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sim_ballbot2D_v2.m
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sim_ballbot2D_v2.m
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function sim_ballbot2D_v2(X0, sim_params, sim_opts)
close all;
%% ----------------------------------------------------------
% Input verification
% -----------------------------------------------------------
% Check for inputs, if not inputs set default values
if(nargin < 3)
% Simulation options
sim_opts.ode_type = 0;
sim_opts.animate = 1;
sim_opts.animate_fun = @plot_bb;
sim_opts.save = 0;
sim_opts.plot = 0;
% Simulation parameteres
if(nargin < 2)
sim_params.model_params = get_model_params;
sim_params.t_range = [0 10];
sim_params.ctrl_params.c3 = 0.5;
sim_params.ctrl_params.epsilon = 0.8;
sim_params.ctrl = @RES_CLFQP_controller;
% Intial condition
if(nargin < 1)
X0 = [0; -2*pi/180; 0; 0] ;
end
end
end
%% Load constants and perofm one time setup
model_params = sim_params.model_params;
% one-time setup
%ctrl = initial_setup(x0, model_params);
%% ----------------------------------------------------------
% Simulation
% -----------------------------------------------------------
ode_opts = odeset('Events',@bbfallEvent2) ;
if(sim_opts.ode_type == 0)
[t_out X_out] = ode45(@(t,x)odefun_dynamicsBB(t,x,sim_params), sim_params.t_range, X0,ode_opts) ;
elseif(sim_opts.ode_type == 1)
[t_out X_out] = ode23(@(t,x)odefun_dynamicsBB(t,x,sim_params), sim_params.t_range, X0,ode_opts);
else
[t_out X_out] = ode23s(@(t,x)odefun_dynamicsBB(t,x,sim_params), sim_params.t_range, X0,ode_opts) ;
end
% Record control inputs
u_out = zeros(length(t_out),1);
X_d_out = zeros(length(t_out),size(X0,1));
u_fb = zeros(length(t_out),2);
u_ff = zeros(length(t_out),1);
psi0 = zeros(length(t_out),1);
psi1 = zeros(length(t_out),1);
phi_d = zeros(length(t_out),1);
kerr = zeros(length(t_out),1);
V_eps = zeros(length(t_out),1);
d1 = zeros(length(t_out),1);
phi_des = zeros(1,1);
for j = 1:length(t_out)
[~, u, xd] = odefun_dynamicsBB(t_out(j),X_out(j,:)',sim_params);
u_out(j,:) = u';
u_ff(j,:) = xd.uparts.u_ff;
u_fb(j,:) = xd.uparts.u_fb;
psi0(j,:) = xd.uparts.psi0;
psi1(j,:) = xd.uparts.psi1;
phi_d(j,:) = xd.uparts.phi_d;
kerr(j,:) = xd.uparts.kerr;
V_eps(j,:) = xd.uparts.V_eps;
d1(j,:) = xd.uparts.d1;
x_d = xd.ref_traj;
phi_des(j,:) = xd.phi_des;
X_d_out(j,:) = x_d';
end
%% ----------------------------------------------------------
% SAVE MODEL
% -----------------------------------------------------------
save_opts = sim_opts.save_opts;
if(save_opts.save)
data = packResults( X0, t_out, X_out, u_out, model_params, sim_params);
notes = save_opts.notes;
if ~exist('sim_opts.overWrite','var')
save_opts.overWrite = 0;
end
save_results( save_opts.folderName, save_opts.fileName, save_opts.overWrite,data,notes)
end
%% ----------------------------------------------------------
% Animation
% -----------------------------------------------------------
if(sim_opts.animate)
Anim.speed = sim_opts.animate_speed;
Anim.plotFunc = sim_opts.animate_fun;
animate(t_out,X_out,Anim);
end
%% ----------------------------------------------------------
% Plots
% -----------------------------------------------------------
if(sim_opts.plot)
if(isempty(sim_opts.plot_fun))
figure(2)
% Ball angle
subplot(3,2,1)
plot(t_out,X_out(:,1)*180/pi)
xlabel('Time (sec)')
ylabel('\theta (deg)')
% Body angle
subplot(3,2,2)
plot(t_out,X_out(:,2)*180/pi,t_out,phi_des*180/pi)
xlabel('Time (sec)')
ylabel('\psi (deg)')
% Ball angular velocity
subplot(3,2,3)
plot(t_out,X_out(:,3)*180/pi)
xlabel('Time (sec)')
ylabel('$\dot{\theta}$ (deg)','interpreter','latex')
% Body angular velocity
subplot(3,2,4)
plot(t_out,X_out(:,4)*180/pi)
xlabel('Time (sec)')
ylabel('$\dot{\psi}$ (deg)','interpreter','latex')
% Ball center x-translation
subplot(3,2,5)
plot(t_out,model_params.r*(X_out(:,1)+X_out(:,2)))
xlabel('Time (sec)')
ylabel('$x$ (m)','interpreter','latex')
% Ball center linear velocity
subplot(3,2,6)
plot(t_out,model_params.r*(X_out(:,3)+X_out(:,4)))
xlabel('Time (sec)')
ylabel('$\dot{x}$ (m/s)','interpreter','latex')
% Control input
figure(3)
subplot(3,1,1)
plot(t_out,u_out);
xlabel('Time (sec)');
ylabel('Input (Nm)');
subplot(3,1,2)
plot(t_out,u_fb);
ylabel('u_fb')
subplot(3,1,3)
plot(t_out,u_ff);
ylabel('u_ff');
figure(4)
subplot(3,1,1)
plot(t_out,phi_des*180/pi);
ylabel('phi_des')
subplot(3,1,2)
plot(t_out,phi_d*180/pi);
ylabel('phi_d')
subplot(3,1,3)
plot(t_out,kerr*180/pi);
ylabel('kerr');
figure(5)
subplot(2,1,1)
plot(t_out,psi0);
ylabel('psi0');
subplot(2,1,2);
plot(t_out,psi1);
ylabel('psi1');
figure
plot(t_out,V_eps);
ylabel('V_eps');
figure
plot(t_out,d1);
ylabel('d1');
else
sim_opts.plot_fun(t_out,X_out,X_d_out,u_out,u_fb,phi_des,sim_params.model_params);
end
end
end
% Function to describe the dynamics of the rocket
function [dx u x_d] = odefun_dynamicsBB(t, x, u, sim_params)
% Print integration time step
%t
% Call dynamic equation (dx)
dx = sim_params.model(t,x,u);
% check for fall
if (abs(x(2)) >= pi/2)
dx = zeros(size(x));
end
end
function [value,isterminal,direction] = bbfallEvent2( t, x, sim_params )
value = abs(x(2)) - pi/2;
isterminal = 1;
direction = 1;
end
function data = packResults( X0, t_out, X_out, u_out, model_params, sim_params )
data.model_params = model_params;
data.X0 = X0;
data.t_out = t_out;
data.X_out = X_out;
data.u_out = u_out;
data.sim_params = sim_params;
end
function [t_out_hist,X_out_hist] = simulate()
ode_opts = odeset('Events',@bbfallEvent2) ;
Ti = sim_params.t_range(1);
Tf = sim_params.t_range(end);
dt = sim_params.dt;
% Initialize variables
err = 0; % Error
err_dot = 0; % First derivative of error
err_ddot = 0; % Seocnd derivative of error
i = 1; % loop counter
X_hist = [X0];
t_hist = 0;
u_hist = 0;
for t = sim_params.t_range
% loop counter
i=i+1;
% Update controls
% Call reference trajectory generators
x_d.ref_traj = sim_params.ctrl_ref_traj(t,x);
err =
err_ddot = err_dot + (phi - phie);
sim_params.ctrl_params.err = err;
sim_params.ctrl_params.err_dot = err_dot;
sim_params.ctrl_params.err_ddot = err_ddot;
% Call controller
[u,uparts] = sim_params.ctrl(t,x,x_d,sim_params.ctrl_params);
% Integration step
[t_out X_out] = ode45(@(t,x)odefun_dynamicsBB(t,x,u,sim_params), [t t+dt], X0,ode_opts) ;
% Initial conditions for differential equaitons
X0 = X_out(end,:);
% Record history of states and inputs
X_hist(i,:) = X_out(end,:);
u_hist(i) = u;
t_hist(i) = t;
end
end