Portal:Tutorials

Verification Tools & Processes Tutorials

Autonomy Tools & Processes Tutorials

Verification of Autonomous Systems Tools & Processes Tutorials

• Andre Platzer Tutorial on how to use Keymaera-X

KeyMaeraX - Garage Door

ArchiveEntry "Garage Door"
Definitions 
 Real m = 50;
 Real k = 600; 
 Real K = 0.6; 
 Real R = 0.005; 
 Real J = 0.02;
 Real Kp = 240; 

 Real error(Real ref, Real theta) = (ref - theta); 
 
 HP ctrl ::= {u := Kp*error;};
 
 HP motion ::= {{
     theta' = thetadt, 
     thetadt' = (K*R^2)/(J+m*R^2)*theta + (K*R)/(J+m*R^2)*u 
     & theta >=0}};
 
End. 
ProgramVariables
 Real theta;       /*position*/
 Real thetadt;     /*velocity*/
 Real u;           /*control input*/
End. 
Problem
   theta > 0 -> [{ctrl; motion;}*] theta >= 0
End.
End.

ArchiveEntry "DrivelineDynamics"

Definitions 
 Real Jf = 0.625;
 Real Jc = 6250; 
 Real cs = 65000; 
 Real ds = 1000; 
 Real Tload = 7000;
 Real r = 12.5; 
 Real K1 = 5.4567;
 Real K2 = 57.1911;
 Real K3 = -12.9458;

 HP ctrl ::= {u := -(K1*Weng + K2*Wwheel + K3*phi);};
 
 HP driveline ::= {{
     Weng' = (1/Jf)*(u - (1/r)*(cs*phi + ds*((Weng/r)-Wwheel))),
     Wwheel' = (1/Jc)*(cs*phi + ds*((Weng/r)-Wwheel)-Tload),
     phi' = (Weng/r) - Wwheel 
 }};
 
End. 

ProgramVariables
 Real Weng;       /*engine speed*/
 Real Wwheel;     /*wheel speed*/
 Real phi;        /*torsion*/
 Real u;          /*control input*/
End. 

Problem
   Weng > 0 & Wwheel > 0 & phi > 0 -> [{ctrl; driveline;}*] Weng >= 0 & Wwheel > 0 & phi = 0
End.
End.