We approach dynamic collision avoidance problem from the perspective of designing collision avoidance systems for unmanned aerial vehicles. Before unmanned aircraft can fly safely in civil airspace, robust airborne collision avoidance systems must be developed. Instead of hand-crafting a collision avoidance algorithm for every combination of sensor and aircraft configurations, we investigate automatic generation of collision avoidance algorithms given models of aircraft dynamics, sensor performance, and intruder behavior. We first formulate the problem within the Partially Observable Markov Decision Process (POMDP) framework, and use generic MDP/POMDP solvers offline to compute vertical-only avoidance strategies that optimize a cost function to balance flight-plan deviation with risk of collision. We then describe a second framework that performs online planning and allows for 3-D escape maneuvers by starting with possibly dangerous initial flight plans and improving them iteratively. Experimental results with four different sensor modalities and a parametric aircraft performance model demonstrate the suitability of both approaches.