151 lines
6.0 KiB
Python
151 lines
6.0 KiB
Python
import numpy as np
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import csv
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def C(x):
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return np.cos(x)
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def S(x):
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return np.sin(x)
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def earth_to_body_frame(ii, jj, kk):
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# C^b_n
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R = [[C(kk) * C(jj), C(kk) * S(jj) * S(ii) - S(kk) * C(ii), C(kk) * S(jj) * C(ii) + S(kk) * S(ii)],
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[S(kk) * C(jj), S(kk) * S(jj) * S(ii) + C(kk) * C(ii), S(kk) * S(jj) * C(ii) - C(kk) * S(ii)],
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[-S(jj), C(jj) * S(ii), C(jj) * C(ii)]]
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return np.array(R)
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def body_to_earth_frame(ii, jj, kk):
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# C^n_b
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return np.transpose(earth_to_body_frame(ii, jj, kk))
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class PhysicsSim():
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def __init__(self, init_pose=None, init_velocities=None, init_angle_velocities=None, runtime=5.):
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self.init_pose = init_pose
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self.init_velocities = init_velocities
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self.init_angle_velocities = init_angle_velocities
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self.runtime = runtime
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self.gravity = -9.81 # m/s
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self.rho = 1.2
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self.mass = 0.958 # 300 g
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self.dt = 1 / 50.0 # Timestep
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self.C_d = 0.3
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self.l_to_rotor = 0.4
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self.propeller_size = 0.1
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width, length, height = .51, .51, .235
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self.dims = np.array([width, length, height]) # x, y, z dimensions of quadcopter
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self.areas = np.array([length * height, width * height, width * length])
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I_x = 1 / 12. * self.mass * (height**2 + width**2)
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I_y = 1 / 12. * self.mass * (height**2 + length**2) # 0.0112 was a measured value
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I_z = 1 / 12. * self.mass * (width**2 + length**2)
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self.moments_of_inertia = np.array([I_x, I_y, I_z]) # moments of inertia
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env_bounds = 300.0 # 300 m / 300 m / 300 m
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self.lower_bounds = np.array([-env_bounds / 2, -env_bounds / 2, 0])
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self.upper_bounds = np.array([env_bounds / 2, env_bounds / 2, env_bounds])
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self.reset()
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def reset(self):
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self.time = 0.0
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self.pose = np.array([0.0, 0.0, 10.0, 0.0, 0.0, 0.0]) if self.init_pose is None else np.copy(self.init_pose)
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self.v = np.array([0.0, 0.0, 0.0]) if self.init_velocities is None else np.copy(self.init_velocities)
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self.angular_v = np.array([0.0, 0.0, 0.0]) if self.init_angle_velocities is None else np.copy(self.init_angle_velocities)
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self.linear_accel = np.array([0.0, 0.0, 0.0])
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self.angular_accels = np.array([0.0, 0.0, 0.0])
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self.prop_wind_speed = np.array([0., 0., 0., 0.])
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self.done = False
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def find_body_velocity(self):
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body_velocity = np.matmul(earth_to_body_frame(*list(self.pose[3:])), self.v)
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return body_velocity
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def get_linear_drag(self):
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linear_drag = 0.5 * self.rho * self.find_body_velocity()**2 * self.areas * self.C_d
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return linear_drag
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def get_linear_forces(self, thrusts):
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# Gravity
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gravity_force = self.mass * self.gravity * np.array([0, 0, 1])
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# Thrust
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thrust_body_force = np.array([0, 0, sum(thrusts)])
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# Drag
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drag_body_force = -self.get_linear_drag()
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body_forces = thrust_body_force + drag_body_force
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linear_forces = np.matmul(body_to_earth_frame(*list(self.pose[3:])), body_forces)
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linear_forces += gravity_force
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return linear_forces
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def get_moments(self, thrusts):
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thrust_moment = np.array([(thrusts[3] - thrusts[2]) * self.l_to_rotor,
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(thrusts[1] - thrusts[0]) * self.l_to_rotor,
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0])# (thrusts[2] + thrusts[3] - thrusts[0] - thrusts[1]) * self.T_q]) # Moment from thrust
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drag_moment = self.C_d * 0.5 * self.rho * self.angular_v * np.absolute(self.angular_v) * self.areas * self.dims * self.dims
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moments = thrust_moment - drag_moment # + motor_inertia_moment
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return moments
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def calc_prop_wind_speed(self):
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body_velocity = self.find_body_velocity()
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phi_dot, theta_dot = self.angular_v[0], self.angular_v[1]
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s_0 = np.array([0., 0., theta_dot * self.l_to_rotor])
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s_1 = -s_0
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s_2 = np.array([0., 0., phi_dot * self.l_to_rotor])
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s_3 = -s_2
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speeds = [s_0, s_1, s_2, s_3]
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for num in range(4):
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perpendicular_speed = speeds[num] + body_velocity
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self.prop_wind_speed[num] = perpendicular_speed[2]
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def get_propeler_thrust(self, rotor_speeds):
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'''calculates net thrust (thrust - drag) based on velocity
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of propeller and incoming power'''
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thrusts = []
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for prop_number in range(4):
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V = self.prop_wind_speed[prop_number]
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D = self.propeller_size
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n = rotor_speeds[prop_number]
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J = V / n * D
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# From http://m-selig.ae.illinois.edu/pubs/BrandtSelig-2011-AIAA-2011-1255-LRN-Propellers.pdf
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C_T = max(.12 - .07*max(0, J)-.1*max(0, J)**2, 0)
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thrusts.append(C_T * self.rho * n**2 * D**4)
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return thrusts
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def next_timestep(self, rotor_speeds):
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self.calc_prop_wind_speed()
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thrusts = self.get_propeler_thrust(rotor_speeds)
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self.linear_accel = self.get_linear_forces(thrusts) / self.mass
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position = self.pose[:3] + self.v * self.dt + 0.5 * self.linear_accel * self.dt**2
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self.v += self.linear_accel * self.dt
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moments = self.get_moments(thrusts)
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self.angular_accels = moments / self.moments_of_inertia
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angles = self.pose[3:] + self.angular_v * self.dt + 0.5 * self.angular_accels * self.angular_accels * self.dt ** 2
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angles = (angles + 2 * np.pi) % (2 * np.pi)
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self.angular_v = self.angular_v + self.angular_accels * self.dt
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new_positions = []
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for ii in range(3):
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if position[ii] <= self.lower_bounds[ii]:
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new_positions.append(self.lower_bounds[ii])
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self.done = True
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elif position[ii] > self.upper_bounds[ii]:
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new_positions.append(self.upper_bounds[ii])
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self.done = True
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else:
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new_positions.append(position[ii])
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self.pose = np.array(new_positions + list(angles))
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self.time += self.dt
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if self.time > self.runtime:
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self.done = True
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return self.done
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