Version 2.1: documentation, public API headers, and sample programs.

PiperOrigin-RevId: 403900419
2021-10-18 12:23:02 +01:00
commit 1f7eaae62e
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+% Force-Length-Velocity function of MuJoCo muscle model
+% Defaults: FLV(0.5, 1.6, 1.5, 1.3, 1.2)
+
+
+function FLV(lmin, lmax, vmax, fpmax, fvmax)
+
+    % derived quantities
+  a = 0.5*(lmin+1);
+  b = 0.5*(1+lmax);
+  c = fvmax-1;
+
+    % length and velocity ranges to plot
+    LL = linspace(lmin, lmax, 51);
+    VV = linspace(-vmax, vmax, 51);
+
+    % length-passive
+    FP = zeros(size(LL));
+    for i=1:length(LL)
+        L = LL(i);
+
+        if L<=1
+            FP(i) = 0;
+        elseif L<=b
+            x = (L-1)/(b-1);
+            FP(i) = 0.25*fpmax*x*x*x;
+        else
+            x = (L-b)/(b-1);
+            FP(i) = 0.25*fpmax*(1+3*x);
+        end
+    end
+
+    % length-active
+    FL = zeros(size(LL));
+    for i=1:length(LL)
+        L = LL(i);
+
+        FL(i) = bump(L, lmin, 1, lmax) + 0.15*bump(L, lmin, 0.5*(lmin+0.95), 0.95);
+    end
+
+    % velocity-active
+    FV = zeros(size(VV));
+    for i=1:length(VV)
+        V = VV(i)/vmax;
+
+        if V<=-1
+            FV(i) = 0;
+        elseif V<=0
+            FV(i) = (V+1)*(V+1);
+        elseif V<=c
+            FV(i) = fvmax - (c-V)*(c-V)/c;
+        else
+            FV(i) = fvmax;
+        end
+    end
+
+    % plot length
+    figure(1);
+    clf;
+    subplot(2,2,1);
+    plot(LL, FL, 'r', 'linewidth', 1);
+    hold on;
+    plot(LL, 0.5*FL, 'b', 'linewidth', 1);
+    plot(LL, FP, 'k', 'linewidth', 1);
+    axis tight;
+    xlabel('length (L0)');
+    ylabel('force (F0)');
+    text(0.9, 0.85, 'act = 1.0');
+    text(0.9, 0.4, 'act = 0.5');
+    text(1.3, 1.2, 'passive');
+    box off;
+    grid on;
+    set(gca, 'xtick', [lmin 1 lmax], 'xticklabel', {'lmin', '1', 'lmax'}, ...
+    'ytick', [0 1 fpmax], 'yticklabel', {'0', '1', 'fpmax'});
+
+    % plot velocity
+    subplot(2,2,2);
+    set( plot(VV, FV, 'linewidth', 1), 'color', [.1 .5 .1]);
+    axis tight;
+    xlabel('velocity (L0/s)');
+    ylabel('force (F0)');
+    box off;
+    grid on;
+    set(gca, 'xtick', [-vmax 0 vmax], 'xticklabel', {'-vmax', '0', 'vmax'}, ...
+    'ytick', [0 1 fvmax], 'yticklabel', {'0', '1', 'fvmax'});
+
+    % plot full activation
+    subplot(2,2,3);
+    surf(LL, VV, FV'*FL + ones(size(VV))'*FP);
+    axis tight;
+    xlabel('length');
+    ylabel('velocity');
+    zlabel('force');
+    title('act = 1.0');
+    box off;
+    set(gca, 'xtick', [lmin, 1, lmax], 'ytick', [-vmax, 0, vmax], 'ztick', [0, 1]);
+
+    % plot half activation
+    subplot(2,2,4);
+    surf(LL, VV, 0.5*FV'*FL + ones(size(VV))'*FP);
+    axis tight;
+    xlabel('length');
+    ylabel('velocity');
+    zlabel('force');
+    title('act = 0.5');
+    box off;
+    set(gca, 'xtick', [lmin, 1, lmax], 'ytick', [-vmax, 0, vmax], 'ztick', [0, 1]);
+end
+
+
+% skewed bump function: quadratic spline
+function y = bump(L, A, mid, B)
+    left = 0.5*(A+mid);
+    right = 0.5*(mid+B);
+
+    if (L<=A) || (L>=B)
+        y = 0;
+    elseif L<left
+        x = (L-A)/(left-A);
+        y = 0.5*x*x;
+    elseif L<mid
+        x = (mid-L)/(mid-left);
+        y = 1-0.5*x*x;
+    elseif L<right
+        x = (L-mid)/(right-mid);
+        y = 1-0.5*x*x;
+    else
+        x = (B-L)/(B-right);
+        y = 0.5*x*x;
+    end
+end