#!/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 = 120.0 # [s] num_data = 1200 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) 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] quadcopter_uav=(J_inertia, J_inv, C_T, C_D, L_arm) q0 = np.array([1,1,-1,1])/np.sqrt(4) w0 = np.array([0.1,-0.2,0.1]) r0 = np.array([0,0,-50]) v0 = np.array([0,0,0]) state_0 = np.hstack((q0,w0,r0,v0)) # use global variables only for saving values global global_motor_time_FM_w_all # minimum time interval for saving values to the global dt_save = 0.005 #----------------------------------------------------------------------------- # propellar & motor #----------------------------------------------------------------------------- def propeller_motor_actuator(C_T,C_D,L_arm,w_command): # 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_w_Motor = np.hstack([F_motor, M_motor, w_motor]) return FM_w_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 w_motor_fblr_squared_desired[w_motor_fblr_squared_desired<0] = 0.0 return w_motor_fblr_squared_desired #----------------------------------------------------------------------------- # quaternion feedback & altitude control #----------------------------------------------------------------------------- def quaternion_feedback_and_altitude_control(q_current, w_current, rv_current, J_inertia, C_T, C_D, L_arm, C_BR, mass_quadcopter, grv_acce): zR_desired = -30 #[m] zdotR_desired = 0 #[m/s] K_qf = 0.01*np.eye(3); C_qf = 0.001*np.eye(3) k1 = 0.1 k2 = 0.5 q_13 = q_current[0:3] w = w_current Fmg_R = grv_acce*mass_quadcopter #[N] Falt_R = k1*(zR_desired-rv_current[2])+k2*(zdotR_desired-rv_current[5]) F_desired_R = np.array([0,0,-Fmg_R+Falt_R]) F_desired_B = C_BR@F_desired_R; u_qf = -K_qf@q_13 - C_qf@w - np.cross(w,J_inertia@w); M_Desired = u_qf; F_M_desired = np.hstack((F_desired_B[2], 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) return w_motor_fblr_desired #----------------------------------------------------------------------------- # translational & rotational kinematics & dynamics #----------------------------------------------------------------------------- def drdt_linear_dynamics(rv_true, mass, grv_const, motor_force_in_R): v = rv_true[3::] drdt = v dvdt = np.array([0,0,grv_const]) + motor_force_in_R/mass drv_dt = np.hstack((drdt, dvdt)) return drv_dt 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 def dqdt_dwdt_drvdt(time,state,quadcopter_uav,dt_save): m_quadcopter = 0.49 #[kg] grv_acce = 9.81 #[m/s^2] global global_motor_time_FM_w_all q_current = state[0:4] q_current = q_current/np.linalg.norm(q_current) w_current = state[4:7] rv_current = state[7::] J_inertia = quadcopter_uav[0] J_inv = quadcopter_uav[1] C_T = quadcopter_uav[2] C_D = quadcopter_uav[3] L_arm = quadcopter_uav[4] q_13 = q_current[0:3] q4 = q_current[3] q13x = np.array([[0, -q_13[2], q_13[1]], [q_13[2], 0, -q_13[0]], [-q_13[1], q_13[0], 0]]) C_BR = (q4**2-q_13@q_13)*np.eye(3) + 2*(q_13.reshape((3,1))*q_13.reshape((1,3)))-2*q4*q13x #-------------------------------- # Begin: this part is controller #-------------------------------- w_motor_fblr_desired = quaternion_feedback_and_altitude_control(q_current, w_current, rv_current, J_inertia, C_T, C_D, L_arm, C_BR, m_quadcopter, grv_acce) #-------------------------------- # End: this part is controller #-------------------------------- # Motor Force & Torque FM_w_Motor = propeller_motor_actuator(C_T, C_D, L_arm, w_motor_fblr_desired) F_motor = np.array([0,0,FM_w_Motor[0]]) M_torque = FM_w_Motor[1:4] motor_force_in_R = C_BR.transpose()@F_motor current_data = np.hstack((time,FM_w_Motor,)) if time < 1e-200: global_motor_time_FM_w_all = current_data.reshape(1,9) elif time > global_motor_time_FM_w_all[-1,0]+dt_save: global_motor_time_FM_w_all = np.vstack((global_motor_time_FM_w_all,current_data,)) dqdt = dqdt_attitude_kinematics(q_current, w_current) dwdt = dwdt_attitude_dynamics(w_current, J_inertia, J_inv, M_torque) drvdt = drdt_linear_dynamics(rv_current, m_quadcopter, grv_acce, motor_force_in_R) dstate_dt = np.hstack((dqdt,dwdt,drvdt)) return dstate_dt #----------------------------------------------------------------------------- # solve ode #----------------------------------------------------------------------------- sol = solve_ivp(dqdt_dwdt_drvdt, (init_time, final_time), state_0, t_eval=tout, atol=1e-9, rtol=1e-6, max_step=0.01, args=(quadcopter_uav,dt_save)) qout = sol.y[0:4,:] wout = sol.y[4:7,:] rout = sol.y[7:10,:] vout = sol.y[10::,:] time_Motor = global_motor_time_FM_w_all[:,0] Force_Motor = global_motor_time_FM_w_all[:,1] Torque_Motor = global_motor_time_FM_w_all[:,2:5] Omega_Motor = global_motor_time_FM_w_all[:,5::]*(60/(2*np.pi)); #[rpm] del global_motor_time_FM_w_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([0,2,4,6,8,10,12])*10 ax.set_xticks(xtick_list) ax.set_xticklabels(xtick_list,fontsize=14) ytick_list = np.array([-1.0,0.0,1.0]) 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((init_time,final_time,-1.1,1.1)) 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([-3.0,-2.0,-1.0,0.0,1.0,2.0,3.0]) 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((init_time,final_time,-3,3)) 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([-10,0]) 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([-0.02, -0.01, 0.0, 0.01, 0.02]) ax3.set_yticks(ytick_list) ax3.set_yticklabels(ytick_list,fontsize=14) ax3.set_xlim([init_time, final_time]) ax3.set_ylim([-0.02,0.02]) ax3.set_ylabel('Torque [Nm]',fontsize=14) ax3.set_xlabel('time [s]',fontsize=14) ax3.legend(('$M_1$','$M_2$','$M_3$'),fontsize=14,loc='upper right') #fig1.set_size_inches(9,6) #fig1.savefig('../figures/quad_motor_Force_Torque.pdf',dpi=250) # motor angular velocity in rpm fig2, ax4 = plt.subplots(nrows=1,ncols=1) ax4.plot(time_Motor,Omega_Motor[:,0],'b-',time_Motor,Omega_Motor[:,1],'r--', time_Motor,Omega_Motor[:,2],'g-.',time_Motor,Omega_Motor[:,3],'m:') ax4.set_xlabel('time [s]',fontsize=14) ax4.set_ylabel('Motor Speed [rpm]',fontsize=14) ax4.set_xticks(xtick_list) ax4.set_xticklabels(xtick_list,fontsize=14) ytick_list = np.array([0,5000,10000,15000]) ax4.set_yticks(ytick_list) ax4.set_yticklabels(ytick_list,fontsize=14) ax4.set_xlim([init_time, final_time]) ax4.set_ylim([0,15000]) ax4.legend(('$\omega_{m1}$','$\omega_{m2}$','$\omega_{m3}$','$\omega_{m4}$'),fontsize=14,loc='lower right') # position & velocity of quadcopter fig3, (ax5,ax6) = plt.subplots(nrows=2,ncols=1) ax5.plot(tout,-rout[2,:]) ax5.set_ylabel('Altitude [m]',fontsize=14) ax5.set_xticks(xtick_list) ax5.set_xticklabels(xtick_list,fontsize=14) ytick_list = np.array([0,20,40,60]) ax5.set_yticks(ytick_list) ax5.set_yticklabels(ytick_list,fontsize=14) ax5.set_xlim([init_time, final_time]) ax5.set_ylim([0,60]) ax6.plot(tout, vout[0,:],'r-',tout,vout[1,:],'b--',tout,vout[2,:],'m-.') ax6.set_xticks(xtick_list) ax6.set_xticklabels(xtick_list,fontsize=14) ytick_list = np.array([-20, 0.0, 20]) ax6.set_yticks(ytick_list) ax6.set_yticklabels(ytick_list,fontsize=14) ax6.set_xlim([init_time, final_time]) ax6.set_ylim([-20,20]) ax6.set_ylabel('Velocity [m/s]',fontsize=14) ax6.set_xlabel('time [s]',fontsize=14) ax6.legend(('$v_1$','$v_2$','$v_3$'),fontsize=14,loc='upper right')