**2) / (I1*(I1-I3)))**0.5 - else: - ω2m = ((H**2 - 2*I3*T) / (I2*(I3-I3)))**0.5 - ω3m = ((2*I1*T - H**2) / (I3*(I1-I3)))**0.5 - - # elliptic modulus - if H**2 >= 2*I2*T: - k = (I2-I3)*(2*I1*T-H**2) / ((I1-I2)*(H**2-2*I3*T)) - else: - k = (I1-I2)*(H**2 - 2*I3*T) / ((I2-I3)*(2*I1*T-H**2)) - - # frequency of ω2(t) - if H**2 >= 2*I2*T: - Ω = ((I1-I2)*(H**2 - 2*I3*T) / (I1*I2*I3))**0.5 - else: - Ω = ((I2-I3)*(2*I1*T - H**2) / (I1*I2*I3))**0.5 - - # imcomplete elliptic integral of the first kind - K = sp.special.ellipk(k**2) - Θ = np.arcsin(w[1] / ω2m) - - t1 = t0 - 1/Ω * (sp.special.ellipkinc(Θ, k**2) + λ*K) - - s1 = np.sign(w[0]) - s3 = np.sign(w[2]) - - τ = Ω * (tf-t1) - τ0 = Ω * (t0-t1) - - sn, cn, dn, _ = sp.special.ellipj(τ, k) - - if H**2 >= 2*I2*T: - f1 = s1 * dn - f3 = -s1 * cn - else: - f1 = -s3 * cn - f3 = s3 * dn - - ω1 = ω1m * f1 - ω2 = ω2m * sn - ω3 = ω3m * f3 - diff --git a/env_original/rpo_detubmling/dynamics/dynamics_trans.py b/env_original/rpo_detubmling/dynamics/dynamics_trans.py deleted file mode 100644 index 5b561c106..000000000 --- a/env_original/rpo_detubmling/dynamics/dynamics_trans.py +++ /dev/null @@ -1,610 +0,0 @@ -########### File containing relevant dynamics models - -# Orbit dynamics -import numpy as np -import numpy.linalg as la -from dyn_misc import * -from oe_conversion import * - -# Constants -J2 = 0.001082635819197 -R_E = 6.3781363e+06 # Earth radius [m] -mu_E = 3.986004415e+14 # Earth gravitational parameter [m^3/s^2] - -# Functions -def map_mtx_roe_to_rtn(oe, t=0): - - a = oe.item(0) - u = oe.item(4) + oe.item(5) - n = np.sqrt(mu_E/a**3) - - map_1 = np.array([1, 0, -np.cos(u), -np.sin(u), 0, 0]).reshape((1,6)) - map_2 = np.array([-(3/2)*n*t, 1, 2*np.sin(u), -2*np.cos(u), 0, 0]).reshape((1,6)) - map_3 = np.array([0, 0, 0, 0, np.sin(u), -np.cos(u)]).reshape((1,6)) - map_4 = np.array([0, 0, np.sin(u)*n, -np.cos(u)*n, 0, 0]).reshape((1,6)) - map_5 = np.array([-(3/2)*n, 0, 2*np.cos(u)*n, 2*np.sin(u)*n, 0, 0]).reshape((1,6)) - map_6 = np.array([0, 0, 0, 0, np.cos(u)*n, np.sin(u)*n]).reshape((1,6)) - - map = np.concatenate((map_1, map_2, map_3, map_4, map_5, map_6), axis=0) - - return map - -def map_roe_to_rtn(roe, oe, t=0): - - map = map_mtx_roe_to_rtn(oe, t) - - return map.dot(roe) - -def map_rtn_to_roe(rtn, oe, t=0): - - map = map_mtx_roe_to_rtn(oe, t) - - return la.solve(map, rtn) - -def state_transition_roe(oe, t): - - # From : Koenig A.W., Guffanti T., D'Amico S.; - # New State Transition Matrices for Spacecraft Relative Motion in Perturbed Orbits; - # Journal of Guidance, Control, and Dynamics, Vol. 40, No. 7, pp. 1749-1768 (September 2017). - - a = oe.item(0) - e = oe.item(1) - i = oe.item(2) - w = oe.item(4) - - n = np.sqrt(mu_E/a**3) - eta=np.sqrt(1-e**2) - k=3/4*J2*R_E**2*np.sqrt(mu_E)/(a**(7/2)*eta**4) - E=1+eta - F=4+3*eta - G=1/eta**2 - P=3*np.cos(i)**2-1 - Q=5*np.cos(i)**2-1 - S=np.sin(2*i) - T=np.sin(i)**2 - - w_dot=k*Q - w_f=w+w_dot*t - e_xi=e*np.cos(w) - e_yi=e*np.sin(w) - e_xf=e*np.cos(w_f) - e_yf=e*np.sin(w_f) - - Phi_11=1 - Phi_12=0 - Phi_13=0 - Phi_14=0 - Phi_15=0 - Phi_16=0 - Phi_1 = np.array([Phi_11,Phi_12,Phi_13,Phi_14,Phi_15,Phi_16]).reshape((1,6)) - Phi_21= -(7/2*k*E*P+3/2*n)*t - Phi_22=1 - Phi_23=k*e_xi*F*G*P*t - Phi_24=k*e_yi*F*G*P*t - Phi_25=-k*F*S*t - Phi_26=0 - Phi_2 = np.array([Phi_21,Phi_22,Phi_23,Phi_24,Phi_25,Phi_26]).reshape((1,6)) - Phi_31=7/2*k*e_yf*Q*t - Phi_32=0 - Phi_33=np.cos(w_dot*t)-4*k*e_xi*e_yf*G*Q*t - Phi_34=-np.sin(w_dot*t)-4*k*e_yi*e_yf*G*Q*t - Phi_35=5*k*e_yf*S*t - Phi_36=0 - Phi_3 = np.array([Phi_31,Phi_32,Phi_33,Phi_34,Phi_35,Phi_36]).reshape((1,6)) - Phi_41=-7/2*k*e_xf*Q*t - Phi_42=0 - Phi_43=np.sin(w_dot*t)+4*k*e_xi*e_xf*G*Q*t - Phi_44=np.cos(w_dot*t)+4*k*e_yi*e_xf*G*Q*t - Phi_45=-5*k*e_xf*S*t - Phi_46=0 - Phi_4 = np.array([Phi_41,Phi_42,Phi_43,Phi_44,Phi_45,Phi_46]).reshape((1,6)) - Phi_51=0 - Phi_52=0 - Phi_53=0 - Phi_54=0 - Phi_55=1 - Phi_56=0 - Phi_5 = np.array([Phi_51,Phi_52,Phi_53,Phi_54,Phi_55,Phi_56]).reshape((1,6)) - Phi_61=7/2*k*S*t - Phi_62=0 - Phi_63=-4*k*e_xi*G*S*t - Phi_64=-4*k*e_yi*G*S*t - Phi_65=2*k*T*t - Phi_66=1 - Phi_6 = np.array([Phi_61,Phi_62,Phi_63,Phi_64,Phi_65,Phi_66]).reshape((1,6)) - - return np.concatenate((Phi_1, Phi_2, Phi_3, Phi_4, Phi_5, Phi_6), axis=0) - -def control_input_matrix_roe(oe): - - a = oe.item(0) - u = oe.item(4) + oe.item(5) - n = np.sqrt(mu_E/a**3) - - b_1 = np.array([0, 2/n, 0]).reshape((1,3)) - b_2 = np.array([-2/n, 0, 0]).reshape((1,3)) - b_3 = np.array([np.sin(u)/n, 2*np.cos(u)/n, 0]).reshape((1,3)) - b_4 = np.array([-np.cos(u)/n, 2*np.sin(u)/n, 0]).reshape((1,3)) - b_5 = np.array([0, 0, np.cos(u)/n]).reshape((1,3)) - b_6 = np.array([0, 0, np.sin(u)/n]).reshape((1,3)) - - return np.concatenate((b_1, b_2, b_3, b_4, b_5, b_6), axis=0) - -def dynamics_roe(state, action, oe, t): - - stm = state_transition_roe(oe, t) - cim = control_input_matrix_roe(oe) - - new_state = stm.dot(state + cim.dot(action)) - - return new_state - -def kepler_dyanmics_oe(oe, dt): - - a = oe.item(0) - n = np.sqrt(mu_E/a**3) - new_oe = np.array([oe.item(0), oe.item(1), oe.item(2), oe.item(3), oe.item(4), oe.item(5) + n*dt]).reshape((6,)) - - return new_oe - -def dynamics_roe_optimization(oe_0, t_0, horizon, n_time): - - a = oe_0.item(0) - n = np.sqrt(mu_E/a**3) - period = 2*np.pi/n - - # Time discretization (given the number of samples defined in rpod_scenario) - if n_time-1 != 0: - dt = horizon*period/(n_time-1) - else: - dt = 0. - - stm = np.empty(shape=(6, 6, n_time-1), dtype=float) - cim = np.empty(shape=(6, 3, n_time), dtype=float) - psi = np.empty(shape=(6, 6, n_time), dtype=float) - - time = np.empty(shape=(n_time,), dtype=float) - oe = np.empty(shape=(6, n_time), dtype=float) - - # Time 0 - time[0] = t_0 - oe[:,0] = oe_0 - - cim[:,:,0] = control_input_matrix_roe(oe[:,0]) - psi[:,:,0] = map_mtx_roe_to_rtn(oe[:,0]) - - # Time Loop - for iter in range(n_time-1): - - # Precompute the STM - stm[:,:,iter] = state_transition_roe(oe[:,iter],dt) # N.B.: is a-dimentional - - # Propagate reference orbit (this assumes keplerian dynamics on the OE, it is an approximation) - time[iter+1] = time[iter] + dt - oe[:,iter+1] = np.array([oe_0.item(0), oe_0.item(1), oe_0.item(2), oe_0.item(3), oe_0.item(4), oe_0.item(5) + n*(time.item(iter+1)-t_0)]).reshape((6,)) - - # Control input matrix - cim[:,:,iter+1] = control_input_matrix_roe(oe[:,iter+1]) # N.B.: has dimension [s] - - # ROE to RTN map - psi[:,:,iter+1] = map_mtx_roe_to_rtn(oe[:,iter+1]) # N.B.: has dimension [-,-,-,1/s,1/s,1/s] - - return stm, cim, psi, oe, time, dt - -def roe_to_rtn_horizon(roe, oe, n_time): - - rtn = np.empty(shape=(6, n_time), dtype=float) - for i in range(n_time): - rtn[:,i] = map_roe_to_rtn(roe[:,i], oe[:,i]) - - return rtn - -def state_transition_hcw(oe, t): - - a = oe.item(0) - n = np.sqrt(mu_E/a**3) - - Phi_11=4-3*np.cos(n*t) - Phi_12=6*(np.sin(n*t)-n*t) - Phi_13=0 - Phi_14=3*n*np.sin(n*t) - Phi_15=6*n*(np.cos(n*t)-1) - Phi_16=0 - Phi_1 = np.array([Phi_11,Phi_12,Phi_13,Phi_14,Phi_15,Phi_16]).reshape((6,1)) # first column - Phi_21=0 - Phi_22=1 - Phi_23=0 - Phi_24=0 - Phi_25=0 - Phi_26=0 - Phi_2 = np.array([Phi_21,Phi_22,Phi_23,Phi_24,Phi_25,Phi_26]).reshape((6,1)) - Phi_31=0 - Phi_32=0 - Phi_33=np.cos(n*t) - Phi_34=0 - Phi_35=0 - Phi_36=-n*np.sin(n*t) - Phi_3 = np.array([Phi_31,Phi_32,Phi_33,Phi_34,Phi_35,Phi_36]).reshape((6,1)) - Phi_41=(1/n)*np.sin(n*t) - Phi_42=(2/n)*(np.cos(n*t)-1) - Phi_43=0 - Phi_44=np.cos(n*t) - Phi_45=-2*np.sin(n*t) - Phi_46=0 - Phi_4 = np.array([Phi_41,Phi_42,Phi_43,Phi_44,Phi_45,Phi_46]).reshape((6,1)) - Phi_51=(2/n)*(1-np.cos(n*t)) - Phi_52=(1/n)*(4*np.sin(n*t)-3*n*t) - Phi_53=0 - Phi_54=2*np.sin(n*t) - Phi_55=4*np.cos(n*t)-3 - Phi_56=0 - Phi_5 = np.array([Phi_51,Phi_52,Phi_53,Phi_54,Phi_55,Phi_56]).reshape((6,1)) - Phi_61=0 - Phi_62=0 - Phi_63=(1/n)*np.sin(n*t) - Phi_64=0 - Phi_65=0 - Phi_66=np.cos(n*t) - Phi_6 = np.array([Phi_61,Phi_62,Phi_63,Phi_64,Phi_65,Phi_66]).reshape((6,1)) - - return np.concatenate((Phi_1, Phi_2, Phi_3, Phi_4, Phi_5, Phi_6), axis=1) - -def state_transition_hcw_jac_dt(oe, t): - - a = oe.item(0) - n = np.sqrt(mu_E/a**3) - - Phi_11=3*n*np.sin(n*t) - Phi_12=6*n*(np.cos(n*t)-1) - Phi_13=0 - Phi_14=3*(n**2)*np.cos(n*t) - Phi_15=-6*(n**2)*np.sin(n*t) - Phi_16=0 - Phi_1 = np.array([Phi_11,Phi_12,Phi_13,Phi_14,Phi_15,Phi_16]).reshape((6,1)) # first column - Phi_21=0 - Phi_22=0 - Phi_23=0 - Phi_24=0 - Phi_25=0 - Phi_26=0 - Phi_2 = np.array([Phi_21,Phi_22,Phi_23,Phi_24,Phi_25,Phi_26]).reshape((6,1)) - Phi_31=0 - Phi_32=0 - Phi_33=-n*np.sin(n*t) - Phi_34=0 - Phi_35=0 - Phi_36=-(n**2)*np.cos(n*t) - Phi_3 = np.array([Phi_31,Phi_32,Phi_33,Phi_34,Phi_35,Phi_36]).reshape((6,1)) - Phi_41=np.cos(n*t) - Phi_42=-2*np.sin(n*t) - Phi_43=0 - Phi_44=-n*np.sin(n*t) - Phi_45=-2*n*np.cos(n*t) - Phi_46=0 - Phi_4 = np.array([Phi_41,Phi_42,Phi_43,Phi_44,Phi_45,Phi_46]).reshape((6,1)) - Phi_51=2*np.sin(n*t) - Phi_52=4*np.cos(n*t)-3 - Phi_53=0 - Phi_54=2*n*np.cos(n*t) - Phi_55=-4*n*np.sin(n*t) - Phi_56=0 - Phi_5 = np.array([Phi_51,Phi_52,Phi_53,Phi_54,Phi_55,Phi_56]).reshape((6,1)) - Phi_61=0 - Phi_62=0 - Phi_63=np.cos(n*t) - Phi_64=0 - Phi_65=0 - Phi_66=-n*np.sin(n*t) - Phi_6 = np.array([Phi_61,Phi_62,Phi_63,Phi_64,Phi_65,Phi_66]).reshape((6,1)) - - return np.concatenate((Phi_1, Phi_2, Phi_3, Phi_4, Phi_5, Phi_6), axis=1) - -def dynamics_hcw_optimization_dt_const(oe_0, t_0, horizon, n_time): - - a = oe_0.item(0) - n = np.sqrt(mu_E/a**3) - period = 2*np.pi/n - - # Time discretization (given the number of samples defined in rpod_scenario) - if n_time-1 != 0: - dt = horizon*period/(n_time-1) - else: - dt = 0. - - stm = np.empty(shape=(6, 6, n_time-1), dtype=float) - stm_jac = np.empty(shape=(6, 6, n_time-1), dtype=float) - - time = np.empty(shape=(n_time,), dtype=float) - oe = np.empty(shape=(6, n_time), dtype=float) - dt_vect = np.empty(shape=(n_time-1,), dtype=float) - - # Time 0 - time[0] = t_0 - oe[:,0] = oe_0 - - # Time Loop - for iter in range(n_time-1): - - # Precompute the STM - stm[:,:,iter] = state_transition_hcw(oe[:,iter],dt) - stm_jac[:,:,iter] = state_transition_hcw_jac_dt(oe[:,iter],dt) - dt_vect[iter] = dt - - # Propagate reference orbit (this assumes keplerian dynamics on the OE, it is an approximation) - time[iter+1] = time[iter] + dt - oe[:,iter+1] = np.array([oe_0.item(0), oe_0.item(1), oe_0.item(2), oe_0.item(3), oe_0.item(4), oe_0.item(5) + n*(time.item(iter+1)-t_0)]).reshape((6,)) - - return stm, stm_jac, oe, time, dt_vect - -def dynamics_hcw_optimization_dt_opt(oe_0, t_0, dt_opt): - - n_time = len(dt_opt) + 1 - - a = oe_0.item(0) - n = np.sqrt(mu_E/a**3) - - stm = np.empty(shape=(6, 6, n_time-1), dtype=float) - stm_jac = np.empty(shape=(6, 6, n_time-1), dtype=float) - - time = np.empty(shape=(n_time,), dtype=float) - oe = np.empty(shape=(6, n_time), dtype=float) - - # Time 0 - time[0] = t_0 - oe[:,0] = oe_0 - - # Time Loop - for iter in range(n_time-1): - - # Precompute the STM - stm[:,:,iter] = state_transition_hcw(oe[:,iter],dt_opt[iter]) - stm_jac[:,:,iter] = state_transition_hcw_jac_dt(oe[:,iter],dt_opt[iter]) - - # Propagate reference orbit (this assumes keplerian dynamics on the OE, it is an approximation) - time[iter+1] = time[iter] + dt_opt[iter] - oe[:,iter+1] = np.array([oe_0.item(0), oe_0.item(1), oe_0.item(2), oe_0.item(3), oe_0.item(4), oe_0.item(5) + n*(time.item(iter+1)-t_0)]).reshape((6,)) - - return stm, stm_jac, oe, time - -def check_ps_cart_hcw(states, oe_vec, n_time, horizon_safe, n_safe, DEED): - - states_ps = np.empty(shape=(6, n_time, n_safe), dtype=float) - min_sep_ps = np.empty(shape=(n_time, ), dtype=float) - - a = oe_vec[0, 0] - n = np.sqrt(mu_E/a**3) - period = 2*np.pi/n - # Time discretization (given the number of samples defined in rpod_scenario) - if n_safe-1 != 0: - dt_safe = horizon_safe*period/(n_safe-1) - else: - dt_safe = 0. - - for k in range(n_time): - sep_k = np.empty(shape=(1, n_safe), dtype=float) - oe_j = oe_vec[:, k] - state_j = states[:, k] - sep_k[:,0] = np.sqrt(np.transpose(state_j).dot(DEED.dot(state_j))) - states_ps[:,k,0] = state_j - for j in range(n_safe-1): - stm_j = state_transition_hcw(oe_j, dt_safe) - state_j = stm_j.dot(state_j) - states_ps[:,k,j+1] = state_j - sep_k[:,j+1] = np.sqrt(np.transpose(state_j).dot(DEED.dot(state_j))) - oe_j = np.array([oe_j.item(0), oe_j.item(1), oe_j.item(2), oe_j.item(3), oe_j.item(4), oe_j.item(5) + n*dt_safe]).reshape((6,)) - t_star_j = np.argmin(sep_k) - min_sep_ps[k] = sep_k[:,t_star_j] - - return states_ps, min_sep_ps - - -### nonlinear dynamics - -# GVE for KOE [a, e, i, Omega, omega, M] -# F = [F_R, F_T, F_N] -def gve_koe(oe,t,mu,F, j2=True, drag=False): - """ - GVE for KOE [a, e, i, Omega, omega, M] - inputs: - oe : orbital elements [a, e, i, Omega, omega, M] - t : time - mu : gravitational parameter - F : non-two-body forces [F_R, F_T, F_N] - j2 : boolean for J2 perturbation - returns: - d_oe : time derivative of the KOE - """ - - a = oe.item(0) - e = oe.item(1) - i = oe.item(2) - Omega = oe.item(3) - w = oe.item(4) - M = oe.item(5) - - E = solve_kepler(M, e) - nu = 2*np.arctan(np.sqrt((1+e)/(1-e))*np.tan(E/2)) - - if np.isnan(nu): - print("e = ", e) - print("nu = ", nu) - print(" X = ", (1+e)/(1-e)) - - h = np.sqrt(mu*a*(1-e**2)) - n = np.sqrt(mu/a**3) - p = a*(1-e**2) - r = a*(1-e**2)/(1+e*np.cos(nu)) - L = Omega + w + nu - - if j2: - J2 = 1082.64e-6 - Re = 6378.1363e3 - h_ = np.tan(i/2)*np.cos(Omega) - k_ = np.tan(i/2)*np.sin(Omega) - Delta_J2r = (-3 * mu * J2 * Re**2 / (2 * r**4)) * (1 - 12 * (h_ * np.sin(L) - k_ * np.cos(L))**2 / (1 + h_**2 + k_**2)**2) - Delta_J2t = (-12 * mu * J2 * Re**2 / r**4) * ((h_ * np.sin(L) - k_ * np.cos(L)) * (h_ * np.cos(L) + k_ * np.sin(L)) / (1 + h_**2 + k_**2)**2) - Delta_J2n = (-6 * mu * J2 * Re**2 / r**4) * ((1 - h_**2 - k_**2) * (h_ * np.sin(L) - k_ * np.cos(L)) / (1 + h_**2 + k_**2)**2) - F = np.array([F[0] + Delta_J2r, F[1] + Delta_J2t, F[2] + Delta_J2n]).reshape((3,1)) - - if drag: - rho = 0 # atmospheric density [kg/m^3] - S = 0 # surface area [m^2] - CD = 0 # drag coefficient [-] - # velocity in ECI (I know there should be a easier way to do this... later work) - f = e * np.cos(w + Omega) - g = e * np.sin(w + Omega) - - v = np.sqrt(mu * (2/r - 1/a)) - vr = np.sqrt(mu/p)*(f*np.sin(L) - g*np.cos(L)) - vt = np.sqrt(mu/p)*(1 + f*np.cos(L) + g*np.sin(L)) - - Delta_Dr = - 0.5 * rho * S * CD * v * vr - Delta_Dt = - 0.5 * rho * S * CD * v * vt - - F = np.array([F[0] + Delta_Dr, F[1] + Delta_Dt, F[2]]).reshape((3,1)) - - # a - A11 = (2 * a**2 * e * np.sin(nu)) / h - A12 = (2 * a**2 * p) / (r * h) - A13 = 0 - # e - A21 = np.sqrt(1-e**2) / (n*a) * np.sin(nu) - A22 = np.sqrt(1-e**2) / (n*a) * ( np.cos(nu) + (e+np.cos(nu))/(1+e*np.cos(nu)) ) - A23 = 0 - # i - A31 = 0 - A32 = 0 - A33 = (r * np.cos(nu + w)) / h - # Omega - A41 = 0 - A42 = 0 - A43 = (r * np.sin(nu + w)) / (h * np.sin(i)) - # omega - A51 = np.sqrt(1-e**2)/(n*a*e) * (- np.cos(nu)) - A52 = np.sqrt(1-e**2)/(n*a*e) * np.sin(nu) * (1 + r/p) - A53 = - (r * np.sin(nu + w) * np.cos(i)) / (h * np.sin(i)) - # M - A61 = h/mu * np.sqrt(1-e**2)/e * (np.cos(nu) - 2*e/(1-e**2)*r/a) - A62 = - h/mu * np.sqrt(1-e**2)/e * (1+1/(1-e**2)*r/a)*np.sin(nu) - A63 = 0 - - row1 = np.array([A11, A12, A13]).reshape(1, 3) - row2 = np.array([A21, A22, A23]).reshape(1, 3) - row3 = np.array([A31, A32, A33]).reshape(1, 3) - row4 = np.array([A41, A42, A43]).reshape(1, 3) - row5 = np.array([A51, A52, A53]).reshape(1, 3) - row6 = np.array([A61, A62, A63]).reshape(1, 3) - - A = np.concatenate((row1, row2, row3, row4, row5, row6), axis=0) - B = np.array([0, 0, 0, 0, 0, n]) #.reshape(6,1) - return (A.dot(F.flatten()) + B).flatten() - - -def gve_qnsroe_full(x, t, mu_E, F, j2=True, drag=False): - """ - nonlinear GVE for the QNSROE dynamics - input: - x : [qnsroe_d(t), koe_c(t)] (12 x 1) - t : time - mu_E : gravitational parameter of the Earth - F : control input - j2 : boolean for J2 perturbation - drag : boolean for drag perturbation - """ - - ac = x.item(6) - ec = x.item(7) - ic = x.item(8) - Omegac = x.item(9) - omegac = x.item(10) - Mc = x.item(11) - - # re-scale the sma term - qnsroe = x[0:6] - koe_d = qnsroe_to_koe(qnsroe, x[6:12]).flatten() - - ad = koe_d.item(0) - ed = koe_d.item(1) - id = koe_d.item(2) - Omegad = koe_d.item(3) - omegad = koe_d.item(4) - Md = koe_d.item(5) - - F0 = np.array([0,0,0]) - - dkoe_c = gve_koe(x[6:12], t, mu_E, F0, j2, drag) - dkoe_d = gve_koe(koe_d, t, mu_E, F, j2, drag) - - dad = dkoe_d.item(0) - ded = dkoe_d.item(1) - did = dkoe_d.item(2) - dOmegad = dkoe_d.item(3) - domegad = dkoe_d.item(4) - dMd = dkoe_d.item(5) - - dac = dkoe_c.item(0) - dec = dkoe_c.item(1) - dic = dkoe_c.item(2) - dOmegac = dkoe_c.item(3) - domegac = dkoe_c.item(4) - dMc = dkoe_c.item(5) - - droe1 = ((dad - dac)*ac - qnsroe[0]*dac) / ac**2 - droe2 = (dMd + domegad) - (dMc + domegac) + (dOmegad - dOmegac) * np.cos(ic) - dic * (Omegad - Omegac) * np.sin(ic) - droe3 = ded * np.cos(omegad) - ed * domegad * np.sin(omegad) \ - - dec * np.cos(omegac) + ec * domegac * np.sin(omegac) - droe4 = ded * np.sin(omegad) + ed * domegad * np.cos(omegad) \ - - dec * np.sin(omegac) - ec * domegac * np.cos(omegac) - droe5 = did - dic - droe6 = (dOmegad - dOmegac) * np.sin(ic) + dic * (Omegad - Omegac) * np.cos(ic) - - # print(np.array([ droe1, droe2, droe3, droe4, droe5, droe6 ]).flatten()) - return np.array([ droe1, droe2, droe3, droe4, droe5, droe6, dac, dec, dic, dOmegac, domegac, dMc ]).flatten() - - - -### Linearization model - -def linearize_trans(oe, time): - """ - linearize the nonlinear dynamics of 6DoF relative motion - input: - oe: OE (chief); 6 x (n_time+1) - qw: attitude (deputy); 7 x (n_time+1) - time: time; 1 x (n_time+1) - J: inertia matrix - return: - mats: dictionary containing the linearized matrices - stm: state transition matrix; 6 x 6 x n_time - stm_qw: state transition matrix for attitude; 7 x 7 x n_time - cim: control input matrix; 6 x 3 x n_time - cim_qw: control input matrix for attitude; 7 x 3 x n_time - psi: ROE -> RTN map; 6 x 6 x (n_time+1) - rs: residual for translational motion; 6 x n_time - rqw: residual for rotational motion; 7 x n_time - """ - - n_time = len(time) - 1 - dt = time[1]-time[0] - - psi = np.empty(shape=(6, 6, n_time+1), dtype=float) # ROE -> RTN map - stm = np.empty(shape=(6, 6, n_time), dtype=float) - cim = np.empty(shape=(6, 3, n_time), dtype=float) - rs = np.empty(shape=(6, n_time), dtype=float) - - # Time Loop - for i in range(n_time+1): - - # ROE to RTN map (TODO: check only translational motion matters (i think so?)) - psi[:,:,i] = map_mtx_roe_to_rtn(oe[:,i]) # N.B.: has dimension [-,-,-,1/s,1/s,1/s] - - if i < n_time: - stm[:,:,i] = state_transition_roe(oe[:,i],dt) # N.B.: is a-dimentional - cim[:,:,i] = control_input_matrix_roe(oe[:,i]) # N.B.: has dimension [s] - - # no residual computation for now - - mats = {"stm_r": stm, "cim_r": cim, "psi": psi, "rs": rs} - - return mats - diff --git a/env_original/rpo_detubmling/dynamics/oe_conversion.py b/env_original/rpo_detubmling/dynamics/oe_conversion.py deleted file mode 100644 index 7ee8c1fb8..000000000 --- a/env_original/rpo_detubmling/dynamics/oe_conversion.py +++ /dev/null @@ -1,143 +0,0 @@ -""" - Conversions of orbital elemnts: - - koe_to_rv - - rv_to_koe - - qnsroe_to_koe - - cart2rtn -""" - -import numpy as np -import numpy.linalg as la -from dyn_misc import * - -def koe_to_rv(koe, mu): - """ - inputs: - koe: [a,e,i,Omega,omega,M] (Keplarian orbital elements) - mu: gravitational parameter of primary - output: - rv: 6-element [r,v] in Cartesian coordinate - """ - - a,e,i,Omega,omega,M = koe - - E = solve_kepler(M, e) - nu = 2*np.arctan(np.sqrt((1+e)/(1-e))*np.tan(E/2)) - - p = a*(1-e**2) - r = p/(1+e*np.cos(nu)) - - # perifocal frame - rp = r*np.array([np.cos(nu), np.sin(nu), 0]).reshape((3,1)) - vp = np.sqrt(mu/p)*np.array([-np.sin(nu), e+np.cos(nu), 0]).reshape((3,1)) - - # rotation matrix from perifocal to ECI - r_cart = Rz(-Omega).dot(Rx(-i)).dot(Rz(-omega)).dot(rp) - v_cart = Rz(-Omega).dot(Rx(-i)).dot(Rz(-omega)).dot(vp) - - # return np.concatenate((r_cart, v_cart), axis=0) - return r_cart.flatten(), v_cart.flatten() - - -def rv_to_koe(rv, mu): - """ - inputs: - rv: 6-element [r,v] in Cartesian coordinate - mu: gravitational parameter of primary - output: - oe: [a,e,i,Omega,omega,M] (Keplarian orbital elements) - """ - rvec = rv[0:3] - vvec = rv[3:6] - hvec = np.cross(rvec, vvec) - - r = la.norm(rvec) - v = la.norm(vvec) - h = la.norm(hvec) - - nvec = np.cross(np.array([0,0,1]), hvec) / np.linalg.norm(np.cross(np.array([0,0,1]), hvec)) - - ene = 1/2*v**2 - mu/r - a = -mu/(2*ene) - evec = (np.cross(vvec, hvec) - mu*rvec/r) / mu - e = la.norm(evec) - i = np.arccos(hvec[2]/h) - Omega = np.arctan2(nvec[1], nvec[0]) - omega = np.arccos(np.dot(evec, nvec)/e) - if np.dot(evec, np.array([0,0,1])) < 0: - omega = -omega - - nu = np.arccos(np.dot(evec, rvec)/(e*r)) - if np.dot(rvec, vvec) < 0: - nu = -nu - - if e > 1 - 1e-5: - raise ValueError('Hyperbolic orbit') - - E = 2 * np.arctan(np.sqrt((1-e)/(1+e))*np.tan(nu/2)) - M = E - e*np.sin(E) - - return np.array([a, e, i, Omega, omega, M]) - - -def qnsroe_to_koe(qnsroe, koe_c): - """ - return deputy's KOE based on the chief's KOE and the deputy's ROE - inputs: - qnsroe: [da, dl, dex, dey, dix, diy] - koe_c: [a,e,i,Omega,omega,M] - returns: - koe_d: [ad, ed, id, Omegad, omegad, Md] - """ - - da = qnsroe.item(0) - dl = qnsroe.item(1) - dex = qnsroe.item(2) - dey = qnsroe.item(3) - dix = qnsroe.item(4) - diy = qnsroe.item(5) - - a = koe_c.item(0) - e = koe_c.item(1) - i = koe_c.item(2) - Omega = koe_c.item(3) - omega = koe_c.item(4) - M = koe_c.item(5) - - ad = da * a + a - exd = dex + e*np.cos(omega) - eyd = dey + e*np.sin(omega) - ed = np.sqrt(exd**2 + eyd**2) - omegad = np.arctan2(eyd, exd) - id = dix + i - Omegad = diy / np.sin(i) + Omega - Md = dl - (Omegad - Omega) * np.cos(i) + (M + omega) - omegad - - return np.array([ ad, ed, id, Omegad, omegad, Md ]).reshape((6,1)) - - -# returns the RTN coordinate frame of the deputy w.r.t. the chief's RTN -def cart2rtn(cart_d, cart_c): - - r_d = cart_d[0:3] - v_d = cart_d[3:6] - r_c = cart_c[0:3] - v_c = cart_c[3:6] - - r_rel = r_d - r_c - v_rel = v_d - v_c - - # radial vector - ur = r_d/la.norm(r_c) - un = np.cross(r_c,v_c)/la.norm(np.cross(r_c,v_c)) - ut = np.cross(un,ur) - - # relative position vector in RTN - r_r = np.dot(r_rel,ur) - r_t = np.dot(r_rel,ut) - r_n = np.dot(r_rel,un) - v_r = np.dot(v_rel,ur) - v_t = np.dot(v_rel,ut) - v_n = np.dot(v_rel,un) - - return np.array([r_r, r_t, r_n, v_r, v_t, v_n]) \ No newline at end of file diff --git a/env_original/rpo_detubmling/dynamics/plot_misc.py b/env_original/rpo_detubmling/dynamics/plot_misc.py deleted file mode 100644 index 55b204a59..000000000 --- a/env_original/rpo_detubmling/dynamics/plot_misc.py +++ /dev/null @@ -1,100 +0,0 @@ -""" -Plotting / Animation functions from the history of quaternion -""" - -import numpy as np -import matplotlib.pyplot as plt -from dynamics_rot import * -from mpl_toolkits.mplot3d import Axes3D -from matplotlib.animation import FFMpegWriter, PillowWriter # Import FFMpegWriter -import matplotlib.animation as animation - - -def plot_attitude(ax, rtn, qw, height=20): - """ - plot attiude in 3D (just one frame) - """ - R_i = q2rotmat(qw[0:4]) - ex, ey, ez = R_i @ np.array([height, 0, 0]), R_i @ np.array([0, height, 0]), R_i @ np.array([0, 0, height]) - # plot axis - ax.plot3D([rtn[1], rtn[1] + ex[1]], [rtn[2], rtn[2] + ex[2]], [rtn[0], rtn[0] + ex[0]], '-r', linewidth=2) - ax.plot3D([rtn[1], rtn[1] + ey[1]], [rtn[2], rtn[2] + ey[2]], [rtn[0], rtn[0] + ey[0]], '-g', linewidth=2) - ax.plot3D([rtn[1], rtn[1] + ez[1]], [rtn[2], rtn[2] + ez[2]], [rtn[0], rtn[0] + ez[0]], '-b', linewidth=2) - - -def plot_attitude_track(ax, rtn, qw, coneAngle, height=20): - if rtn.shape[1] != qw.shape[1]: - raise ValueError("rtn and qw have different length. Check the input variable") - - Nfreq = rtn.shape[1] // 10 # frequency of plotting axes - N = rtn.shape[1] - - # Cone parameters - radius = height * np.tan(coneAngle) - # Meshgrid for polar coordinates - r = np.linspace(0, radius, 50) - theta = np.linspace(0, 2*np.pi, 50) - r, theta = np.meshgrid(r, theta) - # Convert polar to cartesian coordinates - coneX = r * np.cos(theta) - coneY = r * np.sin(theta) - coneZ = r * height / radius # Scale Z based on height and radius - coneX, coneY, coneZ = coneZ, coneX, coneY # RTN trick - - for i in range(N): - if i % Nfreq == 0 or i == N-1: - R_i = q2rotmat(qw[:4, i]) - ex, ey, ez = R_i @ np.array([height, 0, 0]), R_i @ np.array([0, height, 0]), R_i @ np.array([0, 0, height]) - - # plot axis - ax.plot3D([rtn[1, i], rtn[1, i] + ex[1]], [rtn[2, i], rtn[2, i] + ex[2]], [rtn[0, i], rtn[0, i] + ex[0]], '-r', linewidth=2) - ax.plot3D([rtn[1, i], rtn[1, i] + ey[1]], [rtn[2, i], rtn[2, i] + ey[2]], [rtn[0, i], rtn[0, i] + ey[0]], '-g', linewidth=2) - ax.plot3D([rtn[1, i], rtn[1, i] + ez[1]], [rtn[2, i], rtn[2, i] + ez[2]], [rtn[0, i], rtn[0, i] + ez[0]], '-b', linewidth=2) - - # plot cone - # coneVertices = np.vstack([coneX.flatten(), coneY.flatten(), coneZ.flatten()]) - # coneVertices = R_i @ coneVertices - # coneVertices = coneVertices + rtn[:3, i].reshape(-1, 1) - # coneXRotated = coneVertices[0, :].reshape(coneX.shape) - # coneYRotated = coneVertices[1, :].reshape(coneY.shape) - # coneZRotated = coneVertices[2, :].reshape(coneZ.shape) - # ax.plot_surface(coneYRotated, coneZRotated, coneXRotated, color='red', alpha=0.2, linewidth=0, antialiased=False) - - -def animate_attitude(rtn,qw): - - fig = plt.figure() - ax = fig.add_subplot(111, projection='3d') - - # Writer = animation.writers['ffmpeg'] - # writer = Writer(fps=15, metadata=dict(artist='Me'), bitrate=1800) - writer = PillowWriter(fps=15, metadata=dict(artist='Me'), bitrate=1800) - - lines = [ax.plot([], [], [], color)[0] for color in ['r', 'g', 'b']] - - e_b = np.array([[1,0,0],[0,1,0],[0,0,1]]) - - def init(): - ax.set_xlim(-3, 3) - ax.set_ylim(-3, 3) - ax.set_zlim(-3, 3) - return lines - - def update(i): - R_i = q2rotmat(qw[0:4,i]) - e_i = R_i @ e_b - for k, color in enumerate(['r', 'g', 'b']): - lines[k].set_data([rtn[1, i], rtn[1, i] + e_i[1,k]], - [rtn[2, i], rtn[2, i] + e_i[2,k]]) - lines[k].set_3d_properties([rtn[0, i], rtn[0, i] + e_i[0,k]]) - lines[k].set_color(color) - return lines - - ani = animation.FuncAnimation(fig, update, rtn.shape[1], init_func=init, blit=True, interval=10) - # ani.save('test.gif', writer=writer) - plt.show() - - - - - diff --git a/env_original/rpo_detubmling/dynamics/test.gif b/env_original/rpo_detubmling/dynamics/test.gif deleted file mode 100644 index babb99dfa1316ccbc3a5d5c167821151ca7ff4e7..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 1648836 zcmeGERa6||yZwn*H;r5465KtwLvVMu;O@aajk~+MLvV-SF2OC3;2uE(1j2CsGIM6G 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