Arnab Nilim

A probabilistic framework for aircraft conflict detection

A PROBABILISTIC FRAMEWORK FOR AIRCRAFT CONFLICT DETECTION Maria Prandini, John Lygeros, Arnab Nilim and Shankar Sastry Department of Electrical Engineering and Computer Sciences University of California at Berkeley Berkeley CA 94720 fprandini, lygeros, nilim, sastryg@robotics.eecs.berkeley.edu ABSTRACT We describe a general con ict detection/resolution scheme, focusing on the con ict detection component for a pair of aircraft ying at the same altitude. The proposed approach is formulated in a probabilistic framework, thus allowing uncertainty in the aircraft positions to be explicitly taken into account when detecting a potential con ict. The computational issues involved in the application of the proposed con ict alerting system are addressed by resorting to randomized algorithms. Finally, the validation of the proposed detection scheme is performed by Monte Carlo simulation on a stochastic ODE model of the aircraft motion. Our simulations show very promising results. The detection scheme will be used as the basis for a con ict resolution scheme in forthcoming work. INTRODUCTION Safety, of which con ict prediction and resolution form an integral part, is the primary concern of all advanced air tra c management systems. Con ict prediction and resolution are considered at three di erent levels in the air tra c management process: Long range: Some form of con ict prediction and resolution is carried out at the level of the entire National Airspace System (NAS), over a horizon of several hours. It involves composing ight plans and airline schedules (on a daily basis, for example) to ensure that airport and sector capacities are not exceeded. This is typically accomplished by large scale integer and linear programming techniques1;2. Research supported by DARPA under grant F33615-98-C-3614, by NASA under grant NAG 2-1039 and by ARO under grant MURI DAAH 04-96-1-0341. The authors would like to thank Dr. George J. Pappas for the stimulating discussions. Copyright c 1999 by the Regents of the University of California. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Sampled estimates of aircraft positions Conflict probability information

Robust dynamic routing of aircraft under uncertainty

Much of the delay in the US National Airspace System (NAS) arises from convective weather. One major objective of our research is to take a less conservative route, where we take a risk of higher delay to attain a better expected delay, instead of avoiding the bad weather zone completely. We address the single aircraft problem using a Markov decision process model and a stochastic dynamic programming algorithm, where the evolution of the weather is modeled as a stationary Markov chain. Our solution provides a dynamic routing strategy for an aircraft that minimizes the expected delay. A significant improvement in delay is obtained by using our methods over the traditional methods. In addition, we propose an algorithm for dynamic routing where the solution is robust with respect to the estimation errors of the storm probabilities. To the Bellman equations, which are derived in solving the dynamic routing strategy of an aircraft, we add a further requirements: we assume that the transition probabilities are unknown, but bounded within a convex set. The uncertainty described in our approach is based on likelihood functions.

Randomized algorithms for probabilistic aircraft conflict detection

A mid-range conflict alerting system is proposed, based on a measure of criticality which directly takes into account the uncertainty in the prediction of the aircraft positions. The use of randomized algorithms makes the computation of the criticality measure tractable. The performance of the algorithm is evaluated by Monte Carlo simulation on a stochastic ODE model of the aircraft motion.

Optimal path planning for air traffic flow management under stochastic weather and capacity constraints

In the US, delays in the Air Traffic Management Systems (ATMS) are most often caused by weather events, which are stochastic in nature. In practice however, for complexity reasons, these stochastic obstacles are dealt with using overly conservative, deterministic strategies. This means avoiding en- tirely storm zones that have a very good chance of vanishing in the near future, which translates into lost airspace capacity and unnecessary delays. In Europe, the situation is slightly different. There, sector capacity constraints rather than weather are the key limiting factor in ATM. Again, these disturbances are stochastic in nature and there too, overly conservative deterministic routing strategies result in lost airspace. In this work we try to reduce the amount of wasted capacity by solving the optimal path planning problem in a framework that models both the weather patterns and the sector capacity constraints by a stationary Markov chain. If we assume that a priority order is given ranking the various aircraft priorities, our algorithm has a complexity that only grows linearly with the number of aircraft. In simulated examples, as weather and traffic intensity increase, we show a significant improvement over conservative routing strategies. We also study large-scale numerical performance on a simplified European airspace with a large number of aircraft.