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geometric_tracking_controller.m
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geometric_tracking_controller.m
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% function[varargout] = geometric_tracking_controller(varargin)
%%% INITIALZING WORKSPACE
close all;
addpath('./Geometry-Toolbox/');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Using Geometry-Toolbox; thanks to Avinash Siravuru %%
% https://github.com/sir-avinash/geometry-toolbox %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%Implemeting The two cases mentioned in the paper
for iter = 1:2
switch(iter)
case 1
clear;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% INITIALZING SYSTEM PARAMETERS %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% moment of Inertia in Kg(m^2)
quad_params.params.mass = 0.5 ;
% moment of Inertia in Kg(m^2)
quad_params.params.J = diag([0.557, 0.557, 1.05]*10e-2);
% acceleration via gravity contant
quad_params.params.g = 9.81 ;
% interial fram axis
quad_params.params.e1 = [1;0;0] ;
quad_params.params.e2 = [0;1;0] ;
quad_params.params.e3 = [0;0;1] ;
% distance of center of mass from fram center in m
quad_params.params.d = 0.315;
% fixed constant in m
quad_params.params.c = 8.004*10e-4;
%defining parameters different for each trajectories
quad_params.params.x_desired = nan;
quad_params.params.gen_traj = 1; %change here
quad_params.params.vel = nan;
quad_params.params.acc = nan;
quad_params.params.b1d = nan;
quad_params.params.w_desired = [0;0;0];
quad_params.params.k1 = diag([5, 5 ,9]);
quad_params.params.k2 = diag([5, 5, 10]);
quad_params.params.kR = 200;
quad_params.params.kOm = 1;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% INTIALIZING - INTIAL PARAMETERS x,v,R,w %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Intial position
x_quad_0 = [0;0;0];
% xQ0 = [1;3;2];
% Intial velocity
v_quad_0 = zeros(3,1);
% Initial orientation
% R0 = RPYtoRot_ZXY(0*pi/180, 0*pi/180, 0*pi/180);
R0 = eye(3);
% Intial angular velocity
w0= zeros(3,1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Concatenating the entire initial condition into a single vector
x0 = [x_quad_0; v_quad_0; reshape(R0,9,1); w0];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%% SIMULATION
odeopts = odeset('RelTol', 1e-8, 'AbsTol', 1e-9) ;
% odeopts = [] ;
[t, x] = ode15s(@odefun_quadDynamics, [0 20], x0, odeopts, quad_params) ;
% Computing Various Quantities
disp('Evaluating...') ;
index = round(linspace(1, length(t), round(1*length(t))));
% ind = 0:length(t);
for i = index
[~,xd_,f_,M_] = odefun_quadDynamics(t(i),x(i,:)',quad_params);
xd(i,:) = xd_';
pos_err_fx(i) = norm(x(i,1:3)-xd(i,1:3));
vel_err_fx(i) = norm(x(i,4:6)-xd(i,4:6));
f(i,1)= f_;
M(i,:)= M_';
end
%%% Plotting graphs
plott(t,x,xd,pos_err_fx,vel_err_fx);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%% CASE 2 %%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
case 2
clear;
%%% INITIALZING SYSTEM PARAMETERS %%%
% moment of Inertia in Kg(m^2)
quad_params.params.mass = 0.5 ;
% moment of Inertia in Kg(m^2)
quad_params.params.J = diag([0.557, 0.557, 1.05]*10e-2);
% acceleration via gravity contant
quad_params.params.g = 9.81 ;
% interial fram axis
quad_params.params.e1 = [1;0;0] ;
quad_params.params.e2 = [0;1;0] ;
quad_params.params.e3 = [0;0;1] ;
% distance of center of mass from fram center in m
quad_params.params.d = 0.315;
% fixed constant in m
quad_params.params.c = 8.004*10e-4;
% Desired position
quad_params.params.x_desired = [0;0;0];
quad_params.params.w_desired = [0;0;0];
%defining parameters different for each trajectories
quad_params.params.gen_traj = 0;
quad_params.params.vel = 0;
quad_params.params.acc = 0;
quad_params.params.b1d = [1;0;0];
quad_params.params.k1 = diag([5, 5 ,9]);
quad_params.params.k2 = diag([5, 5, 10]);
quad_params.params.kR = 50;
quad_params.params.kOm = 2.5;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% INTIALIZING - INTIAL PARAMETERS x,v,R,w %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Intial position
x_quad_0 = [0;0;0];
% xQ0 = [1;3;2];
% Intial velocity
v_quad_0 = zeros(3,1);
% Initial orientation
R0 = [1 0 0;0 -0.9995 -0.0314; 0 0.0314 -0.9995];
% Intial angular velocity
w0= zeros(3,1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Concatenating the entire initial condition into a single vector
x0 = [x_quad_0; v_quad_0; reshape(R0,9,1); w0];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%% SIMULATION
odeopts = odeset('RelTol', 1e-8, 'AbsTol', 1e-9) ;
% odeopts = [] ;
[t, x] = ode15s(@odefun_quadDynamics, [0 20], x0, odeopts, quad_params) ;
% Computing Various Quantities
disp('Evaluating...') ;
index = round(linspace(1, length(t), round(1*length(t))));
% ind = 0:length(t);
for i = index
[~,xd_,f_,M_] = odefun_quadDynamics(t(i),x(i,:)',quad_params);
xd(i,:) = xd_';
pos_err_fx(i) = norm(x(i,1:3)-xd(i,1:3));
vel_err_fx(i) = norm(x(i,4:6)-xd(i,4:6));
f(i,1)= f_;
M(i,:)= M_';
end
%%% Plotting graphs
plott(t,x,xd,pos_err_fx,vel_err_fx);
otherwise
fprintf('\n invalid case');
end
end
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%% INTIALIZING - INTIAL PARAMETERS x,v,R,w %%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % Intial position
% x_quad_0 = [0;0;0];
% % xQ0 = [1;3;2];
% % Intial velocity
% v_quad_0 = zeros(3,1);
% % Initial orientation
% % R0 = RPYtoRot_ZXY(0*pi/180, 10*pi/180, 20*pi/180);
% R0 = RPYtoRot_ZXY(0*pi/180, 0*pi/180, 0*pi/180);
% % Intial angular velocity
% w0= zeros(3,1);
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % Concatenating the entire initial condition into a single vector
% x0 = [x_quad_0; v_quad_0; reshape(R0,9,1); w0];
% %%%%%%%% SIMULATION
% odeopts = odeset('RelTol', 1e-8, 'AbsTol', 1e-9) ;
% % odeopts = [] ;
% [t, x] = ode15s(@odefun_quadDynamics, [0 20], x0, odeopts, quad_params) ;
%
% % Computing Various Quantities
% disp('Evaluating...') ;
% index = round(linspace(1, length(t), round(1*length(t))));
% % ind = 0:length(t);
% for i = index
% [~,xd_,f_,M_] = odefun_quadDynamics(t(i),x(i,:)',quad_params);
% xd(i,:) = xd_';
% pos_err_fx(i) = norm(x(i,1:3)-xd(i,1:3));
% vel_err_fx(i) = norm(x(i,4:6)-xd(i,4:6));
% f(i,1)= f_;
% M(i,:)= M_';
% end
%
% %%% Plotting graphs
% plott(t,x,xd,pos_err_fx,vel_err_fx);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%% Function definitions %%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function[dx, xd, f,M] = odefun_quadDynamics(t,x,quad_params)
mass = quad_params.params.mass;
J = quad_params.params.J;
g = quad_params.params.g;
e1 = quad_params.params.e1;
e2 = quad_params.params.e2;
e3 = quad_params.params.e3;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% fetching desired states %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if(quad_params.params.gen_traj)
[traj_desired] = return_traj(t);
% x_des = traj_desired.pos;
x_des = traj_desired.pos;
v_des = traj_desired.vel;
a_des = traj_desired.acc;
b1d = traj_desired.b1d;
w_desired = quad_params.params.w_desired;
w_desired_dot = zeros(3,1);
else
x_des = quad_params.params.x_desired;
v_des = [0;0;0];
a_des = [0;0;0];
b1d = quad_params.params.b1d;
Rd = eye(3);
w_desired = quad_params.params.w_desired;
w_desired_dot = zeros(3,1);
end
x_curr = x(1:3);
v_curr = x(4:6);
R = reshape(x(7:15),3,3);
w = x(16:18);
b3 = R(:,3);
dx = [];
%%%%%%%%%%%
% CONTROL %
%%%%%%%%%%%
% Position Control
err_x = x_curr - x_des;
err_v = v_curr - v_des;
% constants for force and moment
k1 = quad_params.params.k1;
k2 = quad_params.params.k2;
A = (-k1*err_x - k2*err_v + mass*a_des + mass*g*e3);
normA = norm(A);
b3_desired = A/normA;
f = vec_dot(A,b3);
%%%%%%%%%%%%%%%%%%%%
% Attitude Control %
%%%%%%%%%%%%%%%%%%%%
%b1d definded above;
b2d = vec_cross(b3_desired,b1d);
norm_b2d = norm(b2d);
b2d = b2d/norm_b2d;
projection_b1d = -vec_cross(b3_desired,b2d);
Rd = [vec_cross(b2d,b3_desired) b2d b3_desired];
%angluar velocity and rotation matrix constants
kR = quad_params.params.kR;
kOm = quad_params.params.kOm;
%calculating error in angular velocity and attitude
% psi_R = ;
err_R = 1/2 * vee_map(Rd'*R - R'*Rd) ;
err_Om = w - R'*Rd*w_desired ;
M = -kR*err_R - kOm*err_Om + vec_cross(w, J*w)...
- J*(hat_map(w)*R'*Rd*w_desired - R'*Rd*w_desired_dot) ;
% Equations of Motion
% -------------------
xQ_dot = v_curr;
vQ_dot = -g*e3 + (f/mass)*R*e3;
R_dot = R*hat_map(w) ;
Omega_dot = J\( -vec_cross(w, J*w) + M ) ;
% Computing xd
xd = [x_des; v_des; reshape(Rd, 9,1); w_desired];
% Computing dx
%-------------
dx = [xQ_dot;
vQ_dot;
reshape(R_dot, 9,1) ;
Omega_dot;];
% if nargout <= 1
% fprintf('Sim time %0.4f seconds \n',t);
% end
end
function[traj] = return_traj(t)
%desired trajectory xd(t) = [0.4t,0.4sin(pi*t), 0.6cos(pi*t)]
traj.pos = [0.4*t; 0.4*sin(pi*t); 0.6*cos(pi*t)];
traj.vel = [0.4; 0.4*pi*cos(pi*t); -0.6*pi*sin(pi*t)];
traj.acc = [0; -0.4*pi*pi*sin(pi*t); -0.6*pi*pi*cos(pi*t)];
traj.b1d = [cos(pi*t); sin(pi*t); 0];
% traj.b1d = [1; 0; 0];
end
function plott(t,x,xd,pos_err_fx,vel_err_fx)
disp('Plotting graphs...');
index = round(linspace(1, length(t), round(1*length(t))));
figure;
subplot(2,2,1);
plot(t(index),x(index,1),'-b','LineWidth',2); hold on;
plot(t(index),xd(index,1),':r','LineWidth',2); hold off;
grid on; title('x');legend('x pos','desired x pos');%axis equal;
xlabel('time');ylabel('x');
subplot(2,2,2);
plot(t(index),x(index,2),'-b','LineWidth',2); hold on;
plot(t(index),xd(index,2),':m','LineWidth',2); hold off;
grid on; title('y');legend('y pos','desired y pos');%axis equal;
xlabel('time');ylabel('y');
subplot(2,2,3);
plot(t(index),x(index,3),'-b','LineWidth',2); hold on;
plot(t(index),xd(index,3),':m','LineWidth',2); hold off;
grid on; title('z');legend('z pos','desired z pos');%axis equal;
xlabel('time');ylabel('z');
subplot(2,2,4);
plot3(x(index,1),x(index,2),x(index,3),'-b','LineWidth',2);hold on;
plot3(xd(index,1),xd(index,2),xd(index,3),':m','LineWidth',2); hold off;
grid on; title('trajectory');legend('trajectory','desired trajectory');%axis equal;
xlabel('x-axis');ylabel('y-axis');zlabel('z-axis');
%%%Plotting error functions
figure;
subplot(2,1,1);
plot(t(index),pos_err_fx(index),'-b','LineWidth',2);
grid on; title('error in position');
legend('{e}_x');
xlabel('Time');ylabel('{x}-{x}_d');
subplot(2,1,2);
plot(t(index),vel_err_fx(index),'-b','LineWidth',2);
grid on; title('error in velocity');legend('{e}_v');
xlabel('Time');ylabel('{v}-{v}_d');
%%%Plotting force and Moments
% figure;
% subplot(2,2,1);
% plot(t(index),f(index,1),'-b','LineWidth',2); %hold on;
% % plot(t(index),xd(index,1),':r','LineWidth',2); hold off;
% grid on; title('f');%legend('x','x_d');%axis equal;
% xlabel('time');ylabel('x [m]');
% subplot(2,2,2);
% plot(t(index),M(index,1),'-b','LineWidth',2); %hold on;
% % plot(t(index),xd(index,2),':m','LineWidth',2); hold off;
% grid on; title('M_x');%legend('y','y_d');%axis equal;
% xlabel('time');ylabel('M in x direction');
% subplot(2,2,3);
% plot(t(index),M(index,2),'-b','LineWidth',2); %hold on;
% % plot(t(index),xd(index,3),':m','LineWidth',2); hold off;
% grid on; title('z');%legend('z','z_d');%axis equal;
% xlabel('time');ylabel('M in y direction');
% subplot(2,2,4);
% plot(t(index),M(index,3),'-b','LineWidth',2); %hold on;
% % plot(t(index),xd(index,3),':m','LineWidth',2); hold off;
% grid on; title('M_z');%legend('z','z_d');%axis equal;
% xlabel('time');ylabel('M in z direction');
end