Automatic Collision Avoidance System based on Geometric Approach - PowerPoint PPT Presentation

6th International Conference on Research in Air Transportation May 26-30, 2014 - Istambul Technical University, Turkey Automatic Collision Avoidance System based on Geometric Approach applied to Multiple Aircraft Paulo Machado University of Beira Interior May 27, 2014 1 of 36 Automatic Collision Avoidance System based on Geometric Approach applied to Multiple Aircraft

6th International Conference on Research in Air Transportation May 26-30, 2014 - Istambul Technical University, Turkey General Picture It is known that nowadays we face several challenges related with Air Traffic as, • Constant growing of Air Traffic • Free-Flight • Environment impact • Departures and Arrivals Scheduling • Possible UAV inclusion • . . . Beside of that several issues related with Air Traffic Management (ATM), it is always necessary to ensure SAFETY . 2 of 36 Automatic Collision Avoidance System based on Geometric Approach applied to Multiple Aircraft

6th International Conference on Research in Air Transportation May 26-30, 2014 - Istambul Technical University, Turkey Subject And Motivation 1. In this sense, our intention is to approach the Collision Avoidance Problem ; 2. And in this huge particularly subject we will address it on a Generalized point of view; 3. Our main goal is try to find a Real Time solution for the problem; 4. Additionally, we also want a solution computed with few Computationally Resources . 3 of 36 Automatic Collision Avoidance System based on Geometric Approach applied to Multiple Aircraft

6th International Conference on Research in Air Transportation May 26-30, 2014 - Istambul Technical University, Turkey Hypothesis The main idea behind the collision avoidance problem is to avoid the distance between aircraft became dangerous for both. In that way, considering the case of two aircraft represented by points P 0 and P 1 with velocities V 0 and V 1 respectively, the distance between them is represented by the vector � r . Then for collision avoidance problem the main requirement to be fulfill is, r � 2 ≥ ∆ � � (1) where ∆ is a value, which independently of aircraft size they never collide (on a general sense). 4 of 36 Automatic Collision Avoidance System based on Geometric Approach applied to Multiple Aircraft

6th International Conference on Research in Air Transportation May 26-30, 2014 - Istambul Technical University, Turkey Hypothesis The equation (1) per se does not solve the problem, indeed with only that equation the problem can not be formulated. Hence, it was considered aircraft with different priorities and assumed relative motions. Hence, from now on, we consider the following Hypothesis; • The system is based on a Priority System; • Aircraft keep their velocity vectors during the computation. 5 of 36 Automatic Collision Avoidance System based on Geometric Approach applied to Multiple Aircraft

. . . . . . . . . X Z . Y 6th International Conference on Research in Air Transportation May 26-30, 2014 - Istambul Technical University, Turkey Two Aircraft Formulation Definition (Object to Object System) Consider the referential OXYZ where a point of mass with position P 0 and velocity V 0 coincide with origin of that � P 1 referential. Suppose also there is other V 1 point of mass with position P 1 , relatively to referential OXYZ , and velocity V 1 . r � � V 0 The system formed by that two points of β mass in the referred configuration, O . P 0 separated by the distance || � r || , with α respective velocities, is called Object to Object System 6 of 36 Automatic Collision Avoidance System based on Geometric Approach applied to Multiple Aircraft

. . . . . . . . . X Y . Z 6th International Conference on Research in Air Transportation May 26-30, 2014 - Istambul Technical University, Turkey Two Aircraft Formulation Definition (Line of Sight) P 1 � V 1 The Line formed by the two objects on an Object to Object System, with distance � r � V 0 � � r � , is called Line of Sight . β O . P 0 α 7 of 36 Automatic Collision Avoidance System based on Geometric Approach applied to Multiple Aircraft

. Z . . . . . . . . X . . . . Y 6th International Conference on Research in Air Transportation May 26-30, 2014 - Istambul Technical University, Turkey Two Aircraft Formulation Definition (Safety Sphere) r CAD � P 1 � V 1 The sphere built on Object to Object System where P 1 is its r � center and the safety distance � V 0 radius � � r CAD � , is called Safety β O . Sphere . P 0 α 8 of 36 Automatic Collision Avoidance System based on Geometric Approach applied to Multiple Aircraft

. . Y . . X . . . . Z . . . . . . . . 6th International Conference on Research in Air Transportation May 26-30, 2014 - Istambul Technical University, Turkey Two Aircraft Formulation Definition (Collision Cone) At Object to Object System the � r CAD � V 1 P 1 infinite cone with apex coincident with point of mass P 0 and the � r straight lines tangent to a sphere δ CAD � V 0 δ � V 01 with radius � � r CAD � , where � � r � > � � r CAD � , and center at the β O . P 0 point of mass P 1 is called the α Collision Cone . 9 of 36 Automatic Collision Avoidance System based on Geometric Approach applied to Multiple Aircraft

. . . Z . Y . . . . . . . . . . . . X 6th International Conference on Research in Air Transportation May 26-30, 2014 - Istambul Technical University, Turkey Two Aircraft Formulation Definition (Collision) � r CAD � V 1 P 1 It is considered that two points of � r mass of an Object to Object δ CAD System are in collision if � V 0 δ � V 01 � � r � < � � r CAD � , where � � r CAD � is β the safety distance. O . P 0 α 10 of 36 Automatic Collision Avoidance System based on Geometric Approach applied to Multiple Aircraft

6th International Conference on Research in Air Transportation May 26-30, 2014 - Istambul Technical University, Turkey Two Aircraft Formulation Lemma Let’s be � V 01 the relative velocity vector between the points of mass of an Object to Object System with constant velocities during a time interval ∆ t. For a time t 0 where || � r ( t 0 ) || > || � r CAD || , if the angle δ formed by vector � V 01 and the line of sight � r is greater than the half aperture angle δ CAD of a collision cone, then ∃ ∆ t > 0 : ∀ t ∈ [ t 0 , t 0 + ∆ t ] , || � r ( t ) || > || � r CAD || . 11 of 36 Automatic Collision Avoidance System based on Geometric Approach applied to Multiple Aircraft

6th International Conference on Research in Air Transportation May 26-30, 2014 - Istambul Technical University, Turkey Two Aircraft Formulation Theorem (Set of Solutions) Consider an Object to Object System, where the point of mass P 1 has a sphere of collision centered in it of radius � � r CAD � and � � r � > � � r CAD � . If the point of mass P 1 has constant velocity, then the set of velocity vector variations ∆ � V of point of mass P 0 that produces a non-interception condition with P 1 is given by, V ∈ R 3 | � Γ = { ∆ � 01 = � V 01 + ∆ � V ; arccos( ˆ V ∗ V ∗ 01 · ˆ r ) > δ CAD } where � V 01 is the relative velocity vector and δ CAD is the half aperture angle of collision cone and ˆ 01 , ˆ V ∗ r are the normalized vectors. 12 of 36 Automatic Collision Avoidance System based on Geometric Approach applied to Multiple Aircraft

. . . Z . X . . . Y . . . . . . . . 6th International Conference on Research in Air Transportation May 26-30, 2014 - Istambul Technical University, Turkey Generalised Formulation Definition (Object to Multi Object System) Considering the referential OXYZ where a point of mass with position P 0 and velocity V 0 coincides with origin of that referential. Suppose also there are others point of mass with position � P 1 V 1 P i , relatively to referential OXYZ , and velocity � r 1 V i , where i = 1 , ..., N − 1 with N as the number � � V 0 V 2 � r 2 P 2 β 1 of points of mass. The system formed by that N O . β 2 P 0 α 2 α 1 points of mass in the referred configuration, separated by the distance � � r i � , with respective velocities, is called Object to Multi Object System. 13 of 36 Automatic Collision Avoidance System based on Geometric Approach applied to Multiple Aircraft

. . . . . . . . X . . Z . Y . . . . 6th International Conference on Research in Air Transportation May 26-30, 2014 - Istambul Technical University, Turkey Generalised Formulation P 1 � V 1 � r 1 � � V 0 V 2 r 2 � P 2 β 1 O . β 2 P 0 α 2 α 1 14 of 36 Automatic Collision Avoidance System based on Geometric Approach applied to Multiple Aircraft

. . . . . . . . . . . . . . . . . . . . . . X . Z . Y . O . . . 6th International Conference on Research in Air Transportation May 26-30, 2014 - Istambul Technical University, Turkey Generalised Formulation � r CAD 1 � P 1 V 1 r 1 � � V 2 r CAD 2 � δ CAD 1 P 2 � V 0 δ 1 � r 2 δ CAD 2 � V 01 δ 2 β 1 � β 2 V 02 P 0 α 1 α 2 15 of 36 Automatic Collision Avoidance System based on Geometric Approach applied to Multiple Aircraft