An evolutionary method of ship's anti-collision trajectory planning: new experiments

Transcription

1 An evolutionary method of ship's anti-collision trajectory planning: new experiments R. Kaminski and R. Smierzchalski Gdynia Maritime Academy, ul. Morska 83, Gdynia, Poland, Abstract In a collision situation at sea, the decision support system should help the operator to choose a proper manoeuvre in a given navigational situation, teach him good habits, and enhance his general intuition on how to behave in similar situations in the future. An accepted approach here is the use of a multiple criterion decision problem based system. A new version of the uep/n++ (Evolutionary Planner /Navigator) algorithm equipped with an on - line mode has been used, as a major component of such a system, for computing the near optimum trajectory of a ship in a given environment. The introduction of the time parameter, moving constrains representing approaching ships, and the online mode are the main distinctions of the newly introduced system. The paper presents selected results in the form of ship trajectories obtained for typical navigation situations. 1 Introduction A safe anti-collision manoeuvre is traditionally looked for by drawing radar plots based on the observed echoes of the moving objects. The new-built ships are equipped with special radar anti-collision systems, named Automatic Radar Plotting Aids (ARPA), which facilitate considerably the navigator's work. International Maritime Organisation (IMO) has worked out the timetable of the installation of the ARPA systems on ships built after Functions executed by the ARPA system automate the process of tracking objects and presenting graphically the navigational situation. Due to its ability to process the data and display the development of the navigational situation on the radar screen, the ARPA system allows the navigator to make fast and correct decision about the manoeuvre to take. However, the final decision on how to act in order to avoid the collision must be made individually by the navigator on the basis of information obtained ffom the

2 ARPA system, complemented by his seamanship and intuition. Apart from adequate preparation for normal tracking work, ARPA system also needs additionally algorithms, which, after the implementation, will help the navigator in charge to make correct decisions. Recent tendencies in the automation of the ship navigation lead to automatic calculations of anti-collision manoeuvres, with simultaneous quantitative assessment of the risk of collision, basing on the data obtained from the ARPA system. When determining a safe trajectory for the own-ship, we look for a trajectory that is a compromise between the cost of necessary deviation from a given route, or from the optimum route leading to a target point, and the safety of passing round all static and dynamic obstacles, here bearing the name of strange ships - targets. All trajectories, which meet the condition of avoiding the risk of collision to a satisfactory degree make a set of permissible trajectories. Thus the task of determining the safe trajectory is reduced to the choice of an optimum solution, or a subset of optimum solutions from the set of permissible trajectories, taking into account certain cost criteria and the need to satisfy, in any circumstances, the safety conditions. Normally, the execution of marine functions, such as ferry transportation, coastal fishing, tourist services, and other activities connected with the maintenance of the navigability of water lines, result in crossing the traffic separation regions by certain craft. According to some sources (Dove et al. [2]), 85 per cent of collisions and singings in this situations result from human errors. There is a tendency to work out a versatile automatic system, which would permit the safe navigation in all areas and at all possible weather conditions. The ship guidance systems were studied by Dove et al. [2]. In this work, the system was used for estimating a ship trajectory along given water lines in the harbour. Bums [l] extended the problem by guiding a set of ships along a given route. Iijima et al. [5,6] and Witt et al. [l91 worked out an autonomous ship guidance system. Hayashi et al. [4] proposed a system for avoiding collision in coastal zones in which the function of an electronic map was linked with the radar operation in order to evaluate the ship's position and assess the navigational situation. Sudhendar et al formulated a list of requirements an intelligent guidance system was to comply with, and presented a review of the actual activities in this area. In a series of articles (Smierzchalski [10,11,12]) this problem was formulated as a multi-criterion optimisation task. Then, the problem was solved for static and moving constraints using the decision making system. The collision situation was modelled by the authors in [3] as a fuzzy process with a number of inputs. Smierzchalski [l41 applied in his ship guidance system a new computer technique - evolutionary algorithms. Basing on the concept of the EPN (EvolutionaryiPlanner Navigator) guidance system, presented by Michalewicz et al. [9,10], Lin et al. 171, Trojanowski et al. [l81 and Michalewicz [S], and Xiao et al. [20], a modified version of that system was prepared for solving collision problems. The present paper is a continuation of author's earlier works (Smierzchalski [l 3,14,15,16]). Comparing to them, an additional parameter, the speed of the own ship, was introduced to the system. In the present work, the

3 authors present a new version of the vepm++ (Evolutionary Planner/Navigator) algorithm, in which especial attention is paid to the trajectory planing in on-line mode in the presence of fixed and moved constraints of the navigational area. 2 Anti-collision problem and evolutionary planner The compromise in anti-collision problem has to be reached between the costs of the diversion from an assumed, or the shortest route, and the acceptable safety of passing round static and dynamic constraints. Due to those contrasting criteria the problem can be reduced to a multi-criterion task for optimum trajectory planning. In a sea variant, all trajectories whose vector of echo motion in a relative visualisation obtained from ARPA does not cross the area of danger defined by a safe distance Db around the actual position of the own ship are permissible trajectories. The optimisation problem consists in selecting the optimum trajectory from the permissible trajectories with respect to an assumed fitness function. After adapting the programme EP/N to sea environment, a new programme was developed bearing the name of vep/n++. The introduced changes include different types of constraints resulting from the new environment in which the ship moves, especially dynamic constraints representing other moving ships. They also include new genetic operators, and time parameter for covering the assumed trajectory. The most recent change made in the programme is the option of on-line trajectory planing. To obtain full flexibility of a decision support system in situations which may develop in an unforeseeable way, the ship control in a collision situation must have the hierarchical structure. [14]. Introducing input data to procedures calculating the ship trajectory (for vep/n++ this data is obtained from ARPA), are: calculating an optimum trajectory for the ship moving in given navigational environment, steering the ship along the calculated trajectory (off- line mode), monitoring parameters of moving obstacles, with possible updating of the introduced input data and re-calculation of the optimum trajectory (on-line mode). The last, stage, i.e. the on-line control of the ship motion in the hierarchical structure of ship steering is the main subject discussed in the paper. 3 Environment - dynamic and static constraints All strange ships are attributed moving domains (at course and speed determined by the system ARPA), although only some of them represent real collision threat. It was assumed in the programme that the object representing a real collision threat is the object which has entered the area of observation of the own ship (the distance of 5-8 nautical miles ahead and 2-4 nautical miles astern, depending on the assumed time horizon) an can cross its course at a dangerous distance. The distance of danger is selected by the navigator, depending on the weather conditions, visibility, sailing area, and own ship's speed. Kinetic modelling of

4 the ship motion was used in the programme. The environment in the system EP/N++ consists of static and dynamic constraints. The static constraints represent land, channels, shallows, straits, andlor other navigational constraints like water lines and the areas of traffic separation, for instance. Those areas are modelled by fixed polygons, similar to those used in the process of generating electronic vector maps. Dynamic constraints represent the areas of danger around approaching ships. These areas are called domains and are modelled by hexagons. Their areas depend on the current navigational situation and assumed safety conditions. In modelling the environment the dimension of the own ship is neglected as very small compared to the dimensions of the domains of strange ships. The dynamics of the ship is taken into consideration in the stage of steering along the already calculated safe trajectory. In the first version of the programme the own ship was assumed to move at a constant speed V along the entire trajectory, and at the initial time instant to the motion of strange objects was assumed steady. The present version makes it possible to introduce changes to the parameters of motion of the dynamic constraints. It also includes the mutation operator for the own ship speed. The speed parameters of the dynamic objects, as determined by the system ARPA, include: bearing, distance, course and speed. In the evolutionary algorithm each trajectory is attributed an instantaneous dynamic area connected with each individual moving strange object. The instantaneous position of the dynamic area with respect to the passing trajectory is evaluated by time t, determined from the crossing point (x,,,,y,,,) of the trajectory of the own ship S with the trajectory of the strange object. This crossing point (x,,,,y,,,) is considered the point of collision threat. The time needed for covering the distance from the starting point (xo,y,) to the crossing point (x,,,,y,,,) by the own ship moving at speed V along trajectory S is t. For the same time t the position of the domain of the strange object is calculated in a similar way and taken into account via its trajectory. The static constraints are seen in the same way from all trajectories and do not have to be re-calculated. In the programme vepin++ a new position of the domain is only calculated for the best individual in each population. The level of collision danger is determined using the depth of penetration of the constraint by the trajectory. 4 Simulation studies and programme tests in collision situations In order to test operational correctness of the on-line version of programme vep/n++, certain trajectories were calculated using the both versions and then compared. The test was divided into three phases. In the first phase, passing paths obtained in the off-line mode were tested. Then the real motion was studied of the own ship travelling along the assumed trajectory and passing other objects. The level of identity was assessed with which the positions of passed ships - domains were calculated with respect to the own ship. For the on-line version, a quality assessment was made for the calculated trajectory on the basis of on-line calculations performed after changing parameters of motion of one or more

5 dynamic constraints. The comparison was made for two sample environments characterised by a relatively high level of complexity. The first case (Fig. l) presents the situation in which the own ship passes round four islands and four objects moving from different directions and at different speeds. Input parameters for the simulation, in which the population number was equal to 40, are shown in Fig. 1. Fig. 1. Test environment No. 1. Generation=O. Mode: off-line. Ship trajectory adaptations. made in the off-line mode after the own ship has met four moving objects in a collision situation, are shown in Fig. 2, after 500, and 2000 generations, respectively. The solution obtained after 2000 generations made it possible to pass round the islands, at the same time leaving aside the moving objects. Current speeds of the own ship were individually calculated for each trajectory segment which allowed the ship to reach the target point in a safe way and the shortest possible time. The realisation of the proposed trajectory optimised the ship passage cost with respect both to safety and economic conditions, eliminating the risk of excessive approach to the passed objects. It is noteworthy that the results are presented in a relative form, in which the domains of the dynamic constraints are drawn up in positions which they will reach when the own ship is in front of their bows or behind their sterns. Fig. 2. Test environment No. 1. Generation=500 (a), 2000 (b). Mode: off-line The next phase studies the real motion of the own ship travelling along the assumed trajectory and passing strange objects. This phase makes it possible to assess more accurately the correctness of positions of the passed ships - domains

6 with respect to the own ship. Fig. 3 presents the navigational situation in the real motion after Ti = 10, 20, 30, 40, min (i= 1,..,4). In contrast to the relative presentation (Fig. 2), here the positions of the domains representing dynamic constraints and the position of the own ship on the trajectory are determined after the time which elapsed after the simulation has started (Option,,Runn pressed down) to the time instant when the option,,real time situation" was started. The option,,real time situation" was implemented in order to stop the motion of all objects for a given time instant and to simulate possible changes in parameters of motion of the domains representing passed objects interpreted as dynamic constraints. Changing parameters of passed objects creates a new navigational situation - a new environment which provokes the adaptation of the ship trajectory calculated in the off-line mode. Switching to the on-line mode, the system vep/n++ adapts the ofl-line trajectory version to the new environment, treating the time when the objects were stopped as the starting point of the modified trajectory. Fig. 3. Test environment No. l, T= 20 (a), 40 min (b). Option,,Real time situation" For the test environment, the algorithm switched to the on-line mode at T2 = 20 min. Then selected parameters were changed, namely: the course of the object seen in the right part of the screen, which was changed from 45 degrees to 210 degrees, and the speed of motion of the object seen in the upper left part of the screen, changed from 5,2 to 17,6 knots. These changes were dictated by the requirement to observe the operation of the algorithm in extremely complex environment. Fig. 4 (b) shows a newly calculated safe trajectory (generation number = 2000) which has taken into account the above changes. After comparing Fig. 2 and Fig. 4 (b) one can see that the path calculated in the on-line mode is similar to the trajectory obtained in the oflline mode, with certain differences resulting from trajectory corrections made due to environment changes introduced. This proves the operational correctness of the on-line version. 6 Conclusions The evolutionary system of ship trajectory planning makes it possible to steer the ship in a well known environment both with static, and dynamic navigation

7 constraints, as well as to make adaptation corrections of the ship trajectory in order to follow unforeseeable changes in the situation at sea. The evolutionary method of determining the safe and optimum trajectory in the environment is a new approach to the problem of avoiding collisions at sea. A number of preliminary tests have made it possible to formulate the following conclusions: evolutionary algorithms can be effectively used for solving the problem of planning ship trajectory in areas of extensive traffic, like harbour entrances, coastal regions, introduction the on-line mode makes it possible to solve the problem in a wider range. For particular trajectory sections, the actual trajectory is evaluated with which the ship covers this section in order to pass safely and economically all navigational constraints, both fixed and moving. (a) Fig. 4. Test environment No. 1, T2 = 20 min. Changing parameters of motion of two targets (a). New optimum trajectory (b). Mode: on-line Acknowledgements The research reported in this paper was supported by the DS. 191 from the Polish State Committee for Scientific Research. References 1. Burns RS, An Intelligent Integrated Ship Guidance System. 2nd IFAC Workshop Control Applications in Marine Systems, Genova, Italy Dove MJ, Bums RS, Stockel CT, An Automatic Collision Avoidance and Guidance System for Marine Vehicles in Confmed Waters. Journal of Navigation, Vol Furuhashi T, Nakaoka K, Uchikawa Y, A Study on Classifier System for Finding Control Knowledge of Multi-Input Systems F. Herrera, J.L.Verdegay Editors. Genetic Algorithms and Soft Computing, Phisica-Verlang Hayashi S, Kuwajima S, Sotooka K, Yamakazi H, Murase H, A stranding avoidance system using radar image matching: development and experiment. Journal of Navigation. Vol

8 5. Iijima Y, Hayashi S, Study towards a twenty-first century intelligent ship. Journal of Navigation, Vol Iijirna Y, Hagiwara, H Results of Collision Avoidance Manoeuvre Experiments Using a Knowledge-Based Autonomous Piloting System. Journal of Navigation, Vol. 47, Lin HS, Xiao J, Michalewicz Z, Evolutionary Algorithm for Path Planning in Mobile Robot Environment. Proceeding IEEE Int. Conference of Evolutionary Computation, Orlando, Florida, Michalewicz Z, Genetic Algorithms + Data structures = Evolution Programs. Spriger-Verlang, 3Id edition Michalewicz Z, Xiao J, Evaluation of Paths in Evolutionary Planner/Navigator. Proceedings of the International Workshop on Biologically Inspired Evolutionary Systems, Tokyo, Japan Srnierzchalski R, The Application of the Dynamic Interactive Decision Analysis System to the Problem of Avoiding Collisions at the Sea (in Polish). l" Conference "Awioniki", Jawor, Poland, Smierzchalski R, The Decision Support System to Design the Safe Manoeuvre Avoiding Collision at Sea. 14" International Conference Information Systems Analysis and Synthesis, Orlando, USA, Smierzchalski R, Multi-Criterion Modeling the Collision Situation at Sea for Application in Decision Support. 31d International Symp. on Methods and Models in Automation and Robotics, Miedzyzdroje, Poland Smierzchalski R, Trajectory laming for ship in collision situations at sea by evolutionary computation. 42 IFAC Conference on Manoeuvring and Control of Marine, Brijuni, Creotia, Smierzchalski R, Dynamic Aspect in Evolutionary Computation on Example of Avoiding Collision at Sea. 4' International Symp. on Methods and Models in Automation and Robotics, Miedzyzdroje, Poland Smierzchalski R, Evolutionary Guidance System for Ship in Collisions Situation at Sea. 3rd IFAC Conference Intelligent Autonomous Vehicle, Madrid, Spain Smierzchalski R, Michalewicz Z, Adaptive Modeling of a Ship Trajectory in Collision Situations. 2nd IEEE World Congress on Computational Intelligence, Alaska, USA Sudhendar H, Grabowski M, Evolution of Intelligent Shipboard Piloting Systems: A Distributed System for the St Lawrence Seaway. Journal of Navigation, Vol Trojanowski K, Michalewicz Z, Planning Path of Mobil Robot (in Polish). lst Conference Evolutionary Algorithms, Murzasichle, Poland Witt NA, Sutton R, Miller KM, Recent Technological Advances in the Control and Guidance of Ship. Journal of Navigation Vol. 47, Xiao J, Michalewicz Z, Zhang L, Evolutionary Planner/Navigator: Operator Performance and Self-Tuning. Proceeding IEEE Int. Conference of Evolutionary Computation, Nagoya, Japan 1996.