Implementation of Deconfliction in Multivehicle Autonomous Systems

IMPLEMENTATION OF DECONFLICTION IN MULTIVEHICLE AUTONOMOUS SYSTEMS A. P. Melander*, N. D. Powel*, E. Lalish*, K. A. Morgansen*, J. S. Jang** and J. Vian** *Department of Aeronautics and Astronautics, University of Washington, Seattle, WA, 98195-2400; **The Boeing Company, Seattle, WA, 98124 Keywords: Deconfliction, multivehicle control, autonomous systems Abstract be guaranteed for them to be accepted by their manned counterparts. The focus of the work in this paper is the im- Many conflict resolution strategies have been plementation of a distributed deconfliction algo- proposed using varying degrees of automation. rithm for vehicles with constraints on velocity Some of these strategies are designed specifically and acceleration. The algorithm was tested on for Air Traffic Control (ATC) applications, while two testbeds: a quadrotor system and an under- others are more general in nature. An overview water vehicle system. The quadrotor system has and classification of many collision avoidance al- vehicles that can hover in place and move in arbi- gorithms can be found in [8]. The Distributed trary directions, while the vehicles in the under- Reactive Collision Avoidance (DRCA) algorithm water system move with a constant forward ve- developed in [9] is a conflict resolution scheme locity and can only change direction by changing guaranteeing collision avoidance, either in the heading. Results are demonstrated for a variety plane or in 3D, for an arbitrary number, n, of of numbers of vehicles as well as types of colli- nonholonomic vehicles. The DRCA algorithm is sion directions. designed to work with vehicles that have limited control authority and complex dynamics (such as 1 Introduction aircraft, which have low acceleration compared to speed and must bank to turn). According to the As multi-vehicle autonomous systems are stud- collision avoidance classification in [8], DRCA ied and implemented, the issue of conflict res- is a nominal (projects current states into the fu- olution becomes increasingly important. From ture along a single trajectory), horizontal plane, mobile robots performing a cooperative search global algorithm that combines turning and speed to air traffic control for unmanned aerial vehi- changes and detects conflict. It is most closely cles, collision avoidance is of utmost importance associated with a force field approach, although for safety. Much of the work so far on colli- it does not strictly meet this definition because sion avoidance has been sponsored by the FAA DRCA does not treat vehicles as charged parti- to support a potential move to free-flight air traf- cles. fic control [13], [7], whereby aircraft can avoid An imperative feature for any avoidance algo- each other in a decentralized manner rather than rithm used for automating air or shipping traffic relying on a land-based controller. Similar con- must be a guarantee of collision avoidance. For a cepts have been discussed regarding autonomous collision avoidance guarantee to be valid for real harbor control for ships [11], [6]. These scenarios vehicles, it must also restrict the maximum ac- will become more important as unmanned vehi- celeration. Any collision avoidance scheme that cles are introduced, because safety will need to does not meet this criteria can be ruled out for 1 A. P. MELANDER*, N. D. POWEL*, E. LALISH*, K. A. MORGANSEN*, J. S. JANG** AND J. VIAN** such applications. Many of the approaches pre- tors, hats over unit-vectors, script capital letters viously proposed guarantee avoidance, but only for sets, standard capital letters for matrices and for a limited number of vehicles [15], [2]. Be- functions, and everything else is assumed scalar. cause traffic in the air and on the sea is rapidly Quantities subscripted with t, n, or b refer to the increasing, a higher likelihood exists for a colli- tangent, normal, or binormal direction, respec- sion (or at least a conflict) involving multiple ve- tively. hicles. The DRCA algorithm is ideal for such ap- Each vehicle has a nominal desired control plications because it guarantees collision avoid- input, ud(t), which comes from an arbitrary ance (including a restriction on maximum accel- outer-loop controller. This controller is designed eration) for an arbitrary number of vehicles si- for the vehicle to perform a desired task, which multaneously. could range from target tracking to waypoint nav- Furthermore, a centralized avoidance scheme igation, area searching, etc. The goal of the should be avoided because of the high compu- DRCA algorithm is to adjust the control input tational load required by the central node, lack on each vehicle to guarantee collision avoidance of robustness (what happens if it breaks?), and while simultaneously staying close to the desired inability to respond quickly to emergency situa- control input (keeping in mind that this desired tions. The DRCA algorithm distributes compu- control can change with time). tation among the entire group because each vehi- For this approach to collision avoidance, the cle accounts only for its own interactions. This only vehicle states that matter are position and distribution makes for O(n) calculations on each velocity. Orientations affect performance, as they vehicle, which should be reasonable in most ap- often have bearing on the magnitude of acceler- plications. It is not a centralized algorithm, but ation available in a particular direction, but they it is not strictly decentralized since states of all do not directly affect the underlying features of other vehicles are required (not just the nearest conflict and collision. In this way, many differ- neighbors). Since it is not centralized or decen- ent vehicle models work equivalently with this tralized, the term “distributed” is used in naming approach. To simplify the math, a simple vehi- the algorithm. cle model will be used for most of the following The focus of the work in this paper is to pro- analysis: a 3D double integrator, which for the ith ceed beyond the theoretical and simulation work vehicle is given by developed in [9] by implementing the DRCA al- d r v gorithm on actual hardware. The remainder of i = i dt v u the paper is organized as follows to present the i i (1) d implementation. In Section 2, system modeling Qi = WiQi; is discussed, and the deconfliction algorithm is dt presented. The two testbeds being utilized for im- where r;v 2 R3 are the position and velocity of plementation are discussed in Section 3. Results the vehicle center of mass, and u 2 R3 is the con- of the deconfliction implementation are given in trol input. The matrix Q = [tˆ;nˆ;bˆ] defines the ori- Section 4, and conclusions are given in Section 5. entation of a body-fixed coordinate frame located at the vehicle center of mass relative to an inertial 2 Decentralized Reactive Collision Avoid- coordinate frame, and W is the cross product ma- T ance trix of the body rotation vector w = [wt;wn;wb] . Note that the orientation of the vehicle (defined ˆ 2.1 System Model by the tˆ, nˆ, and b vectors) is only used as a local coordinate frame for the DRCA algorithm. The The work here presents implementation of a orientation does not directly affect the dynamics method for deconflicting n vehicles. The notation (r and v), and as such can be arbitrary. How- throughout this paper will use bold face for vec- ever, many vehicle’s input constraints are related 2 Implementation of Deconfliction in Multivehicle Autonomous Systems to their orientation, and so it can be useful to tie equivalent representation of the system is (1) with this local coordinate frame to the actual body co- u = uatˆ+kvkwbnˆ −kvkwnbˆ. The tangent vector ordinates of the vehicle. must be initialized to the same direction as the We constrain the input by use of an arbitrarily velocity vector, but the dynamics will keep the varying constraint set, ui 2 Ci. The only require- two vectors aligned from then on. In this case, R ment is that Ci always contain the origin. A sim- can be defined by ple example of an input constraint set that limits maximum acceleration and velocity is utmax = −utmin = uamax unmax = −unmin = kvkwbmax n 3 i = ui 2 kuik ≤ umax; C R ubmax = −ubmin = kvkwnmax ; T o kvik ≥ vmax =) ui vi ≤ 0 : (2) and the accompanying saturation function is For the DRCA algorithm, one must choose a ( vuTv T u − ; kvk ≥ smax;u v ≥ 0 set of rectangular constraints R (which can also S = smax vary with time, state, etc.) for each vehicle that u; otherwise: encloses its C, as well as a corresponding saturation function, S : R ! C. The function S must Normally one would not equate a holonomic be continuous, must become the identity map for model to a nonholonomic one, largely because any u 2 C, and must preserve the sign of each of differences in controllability. However, full component of u when decomposed in the tˆ, nˆ, controllability is not essential to the DRCA algo- and bˆ directions. In this example, one can choose rithm since only position and velocity are essential. The DRCA algorithm is designed to use any 3 Ri = ui 2 R − umaxi ≤ uti ≤ umaxi ;::: ; (3) control authority available, assuming controllability in the position and velocity states. Note and that full controllability is generally required for 8 umax the nominal control, ud(t). ui ; kuik > umax > kuik The relative position vector from vehicle i to < T viui vi T Si = u − ; kv k ≥ v ;u v ≥ 0 (4) vehicle j is denoted r˜i j ≡ r j − ri, while the rel- i vmax i max i i > ative velocity vector is defined in the opposite :ui; otherwise: sense: v˜i j ≡ vi − v j. Note that these definitions An example of how more complex vehi- imply that r˜˙i j = −v˜i j, and v˜˙i j = ui − u j.

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