  We propose a novel formulation of the collision-aware task assignment (CATA)
problem and a decentralized auction-based algorithm to solve the problem with
optimality bound. Using a collision cone, we predict potential collisions and
introduce a binary decision variable into the local reward function for task
bidding. We further improve CATA by implementing a receding collision horizon
to address the stopping robot scenario, i.e. when robots are confined to their
task location and become static obstacles to other moving robots. The
auction-based algorithm encourages the robots to bid for tasks with collision
mitigation considerations. We validate the improved task assignment solution
with both simulation and experimental results, which show significant reduction
of overlapping paths as well as deadlocks.
