## Tuesday, December 7, 2010

### Differential steering challenge problem

I posed a challenge problem in today's guest lecture in the Embedded Systems Programming course.  The challenge is to efficiently control a simple differential steering robot.  The Acumen code below presents both the model of the robot (dsbot), a target object, and a very simple controller.  How well the controller performs is measured in the Main object by the total energy (e) at the end of the simulation.  My score was 161.3.  You are welcome to submit to me the code of an controller that performs better.

The only rule is that you can only send me the code for the controller.  In other words, the code for the robot, target, and the main program has to remain the same.

class dsbot () // Differential steering robot
private x=0; x'=0; y=0; y'=0;
a=0; a'=0 ; v=0
end
x' [=] v * cos(a);
y' [=] v * sin(a);
end

class target () // A simple target moving in a circle
private t=0; t'=0; x=0; y=0 end
t' [=] 1;
x = 2*sin(t/1.5);
y = 2*cos(t/1.5);
end

class controller () // A simple controller
private t =0; t'=0; // local time
ex = 0; ey = 0; // Error in x and y
ia = 0; // Input angle
ov = 0; oap = 0; // Ouput v and a'
end
t' [=] 1;
if t>0.1
t = 0;
// Control code goes here
if (ex*ex + ey*ey) < 1 // Robot is close enough. Slow down
ov = 1
else
ov = 4;
if   (   (ex>0 && cos(ia)<0)
|| (ey>0 && sin(ia)<0))
|| (  (ex<0 && cos(ia)>0)
||(ey<0 && sin(ia)>0))
oap = -10
else
oap = 0
end
end
else
end
end

class Main(simulator)
private r = create dsbot ();
t = create target ();
c = create controller ();
d = 0; e = 0; e'= 0; // Measures of success
end
// Controller see robot
c.ex [=] t.x - r.x;
c.ey [=] t.y - r.y;
c.ia [=] r.a;
// Robot listens to controller
r.a' [=] c.oap;
r.v [=] c.ov;
// Error over time
d [=] sqrt(c.ex*c.ex+c.ey*c.ey);
e' [=] r.v*r.v + 2*d*d
end