I hope I can do that without changing the integration step size that the integrater uses. It takes a bit of time to run the simulation, which may be sped up by increasing the time interval between calls to write to the output file. For other initial conditions, this may not be an appropriate simulation time. I've found that a 2 second long simulation, for the hardcoded initial conditions (the velocity in x and y when the foot touches the wall), is sufficient to see where the airplane settles to an equilibrium, at least in terms of the normal and shear forces at the contact point with the wall. I'm now up and running with Alexis' slightly old, but sufficient for now, models of the various phases of flying, attachment, and sliding. *The equilibrium point will be a surface in the overall state space of the plane, since, for example, we don't care about where on the wall we land, as long as we land. In order to get that envelop, I first need to find the ROA of a TI LQR about the equilibrium point/surface*, which is going to be found using the post-landing and stuck (non-sliding) model. I'm not sure, but I think Alexis' successful landing envelope is plotted on a graph of state values some distance away from the wall. Note that Alexis is very interested in our computation of the landing envelop using our (conservative) symbolic methods, rather than "exhaustive simulation." So that is my immediate goal.Īll I have right now is Alexis' flying model-the model whose exit condition is the foot touching the wall. My first though: I have no idea what a reasonable estimate would be! But maybe I can project the level set of x'Sx = rho on to the envelope graphs Alexis made in order to pick a "reasonable" rho.
AQUAMACS FROZE UPDATE
), then email Mark T with a discription of the failure, so that he can update the code to support the case of computing ROA without inputs.Īlso, when calling roaTILQ, Mark T mentioned that I should set set options.rho0 to a "reasonable estimate," which will depend on S. If that fails (to produce anything, or fails to produce a true ROA, or.
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Mark T gave me the following instructions:ġ) Simulate the system to find an equilibrium.Ģ) Linearize the dynamics about that equilibrium.ģ) Solve for a quadratic Lyapunov candidate using the following command in Matlab: S = lyap(A',eye(n)), where n is the number of states.Ĥ) Try calculating a ROA (region of attraction) using Robotlib's roaTILQ command with an empty K and u0 as inputs.
AQUAMACS FROZE VERIFICATION
Russ had apparently grabbed him after skyping in order to discuss the nuts and bolts of applying our verification tools to Alexis' model. On Friday afternoon, shortly after our Skype call with Russ, I received an email from Mark T, the grad student in RLG with the most expertise in verification.
![aquamacs froze aquamacs froze](https://i0.wp.com/hubsidy.com/wp-content/uploads/2021/07/Aquamacs_-Emacs-.png)
advantage of a parametric description for design purposes.ĪutoLev => Matlab symbolic eqns => Verification code Need plane momentum to be sufficient to stay in contact with wall, and then look for whether vertical velocity can reverss => attachment, or whether you instead bounce off.
![aquamacs froze aquamacs froze](https://s.alicdn.com/@sc01/kf/Hd53a32481c9d4f3a8371b43b59ee5e10l.jpg)
AQUAMACS FROZE FREE
Legs essentially massless, so have 1st order dynamics while free - essentially need a timer to know how long it takes for legs to get back to equilibrium position.After detachment, legs slowly relax back to equilibrium position. Look now at upward sliding along wall with Coulomb friction.
![aquamacs froze aquamacs froze](https://i1.wp.com/hubsidy.com/wp-content/uploads/2021/07/best-text-editor-for-Mac-in-2021.jpg)