#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ MIT License Copyright (c) 2022 Jongrae.K Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. """ import numpy as np from numpy import linspace from scipy.integrate import solve_ivp init_time = 0 # [s] final_time = 10.0 # [s] num_data = 200 tout = linspace(init_time, final_time, num_data) J_inertia = np.array([[0.005, -0.001, 0.004], [-0.001, 0.006, -0.002], [0.004, -0.002, 0.004]]) J_inv = np.linalg.inv(J_inertia) J_inv_J_inertia = np.vstack((J_inertia,J_inv)) C_T = 8.8e-7 # motor thruster coefficient [N/(rad/s)^2] C_D = 11.3e-8 # motor drag coefficient [Nm/(rad/s)^2] L_arm = 0.127 # length from the centre of quadcopter to the motor [m] Motor_para = np.array([C_T,C_D,L_arm]) q0 = np.array([0,0,0,1]) w0 = np.array([0,0,0]) #----------------------Added Part--------------------------------------- # first-order motor model tau_motor = 0.01#[s] w_motor = np.array([0,0,0,0]) # [initial 4-motor angular velocity] #----------------------------------------------------------------------- #----------------------Modified Part------------------------------------ state_0 = np.hstack((q0,w0,w_motor)) #----------------------Added Part--------------------------------------- # use global variables only for saving values global global_motor_time_FM_all # minimum time interval for saving values to the global dt_save = 0.05 def propeller_motor_actuator(C_T,C_D,L_arm,w_motor): # this part is replaced by current motor angular velocity # assume perfect motor angular velocity control # w_motor = w_command F_fblr = C_T*(w_motor**2) tau_fblr = C_D*(w_motor**2) F_motor = -np.sum(F_fblr) M_motor = np.array([ L_arm*(F_fblr[2]-F_fblr[3]), L_arm*(F_fblr[0]-F_fblr[1]), np.sum(tau_fblr[0:2])-np.sum(tau_fblr[2::])]) FM_Motor = np.hstack([F_motor, M_motor]) return FM_Motor def propeller_motor_FM2w_conversion(F_M_Desired, C_T, C_D, L_arm): inv_C_T = 1/C_T; inv_C_D = 1/C_D; inv_2_L_C_T = 2/(L_arm*C_T); Conv_Mat = 0.25*np.array([ [-inv_C_T, 0, inv_2_L_C_T, inv_C_D], [-inv_C_T, 0, -inv_2_L_C_T, inv_C_D], [-inv_C_T, inv_2_L_C_T, 0, -inv_C_D], [-inv_C_T, -inv_2_L_C_T, 0, -inv_C_D]]) w_motor_fblr_squared_desired = Conv_Mat@F_M_Desired return w_motor_fblr_squared_desired def dqdt_attitude_kinematics(q_true, w_true): quat=q_true wx=np.array([[0, -w_true[2], w_true[1]], [w_true[2], 0, -w_true[0]], [-w_true[1], w_true[0], 0]]) Omega_13 = np.hstack((-wx,np.resize(w_true,(3,1)))) Omega_4 = np.hstack((-w_true,0)) Omega = np.vstack((Omega_13, Omega_4)) dqdt = 0.5*(Omega@quat) return dqdt def dwdt_attitude_dynamics(w_true,J_inertia,inv_J_inertia, M_torque): Jw = J_inertia@w_true Jw_dot = -np.cross(w_true,Jw) + M_torque dwdt = inv_J_inertia@Jw_dot return dwdt #------------------Updated Part: tau_motor added in the input parameters-- def dqdt_dwdt(time,state,J_inv_J_inertia,Motor_para,dt_save, tau_motor): #------------------------------------------------------------------------- global global_motor_time_FM_all q_current = state[0:4] q_current = q_current/np.linalg.norm(q_current) w_current = state[4:7] #------------------Updated Part: motor state--- w_motor_current = state[7::] #--------------------------------------------- J_inertia = J_inv_J_inertia[0:3,:] J_inv = J_inv_J_inertia[3::,:] C_T = Motor_para[0] C_D = Motor_para[1] L_arm = Motor_para[2] #-------------------------------- # Begin: this part is controller #-------------------------------- M_Desired = np.array([0.00001+0.0005*np.sin(2*time), -0.00002+0.0001*np.cos(0.75*time), -0.0001]) mg = 10.0 #[N] F_M_Desired = np.hstack([-mg, M_Desired]) w_motor_fblr_squared_desired = propeller_motor_FM2w_conversion(F_M_Desired, C_T, C_D, L_arm) w_motor_fblr_desired = np.sqrt(w_motor_fblr_squared_desired) #-------------------------------- # End: this part is controller #-------------------------------- #------------------------added part---------------------------------- dw_motor_dt = (-w_motor_current + w_motor_fblr_desired)/tau_motor # Motor Force & Torque # desired motor angular velocity is replaced with current motor angular velocity FM_Motor = propeller_motor_actuator(C_T, C_D, L_arm, w_motor_current) # updated part M_torque = FM_Motor[1::] current_data = np.hstack((time,FM_Motor,)) if time < 1e-200: global_motor_time_FM_all = current_data.reshape(1,5) elif time > global_motor_time_FM_all[-1,0]+dt_save: global_motor_time_FM_all = np.vstack((global_motor_time_FM_all,current_data,)) dqdt = dqdt_attitude_kinematics(q_current, w_current) dwdt = dwdt_attitude_dynamics(w_current, J_inertia, J_inv, M_torque) dstate_dt = np.hstack((dqdt,dwdt,dw_motor_dt)) # updated part return dstate_dt # solve ode sol = solve_ivp(dqdt_dwdt, (init_time, final_time), state_0, t_eval=tout, atol=1e-9, rtol=1e-6, max_step=0.01, args=(J_inv_J_inertia, Motor_para, dt_save,tau_motor)) qout = sol.y[0:4,:] wout = sol.y[4:7,:] w_motor_out = sol.y[7::,:] time_Motor = global_motor_time_FM_all[:,0] Force_Motor = global_motor_time_FM_all[:,1] Torque_Motor = global_motor_time_FM_all[:,2::] del global_motor_time_FM_all import matplotlib.pyplot as plt # quaternion and omega plot fig, (ax,ax1) = plt.subplots(nrows=2,ncols=1) ax.plot(tout,qout[0,:],'b-',tout,qout[1,:],'r--',tout,qout[2,:],'g-.',tout,qout[3,:],'m:') fig.set_figheight(6) # size in inches fig.set_figwidth(8) # size in inches xtick_list = np.array([0,1,2,3,4,5,6,7,8,9,10]) ax.set_xticks(xtick_list) ax.set_xticklabels(xtick_list,fontsize=14) ytick_list = np.array([-1.0,-0.5,0.0,0.5,1.0]) ax.set_yticks(ytick_list) ax.set_yticklabels(ytick_list,fontsize=14) ax.legend(('$q_1$','$q_2$','$q_3$','$q_4$'),fontsize=14, loc='upper right') ax.axis((0,10,-1.0,1.0)) ax.set_ylabel('quaternion',fontsize=14) ax1.plot(tout,wout[0,:],'r-',tout,wout[1,:],'b--',tout,wout[2,:],'m-.') ax1.set_xticks(xtick_list) ax1.set_xticklabels(xtick_list,fontsize=14) ax1.set_xlabel('time [s]',fontsize=14) ytick_list = np.array([-2.0,-1.0,0.0,1.0,2.0]) ax1.set_yticks(ytick_list) ax1.set_yticklabels(ytick_list,fontsize=14) ax1.legend(('$\omega_1$','$\omega_2$','$\omega_3$'),fontsize=14, loc='upper right') ax1.axis((0,10,-2.0,2.0)) ax1.set_xlabel('time [s]',fontsize=14) ax1.set_ylabel('$\omega$ [rad/s]',fontsize=14) # motor force and torque plot fig1, (ax2,ax3) = plt.subplots(nrows=2,ncols=1) ax2.plot(time_Motor,Force_Motor) ax2.set_ylabel('Force [N]',fontsize=14) ax2.set_xticks(xtick_list) ax2.set_xticklabels(xtick_list,fontsize=14) ytick_list = np.array([-15.0,-10.0,-5.0,0.0]) ax2.set_yticks(ytick_list) ax2.set_yticklabels(ytick_list,fontsize=14) ax2.set_xlim([init_time, final_time]) ax2.set_ylim([-15,0]) ax3.plot(time_Motor,Torque_Motor[:,0],'r-',time_Motor,Torque_Motor[:,1],'b--', time_Motor,Torque_Motor[:,2],'m-.') ax3.set_xticks(xtick_list) ax3.set_xticklabels(xtick_list,fontsize=14) ytick_list = np.array([-0.0006, -0.0003, 0.0, 0.0003, 0.0006]) ax3.set_yticks(ytick_list) ax3.set_yticklabels(ytick_list,fontsize=14) ax3.set_xlim([init_time, final_time]) ax3.set_ylim([-0.0006,0.0006]) ax3.set_ylabel('Torque [Nm]',fontsize=14) ax3.set_xlabel('time [s]',fontsize=14) ax3.legend(('$M_1$','$M_2$','$M_3$'),fontsize=14) # motor angular velocity fig2, ax1 = plt.subplots(nrows=1,ncols=1) ax1.plot(tout, w_motor_out.T*60/(2*np.pi)) ax1.set_ylabel('Motor Angular Velocity [rpm]',fontsize=14) ax1.set_xlabel('time [s]',fontsize=14) ax1.legend(('$\omega_m^{forward}$','$\omega_m^{backward}$','$\omega_m^{left}$','$\omega_m^{right}$')) #fig1.set_size_inches(9,6) #fig1.savefig('../figures/quad_motor_Force_Torque.pdf',dpi=250)