The Spatial Semantic Hierarchy is a model of knowledge of large-scale space consisting of multiple interacting representations, both qualitative and quantitative. The SSH is inspired by the properties of the human cognitive map, and is intended to serve both as a model of the human cognitive map and as a method for robot exploration and map-building. The multiple levels of the SSH express states of partial knowledge, and thus enable the human or robotic agent to deal robustly with uncertainty during both learning and problem-solving. The control level represents useful patterns of sensorimotor interaction with the world in the form of trajectory-following and hill-climbing control laws leading to locally distinctive states. Local geometric maps in local frames of reference can be constructed at the control level to serve as observers for control laws in particular neighborhoods. The causal level abstracts continuous behavior among distinctive states into a discrete model ...

Applications of fuzzy logic in heuristic control have been highly successful, but which aspects of fuzzy logic are essential to its practical usefulness? This paper shows that an apparently reasonable version of fuzzy logic collapses mathematically to two-valued logic. Moreover, there are few if any published reports of expert systems in real-world use that reason about uncertainty using fuzzy logic. It appears that the limitations of fuzzy logic have not been detrimental in control applications because current fuzzy controllers are far simpler than other knowledge-based systems. In the future, the technical limitations of fuzzy logic can be expected to become important in practice, and work on fuzzy controllers will also encounter several problems of scale already known for other knowledge-based systems. 1

. Research in Qualitative Reasoning builds and uses discrete symbolic models of the continuous world. Inference methods such as qualitative simulation are grounded in the theory of ordinary differential equations. We argue here that cognitive mapping --- building and using symbolic models of the large-scale spatial environment --- is a highly appropriate domain for qualitative reasoning research. We describe the Spatial Semantic Hierarchy (SSH), a set of distinct representations for space, each with its own ontology, each with its own mathematical foundation, and each abstracted from the levels below it. At the control level, the robot and its environment are modeled as a continuous dynamical system, whose stable equilibrium points are abstracted to a discrete set of "distinctive states." Trajectories linking these states can be abstracted to actions, giving a discrete causal graph level of representation for the state space. Depending on the properties of the actions, th...

Abstract. Fuzzy control is a very successful way to transform the expert’s knowledge of the type “if the velocity is big and the distance from the object is small, hit the brakes and decelerate as fast as possible ” into an actual control. To apply this transformation one must: 1) choose fuzzy variables corresponding to words like “small”, “big”; 2) choose operations corresponding to “and ” and “or”; 3) choose a method that transforms the resulting fuzzy variable for a into a single value ā. The wrong choice can drastically affect the quality of the resulting control, so the problem of choosing the right procedure is very important. From mathematical viewpoint these choice problems correspond to non-linear optimization and are therefore extremely difficult. We develop a new mathematical formalism (based on group theory) that allows us to solve the problem of optimal choice and thus: 1) explain why the existing choices are really the best (in some situations); 2) explain a rather mysterious fact that the fuzzy control based on the experts’ knowledge is often better than the control by these same experts; 3) give choice recommendations for the cases when traditional choices do not work. Perspectives of space applications will be also discussed.

Fuzzy control is a methodology that transforms control rules (described by an expert in words of a natural language) into a precise control strategy. There exist several versions of this transformation. The main difference between these versions is in how they interpret logical connectives “and” and “or”, i.e., in other words, what reasoning method a version uses. Which of these versions should we choose? It turns out that on different stages of control, different reasoning methods lead to better control results. Therefore, a natural idea is not to fix a reasoning method once and forever, but to switch between different reasoning methods. In this chapter, we describe the optimal choice of the reasoning methods between which we switch.

We present a method for creating and validating a nonlinear controller by the composition of heterogeneous local control laws appropriate to different operating regions. Like fuzzy logic control, these methods apply even in the presence of incomplete knowledge of the structure of the system, the boundaries of the operating regions, or even the control action to take. Unlike fuzzy logic control, these methods can be analyzed by a combination of classical and qualitative methods. Each operating region of the system has a classical control law, which provides highresolution control and can be analyzed by classical methods. Operating regions are defined by fuzzy set membership functions. The global control law is the weighted average of the local control laws, where the weights are provided by the operating region membership functions. A heterogeneous control law can be analyzed, even in the presence of incomplete knowledge, by representing it as a qualitative differential equation and usi...

One of the main problems of interval computations is, given a function f(x 1 ; :::; x n ) and n intervals x 1 ; :::; x n , to compute the range y = f(x 1 ; :::; x n ). This problem is feasible for linear functions f , but for generic polynomials, it is known to be computationally intractable. Because of that, traditional interval techniques usually compute the enclosure of y, i.e., an interval that contains y. The closer this enclosure to y, the better. It is desirable to describe cases in which we can compute the optimal enclosure, i.e., the range itself.

This paper presents an evolutionary design method for fuzzy logic controllers, which is based on a self-organizing process that learns the appropriate relationship between control input and output. Our approach employs an evolution strategy that operates on vectors of real numbers which correspond to the gain factors in the conclusion part of fuzzy rules. An incremental learning scheme gradually expands the genome and thereby refines the fuzzy knowledge base that acquires additional fuzzy rules. The paper describes the hybrid architecture of a flight vehicle management system, which governs the operation of an autonomous model helicopter. The autopilot is composed of four modules that control the longitudinal and lateral motion, altitude and heading. The autopilot that constitutes the continuous regulation layer of the hybrid system is implemented by a set of fuzzy controllers. The evolutionary algorithm optimizes the fuzzy rule bases off-line. We compare two design approaches, learnin...

this paper, we prove that ab and a+b \Gamma ab are "in the average" the least sensitive &\Gamma and \Gammaoperations. This result is in good accordance with the experimental data according to which in many cases, these operations provide the best description of how experts actually think. We also show how this idea can be applied to other logical connectives (e.g., "not"), and to the choice of membership functions. Keywords: Fuzzy Logic; Average Sensitivity; &\Gamma and \GammaOperations. 1. Introduction Experts usually express their uncertainty by words of natural languages (like "for sure", "maybe", etc). However, in the majority of expert systems and intelligent control systems uncertainty of expert's statements is represented by a number from the interval [0,1]: t(A) = 1

Abstract—There is a broad range of diverse technologies under the generic topic of intelligent transportation systems (ITS) that holds the answer to many of the transportation problems. In this paper, one approach to ITS is presented. One of the most important research topics in this field is adaptive cruise control (ACC). The main features of this kind of controller are the adaptation of the speed of the car to a predefined one and the keeping of a safe gap between the controlled car and the preceding vehicle on the road. We present an ACC controller based on fuzzy logic, which assists the speed and distance vehicle control, offering driving strategies and actuation over the throttle of a car. The driving information is supplied by the car tachometer and a RTK differential GPS, and the actuation over the car is made through an electronic interface that simulates the electrical signal of the accelerator pedal directly to the onboard computer. This control is embedded in an automatic driving system installed in two testbed mass-produced cars instrumented for testing the work of these controllers in a real environment. The results obtained in these experiments show a very good performance of the gap controller, which is adaptable to all the speeds and safe gap selections. Index Terms—Autonomous vehicles, longitudinal control, intelligent vehicles, field experiments, fuzzy logic, adaptive cruise control (ACC), safe gap, Stop&Go, platoon driving, wireless communications, intelligent transportation systems (ITS). I.