Type-2 fuzzy logic based linguistic pursuing strategy design with a real world application

The Interest in fuzzy logic has grown significantly in various working areas such as control system design, decision making, image processing, robotics, modelling and computing with words. The reason behind this huge interest is that fuzzy logic systems perform well against nonlinearities, uncertainties or unknown system dynamics since they imitate the human's way of thinking and act accordingly against not-well known or not clear enough situations. In this context, fuzzy logic systems have been implemented into various engineering applications where uncertainties and nonlinearities are high. In recent works, it has been shown that the performance of the conventional fuzzy logic systems, also known as the type-1 fuzzy logic systems, might be inadequate in defining the nonlinearities and uncertainties in some cases. Besides, it is seen that this insufficient performance of conventional fuzzy logic system moderately caused from the crisp membership grades of the implemented conventional or type-1 fuzzy sets. Thus, researchers have been proposed the type-2 fuzzy logic systems as the alternatives of type-1 fuzzy logic systems. It has been shown in several studies that type-2 fuzzy logic systems have the capability to handle or represent the uncertainties in a better way since they have an extra degree of freedom that is provided by the footprint of uncertainty. Type-2 fuzzy logic systems can be defined as the generalized versions of their type-1 counterparts. However, in handling of the type-2 fuzzy logic systems, an additional procedure is needed in type-2 fuzzy inference system that is defined as type reduction unlike their type-1 counterparts. The type reduction is applied to the antecedent type-2 membership functions of the fuzzy rules in order to reduce them into type-1 form before the defuzzification process. Type-2 fuzzy logic systems still have open problems since they have a complex internal structure and their high computational costs caused from the type reduction operation of type-2 fuzzy sets. Therefore, interval type-2 fuzzy logic systems, a special form of type-2 fuzzy logic systems, have been proposed to overcome this computational problem. Interval type-2 form of the fuzzy logic systems have becoming a dominating subject in the related fuzzy logic areas. In this context, it has been seen in several studies that especially interval type-2 fuzzy logic systems are widely used and employed since their capability to represent uncertainties in a better way and also their lower computational cost. In most of the applications of type-2 and interval type-2 fuzzy logic systems, the parameter footprint of uncertainty is usually handled as a design parameter and mostly it is tuned in order to decrease the effects of uncertainties and nonlinearities on the system performance. Therefore, there are also some studies have been performed in literature on how the size or shape of the footprint of uncertainty affects the interval type-2 fuzzy mapping. On the other hand, researchers have also worked on describing an interpretable relationship between the size of the footprint of uncertainty and the output of the interval type-2 fuzzy logic systems to use the advantages of the linguistic meaning of the interval type-2 fuzzy sets and fuzzy logic systems. In the light of these studies, interval type-2 fuzzy logic systems have become popular and widely employed to the real-world applications where unknowns, uncertainties and complexities are high such as control system design, computing with words, decision making and recently in computer and real-world games. Recently, games are gaining more and more attention among the researchers since they provide challenging, realistic and complex testbeds for computational intelligence and artificial intelligence structures and methods. In particular, pursuit-evasion game types have been commonly used in various studies as they can be defined as general problem of the many other robotic problems such as obstacle avoidance, leader-following and path-planning. The main goal of the pursuit-evasion games can be defined as; one or more pursuer tries to catch one or more evader in the probable shortest time while one or more evader tries to escape as much as possible. The various types of scenarios of the pursuit-evasion games are generally handled by the researchers who work on the area of mobile robotic. In the mobile robotic field, the pursuit-evasion games are mainly implemented to solve motion planning problems in complex, unknown and dynamic environments. In literature, the types of developed pursuit-evasion game scenarios have been shaped with respect to the limitation of the moving capabilities of the agents, number of the agents, the definition of the capture and structure of the game space. In order to solve this challenging pursuit-evasion game problem, different types of methods have been employed in literature such as dynamic programming, game theory and fuzzy logic theory. In this master thesis, we have proposed a type-2 fuzzy logic based novel approach in order to solve the pursuing problem of the real-world pursuit-evasion game; "Game of Spheros" with a new experimental setup that is constructed with spherical droids Sphero 2.0 and the BB-8. The game model has been implemented to a bounded game environment with the following specifications; the pursuer is adjusted to be faster than the evader, but at the same time to make it less maneuverable the maximum steering angle of the pursuer is restricted. In the constructed pursuit-evasion game scenario, the evader droid BB-8 is controlled by a human user while the pursuing droid Sphero 2.0 is controlled by the propose type-2 fuzzy logic based pursuing system. The proposed intelligent type-2 fuzzy logic based pursuing system is mainly composed of five components that are the vision based localization, error signal generator, control system, type-2 fuzzy strategy planner and type-1 fuzzy decision making mechanism. The vision based localization mechanism is established with a low cost webcam to localize the droids in the game environment. This feedback information is used by error signal generator to provide the necessary inputs to the type-2 fuzzy strategy planner and type-1 fuzzy decision making mechanism. Type-2 fuzzy strategy planner and type-1 fuzzy decision making mechanism are the key blocks of these intelligent pursuing system since the type-2 fuzzy strategy planner generates the reference trajectories to be followed by the pursuer and type-1 fuzzy decision making mechanism regulates the approaching behavior of the pursuer by regulating the footprint of uncertainty sizes of the type-2 fuzzy strategy planner. In the analysis of the internal structure of the type-2 fuzzy strategy planner, we have analytically derived and presented four novel type-2 fuzzy logic based pursuing strategies which are the aggressive right pursuing strategy, aggressive left pursuing strategy, smooth right pursuing strategy and smooth left pursuing strategy for the pursuit-evasion games through detailed theoretical analyses. Type-2 fuzzy strategy planner has been constructed with single input interval type-2 fuzzy logic systems and it creates pursuing trajectories to be followed by the pursuer with respect to the change of the size of the footprint of uncertainty or the height of the lower membership functions of the interval type-2 fuzzy sets. We can determine the pursuer's approaching behavior and approaching side according to the evader by regulating only one parameter besides generating pursuing trajectories with our proposed type-2 fuzzy strategy planner which can be defined as the superior part of the proposed structure. In other words, the result of this thesis study will show that it is possible to design pursuing strategies linguistically in terms of both the approaching behavior (Aggressive, Smooth) and approaching side (Left or Right) to the evader by simply tuning the footprint of uncertainty sizes of the interval type-2 fuzzy sets. We have also presented the type-1 fuzzy decision making mechanism to regulate type-2 pursuing strategy in an online manner as there is a need to change the pursuing strategy in an intelligent way. Decision making mechanism has been constructed with type-1 fuzzy logic systems based on the expert knowledge. Proposed fuzzy decision making mechanism can be also defined as a self-tuning mechanism for the type-2 fuzzy strategy planner since it regulates the footprint of uncertainty sizes of the antecedent type-2 fuzzy sets of the type-2 fuzzy strategy planner to give the chance of increasing the pursuing performance. The fuzzy decision mechanism tuned pursuing strategy is named as the intelligent pursuing strategy in this thesis. The outcomes of the thesis study will show that the superiority of the proposed intelligent pursuing strategy since fuzzy decision making mechanism provides the advantages of both aggressive and smooth pursuing strategies by regulating the footprint of uncertainty sizes of the type-2 fuzzy strategy planner in an online manner. Finally, in order to validate that the analyses on the linguistic relationships of the interval type-2 fuzzy sets of the footprint of uncertainty and also show that the performances of the proposed structure, we have performed real-world game experiments. Firstly, we will present several experimental results to validate that whether the proposed type-2 fuzzy strategy planner has an interpretable relationship between its footprint of uncertainty size and its output. Then, the pursuing performances of the proposed linguistic pursuing strategies will be also examined against a human user. Comparative experimental results of the type-2 fuzzy logic based pursuing strategies will be presented to show that resulting performances are satisfactory. It will be demonstrated that intelligent pursuing strategy, generated from the type-2 fuzzy strategy planner and fuzzy decision making mechanism structures, improved the pursuing performance as it has the capability to change the employed pursuing strategy in the dynamic pursuit-evasion game against a human controlled evader.