Time variable for robot trajectory
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Hi,
I am trying to build robot trajectory to work on inverse dynamics.Trajectory is using polynomial expressions as below.
a0=2;
a1=0;
a2=9.75;
a3=3.25;
theta1=a0+(a1*t)+(a2*t*t)+(a3*t*t*t);Joint angle
v1=a1+(2*a2*t)+(3*a3*t*t); Joint velocity
a1=(2*a2)+(6*a3*t); Joint acceleration
I have used clok block of simulink to provide time input t. I dont think it is the right process. Do we have any other block in simulink to provide time input?
2 个评论
I don't see any issue so far. What problem did you encounter in Simulink?
t = linspace(0, 2, 10001);
a0 = 2;
a1 = 0;
a2 = 9.75;
a3 = 3.25;
theta1 = a0 + a1*t + a2*t.^2 + a3*t.^3; % Joint angle
v1 = a1 + 2*a2*t + 3*a3*t.^2; % Joint velocity
a1 = 2*a2 + 6*a3*t; % Joint acceleration
Claude Mathias
2023-7-14
采纳的回答
After checking your comment, I think you need to update the polynomials for each time interval. For one-time use, it maybe okay to use the Clock block. That Clock block outputs the current simulation time at each simulation step. The following example shows how to compute the Quintic Polynomial Trajectories for 
, based your desired initial and final values.
, based your desired initial and final values.t0 = 1; % start time
t1 = 2; % end time
A = [1 t0 t0^2 t0^3 t0^4 t0^5;
0 1 2*t0 3*t0^2 4*t0^3 5*t0^4;
0 0 2 6*t0 12*t0^2 20*t0^3;
1 t1 t1^2 t1^3 t1^4 t1^5;
0 1 2*t1 3*t1^2 4*t1^3 5*t1^4;
0 0 2 6*t1 12*t1^2 20*t1^3]
B = [3; 2; 1; 4; 3; 2]; % desired initial and final values
x = A\B
t = linspace(t0, t1, 10001);
y = x(1) + x(2)*t + x(3)*t.^2 + x(4)*t.^3 + x(5)*t.^4 + x(6)*t.^5;
dy = gradient(y)./gradient(t);
ddy = gradient(dy)./gradient(t);
tiledlayout(3, 1, 'TileSpacing', 'compact')
nexttile
plot(t, y, 'linewidth', 1.5, 'color', '#cc3232'), grid on
ylabel({'$\theta$ / rad'}, 'interpreter', 'latex', 'fontsize', 12)
title('Quintic Polynomial Trajectories', 'fontsize', 12)
nexttile
plot(t, dy, 'linewidth', 1.5, 'color', '#e6b415'), grid on
ylabel({'$\dot{\theta}$ / (rad/s)'}, 'interpreter', 'latex', 'fontsize', 12)
nexttile
plot(t, ddy, 'linewidth', 1.5, 'color', '#2dc937'), grid on
ylabel({'$\ddot{\theta}$ / (rad/s$^2$)'}, 'interpreter', 'latex', 'fontsize', 12)
xlabel({'$t$ / s'}, 'interpreter', 'latex', 'fontsize', 12)
更多回答（1 个）
Parth Saraf
2023-7-13
0 个投票
Hi,
If you want to avoid using Clock block, you may use the Ramp block or the "From Workspace" block.
You can create a time vector in the workspace which may be useful.
Hope this helps!
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