Distributed Reactive Collision Avoidance - University of Washington

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in D.
If D is empty, then each vehicle uses ξ i (j) to determine when to maneuver, where j is
the nearest vehicle. If vehicle i is less maneuverable than vehicle j, then ξ i (j) will turn
false before ξ j (i) does. In this case, vehicle i becomes an element of D, making D = {i},
but vehicle i does not perform a deconfliction maneuver, since vehicle j will be able to
safely deconflict even if the vehicles move closer together. Now that D is nonempty, the
system then follows the previous directions. Once ξ i (D) becomes true again, vehicle i is
removed from D and solely follows its desired control.
The deconfliction maneuvers used here are in fact simple optimization schemes with
the goal of finding the smallest velocity change necessary to attain a conflict-free state.
In this sense, the maneuvers are most similar to [8, 24] (in fact, because these authors’
optimization schemes use the same definition of conflict, they could also be used as deconfliction
maneuvers here). However, these two optimization schemes are centralized and
computationally expensive. More importantly, they do not give a bound on how far apart
the vehicles must be for a feasible solution to exist. This bound is of the utmost importance
for designing a safe system.
This algorithm is greedy in the sense that each vehicle minimizes its own cost function
(‖∆v i ‖), meaning that the solution will not be a global optimum for some overarching cost
function of the group. However, given the nonconvexity of the problem, finding any global
optimum is nontrivial. For instance [8] used a semidefinite relaxation, but still required a
random initial guess, and hence could not guarantee a global optimum either. Additionally,
the actual cost function for the system is unknown in general, since any desired controller
can have its own unique cost function associated with it, depending on the task. Therefore,
instead of attempting to minimize an arbitrary cost function, a suboptimal solution will be
allowed, with the focus instead on feasibility and low computation load.
The only information the DRCA algorithm needs on a continuous basis is the position
and velocity of each vehicle in D, which can either come from broadcast communication
(e.g. a transponder) or sensing (e.g. radar). If the system is heterogeneous, then the vehicles