Error in odearguments (line 90) f0 = feval(ode,​t0,y0,args​{:}); % ODE15I sets args{1} to yp0. Error in ode45 (line 115) odeargumen​ts(FcnHand​lesUsed, solver_name, ode, tspan, y0, options, varargin); Error in pendulum_sim (line 30) [t,f] = ode

I keep getting this error message whenever I run my code. I have attached my code for reference.

Appreciate some help on this :)

%% Pendulum - Muscle  Model
% Create your own pendulum_muscle_equation function. It should be solvable
% with ode45 and the solution you return both theta and theta dot. 

% PART 1:  Study how co-contraction influences the stability and position/orientation of the forearm. To do this use three values of co-contraction u=0, u=0.5 and u=1. 
% Plot the evolution of theta and thetadot for two different set of initial conditions, for which the system:
%       1) Does not fall to the ground for both small (u = 0.5) and large (u = 1) activation level; 
%       2) Does not fall to the ground for large (u = 1) activation level and falls for smaller ones (u = 0.5);

figure()
ax1 = subplot(2,1,1);
ax2 = subplot(2,1,2);

%activation
u_set =  [0,0;0.5,0.5;1,1];
tspan = [0 5];
n = size(u_set);

% Set the initial conditions
syms theta(t);
initial_cond = theta(0) == 0 ;  %% INSERT YOUR CODE %%
options = odeset('Events',@ fallEventsFcn);

for i = 1:n(1)
    u_set_i = u_set(i,:); 
    u1 = u_set_i(1);
    u2 = u_set_i(2);
    % Compute theta and thetadot using your own pendulum_muscle_equation
    [t,f] = ode45(@(t,theta) pendulum_muscle_equation(t,theta,u1,u2),tspan,initial_cond,options); 
    
    subplot(ax1)
    plot(t(:),f(:,1)*180/pi,'DisplayName',['u1 =' num2str(u_set_i(1)) '; u2 = ' num2str(u_set_i(2))]);
    hold on;
    subplot(ax2)
    plot(t(:),f(:,2),'DisplayName',['u1 =' num2str(u_set_i(1)) '; u2 = ' num2str(u_set_i(2))]);
    hold on;
end
ylabel(ax1,'Theta [°]');
ylabel(ax2,'Thetadot [rad/s]');
xlabel(ax2,'Time [s]');
title(ax1,'Angle');
title(ax2,'Velocity');
legend(ax1);
legend(ax2);



% Function to be called to solve ODE% Function to be called to solve ODE
function theta_dot = pendulum_muscle_equation(t, theta, u1,u2)

% Parameters
g = 9.81;
r = 0.3;
m = 1; 
a1 = 0.0436;
a2 = 0.09;
alpha = 0.0218;
k_0 = 810.8;
k = 1621.6;
damping_ratio = 0.26;
delta = 2*damping_ratio*sqrt(k*m);
delta_0 = 2*damping_ratio*sqrt(k_0*m);

% use cosine rule to find l1 and l2
l1 = sqrt(a1^2+a2^2+2*a1*a2*sin(theta(1)));
l2 = sqrt(a1^2+a2^2-2*a1*a2*sin(theta(1)));
l_0 = sqrt(a1^2 + a2^2); % muscle inital length
 
% Find l_dot for both muscles
l1_dot = diff(sqrt(a1^2+a2^2+2*a1*a2*sin(theta(1))),t);
l2_dot = diff(sqrt(a1^2+a2^2-2*a1*a2*sin(theta(1))),t);

% use sine rule to find h1 and h2
h1 = a1*a2*cos(theta(1))/l1;
h2 = a1*a2*cos(theta(1))/l2;


% Find K_tot and D_tot for both muscles
K_tot1 = k_0 + k*u1;
D_tot1 = delta_0 + delta * sqrt(u1);

K_tot2 = k_0 + k*u2;
D_tot2 = delta_0 + delta * sqrt(u2);

% Muscle tensions

if l1 < l_0 - alpha * u1
    mu1 = 0;    % if muscle length < rest length -> tension = 0
else
    mu1 = K_tot1 * (l_0 - alpha*u1 -l1) - D_tot1 * l1_dot;
    % if muscle length > rest length -> tension follows muscle model eq
end

if l2 < l_0 - alpha * u2
    mu2 = 0;    % if muscle length < rest length -> tension = 0
else
    mu2 = K_tot2 * (l_0 - alpha*u2 -l2) - D_tot2 * l2_dot;
    % if muscle length > rest length -> tension follows muscle model eq
end

% Pendulum angular velocity and acceleration, to be integrated with ode45
theta_dot = zeros(2,1);
theta_dot(1) = theta(2);
theta_dot(2) = (m*g*r*sin(theta(1)) + mu1*h1 - mu2*h2)/(m*r^2);
% total torque about the elbow (load+muscle1+muscle2)


end

Answer 1

[Kiran Felix Robert]

Hi Ai,

The cause for this error is due to an incorrect call to the sine function at line 65.

The argument passed to the sine function is a symbolic equation and not a valid symbolic expression (refer sin function). This error can be resolved if the symbolic sine function is called with a valid argument.