Enter a velocity and a specific acceleration to a motion

I want to give a revolute joint a certain velocity. However, the velocity is to be achieved via a specific acceleration. How can I enter the required velocity, but at the same time the acceleration with which the joint should reach the velocity?

Optimally, I could specify the duration for which the joint should maintain the specified speed (via a variable). In addition, the joint should also decelerate the movement afterwards - receive a negative acceleration until a speed of 0 is reached. As an example, I have simulated a cube that is driven by a joint with a specific velocity.

I hope you can help me!

[Nathan Hardenberg]

There is an easier way of providing the position input of the joint: Use the "Simulink-PS Converter" - Block (Stands for Simulink to Physical Converter) and in it's settings do the following:

Then you can connect any simulink signal without providing derivatives.

Answer 1

[Nathan Hardenberg]

There are multiple ways of doing it. I'm just using constant acceleration examples since those are the easiest. But I just want to note that there are more ways of accelerating e.g. jerk-limited.

1 Trapezoidal Velocity Profile Trajectory - Block

To use this Block the the Robotics System Toolbox is needed. I find it quite unintuitive to use (e.g. I do not understand the Waypoints quite fully), but it does the job with a bit of fiddeling around. It gives the position, velocity and acceleration at a given time

2 Manual acceleration with integration and Step - Block

For this you only need to know how the acceleration time gets calculated: As Initial value you choose the acceleration. But be aware that the integraion process is not very reliable if your simulation step time is high. So if you use this check the results and keep you maximum simulation step size low. Also this just accelerates and does not decelerate.

3 Own MATLAB function

You can write your own function using a MATLAB-Function-Block. This should also have the time as one input. Then you can either

a) calculate the acceleration time (see above) and output the acceleration similar to the Step-Block above. Then you can integrate again to get the velocity/position. [also as above: Integration problem on long step times]

b) or calculate the position by hand and output it directly. Here you implement the functionality of the above mentioned "Trapezoidal Velocity Profile Trajectory - Block" yourself. But probably with less features. I'll post some function code as a comment on this Answer

With both you can also easily decelerate by providing a negative acceleration/decelerating position.

4 ???

There are probably other ways of doing it aswell, But I don't know them yet

[Nathan Hardenberg]

As promised the code for the movment of the axis. Note that this moves the joint to a given position (s_soll), but you can specify acceleration and velocity. So if you want to go at a fixed velocity for a long time, just choose a big number for the s_soll input

function [currPos, currVel, t_needed, isDone] = ...
    trapz_traj_pos1D(time0ToEnd, s_soll, v_max, a_max)
t = time0ToEnd;
isDone = 0;

if t < 0
    currPos = 0;
    currVel = 0;
    t_needed = 0;
    return;
end

T_VMax = (a_max*s_soll - v_max^2)/(a_max*v_max);
if T_VMax > 0  % Default
    T_AMax = v_max/a_max;
else  % No Velocity limit reached
    T_VMax = 0;
    T_AMax = sqrt(s_soll/a_max);
    v_maxNew = sqrt(a_max)*sqrt(s_soll);
    v_max = v_maxNew;
end

t_ges = 2*T_AMax + T_VMax;
t_needed = t_ges;

if t <= T_AMax % acceleration
    currPos = 1/2*a_max*t^2;
    currVel = a_max*t;
elseif t <= T_AMax + T_VMax  % constant velocity
    posVMaxBegin = 1/2*a_max*T_AMax^2;
    currPos = v_max*(t-T_AMax) + posVMaxBegin;
    currVel = v_max;
elseif t <= 2*T_AMax + T_VMax  % deceleration
    posVMaxBegin = 1/2*a_max*T_AMax^2;
    posBegin = v_max*T_VMax + posVMaxBegin;

    currPos = posBegin - 1/2*a_max*(t-(2*T_AMax+T_VMax))^2 + posVMaxBegin;
    currVel = v_max - (t - (T_AMax + T_VMax))*a_max;
else  % standstill
    currPos = s_soll;
    currVel = 0;
    isDone = 1;
end

end