Balance Lab

David
/
Balance Lab
on 2 Nov 2026
2
20
10
1
8026
game.m
function g = game()
%game  BALANCE LAB - bang-bang control of an inverted pendulum on a cart.
%
%   The cart motor always pushes at full force; SPACE (or click) flips
%   its direction. Keep the pendulum upright in Pluto gravity while wind
%   gusts push it around. Survive and the lab bolts on a 2nd and 3rd arm,
%   with ever softer joints. Time balanced is your score.
%
%   Built using Claude Code and Opus 5.5
%
%   >> minihackContest.validate
%   >> minihackContest.play
g.init   = @initState;
g.update = @updateState;
g.render = @renderFrame;
end

function s = initState(ax)
set(ax,'YDir','normal','XLim',[0 800],'YLim',[0 600],'Color',[.03 .07 .16],'ALim',[0 1],'SortMethod','childorder');
E = {'EdgeColor','none'};
C = [.35 .85 1];   % blueprint cyan

% Blueprint grid: minor and major lines
for k = 1:2
    d = 25*4^(k-1);
    [x,y] = seg(0:d:800,0,600); line(ax,x,y,'Color',[C .05+.07*k]);
    [y,x] = seg(0:d:600,0,800); line(ax,x,y,'Color',[C .05+.07*k]);
end

% Track, ruler ticks every 0.5 m, end stops
patch(ax,[60 740 740 60],[0 0 104 104],[.02 .04 .1],E{:});
line(ax,[90 710],[104 104],'Color',C,'LineWidth',2);
[x,y] = seg(100:50:700,104,104 - 6*(1 + mod(0:12,2)));
line(ax,x,y,'Color',[C .6]);
for k = [-1 1]   % end stops, and red warning zones the cart edge enters near them
    patch(ax,400 + k*[313 337 337 313],[104 104 160 160],[.9 .45 .2],'FaceAlpha',.8,E{:});
    patch(ax,400 + k*[265 313 313 265],[104 104 220 220],[1 .2 .15],'FaceVertexAlphaData',[.3;.3;0;0],'FaceAlpha','interp',E{:});
end
for k = -3:3
    text(ax,400 + 100*k,82,sprintf('%+d m',k),'Color',[C .6],'FontSize',8,'HorizontalAlignment','center');
end

% Wind streak pool
s.wx = 800*rand(1,40); s.wy = 110 + 420*rand(1,40);
s.h.wd = scatter(ax,s.wx,s.wy,6,[.7 .85 1],'filled','MarkerFaceAlpha',.5,'MarkerEdgeColor','none');

% Cart: body, wheels, motor force arrow
s.h.ct = patch(ax,0,0,[.12 .2 .35],'EdgeColor',C,'LineWidth',1.5);
s.h.wh = line(ax,0,0,'LineStyle','none','Marker','o','MarkerSize',11,'MarkerFaceColor',[.05 .1 .2],'Color',C,'LineWidth',1.5);
s.h.ar = patch(ax,0,0,[1 .6 .2],E{:});

% Pendulum: soft glow, bright core, joints, tip masses
s.h.pg = line(ax,0,0,'Color',[C .25],'LineWidth',9);
s.h.pc = line(ax,0,0,'Color',[.85 .97 1],'LineWidth',3);
s.h.pj = scatter(ax,0,0,60,[.85 .97 1],'filled','MarkerEdgeColor',C,'LineWidth',1.5);

% Oscilloscope: top-arm angle (cyan) and motor command (orange)
patch(ax,[560 780 780 560],[440 440 540 540],[.01 .03 .07],'EdgeColor',C,'EdgeAlpha',.5);
line(ax,[560 780],[490 490],'Color',[C .2]);
s.hx = linspace(562,778,150);
s.ha = zeros(1,150); s.hm = s.ha;
s.h.sa = line(ax,s.hx,s.ha+490,'Color',C,'LineWidth',1.5);
s.h.sm = line(ax,s.hx,s.hm+490,'Color',[1 .6 .2 .7]);
text(ax,565,532,'SCOPE  angle / motor','Color',[C .7],'FontSize',8);

% HUD
T = {'HorizontalAlignment','center','FontWeight','bold'};
F = {'FontName','Consolas','FontSize',11};
s.h.sc = text(ax,20,575,'','Color',[.85 .95 1],'FontSize',15,'FontWeight','bold');
s.h.rd = text(ax,20,500,'','Color',C,F{:},'VerticalAlignment','top');
s.h.wn = text(ax,400,555,'','Color',[1 .75 .4],'FontSize',13,T{:});
s.h.t1 = text(ax,400,400,'','Color',[.9 .97 1],'FontSize',38,T{:});
s.h.t2 = text(ax,400,350,'','Color',C,'FontSize',13,T{1:2});
s.h.fl = patch(ax,[0 800 800 0],[0 0 600 600],[1 .3 .2],'FaceAlpha',0,E{:});
set(ax.Children,'HitTest','off','PickableParts','none');

% Lab constants: Pluto gravity (slow, so it is human-playable), tip masses (kg) and arm lengths (m)
s.g = .62; s.mc = 2; s.m = [1 .5 .3]; s.L = [1.5 .7 .5];
s.Fm = 2.5; s.ks = 1.5; s.t = 0; s.best = 0;
s = rst(s);
s.m0 = 0;   % mode: 0 title, 1 playing, 2 toppling, 3 game over
end

function s = updateState(s,dt,p)
s.t = s.t + dt;
s.fa = max(0,s.fa - 2*dt);
s.bt = max(0,s.bt - dt);
if p && ~mod(s.m0,3)
    s = rst(s); p = 0;
end

if s.m0 == 1
    s.rt = s.rt + dt;
    if p, s.d = -s.d; end

    % Bolt on another arm, aligned with the current top arm
    n = numel(s.q) - 1;
    if n < 3 && s.rt > 25*n - 5
        s.q(end+1) = s.q(end); s.v(end+1) = s.v(end); s.bt = 2;
    end

    % Joints soften and gusts strengthen over time
    s.k = max(.6,3*exp(-s.rt/60));
    s.gt = s.gt - dt;
    if s.gt <= 0
        s.gw = s.gn; s.gt = 1.5 + 2*rand;
        s.gn = (rand > .35)*min(.17,.04 + s.rt/500)*(2*rand - 1);
    end
elseif s.m0
    s.d = 0; s.gw = 0;
    if s.t > s.td, s.m0 = 3; end
end

% Physics: 4 symplectic Euler substeps; motor is a first-order actuator
h = dt/4;
for i = 1:4
    s.f = s.f + (s.d*s.Fm - s.f)*h/.05;
    x = s.q(1);
    % Cubic centering spring (a bungee) plus a stiff bumper where the cart meets the stops
    b = -s.ks*s.Fm*(x/2.68)^3 + (abs(x) > 2.68)*(-300*(x - 2.68*sign(x)) - 20*s.v(1));
    if s.m0
        s.v = s.v + h*acc(s,s.f + b);
        s.q = s.q + h*s.v;
    end
    o = [0 abs(s.q(2:end)) > 1.6] > 0;   % toppled arms rest on the deck
    s.q(o) = 1.6*sign(s.q(o)); s.v(o) = 0;
end
if s.m0 == 1 && any(abs(s.q(2:end)) > 1.2)
    s.m0 = 2; s.td = s.t + 1.5; s.fa = .5;
    s.best = max(s.best,s.rt);
end

% Scope history and wind streaks
s.ha = [s.ha(2:end) min(48,max(-48,40*s.q(end)/1.2))];
s.hm = [s.hm(2:end) 30*s.f/s.Fm];
s.wx = mod(s.wx + (60 + 900*abs(s.gw))*sign(s.gw + eps)*dt,800);
end

function a = acc(s,F)
% Lagrangian N-link inverted pendulum on a cart, point masses at the tips
n = numel(s.q) - 1; th = s.q(2:end); w = s.v(2:end);
m = s.m(1:n); L = s.L(1:n);
mu = flip(cumsum(flip(m)));
[J,K] = ndgrid(1:n);
D = th(J) - th(K);
Mt = L(J).*L(K).*mu(max(J,K));
c = L.*mu;
r = [0 diff(th)]; rd = [0 diff(w)];
tq = -s.k*r - .05*s.k*rd; tq = tq - [tq(2:end) 0];
M = [s.mc+sum(m) c.*cos(th); (c.*cos(th))' Mt.*cos(D)];
f = [F + sum(c.*sin(th).*w.^2) + s.gw*sum(m) - .5*s.v(1), ...
    s.g*c.*sin(th) - sum(Mt.*sin(D).*w(K).^2,2)' + tq + s.gw*c.*cos(th) - .05*w];
a = (M\f')';
end

function renderFrame(~,s)
h = s.h;
n = numel(s.q) - 1;
X = 400 + 100*s.q(1); Y = 150;
P = [X Y; X + 100*cumsum(s.L(1:n).*sin(s.q(2:end)))' Y + 100*cumsum(s.L(1:n).*cos(s.q(2:end)))'];
set([h.pg h.pc],'XData',P(:,1),'YData',P(:,2));
set(h.pj,'XData',P(:,1),'YData',P(:,2),'SizeData',[50 260*s.m(1:n)]);
set(h.ct,'XData',X + [-45 45 45 -45],'YData',[118 118 Y Y],'EdgeColor',[.35 .85 1] + (abs(s.q(1)) > 2.2)*[.65 -.6 -.8]);
set(h.wh,'XData',X + [-28 28],'YData',[112 112]);
u = s.f/s.Fm;
h.ar.XData = X + 55*u*[0 .6 .6 1 .6 .6 0];
h.ar.YData = 134 + [-4 -4 -10 0 10 4 4];

set(h.sa,'YData',490 + s.ha);
set(h.sm,'YData',490 + s.hm);
set(h.wd,'XData',s.wx,'MarkerFaceAlpha',.15 + 1.5*abs(s.gw));

q = round(s.q(2:end)*180/pi,1);
r = sprintf('ARM%d %+6.1f deg\n',[1:n; q]);
h.rd.String = sprintf('%sMOTOR %s %3.0f%%\nJOINT k %.1f Nm\nWIND %+5.2f',r, ...
    char(60 + 2*(s.d > 0)),100*abs(u),s.k,s.gw);
set(h.rd,'Visible',s.m0 > 0);
set(h.sc,'Visible',s.m0 > 0,'String',sprintf('%.1f s     best %.1f s',s.rt,s.best));

w = '';
if s.m0 == 1 && s.gt < .9 && s.gn
    w = sprintf('GUST INCOMING %s',repmat(char(60 + 2*(s.gn > 0)),1,1 + round(6*abs(s.gn))));
end
if s.bt > 0, w = sprintf('+1 ARM  (%d arms)',n); end
h.wn.String = w;
h.fl.FaceAlpha = s.fa;

z = {'BALANCE LAB','Motor never stops. SPACE flips it. Keep the arms up!'; '' ''; '' ''; ...
    'TOPPLED',sprintf('%.1f s with %d arm%s   |   SPACE to retry',s.rt,n,repmat('s',1,n > 1))};
h.t1.String = z{s.m0+1,1};
h.t2.String = z{s.m0+1,2};
end

function [P,Q] = seg(v,a,b)
% NaN-separated segments from (v,a) to (v,b), for drawing many lines as one
P = [v; v; NaN*v]; P = P(:);
Q = [a + 0*v; b + 0*v; NaN*v]; Q = Q(:);
end

function s = rst(s)
% New round: one arm, slightly off vertical, motor pushing right
s.m0 = 1; s.rt = 0; s.d = 1; s.f = 0;
s.q = [0 .03*sign(rand - .5)]; s.v = [0 0];
s.k = 3; s.gw = 0; s.gn = 0; s.gt = 3;
s.fa = 0; s.bt = 0; s.td = 0;
s.ha(:) = 0; s.hm(:) = 0;
end
Play Game
Preview

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