next up previous
Next: Rendezvous without connectivity or Up: Condition on Angular Velocity Previous: Condition on Angular Velocity

Angular Velocity Condition

So far, all of our results assume that agents must maintain their targets in some appropriate $ (-\phi, \phi)$ range. We now show that agents do not need to rotate arbitrarily fast to achieve this by providing an upper bound on the rotational speed for the bounded speed pursuit case; the result readily generalizes to other cases.

Proposition 16   In bounded speed pursuit of $ n$ Dubins car agents with windshield span $ (-\phi, \phi)$ , for any $ \rho > 0$ , selecting

$\displaystyle \omega_i > \frac{v_{\max}}{\rho}$ (40)

is sufficient for an agent to either keep its target within its windshield or merge with its target.



Jingjin Yu 2011-01-18