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Plots.m
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function Plots()
% Version 0.4 - 14/06/2012
% close all
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %
% To get great plots for printing use these 2 lines for each figure: %
% set(gcf,'PaperType','A2') %
% print -dtiffn -r600 %
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %
% Set format parameters
FontSize=18;
LineWidth=2;
% Select to display slope in radians or degrees
RadORDeg=1; % 1 for Deg, 2 for Rad
RMult=pi/180;
% Select to display leg angles from perpendicular
% to the horizon or to the surface
% 1 for symmetrical, 0 for real values
Symmetric=0;
Plots=zeros(1,19);
% Plots to display:
% Plots(1)=1; % Initial conditions: q_1 q_2 \phi
% Plots(2)=1; % Initial conditions: q_1dot q_2dot
% Plots(3)=1; % Interactive Phase Plane
% Plots(4)=1; % Poincare eigenvalues
% Plots(5)=1; % Interactive Poincare Map
% Plots(6)=1; % Poincare Map eigenvalues locus
% Plots(7)=1; % Limit Cycle plots for paper
% Plots(8)=1; % Compass Gait Model Figure
% Plots(9)=1; % Interactive GRF plot
% Plots(10)=1; % Energy plots
Plots(11)=1; % Mega interactive plot
Plots(12)=1; % ZMP and friction coeff. plot
% %%%% !!!! Following plots not yet updated !!!! %%%% %
% Plots(13)=1; % Muscle Torques
% Plots(14)=1; % Potential, Kinetic and Total Energy
% Plots(15)=1; % Energy Loss by Leg Apperture
% Plots(16)=1; % Off COM Distance
% Plots(17)=1; % Off COM Distance by Slope and Leg Apperture
% Plots(18)=1; % Plots for paper
% Plots(19)=1; % Stick-figure images
% If both initial condition plots are selected define
% whether to plot them as separate figures or as subplots
InitCondSubplots=1;
% If both interactive plots are selected define
% whether to plot them as separate figures or as subplots
InterSubplots=1;
% Define whether to print PM locus as subplots
LocusSubplots=1;
% Define whether to add direction to the locus (increasing with slope)
LocusDirection=1;
% Define whether to add an index number to the direction arrows
LocusDirNumber=0;
S=load('NumericalData.mat'); % Load precomputed numerical data
Slopes=S.Slopes;
LimitCycle_Period=S.LimitCycle_Period;
LimitCycle_IC=S.LimitCycle_IC;
LimitCycle_X=S.LimitCycle_X;
LimitCycle_T=S.LimitCycle_T;
LimitCycle_Torques=S.LimitCycle_Torques;
LimitCycle_GRF=S.LimitCycle_GRF;
LimitCycle_ZMP=S.LimitCycle_ZMP;
LimitCycle_eig=S.LimitCycle_eig;
MaxZMP = S.MaxZMP;
MaxFriction = S.MaxFriction;
StepLength=S.StepLength;
dKineticEIm=S.dKineticEIm;
dKineticEFr=S.dKineticEFr;
dPotentialE=S.dPotentialE;
ControllerE=S.ControllerE;
% AbsControllerE=S.AbsControllerE;
DPSlopes=S.DPSlopes;
DPStepLength=S.DPStepLength;
DPdKineticEIm=S.DPdKineticEIm;
DPdKineticEFr=S.DPdKineticEFr;
DPdPotentialE=S.DPdPotentialE;
DPControllerE=S.DPControllerE;
% DPAbsControllerE=S.DPAbsControllerE;
GRF=S.GRF;
MeasuredGRF=S.MeasuredGRF;
MeanMeasuredGRF=S.MeanMeasuredGRF;
MaxGRFRatio=S.MaxGRFRatio;
Sections=length(Slopes); % Obtain number of sections
IPPIndex=ceil(Sections/2); % Set interactive phase plane plot index to middle of range
IPMIndex=ceil(Sections/2); % Set interactive PM locus plot index to middle of range
IGRFIndex=ceil(Sections/2); % Set interactive GRF plot index to middle of range
IMIPIndex=ceil(Sections/2); % Set mega interactive plot index to middle of range
% Apply modifications to display units as deg or rad
if RadORDeg==1
SlopeLabel='Slope [deg]';
end
if RadORDeg==2
Slopes=Slopes*RMult;
SlopeLabel='Slope [rad]';
RMult=1;
end
% Assign sets of data to each coordinate
nSets=floor(size(LimitCycle_IC,1)/5);
switch nSets
case 1
Coords=(1:5)';
case 2
Coords=[1:5; 6:10]';
case 3
Coords=[1:5; 6:10; 11:15]';
case 4
Coords=[1:5; 6:10; 11:15; 16:20]';
end
% We know that there's only one region where there is a period
% bifurcation so we'll split the slopes into 3 regions
Split1=find(LimitCycle_Period==2,1,'first');
Split2=find(LimitCycle_Period==2,1,'last');
Region1=1:Split1-1;
Region2=Split1:Split2;
Region3=Split2+1:length(Slopes);
Colors={[0.7 0.7 0], [1 0 1], [0 0.7 0.7], [0 0.7 0], [0 0 1], [0 0 0], [0.5 1 0.5], [0.5 0 1], [0.5 0.5 1], [1 0.5 0.25]};
LineStyles={'-', '-.', '--', '-.', '--'};
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%% Initial conditions: q_1 q_2 \phi %%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if Plots(1)
figure(1);
if InitCondSubplots==1 && Plots(2)==1
subplot(8,1,1:3);
end
if nSets>1
h1=plot(Slopes,LimitCycle_IC(Coords(1,1),:)-Symmetric*repmat(Slopes*RMult,1,1),'b','LineWidth',LineWidth);
hold on
h2=plot(Slopes,LimitCycle_IC(Coords(2,1),:)-Symmetric*repmat(Slopes*RMult,1,1),'--r','LineWidth',LineWidth);
for i=2:nSets
RepIndex=find(abs(LimitCycle_IC(Coords(1,1),:)-LimitCycle_IC(Coords(1,i),:))>1e-6);
plot(Slopes(RepIndex),LimitCycle_IC(Coords(1,i),RepIndex)-Symmetric*repmat(Slopes(RepIndex)*RMult,1,1),'b','LineWidth',LineWidth);
RepIndex=find(abs(LimitCycle_IC(Coords(2,1),:)-LimitCycle_IC(Coords(2,i),:))>1e-6);
plot(Slopes(RepIndex),LimitCycle_IC(Coords(2,i),RepIndex)-Symmetric*repmat(Slopes(RepIndex)*RMult,1,1),'--r','LineWidth',LineWidth);
end
else
h1=plot(Slopes,LimitCycle_IC(Coords(1,:),:)-Symmetric*repmat(Slopes*RMult,nSets,1),'b','LineWidth',LineWidth);
hold on
h2=plot(Slopes,LimitCycle_IC(Coords(2,:),:)-Symmetric*repmat(Slopes*RMult,nSets,1),'--r','LineWidth',LineWidth);
end
if InitCondSubplots==1 && Plots(2)==1
t1=title('Steady state initial conditions: \theta_1,\theta_2,\theta_1_t,\theta_2_t,\phi versus slope');
set(gca,'XTickLabel','');
else
t1=title('Steady state initial conditions for \theta_1,\theta_2 versus slope');
xh=xlabel(SlopeLabel);
set(xh,'FontSize',FontSize);
end
yh=ylabel('Angle [rad]');
legend([h1(1);h2(1)],{'\theta_1';'\theta_2'},'Orientation','Horizontal','Location','SouthEast');
axis([min(Slopes) max(Slopes) -0.5 0.4]);
set(gca,'FontSize',FontSize-2);
set(yh,'FontSize',FontSize);
set(t1,'FontSize',FontSize);
if InitCondSubplots==1 && Plots(2)==1
subplot(8,1,7:8);
else
figure(2);
end
if nSets>1
plot(Slopes,LimitCycle_IC(Coords(5,1),:),'k','LineWidth',LineWidth);
hold on
for i=2:nSets
RepIndex=find(abs(LimitCycle_IC(Coords(5,1),:)-LimitCycle_IC(Coords(5,i),:))>1e-6);
plot(Slopes(RepIndex),LimitCycle_IC(Coords(5,i),RepIndex),'k','LineWidth',LineWidth);
end
else
plot(Slopes,LimitCycle_IC(Coords(5,:),:),'k','LineWidth',LineWidth);
end
if InitCondSubplots==0 || Plots(2)==0
t1=title('Steady state initial conditions for CPG phase \phi versus slope');
set(t1,'FontSize',FontSize);
end
xh=xlabel(SlopeLabel);
set(xh,'FontSize',FontSize);
yh=ylabel('CPG Phase \phi');
axis([min(Slopes) max(Slopes) 0.65 1]);
set(gca,'FontSize',FontSize-2);
set(yh,'FontSize',FontSize);
end
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%% Initial conditions: q_1dot q_2dot %%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if Plots(2)
if InitCondSubplots==1 && Plots(1)==1
subplot(8,1,4:6);
else
figure(3);
end
if nSets>1
h1=plot(Slopes,LimitCycle_IC(Coords(3,1),:),'b','LineWidth',LineWidth);
hold on
h2=plot(Slopes,LimitCycle_IC(Coords(4,1),:),'--r','LineWidth',LineWidth);
for i=2:nSets
RepIndex=find(abs(LimitCycle_IC(Coords(3,1),:)-LimitCycle_IC(Coords(3,i),:))>1e-6);
plot(Slopes(RepIndex),LimitCycle_IC(Coords(3,i),RepIndex),'b','LineWidth',LineWidth);
RepIndex=find(abs(LimitCycle_IC(Coords(4,1),:)-LimitCycle_IC(Coords(4,i),:))>1e-6);
plot(Slopes(RepIndex),LimitCycle_IC(Coords(4,i),RepIndex),'--r','LineWidth',LineWidth);
end
else
h1=plot(Slopes,LimitCycle_IC(Coords(3,:),:),'b','LineWidth',LineWidth);
hold on
h2=plot(Slopes,LimitCycle_IC(Coords(4,:),:),'--r','LineWidth',LineWidth);
end
if InitCondSubplots==0 || Plots(1)==0
t1=title('Steady state initial conditions for \theta_{1t}, \theta_{2t} versus slope');
set(t1,'FontSize',FontSize);
xh=xlabel(SlopeLabel);
set(xh,'FontSize',FontSize);
end
yh=ylabel('Angular Velocity [rad/s]');
legend([h1(1);h2(1)],{'\theta_{1t}';'\theta_{2t}'},'Orientation','Horizontal','Location','SouthEast');
axis([min(Slopes) max(Slopes) -1.25 -0.45]);
set(gca,'FontSize',FontSize-2);
set(yh,'FontSize',FontSize);
if InitCondSubplots==1 && Plots(1)==1
set(gca,'XTickLabel','');
end
end
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%% Interactive Phase Plane %%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if Plots(3)
X=LimitCycle_X{IPPIndex};
% Initialize figure
IPPh_fig=figure(4);
% Set the keyboard input handling function
set(IPPh_fig,'KeyPressFcn',@KeybHandle);
% Plot
if InterSubplots==1 && Plots(3)+Plots(5)==2
subplot(1,2,1);
end
IPPh1=plot(X(:,3),X(:,5),'b','LineWidth',LineWidth);
hold on
IPPh2=plot(X(:,4),X(:,6),'b','LineWidth',LineWidth);
axis([-0.5 0.8 -2.8 3.2]);
xh=xlabel('Angle [rad]');
yh=ylabel('Angular Velocity [rad/s]');
IPPt1=title(sprintf('Interactive Phase Plane - Slope=%.2f\\circ',Slopes(IPPIndex)));
set(gca,'FontSize',FontSize);
set(xh,'FontSize',FontSize);
set(yh,'FontSize',FontSize);
set(IPPt1,'FontSize',FontSize);
end
%%%%%%%%%%%%%%%%%%%%%%% KeybHandle %%%%%%%%%%%%%%%%%%%%%%%
% Handle keyboard input
function KeybHandle(h_obj,evt) %#ok<INUSL>
if strcmp(evt.Key,'uparrow')
IPPIndex=IPPIndex+1;
if IPPIndex>Sections
IPPIndex=Sections;
end
end
if strcmp(evt.Key,'downarrow')
IPPIndex=IPPIndex-1;
if IPPIndex<1
IPPIndex=1;
end
end
if strcmp(evt.Key,'rightarrow')
IPPIndex=IPPIndex+20;
if IPPIndex>Sections
IPPIndex=Sections;
end
end
if strcmp(evt.Key,'leftarrow')
IPPIndex=IPPIndex-20;
if IPPIndex<1
IPPIndex=1;
end
end
X=LimitCycle_X{IPPIndex};
Slope=Slopes(IPPIndex);
set(IPPh1,'XData',X(:,3));
set(IPPh1,'YData',X(:,5));
set(IPPh2,'XData',X(:,4));
set(IPPh2,'YData',X(:,6));
set(IPPt1,'String',sprintf('Interactive Phase Plane - Slope=%.2f\\circ',Slope));
if Plots(5)==1 % If interactive PM locus is active, apply change to it as well
if ~isfield(evt,'Called') % check if this handle was called from the other handle
evt.Called=1;
PMKeybHandle([],evt);
end
end
end
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%% Linearized Poincare Matrix eigenvalues %%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if Plots(4)
figure(5);
subplot(6,1,1:3);
hold on
for i=1:5
plot(Slopes(Region1),abs(LimitCycle_eig(i,Region1)),LineStyles{i},'LineWidth',LineWidth,'Color',Colors{i});
plot(Slopes(Region2),abs(LimitCycle_eig(i,Region2)),LineStyles{i},'LineWidth',LineWidth,'Color',Colors{i});
plot(Slopes(Region3),abs(LimitCycle_eig(i,Region3)),LineStyles{i},'LineWidth',LineWidth,'Color',Colors{i});
end
% Draw bifurcation lines
X1=Slopes(Region1(end));
X2=Slopes(Region3(1));
line([X1 X1],[0 1],'LineWidth',3,'LineStyle','--','Color',[0 0 0]);
line([X2 X2],[0 1],'LineWidth',3,'LineStyle','--','Color',[0 0 0]);
% Add labels to different areas
LX1=(Slopes(Region1(end))+Slopes(Region1(1)))/2;
LX2=(Slopes(Region2(end))+Slopes(Region2(1)))/2;
LX3=(Slopes(Region3(end))+Slopes(Region3(1)))/2;
text(LX1,0.96,'I','FontSize',FontSize,'FontName','Times New Roman','FontWeight','bold','HorizontalAlignment','center');
text(LX2,0.96,'IIa','FontSize',FontSize,'FontName','Times New Roman','FontWeight','bold','HorizontalAlignment','center');
text(LX3,0.96,'III','FontSize',FontSize,'FontName','Times New Roman','FontWeight','bold','HorizontalAlignment','center');
t1=title('Absolute value of Poincare Map eigenvalues versus slope');
% xh=xlabel(SlopeLabel);
yh=ylabel('|\lambda_i|');
axis([min(Slopes) max(Slopes) -0.05 1]);
set(gca,'FontSize',FontSize);
% set(xh,'FontSize',FontSize);
set(yh,'FontSize',FontSize+2);
set(t1,'FontSize',FontSize);
set(gca,'XTickLabel','');
subplot(6,1,4:6);
hold on
for i=1:5
plot(Slopes(Region1),abs(LimitCycle_eig(i,Region1)),LineStyles{i},'LineWidth',LineWidth,'Color',Colors{i});
plot(Slopes(Region2),abs(LimitCycle_eig(i+5,Region2)),LineStyles{i},'LineWidth',LineWidth,'Color',Colors{i});
plot(Slopes(Region3),abs(LimitCycle_eig(i,Region3)),LineStyles{i},'LineWidth',LineWidth,'Color',Colors{i});
end
% Draw bifurcation lines
X1=Slopes(Region1(end));
X2=Slopes(Region3(1));
line([X1 X1],[0 1],'LineWidth',3,'LineStyle','--','Color',[0 0 0]);
line([X2 X2],[0 1],'LineWidth',3,'LineStyle','--','Color',[0 0 0]);
% Add labels to different areas
LX1=(Slopes(Region1(end))+Slopes(Region1(1)))/2;
LX2=(Slopes(Region2(end))+Slopes(Region2(1)))/2;
LX3=(Slopes(Region3(end))+Slopes(Region3(1)))/2;
text(LX1,0.96,'I','FontSize',FontSize,'FontName','Times New Roman','FontWeight','bold','HorizontalAlignment','center');
text(LX2,0.96,'IIb','FontSize',FontSize,'FontName','Times New Roman','FontWeight','bold','HorizontalAlignment','center');
text(LX3,0.96,'III','FontSize',FontSize,'FontName','Times New Roman','FontWeight','bold','HorizontalAlignment','center');
% t1=title('Absolute value of Poincare Map eigenvalues versus slope');
xh=xlabel(SlopeLabel);
yh=ylabel('|\lambda_i|');
axis([min(Slopes) max(Slopes) -0.05 1]);
set(gca,'FontSize',FontSize);
set(xh,'FontSize',FontSize);
set(yh,'FontSize',FontSize+2);
set(t1,'FontSize',FontSize);
end
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%% Interactive Poincare Map %%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if Plots(5)==1
if InterSubplots==1 && Plots(3)+Plots(5)==2
figure(IPPh_fig);
subplot(1,2,2);
else
% Initialize figure
IPMh_fig=figure(6);
% Set the keyboard input handling function
set(IPMh_fig,'KeyPressFcn',@PMKeybHandle);
end
% Plot the unit circle
Circle();
hold on
% Select the eigenvalues by index
switch LimitCycle_Period(IPMIndex)
case 1
EigVa=LimitCycle_eig(1:5,IPMIndex);
EigVb=[];
case 2
EigVa=LimitCycle_eig(1:5,IPMIndex);
EigVb=LimitCycle_eig(6:10,IPMIndex);
otherwise
EigVa=[];
EigVb=[];
end
% Plot
IPMha=plot(real(EigVa),imag(EigVa),'*','MarkerSize',10);
IPMhb=plot(real(EigVa),imag(EigVa),'*r','MarkerSize',10);
IPMt1=title(sprintf('Numerical PM eigenvalues locus - Slope=%.2f\\circ',Slopes(IPMIndex)));
xh=xlabel('Real(\lambda)');
yh=ylabel('Imag(\lambda)');
IPMtext1=text(0.95,0.95,'Period: 1','FontWeight','bold','HorizontalAlignment','Right');
IPMaxis=gca;
% Set axis to show the complete unit circle
axis equal
if max(abs(LimitCycle_eig(1:5*LimitCycle_Period(IPMIndex),IPMIndex)))<1.05
set(IPMaxis,'XLim',[-1.05 1.05]);
set(IPMaxis,'YLim',[-1.05 1.05]);
else
set(IPMaxis,'XLimMode','auto');
set(IPMaxis,'YLimMode','auto');
end
set(gca,'FontSize',FontSize);
set(xh,'FontSize',FontSize);
set(yh,'FontSize',FontSize);
set(IPMt1,'FontSize',FontSize);
end
%%%%%%%%%%%%%%%%%%%%%%% PMKeybHandle %%%%%%%%%%%%%%%%%%%%%%%
% Handle keyboard input
function PMKeybHandle(h_obj,evt) %#ok<INUSL>
if strcmp(evt.Key,'uparrow')
IPMIndex=IPMIndex+1;
if IPMIndex>Sections
IPMIndex=Sections;
end
end
if strcmp(evt.Key,'downarrow')
IPMIndex=IPMIndex-1;
if IPMIndex<1
IPMIndex=1;
end
end
if strcmp(evt.Key,'rightarrow')
IPMIndex=IPMIndex+20;
if IPMIndex>Sections
IPMIndex=Sections;
end
end
if strcmp(evt.Key,'leftarrow')
IPMIndex=IPMIndex-20;
if IPMIndex<1
IPMIndex=1;
end
end
set(IPMtext1,'string',['Period: ',num2str(LimitCycle_Period(IPMIndex))]);
% Select the eigenvalues by index
switch LimitCycle_Period(IPMIndex)
case 1
EigVa=LimitCycle_eig(1:5,IPMIndex);
EigVb=[];
case 2
EigVa=LimitCycle_eig(1:5,IPMIndex);
EigVb=LimitCycle_eig(6:10,IPMIndex);
otherwise
EigVa=[];
EigVb=[];
end
set(IPMha,'XData',real(EigVa),'YData',imag(EigVa));
set(IPMhb,'XData',real(EigVb),'YData',imag(EigVb));
% Set axis to show the complete unit circle
if max(abs(LimitCycle_eig(1:5*LimitCycle_Period(IPMIndex),IPMIndex)))<1.05
set(IPMaxis,'XLim',[-1.05 1.05]);
set(IPMaxis,'YLim',[-1.05 1.05]);
else
set(IPMaxis,'XLimMode','auto');
set(IPMaxis,'YLimMode','auto');
end
set(IPMt1,'String',sprintf('Numerical PM eigenvalues locus - Slope=%.2f\\circ',Slopes(IPMIndex)));
if Plots(3)==1 % If interactive phase plane is active, apply change to it as well
if ~isfield(evt,'Called') % check if this handle was called from the other handle
evt.Called=1;
KeybHandle([],evt);
end
end
end
%%%%%%%%%%%%%%%%%%%%%%% Circle %%%%%%%%%%%%%%%%%%%%%%%
% Draws a circle
function [ res ] = Circle()
Resolution=36;
coordX=zeros(1,Resolution);
coordY=zeros(1,Resolution);
for r=1:Resolution
coordX(1,r)=cos(r/Resolution*2*pi);
coordY(1,r)=sin(r/Resolution*2*pi);
end
h=patch(coordX,coordY,[1 1 1]);
set(h,'EdgeColor',[0 0 0]);
set(h,'LineWidth',2,'LineStyle','--');
res=h;
end
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%% Poincare Map eigenvalues locus %%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if Plots(6)
% First we split the slopes into 3 regions
EigV1=LimitCycle_eig(1:5,Region1)';
EigV2a=LimitCycle_eig(1:5,Region2)';
EigV2b=LimitCycle_eig(6:10,Region2)';
EigV3=LimitCycle_eig(1:5,Region3)';
% We have 3 regions so we'll do 3 subplots
if LocusSubplots==1
subplot(4,4,[1 2 5 6]);
else
figure(7)
end
% Plot the unit circle
Circle();
hold on
line([-1.2 1.2],[0 0],'Color',[0 0 0]);
line([0 0],[-1.2 1.2],'Color',[0 0 0]);
% Plot the eigenvalues locus
for i=1:5
plot(real(EigV1(:,i)),imag(EigV1(:,i)),'-','LineWidth',LineWidth,'MarkerSize',8,'Color',Colors{i});
end
t1=title(sprintf('Region I: %.2f\\circ to %.2f\\circ',Slopes(1),Slopes(Split1-1)));
yh=ylabel('Imag(\lambda)');
if LocusSubplots==0
xh=xlabel('Real(\lambda)');
set(xh,'FontSize',FontSize);
end
if LocusDirection==1
b=find(imag(EigV1)==max(max(imag(EigV1))));
col=floor(b/size(EigV1,1));
Start=EigV1(b-col*size(EigV1,1),:);
for jl=1:5
plot(real(Start(jl)),imag(Start(jl)),'.','MarkerSize',26,'Color',Colors{jl});
end
AddDirection(EigV1,3.5);
end
% Set axis to show the complete unit circle
axis([-1.05 1.05 -1.05 1.05]);
axis image
axis off
set(gcf,'Color',[1 1 1]);
set(gca,'FontSize',FontSize);
set(yh,'FontSize',FontSize);
set(t1,'FontSize',FontSize);
if LocusSubplots==1
subplot(4,4,[9 10 13 14]);
else
figure(8)
end
% Plot the unit circle
Circle();
hold on
line([-1.2 1.2],[0 0],'Color',[0 0 0]);
line([0 0],[-1.2 1.2],'Color',[0 0 0]);
% Plot the eigenvalues locus
for i=1:5
plot(real(EigV2a(:,i)),imag(EigV2a(:,i)),'-','LineWidth',LineWidth,'MarkerSize',8,'Color',Colors{i});
end
t1=title(sprintf('Region IIa: %.2f\\circ to %.2f\\circ',Slopes(Split1),Slopes(Split2)));
xh=xlabel('Real(\lambda)');
if LocusSubplots==0
yh=ylabel('Imag(\lambda)');
set(yh,'FontSize',FontSize);
end
if LocusDirection==1
Start=EigV2a(1,:);
for jl=1:5
plot(real(Start(jl)),imag(Start(jl)),'.','MarkerSize',26,'Color',Colors{jl});
end
AddDirection(EigV2a,3);
end
% Set axis to show the complete unit circle
axis([-1.05 1.05 -1.05 1.05]);
axis image
axis off
set(gcf,'Color',[1 1 1]);
set(gca,'FontSize',FontSize);
set(xh,'FontSize',FontSize);
set(t1,'FontSize',FontSize);
if LocusSubplots==1
subplot(4,4,[11 12 15 16]);
else
figure(9)
end
% Plot the unit circle
Circle();
hold on
line([-1.2 1.2],[0 0],'Color',[0 0 0]);
line([0 0],[-1.2 1.2],'Color',[0 0 0]);
% Plot the eigenvalues locus
for i=1:5
plot(real(EigV2b(:,i)),imag(EigV2b(:,i)),'-','LineWidth',LineWidth,'MarkerSize',8,'Color',Colors{i});
end
t1=title(sprintf('Region IIb: %.2f\\circ to %.2f\\circ',Slopes(Split1),Slopes(Split2)));
xh=xlabel('Real(\lambda)');
if LocusSubplots==0
yh=ylabel('Imag(\lambda)');
set(yh,'FontSize',FontSize);
end
if LocusDirection==1
Start=EigV2b(1,:);
for jl=1:5
plot(real(Start(jl)),imag(Start(jl)),'.','MarkerSize',26,'Color',Colors{jl});
end
AddDirection(EigV2b,4.5);
end
% Set axis to show the complete unit circle
axis([-1.05 1.05 -1.05 1.05]);
axis image
axis off
set(gcf,'Color',[1 1 1]);
set(gca,'FontSize',FontSize);
set(xh,'FontSize',FontSize);
set(t1,'FontSize',FontSize);
if LocusSubplots==1
subplot(4,4,[3 4 7 8]);
else
figure(10)
end
% Plot the unit circle
Circle();
hold on
line([-1.2 1.2],[0 0],'Color',[0 0 0]);
line([0 0],[-1.2 1.2],'Color',[0 0 0]);
% Plot the eigenvalues locus
for i=1:5
plot(real(EigV3(:,i)),imag(EigV3(:,i)),'-','LineWidth',LineWidth,'MarkerSize',8,'Color',Colors{i});
end
t1=title(sprintf('Region III: %.2f\\circ to %.2f\\circ',Slopes(Split2+1),Slopes(end)));
if LocusSubplots==0
xh=xlabel('Real(\lambda)');
set(xh,'FontSize',FontSize);
yh=ylabel('Imag(\lambda)');
set(yh,'FontSize',FontSize);
end
if LocusDirection==1
Start=EigV3(1,:);
for jl=1:5
plot(real(Start(jl)),imag(Start(jl)),'.','MarkerSize',26,'Color',Colors{jl});
end
AddDirection(EigV3,3.5);
end
% Set axis to show the complete unit circle
axis([-1.05 1.05 -1.05 1.05]);
axis image
axis off
set(gcf,'Color',[1 1 1]);
set(gca,'FontSize',FontSize);
set(t1,'FontSize',FontSize);
end
function [] = AddDirection(Values,nArrows)
[N,M]=size(Values);
% Find length of locus to evenly distribute arrows
LocusDist=zeros(1,M);
for j=1:M
for a=1:N-1
LocusDist(j)=LocusDist(j)+sqrt((real(Values(a+1,j))-real(Values(a,j)))^2+(imag(Values(a+1,j))-imag(Values(a,j)))^2);
end
end
Step=LocusDist/(nArrows+1);
LocusDist=zeros(1,M);
for j=1:M
for a=1:N-1
LocusDist(j)=LocusDist(j)+sqrt((real(Values(a+1,j))-real(Values(a,j)))^2+(imag(Values(a+1,j))-imag(Values(a,j)))^2);
if LocusDist(j)>Step
LocusDist(j)=0;
Vec1=[real(Values(a,j)) imag(Values(a,j))];
Vec2=[real(Values(a+1,j)) imag(Values(a+1,j))];
Dir=Vec2-Vec1;
Dir=Dir/norm(Dir);
Length=0.075;
% Plot arrow
TrDir=[-Dir(2) Dir(1)];
Points=[Vec2; Vec2-Length*Dir-Length/2*TrDir; Vec2-Length*Dir+Length/2*TrDir];
patch(Points(:,1), Points(:,2),Colors{j},'EdgeColor',Colors{j});
Point4=Vec2-Length*Dir+2*Length*TrDir;
if LocusDirNumber==1
text(Point4(1),Point4(2),num2str(a),'FontSize',14);
end
end
end
end
end
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%% Limit Cycle plots for paper %%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if Plots(7)==1
figure(11)
PlotSlopes=[-10 -5 0 3 7 10];
SubPlots=[4 7 10 13 16; 5 8 11 14 17; 6 9 12 15 18; 22 25 28 31 34; 23 26 29 32 35; 24 27 30 33 36];
for i=1:6
if i==4
subplot(12,3,SubPlots(i,:));
CurSlope=find(Slopes>=PlotSlopes(i),1,'first');
ID=find(abs(diff(LimitCycle_X{CurSlope}(:,6)))>0.1,1,'first');
plot(LimitCycle_X{CurSlope}(1:ID+1,3),LimitCycle_X{CurSlope}(1:ID+1,5),'--','LineWidth',LineWidth);
hold on
plot(LimitCycle_X{CurSlope}(1:ID+1,4),LimitCycle_X{CurSlope}(1:ID+1,6),'r','LineWidth',LineWidth);
plot(LimitCycle_X{CurSlope}(ID+1:end,3),LimitCycle_X{CurSlope}(ID+1:end,5),'LineWidth',LineWidth);
plot(LimitCycle_X{CurSlope}(ID+1:end,4),LimitCycle_X{CurSlope}(ID+1:end,6),'--r','LineWidth',LineWidth);
plot(LimitCycle_X{CurSlope}(1,3),LimitCycle_X{CurSlope}(1,5),'.','MarkerSize',25);
plot(LimitCycle_X{CurSlope}(1,3),LimitCycle_X{CurSlope}(1,5),'.w','MarkerSize',10);
plot(LimitCycle_X{CurSlope}(1,4),LimitCycle_X{CurSlope}(1,6),'.r','MarkerSize',25);
plot(LimitCycle_X{CurSlope}(ID+1,3),LimitCycle_X{CurSlope}(ID+1,5),'.','MarkerSize',25);
plot(LimitCycle_X{CurSlope}(ID+1,4),LimitCycle_X{CurSlope}(ID+1,6),'.r','MarkerSize',25);
plot(LimitCycle_X{CurSlope}(ID+1,4),LimitCycle_X{CurSlope}(ID+1,6),'.w','MarkerSize',10);
else
subplot(12,3,SubPlots(i,:));
CurSlope=find(Slopes>=PlotSlopes(i),1,'first');
plot(LimitCycle_X{CurSlope}(:,3),LimitCycle_X{CurSlope}(:,5),'--','LineWidth',LineWidth);
hold on
plot(LimitCycle_X{CurSlope}(:,4),LimitCycle_X{CurSlope}(:,6),'LineWidth',LineWidth);
plot(LimitCycle_X{CurSlope}(1,3),LimitCycle_X{CurSlope}(1,5),'.','MarkerSize',25);
plot(LimitCycle_X{CurSlope}(1,3),LimitCycle_X{CurSlope}(1,5),'.w','MarkerSize',10);
plot(LimitCycle_X{CurSlope}(1,4),LimitCycle_X{CurSlope}(1,6),'.','MarkerSize',25);
end
% switch i
% case 4
% AddArrows([LimitCycle_X{CurSlope}(:,3), LimitCycle_X{CurSlope}(:,5)], 2, [0 0 1], 5.537, 0);
% case 5
% AddArrows([LimitCycle_X{CurSlope}(:,3), LimitCycle_X{CurSlope}(:,5)], 6, [0 0 1], 5.537, [1 2 3 5]);
% case 6
% AddArrows([LimitCycle_X{CurSlope}(:,3), LimitCycle_X{CurSlope}(:,5)], 6, [0 0 1], 5.537, [1 2 3 5]);
% otherwise
% AddArrows([LimitCycle_X{CurSlope}(:,3), LimitCycle_X{CurSlope}(:,5)], 5, [0 0 1], 5.537, [2 3 5]);
% end
axis([-0.5 0.62 -2.8 3.4]);
set(gca,'FontSize',FontSize);
if Slopes(CurSlope)<=0
title(['Slope: ',num2str(Slopes(CurSlope)),'\circ'],'FontSize',FontSize);
set(gca,'XTickLabel','');
else
title(['Slope: +',num2str(Slopes(CurSlope)),'\circ'],'FontSize',FontSize);
end
if i~=1 && i~=4
set(gca,'YTickLabel','');
end
end
subplot(12,3,SubPlots(5,:));
xlabel('Leg angle [rad]','FontSize',FontSize);
% subplot(2,3,SubPlots(1,:));
% ylabel('Leg angular velocity [rad/s] ','FontSize',FontSize);
hax = axes('Position', [0, 0, 1, 1],'Visible','off');
text(0.05,0.5,'Leg angular velocity [rad/s]','FontSize',FontSize,'Units','normalized','rotation',90,'HorizontalAlignment','center');
text(0.5,0.99,'Limit cycles generated by the Full Feedback Controller for different slopes',...
'FontSize',FontSize,'Units','normalized','HorizontalAlignment','center','VerticalAlignment','top');
end
% function [] = AddArrows(Values,nArrows,Color,AR,skip)
% N=length(Values);
%
% % Find length of locus to evenly distribute arrows
% LocusDist=0;
% for lo=1:N-1
% LocusDist=LocusDist+sqrt((Values(lo+1,1)-Values(lo,1))^2+(Values(lo+1,2)-Values(lo,2))^2);
% end
% Step=LocusDist/(nArrows+1);
%
% LocusDist=0;
% count=0;
% for lo=1:N-1
% LocusDist=LocusDist+sqrt((Values(lo+1,1)-Values(lo,1))^2+(Values(lo+1,2)-Values(lo,2))^2);
% if LocusDist>Step
% LocusDist=0;
%
% count=count+1;
% if ~isempty(find(count==skip,1,'first'))
% continue
% end
%
% Vec1=[Values(lo,1) Values(lo,2)];
% Vec2=[Values(lo+1,1) Values(lo+1,2)];
% Dir=Vec2-Vec1;
% Dir=Dir/norm(Dir);
% Length=0.1*Step;
%
% % Plot arrow
% TrDir=[-Dir(2) Dir(1)];
% Points=[Vec2; Vec2-Length*Dir-Length/2*TrDir; Vec2-Length*Dir+Length/2*TrDir];
%
% % Correct aspect ratio
% CoM=mean(Points,1);
% Points=Points-repmat(CoM,3,1);
% Points(:,2)=Points(:,2)*AR;
% Points=Points+repmat(CoM,3,1);
%
% patch(Points(:,1), Points(:,2),Color,'EdgeColor',Color);
% end
% end
% end
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%% Compass Gait Model Figure %%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if Plots(8)==1
Robot=CompassBiped();
InitCond=[1.88*pi, 0.2*pi, 0, 0];
Robot.CircRes=72;
Robot.LinkRes=24;
Robot.RenderParams=1;
Floor=Terrain(0,1,1);
figure(12)
Robot.Render(InitCond);
Floor.Render(-0.4,1.2);
axis([-0.4 1.2 -0.5 1.5])
axis off
set(gcf,'Color',[1 1 1])
set(0,'Units','Pixels');
ScSize=get(0,'ScreenSize');
set(12,'Units','Pixels');
set(12,'OuterPosition',ScSize+[600 200 -1200 -325]);
addpath('ExportFig');
export_fig 'CompassBiped' -r600 -painters -tif -nocrop -transparent
end
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%% Interactive Ground Reaction Forces Plot %%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if Plots(9)==1
Robot=CompassBiped();
ThisGRF=GRF{IGRFIndex};
ThisMeasGRF=MeasuredGRF{IGRFIndex};
ThisT=LimitCycle_T{IGRFIndex};
% Initialize figure
IGRFh_fig=figure(4);
% Set the keyboard input handling function
set(IGRFh_fig,'KeyPressFcn',@KeybHandleGRF);
% Plot GRF Fy
subplot(3,1,1);
IGRFh1=plot(ThisT,ThisGRF(2,:),'LineWidth',LineWidth);
hold on
plot(ThisT,Robot.GetWeight()*ones(size(ThisT)),'--k','LineWidth',LineWidth);
yh=ylabel('GRF F_y [N]');
IGRFt1=title(sprintf('Interactive GRF Plot - Slope=%.2f\\circ',Slopes(IGRFIndex)));
set(gca,'FontSize',FontSize);
set(yh,'FontSize',FontSize);
set(IGRFt1,'FontSize',FontSize);
axis([ThisT(1) ThisT(end) 0.995*min(ThisGRF(2,:)) 1.005*max(ThisGRF(2,:))]);
% Plot GRF Fx
subplot(3,1,2);
IGRFh2=plot(ThisT,ThisGRF(1,:),'LineWidth',LineWidth);
yh=ylabel('GRF F_x [N]');
set(gca,'FontSize',FontSize);
set(yh,'FontSize',FontSize);
axis([ThisT(1) ThisT(end) 1.05*min(ThisGRF(1,:)) 1.05*max(ThisGRF(1,:))]);
% Plot Measured GRF
subplot(3,1,3);
IGRFh3=plot(ThisT,ThisMeasGRF,'LineWidth',LineWidth);
hold on
IGRFh4=plot(ThisT,MeanMeasuredGRF(IGRFIndex)*ones(size(ThisT)),'--k','LineWidth',LineWidth);
xh=xlabel('Time [sec]');
yh=ylabel('GRF MEasured [N]');
set(gca,'FontSize',FontSize);
set(xh,'FontSize',FontSize);
set(yh,'FontSize',FontSize);
axis([ThisT(1) ThisT(end) 0.995*min(ThisMeasGRF) 1.005*max(ThisMeasGRF)]);
end
%%%%%%%%%%%%%%%%%%%%%%% KeybHandle %%%%%%%%%%%%%%%%%%%%%%%
% Handle keyboard input
function KeybHandleGRF(h_obj,evt) %#ok<INUSL>
if strcmp(evt.Key,'uparrow')
IGRFIndex=IGRFIndex+1;
if IGRFIndex>Sections
IGRFIndex=Sections;
end
end
if strcmp(evt.Key,'downarrow')
IGRFIndex=IGRFIndex-1;
if IGRFIndex<1
IGRFIndex=1;
end
end
if strcmp(evt.Key,'rightarrow')
IGRFIndex=IGRFIndex+20;
if IGRFIndex>Sections
IGRFIndex=Sections;
end
end
if strcmp(evt.Key,'leftarrow')
IGRFIndex=IGRFIndex-20;
if IGRFIndex<1
IGRFIndex=1;
end
end
ThisGRF=GRF{IGRFIndex};
ThisMeasGRF=MeasuredGRF{IGRFIndex};
ThisT=LimitCycle_T{IGRFIndex};
set(IGRFh1,'XData',ThisT);
set(IGRFh1,'YData',ThisGRF(2,:));
set(IGRFh2,'XData',ThisT);
set(IGRFh2,'YData',ThisGRF(1,:));
set(IGRFh3,'XData',ThisT);
set(IGRFh3,'YData',ThisMeasGRF);
set(IGRFh4,'XData',ThisT);
set(IGRFh4,'YData',MeanMeasuredGRF(IGRFIndex)*ones(size(ThisT)));
set(IGRFt1,'String',sprintf('Interactive GRF Plot - Slope=%.2f\\circ',Slopes(IGRFIndex)));
subplot(3,1,1);
axis([ThisT(1) ThisT(end) 0.995*min(ThisGRF(2,:)) 1.005*max(ThisGRF(2,:))]);
subplot(3,1,2);
axis([ThisT(1) ThisT(end) 1.05*min(ThisGRF(1,:)) 1.05*max(ThisGRF(1,:))]);
subplot(3,1,3);
axis([ThisT(1) ThisT(end) 0.995*min(ThisMeasGRF) 1.005*max(ThisMeasGRF)]);
end
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Energy %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if Plots(10)==1
figure
plot(Slopes,StepLength);
hold on
plot(DPSlopes,DPStepLength,'r');
title('Step length');
figure