Optimal control based coordinated taxiing path planning and tracking for multiple carrier aircraft on flight deck

Xin-wei Wng ,Hi-jun Peng ,Jie Liu ,Xin-zhou Dong ,Xu-ong Zho ,Chen Lu

a Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian,Liaoning,116024, China

b Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, Liaoning,116024, China

c War Research Institute, Academy of Military Sciences, Beijing,100850, China

d School of Reliability and Systems Engineering, Beihang University, Xueyuan Road, Haidian District, Beijing,100191, China

Keywords:Carrier aircraft Coordinated path planning Centralized optimal control Trajectory tracking Model predictive control

ABSTRACTCoordinated taxiing planning for multiple aircraft on flight deck is of vital importance which can dramatically improve the dispatching efficiency.In this paper,first,the coordinated taxiing path planning problem is transformed into a centralized optimal control problem where collision-free conditions and mechanical limits are considered.Since the formulated optimal control problem is of large state space and highly nonlinear,an efficient hierarchical initialization technique based on the Dubins-curve method is proposed.Then, a model predictive controller is designed to track the obtained reference trajectory in the presence of initial state error and external disturbances.Numerical experiments demonstrate that the proposed “offline planning + online tracking” framework can achieve efficient and robust coordinated taxiing planning and tracking even in the presence of initial state error and continuous external disturbances.

1.Introduction

1.1.An overview of dispatch problems of carrier aircraft on the deck

An aircraft carrier is a complex weapon system where efficiency and safety in the sortie task is an important index to measure its combat effectiveness [1-4], and the dispatch is one of the key processes of the sortie task.However, numerous instances of damage or loss of aircraft during the phase of dispatch since it is difficult to achieve accurate and safe movement of multiple aircraft in such narrow space with limited resources [3,4].To meet the demand for cooperative combat for future war,aircraft carriers are carrying more and more aircraft.Hence, an optimized sortie schedule is expected when multiple aircraft are required to launch from the flight deck.One of the difficulties is that it’s hard to make a reasonable plan to transfer the aircraft from the gate position to the preparing spot with different departure times and prescribed terminal heading angles, where the key issue is to solve the cooperative trajectory planning problem.Traditional planning processes are based on manual experience, where it becomes extremely hard to generate reasonable and optimal cooperative dispatch trajectories when a large number of aircraft are involved.To reduce the executive’s workload and improve the efficiency and safety in the sortie task, it’s necessary to study the cooperative trajectory planning problem for multiple aircraft on deck and the corresponding control problem.

When a carrier aircraft taxiing on the flight deck, various constraints must be considered.Such constraints can be categorized into five aspects:(1)The taxiing velocity should be restricted with a safety range, and a carrier aircraft cannot taxi backwards without extra assisted traction vehicles; (2) The maximum front wheel steering angle is known according to the mechanical design,determining a certain minimum turning radius;(3)The flight deck is a narrow space with many obstacles, and the position of an obstacle may vary with time;(4)Highly accurate satisfaction on the terminal state,which includes position and orientation,is required for following launching procedure; (5) The saturation of control inputs should also be considered for practical control.

1.2.Literature review on path planning of carrier aircraft on the deck

Existing path planning techniques for carrier aircraft on deck are mainly divided into the following five categories[5]:

(1)In this kind of method, an active aircraft is usually considered to be outlined by a circle with a certain radius, while obstacles on the flight deck are considered to be outlined by convex hulls.Therefore, with the knowledge of boundary conditions and obstacles, the search space and threatened zones of the active aircraft are obtained according to the minimum turning radius.Next,one needs to find all way points and further compute the cost of each pair of way points.Finally, graph theory based methods, where Dijkstra’s algorithms are commonly adopted, are required to solve the shortest path.Under this framework, Zhang et al.solve the path planning of taxiing aircraft and traction system in Ref.[6,7], respectively.It is noted that the taxiing velocity of the aircraft is simply considered constant in graph theory based methods.Hence,this kind of method cannot clearly explain the accelerating and the decelerating behavior around the initial and the final position, respectively.Besides, since the search zone and threatened zones severely depend on the position and shape of obstacles, this kind of method, to the best of our knowledge, has not been applied to scenarios where dynamic obstacles exist.

(2)Various improved A*algorithms are proposed under this framework.In this kind of method,to improve the solving efficiency and accuracy, the mechanical constraints must be integrated to narrow the search space.The selection of theneeds much experience, and it directly determines the quality of the generated path.As stated previously,the final heading angle is an important constraint in the taxiing trajectory planning,while this constraint cannot be easily satisfied in the traditional A*algorithm.To overcome this deficiency,Wu and Qu[8]design a dynamic weighted heuristic function,where the expanding node closer to the final node (representing the final destination) in the node sequence is assigned with a larger weight on the desired heading angle,to solve the path planning problem in obstacle-absent situations.Since the obtained path consists of several segment lines, an extra trajectory smoothening procedure is required.By incorporating the theory of model predictive control(MPC)with the A* algorithm, Wu and Qu [9]design a new dynamic weight heuristic function and develop a multi-step optimization algorithm to solve the problem in presence of obstacles.The introduction of MPC guarantees that the generated trajectory is feasible since the kinematics are considered.Meanwhile,the multi-step optimization scheme can extensively decrease the probability that none of the spare path points is available due to the unforeseen obstacle in single-step method and various constraints on state and control variables.

(3)Moving towards the object and obstacle avoidance comprise the path planning behavior modes of carrier aircraft.The velocity and the heading angle are commonly selected as the behavior variables.And the behavior modes are realized by two independent differential equations of these two behavior variables.This kind of method is,to some extent,alike to the artificial potential field method since the design of fields is the major concern(especially for complicated environment)[10,11].When the fields are properly designed,the method is of high efficiency.Zhang et al.[12]proposed an improved strategy for obstacle avoidance based on the generalized symbolic threshold function to solve the taxiing path.Recently, the above method was extended to solve the problem of traction systems [13].However, the constraints on the terminal heading angle and control variables are hard to be taken into consideration.

(4)This kind of method owns strong computational robustness and highly efficient calculation.Han et al.[14]divide the flight deck into segments in-axis direction, and clustered particle swarm optimization(PSO)algorithm is used to optimize the corresponding-axis coordinates.This method has an obvious disadvantage that the “U-turn like” behavior in-axis direction cannot be realized.In addition, the orientation of the aircraft is not considered.In Ref.[15], Wu et al.take the front wheel angular velocity at Chebyshev collocation points as variables to be optimized, and the chicken swarm optimization (CSO)algorithm is taken as the core solver.A strategy of segmented fitness function is developed, numerical results therein demonstrate that the terminal constraints on position and orientation can be restricted within prescribed ranges.Su et al.[16]develop a taxiing path planning method that combines artificial experience in selecting intermediate nodes and the modified artificial bee colony (MABC) algorithm for local optimization.When optimized intermediate path nodes are obtained, the Dubins curve or the Reeds-Shepp curve is used to generate feasible trajectory.Hence,the constraints on minimum turning radius and terminal orientation are strictly satisfied.Swarm intelligence methods can achieve global optimality theoretically.However, due to the limit of computational time in practice, it cannot avoid the possibility of falling into local optimum.

(5)Optimal control-based method has a simple mathematical formulation, various constraints (i.e., boundary conditions, mechanical constraints, input saturation, obstacle avoidance, etc.) can be treated under a uniform framework and strictly satisfied.Along with the trajectory, the profile of control variables is also provided in optimal control based methods.Besides,by regarding the position of obstacles as a function of time,dynamic obstacles can be treated equivalently to static obstacles.Based on the classical bicycle model,Li et al.[17]use direct pseudospectral method to solve the taxiing trajecotry.Liu et al.[18]use the symplectic pseudospectral method(SPM) to solve trajectory planning of traction system.It should be noted that once many obstacles are involved on the flight deck,optimal control-based method could be timeconsuming even fails in extremely complicated situations.Hence, reasonable simplifications and efficient initialization techniques must be incorporated for complicated problems.

The above five kinds of path planning techniques generally fall into geometric methods (including geometry theory based methods, heuristic search methods, and behavior dynamics based methods) and trajectory planning methods (including optimal control based methods)according to whether the kinematic model is considered.As for a swarm intelligence method,its classification depends on the discretization formulation.In geometric methods,only a path that consists of a series way points is provided.However, information on time corresponding to way points is also available in trajectory planning methods.Since information on the start/stop time of each dispatch path is the key input for the mission planning module, trajectory planning methods are much appealing for path planning for carrier aircraft taxiing on the deck.Hence, an efficient and robust path planning module can greatly improve the quality of mission planning module.

It should be noted that the methods mentioned above are only applicable to the path planning of single carrier aircraft.Once coordinated path planning of multiple carrier aircraft is realized, it could dramatically improve the operation efficiency of sortie tasks.However,only a few related studies are seen.Li et al.[19],based on their previous work [9], design a segmented heuristic function to solve the path planning of aircraft fleet launching.Wu et al.[20]develop a mission planning approach for carrier aircraft launching.For the path planning task therein, a distributed path planning algorithm based on the asynchronous planning strategy is proposed.Liu et al.[21]combine the features of reciprocal velocity (RVO)method and the SPM to develop a composite trajectory planning method for multiple aircraft taxiing on the deck.An improved RVO method that considers mechanical constraints of carrier aircraft is proposed therein.When the carrier aircraft approaches around the final destination, the SPM is used to determine the remaining trajectory, hence the terminal boundary conditions can be strictly satisfied.

As for a carrier aircraft taxiing by itself on the deck, its mechanism of motion is partialy similar to that of an automobile on the road.In the field of autonomous driving,the classical bicycle model is widely used for local trajectory optimization.The bicycle model is essentially a kinematic model and it cannot reflect inertial effects of the aircraft.However,the taxiing velocity of aircraft on the deck is relatively low (usually no more than 2 m/s) during the dispatch process for the sake of security.According to Karkee’s conclusion[22],trajectory planning results based on the kinematic model and the dynamic model are almost the same when the vehicle runs at a relatively low speed.Hence, the bicycle model is also used when implementing the trajectory planning process in this paper.

1.3.Literature review on trajectory tracking of carrier aircraft on the deck

Control inputs cannot be provided simultaneously by the path planning methods reviewed in Section 1.2 except for optimal control-based methods.Actually,even the control laws obtained by optimal control-based methods cannot be applied directly since initial state error and various external disturbances exist in practice.Hence,it is of vital importance to adopt a tracking controller to track the reference trajectory.Once robust trajectory tracking techniques are successfully implemented,it is promising to realize the autonomous dispatch control for carrier aircraft on the deck.

Studies on taxiing trajectory tracking of carrier aircraft are rarely seen until recent years.In several existing studies[7,18,21],tracking controllers have coincidentally adopted the MPC method due to its simple mathematical formulation and inherent capability to consider constraints.No perturbations are considered in Ref.[7],external disturbances are considered in Ref.[18,21],and initial state error is considered in Refs.[18].Ref [18]doesn’t consider the constraints on acceleration,thus the acceleration varies within a large range therein.Ref [21]designs the MPC controller based on an oversimplified bicycle model where the taxiing velocity and front wheel are taken as control variables.Numerical simulation therein shows that such two control variables vary extremely fast,which is not applicable in practice.

Based on the above discussions, it is seen that the selection of motion model and the setting of constraints are, to some extent,critical for the tracking performance.Generally speaking, we prefer to conduct path planning based on the kinematic model while designing trajectory tracking controllers based on the dynamic model.Complicated dynamic characteristics such as tire-deck interaction, which are important factors to analyze the mechanism of motion instability,cannot be considered in the kinematic model.It should be noted that the so-called control variables such as acceleration and front wheel steering angular velocity obtained in the path planning moduls are actually not the real control inputs for the aircraft.The real control inputs such as propulsive force are not involved in the kinematic model.

However,existing related researches all develop the MPC based on the classical bicycle model or its simplified version.We believe that the reasons are possibly twofold.One the one hand,as for the aircraft on deck, the trajectory tracking is a totally nascent topic when compared to the path planning.Hence,researchers are used to designing trajectory tracking controllers based on kinematic models since they are frequently used in path planning.On the other hand, researchers may derive the relationships between the virtual control variables and the actual inputs according to geometry and the information on inertia.Hence,once the virtual control variables are generated by the MPC, actual control inputs can be caculated and applied.In this paper, we also develop a trajectory tracking controller based on a kinematic model.

1.4.Contributions

In this paper, we aim at presenting an autonomous dispatch motion control framework for multiple carrier aircraft taxiing on the deck,and an“offline planning+online tracking”framework is developed.To the best knowledge of the authors, this is the first paper that clearly presenting the idea of autonomous dispatch control on deck.

In the offline path planning module, based on the simplified bicycle model and its augmentation,the coordinated path planning problem is transformed into a centralized optimal control problem,where constraints on front wheel steering angle, taxiing velocity and input acceleration are considered.As for the collision-free conditions, extra adequate safety distance is introduced.Since the flight deck is a complex environment with many obstacles,inspired by Li et al.[23], a hierarchical initialization method based on the Dubins curve is developed to improve the computational efficiency and robustness.The developed initialization method is divided into the following three steps.First,the Dubins curve is used to generate a path for every single aircraft.Then, the obtained Dubins curve solutions are taken as initial guesses of an obstacle-absent problem for each aircraft.Finally,the solutions obtained in the previous step are gathered to initialize the real problem.

Once the feasible trajectories are generated, based on an extended bicycle model,an MPC controller is designed to track the reference trajectory in the presence of external disturbances and initial state error.Since adequate safety distances are prescribed in the path planning module, the collision-free conditions can be eliminated in the MPC controller to improve the computational efficiency.

1.5.Organization of the paper

The remainder of the paper is organized as follows.In section 2,the bicycle model is used to describe the motion of carrier aircraft taxiing on the flight deck, and a simplified bicycle model is introduced.In Section 3, various constraints that should be considered are introduced.And based on the simplified bicycle model, the coordinated taxiing problem is transformed into a centralized optimal control problem.Besides, an efficient and robust hierarchical initialization technique is proposed.Then in Section 4, an MPC trajectory tracking controller based on an extended bicycle model is designed in case of initial state error and external disturbances.Section 5 validates the effectiveness of the developed“offline planning + online tracking” framework.Finally, Section 6 concludes the paper.

2.Motion of the carrier aircraft taxiing on the flight deck

Fig.1.An illustration of carrier aircraft taxiing on the flight deck (the subscript is omitted for simplicity).

3.Of fline taxiing path planning based on centralized optimal control

3.1.System equations

This section aims to solve the coordinated path planning under the framework of centralized optimal control problems.For the purpose of distinguishing,the aircraft to be planed are calledones while others are called dumb ones.Hence, whenactive aircraft are involved,based on model(2),one can expand the state space to 4-dimension as follow

Correspondingly, the system equations can be simply obtained by putting those of each aircraft together

3.2.Constraints

For theth active aircraft, its maximum front wheel steering angle has a physical limit, i.e.,φ.Thus, we have

Let Sbe the distance indicator between theth and theth active aircraft, and it is defined as

It is seen that Sis dimensionless.And the collision-free condition in Eq.(9) is equivalent to the following equation

As well as dumb aircraft,some other objects on the flight deck,such as the island and other vehicles (including tractor vehicles,weapon-delivery vehicles, etc.), should also be seen as obstacles.Such obstacles could be in irregular outlines.However, in optimal control-based trajectory planning methods, it’s ideal to model the collision-free condition by a-continuous function to guarantee the numerical stability and computational efficiency.A widely used method is using a quasi-rectangle to describe the outline of an obstacle [25].The featured quasi-rectangle of theth obstacle can be modeled by the following curve

At the initial time instant= t, theth active aircraft parks at（x，y）with the heading angle θ.Hence,the initial state of theth active aircraft can be denoted as follow

And at the final time instant=t,theth active aircraft should have already taxied to its preparing spot locates at （x，y） with the prescribed heading angle θ,conducting the final maintenance before its launching.Similarly, the final state of theth active aircraft is denoted as follow

3.3.Formulation of the optimal control problem

Based on the augmented model in Eq.(4), we aim at obtaining feasible taxiing trajectories foractive aircraft and corresponding control inputs, which satisfy various kinds of constraints as discussed in Section 3.2.We formulate the coordinated taxiing path planning problem into the following centralized optimal control problem

It is seen that the Problem Pis actually highly non-convex since nonlinear system equations and complicated collision-free conditions are involved.Proper initialization techniques must be incorporated otherwise the problem is hard to be solved.Hence, a relatively easier problem, i.e., Problem P, which eliminates the collision-free conditions defined in Eq.(11) and Eq.(13) from Problem P,is formulated and solved in advance.Since no collisionfree conditions are considered in Problem P, it can be decoupled intoindependent sub-problems foractive aircraft themselves,which is denoted as Problem P（= 1，…，）.With the help of the Dubins curve method,a robust hierarchical initialization technique as illustrated in Fig.2 is developed.Its detailed procedure is given as follow:

: Since the initial and final states as well as minimum turning radius of each active aircraft are prescribed, one can first use the Dubins curve to generate a feasible trajectory(considering no collision-free condition) for each active aircraft.

: Based on model (2), the results of position and heading angle obtained in Step 1 for each aircraft are taken as the initial guesses to solve Problem P.

: The results obtained of Problem Pare gathered to constitute the result of Problem P.Finally, the results of Problem Pare taken as the initial guesses to solve Problem P.

4.Online trajectory tracking based on MPC

4.1.Basic idea

4.2.An extended kinematic model

Fig.2.The initialization procedure for the coordinated collision-free taxiing problem.

4.3.Formulation of the MPC

5.Results

5.1.Parameter settings and the numerical algorithm

To verify the model and algorithm developed in this paper, the flight deck of the Nimitz-class aircraft carrier is taken as the simulation environment.For simplicity, as given in Table 1, every aircraft on the flight deck is thought to have the same mechanical parameters and the subscript to indicate the aircraft number is omitted.It is seen that the upper limits of taxiing velocity and acceleration in the tracking module are slightly loosened those that used in the planning module,such that the MPC controller can welltrack the reference trajectory under external disturbances and initial state errors.

Table 1Mechanical parameters for aircraft.

In this paper,the SPM developed in Ref.[26]is taken as the core solver in both the offline planning module and the online tracking module.The SPM is actually an indirect method that utilizes the sequential convexification (SCvx) technique [27], where the original nonlinear optimal control problem is transformed into a series of convexified linear-quadratic (LQ) optimal control problems.Based on the first-order necessary conditions and multiple-interval Legendre-Gauss-Lobatto discretization, each LQ problem is transformed into a linear complementarity problem (LCP) and finally solved by the Lemke’s method.And the convergent criterion is that the relative error of computational results in two adjacent iterations is less than a prescribed acceptable tolerance,i.e.,ε.The SPM has been successfully applied to the path planning [18,21,28,29]and tracking [18,21,28,30]for various mechanical systems.

5.2.Offline coordinated taxiing trajectory planning

In the offline trajectory planning module,aircraft numbered 1,2,3 and 4(black ones)are taken as active aircraft while others(white ones) are considered dumb ones, as depicted in Fig.3.The dumb aircraft and the island are viewed as obstacles for active aircraft,and the safety distance is set as= 1m.The initial states and final desired states of four active aircraft are listed in Table 2.The initial time instant is set to t= 0s, and the aircraft is expected to taxi to the allocated preparing site within t=120s.In the SPM,the time domain is set to 12 sub-intervals and the 6-order LGL approximation scheme is used in each sub-interval.The acceptable tolerance is set to ε = 10.

Table 2Initial parking and final desired state of 4 active aircraft.

Table 3The actual initial state of four active aircraft.

Fig.3.Optimal coordinated taxiing trajectory of four active aircraft.

Fig.4.Taxiing velocities of four active aircraft (unit: m/s).

The computed trajectory for each aircraft is plotted in Fig.3,where the dotted lines and the solid lines are the trajectories obtained in Problem Pand Problem P, respectively.One may find that except for Aircraft 1,the two trajectories for other three active aircraft are almost the same.The velocity for each aircraft is plotted in Fig.4.It is seen that Aircraft 1 begins to taxi at the initial time instant while other three aircraft begin to taxi after some waiting.Though the time span is set fixed,in order to achieve collision-free with minimum effort, four active aircraft have different departure and arrival instants.To further validate the collision-free conditions,the distance indicators as defined in Eq.(10)between 4 active aircraft are reported in Fig.5.It is seen that all six distance indicators keep below zero during the whole diapatch process,implying that the collision-free conditions are strictly satisfied.The accelerations of four active aircraft are plotted in Fig.6, and the front wheel steering angles of four aircraft are given in Fig.7.It is seen that the control inputs vary smoothly and corresponding constraints are strictly satisfied.In addition, the steering angles of four aircraft are all already tuned to zero at the final time instant,though this variable is absent from the state variable of model (2)(see Fig.8).

Fig.5.Distance indicators between four active aircraft.

Fig.6.Optimal acceleration of four active aircraft (unit: m/s2).

Fig.7.Optimal front wheel steering angle of four aircraft (unit: deg).

5.3.Online trajectory tracking

The MPC tracking controller designed in Section 4 is applied to track the four reference trajectories generated in Section 5.2.In the tracking controller,the sampling period is set as δ=0.05s and the length of the prediction time window is selected as=4s.For the open-loop optimal control problem to be solved at each sampling instant, the prediction time window is divided into 3 regular subintervals with 4th order LGL approximation.And the acceptable tolerance is set to ε = 10.To further improve the online computational efficiency,the reference trajectory is interpolated to form the initial guesses.The weighted matrices are selected as=diag（10，10，10） and= diag（1，1）, respectively.

Fig.8.Tracking error of state x of four active aircraft (unit: m).

Two kinds of disturbances,i.e.,perturbations in initial state and continuous external disturbances, are considered during the implementation to validate the robustness of the tracking controller.The actual initial states of four aircraft are listed in Table 3.To simulate the disturbances caused by external loads(such as base motion, wind, friction, etc.) and measurement noise, 0.05 times of the standard Gaussian white noise added to state,and θ at the left end of every prediction time window(for position variables and the orientation variable, the units of corresponding perturbations are m and rad, respectively)(see Fig.9).

Fig.9.Tracking error of state y of four active aircraft (unit: m).

Fig.10.Tracking error of state θ of four active aircraft (unit: deg).

Table 4Tracking performance of four active aircraft.

The tracking errors including state,and θ of four active aircraft are given in Figs.8-10.It is seen that the tracking errors are restricted within small ranges.And the final error of state variables and average computational time are summarized in Table 4.The average online computational time about 7 ms,compared with the sampling period δ=50ms,it can meet the demand for real-time calculation.The profiles of taxiing velocity and front wheel steering angle are plotted in Fig.11 and Fig.12, respectively.It is seen that such two variables vary smoothly and keep within the predefined box constraints strictly.Besides, the front wheel steering angular velocity and acceleration are given in Fig.13 and Fig.14, respectively.Since the rates of these two variables are constrained, they vary smoothly.

Fig.11.Actual taxiing velocity of four active aircraft (unit: m/s).

Fig.12.Actual front wheel steering angle of four active aircraft (unit: deg).

Fig.13.Actual front wheel steering angular velocity of four active aircraft(unit:deg/s).

Fig.14.Actual acceleration of four active aircraft (unit: m/s2).

6.Conclusions

An “offline planning + online tracking” framework for coordinated taxiing trajectory planning and tracking problem of multiple carrier aircraft on the flight deck is developed in this paper.In the offline planning module, based on a simplified bicycle model, the coordinated trajectory planning problem is solved under the framework of a centralized optimal control problem.And a robust hierarchical initialization technique based on the Dubins curve method is developed.In the online tracking module, based on an extended bicycle model, an MPC trajectory tracking controller is designed to track the reference trajectory obtained from the trajectory planning module.In the MPC controller,box constraints on state and control variables are properly loosened to guarantee the tracking performance in the presence of initial state error and external disturbances.

Simulations show the developed framework is promising to be an efficient and robust framework to realize autonomous dispatch control on flight deck.And it can be easily extended to other dispatch modes.However,the trajectory tracking module herein is developed based on the kinematic model where inertial effects of the carrier aircraft are ignored.Our future research directions are to derive a simple and accurate dynamic model for carrier aircraft taxiing on the deck considering the base motion.With the help of such a dynamic model, on the one hand, we can set proper box constraints on motion parameters; on the other hand, we can develop trajectory tracking controllers with higher accuracy and robustness.

The authors declare that they have no conflict of interest.

The authors are grateful for the National Key Research and Development Plan (2017YFB1301103); the China Postdoctoral Science Foundation (2020M670744, 2020M680947); the financial support of the National Natural Science Foundation of China(62003366,11922203, 11772074, 11761131005); the Fundamental Research Funds for the Central Universities (DUT19TD17).