My experience is in solid mechanics and FEA. So I have zero experience in robotics/controls.
I'm developing a control strategy to stabilize a complicated 6-legged dynamical system. Torques Ti from each leg's joints will be used to create a net moment M on the body, stabilizing the system. This moment M is known from the pre-determined control strategy. (Side note: the dynamical solver is of the nonlinear computational type)
Due to my lack of background, I have a fundamental confusion with the dynamical system. I want to use joint torques Ti to create this known net moment M on the body. This moment M is a function of the
- current positions/angles of all the leg segments
- reaction forces and moments (that cannot be controlled) of each leg
- controllable joint torques Ti of each leg
$(*)$ At a given time $(n-1)\Delta$t:
--From the control strategy, the desired net moment M is computed/known
--One can read/sense the legs' positions, angles, reaction forces, and reaction moments (say, from well placed sensors), at this time $t = (n-1)\Delta$t.
--From this information, vector algebra easily yields the desired joint torques Ti required to create the net moment M
$(**)$ At the time $(n)\Delta$t:
--one applies the previously determined joint torques Ti (determined at $t=(n-1)\Delta$t) to create the desired moment M
--of course these torques Ti are applied at the immediate proceeding time step because they cannot be applied instantaneously
So this is exactly where my fundamental confusion exists. The torques Ti were calculated in $(*)$, based on data of angles/positions/reactions in $(*)$, with the objective to create moment M. However, these torques Ti are applied in $(**)$, where the data (angles/positions/reactions) are now different - thus the desired net moment M can never be created (unless you an magically apply actuation at the instantaneous time of sensing). Am I understanding the controls problem correctly?
- Am I understanding the robotics problem correctly? What are the terms and strategies around this dilemma?
- Of course I could create the time steps between the sensing and the actuation to be infinitely small, but this would be unrealistic/dishonest. What is the balance between a realistic time step, but also performs the task well?