We would like to include gravity in a Simscape multi-body model while starting the simulation at the equilibrium.
The basic idea is to first perform a simulation of the system until it goes at it rest position and save the rest position forces and deflection in each joint.
We can then think of three solutions to start a new simulation directly at the steady state position:
- Change the equilibrium position $l_0$ of each joint such that at $t=0$, $k \times l_0$ is equal to the previously measured force in the joint.
Here, it is suppose that we constrain the initial position of the joint to be equal to zero.
Then, these forces cancel each other and the simulation starts at equilibrium.
- Add an External force (or maybe the "Internal Force") in the direction of the joint (the "resolution frame" is fixed to the solids) equal to the opposite of the previously measured force.
- After the first simulation, measure the final change of position of each joint, then set the initial position to be the measured static position.
Then, the simulation will start at equilibrium, but all the elements will be "deflected".
The three solutions are tested below.
* ZIP file containing the data and matlab files :ignore:
#+begin_src bash :exports none :results none
if [ matlab/simscape_gravity.m -nt data/simscape_gravity.zip ]; then
cp matlab/simscape_gravity.m simscape_gravity.m;
zip data/simscape_gravity \
gravity_test.slx \
simscape_gravity.m
rm simscape_gravity.m;
fi
#+end_src
#+begin_note
All the files (data and Matlab scripts) are accessible [[file:data/simscape_gravity.zip][here]].
#+CAPTION: Simulation after changing the equilibrium position of the joint ([[./figs/sim_change_eq_position.png][png]], [[./figs/sim_change_eq_position.pdf][pdf]])
[[file:figs/sim_change_eq_position.png]]
* Add external force
#+begin_src matlab
l0 = 0; % Initial wanted position [m]
leq = 0; % equilibrium position [m]
F_ext = -out_init.Fm.Data(end); % External force [N]
F_act = 0; % Actuator force [N]
#+end_src
#+begin_src matlab :exports none
out = sim('gravity_test.slx');
out.d.Name = 'Displacement';
out.Fm.Name = 'Force Sensor';
#+end_src
#+begin_src matlab :exports none
figure;
subplot(1,2,1)
plot(out.d)
title('');
subplot(1,2,2)
plot(out.Fm)
title('');
#+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
#+CAPTION: Simulater after adding an external force applied to the solid ([[./figs/sim_add_external_force.png][png]], [[./figs/sim_add_external_force.pdf][pdf]])
[[file:figs/sim_add_external_force.png]]
* Change initial position
#+begin_src matlab
l0 = out_init.d.Data(end); % Initial wanted position [m]
leq = 0; % equilibrium position [m]
F_ext = 0; % External force [N]
F_act = 0; % Actuator force [N]
#+end_src
#+begin_src matlab :exports none
out = sim('gravity_test.slx');
out.d.Name = 'Displacement';
out.Fm.Name = 'Force Sensor';
#+end_src
#+begin_src matlab :exports none
figure;
subplot(1,2,1)
plot(out.d)
title('');
subplot(1,2,2)
plot(out.Fm)
title('');
#+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
#+CAPTION: Simulation after changing the initial position of the joint ([[./figs/sim_change_initial_position.png][png]], [[./figs/sim_change_initial_position.pdf][pdf]])
