An Introduction and Literature Review of Fuzzy Logic Applications for Robot Motion Planning
Abstract
This paper reviews fuzzy logic applications for robot motion planning. A short literature review is provided and three applications of fuzzy logic are considered: navigation and obstacle avoidance of a robotic vehicle in a 2D environment; a multilink industrial robot manipulator; and a robotic vehicle in a 3D environment. Scenarios are compared for their assignment of fuzzy sets, inference (rule base format and size), defuzzification technique, and the effectiveness and limitations of algorithms
INTRODUCTION
In the field of mobile robotics, the goal of autonomous robot operation is a topic of considerable research. Robots may frequently find themselves in environments for which a reliable map of obstacles and terrain is unavailable due to the dynamics of the environment, imprecise sensory data or simply a lack of prior knowledge of the environment [4]. In such situations, it may be necessary for a robot to recalculate its trajectory online. While an end-to-end motion plan for the robot in terms of gross motions over longer distances may remain valid, a response to a moving or unforeseen obstacle may force the robot to alter its path amid local obstacles while en route from the initial configuration to the final goal. As a possible means to meet such requirements, fuzzy logic based algorithms have found application in the area of robot motion planning because of their inherent ability to deal with imprecise inputs and their low computational complexity.
Fuzzy algorithms execute in three major stages: fuzzification, inference, and defuzzification. In the fuzzification stage, real world sensory inputs in a given universe of discourse are characterized on the closed interval [0, 1] according to their levels of membership in fuzzy sets. These sets are given names which express qualities of the input variable using easily understood linguistic terms. A membership function maps the value of the input variable to a degree of membership in each of the fuzzy sets. The fuzzified value then, represents the level of truth of each of these linguistic terms for a given input. For example, the angular direction of a near obstacle to a mobile robot might have a universe of discourse of -90° to 90° where 0° denotes the current heading of the robot. Figure 1 below shows a possible definition of fuzzy sets for how a “crisp” (real world) input angle θ might linguistically reflect the level to which the obstacle is left, in front, or right of the vehicle. Here, an angle of 30° represents a direction having fuzzified degrees membership in the set of angles to the right (“rightness”) of R and frontness of F. In this manner, fuzzy sets are capable of handling imprecise inputs. Should an input angle be sensed inaccurately, its levels of truth according to the linguistic terms may vary while its relative membership levels in the sets remain qualitatively the same. Sets are often defined to have the piecewise-linear shape shown so as to reduce the computational complexity of determining set membership [3]. Typical shapes include triangular, square, singleton, Gaussian or asymmetric types. Other variables commonly of interest in robotic applications include distance to an obstacle and speed of the robot with respect to an obstacle.
The inference stage applies the fuzzified input value to a rule base to determine a [still fuzzy] command output. The rule base contains the operational intelligence of the system.
A rule base must cover all permutations of input variables having degrees of truth in all possible linguistic terms. Hence the total number of rules N which must be represented in a rule base either by explicit statement or default action is given by in the relation:
(2) 1 m i i N p   
where m is the number of input variables (angle, speed, distance, etc.), and pi is the number of linguistic terms for the ith variable [5]. Multiple rules in the rule base may have their predicate conditions satisfied to greater or lesser degrees by fuzzified input variables. Such rules are said to have fired. In fact, where fuzzy sets are defined to overlap on their universe of discourse, at least two rules are guaranteed to fire for any input value. Each fired rule, then, possesses an adaptability to the associated output command through the fuzzy operation (AND, OR, sum, bounded sum, product, etc.) stated by the rule [2]. Commonly, the AND (min) operation is used as shown in the example above. In such a case, the minimum fuzzified value of the predicate conditions becomes the adaptability of that rule to its consequence.
The defuzzification stage extracts a crisp command output from inferences drawn from fired rules. Techniques for defuzzification generally involve some analysis of the regions created by cutting the output fuzzy sets using adaptabilities from each fired rule. An example of such a region is given by Figure 2. Common methods for this operation include taking the centroid of largest area (CLA), and mean of maximum value (MOM). Numerous other approaches exist which are not considered here.
This paper discusses three selected applications of fuzzy logic based algorithms to robot motion control and compares/contrasts their approaches. These applications include robotic vehicle navigation in a 2D environment, multilink robot manipulator guidance, and aerial robotic vehicle navigation in a 3D environment. Section 0 includes a concise summary of the articles which present each of these applications. Section 0 includes analysis of the approaches for their relative strengths and weaknesses.
LITERATURE REVIEW OF FUZZY LOGIC APPLICATIONS
Three examples of recent research are reviewed wherein methods are discussed for solutions to issues associated with robots autonomous robot navigation in the presence of incomplete or changing knowledge of their environments. Each of these examples employs a fuzzy logic based algorithm which allows the robot to make online decisions about its local trajectory without recalculation of its end-to-end motion plan.
Mobile Robot Navigation in a 2D Environment
Yang, Maollem and Patel [3] propose an augmentation to previous applications of fuzzy logic to 2D robot motion planning. All figures, equations and algorithm details in this section are attributed to this work unless otherwise stated. Prior work in this area focused on short range reactive control. That is, robots were navigated by simply reacting to near obstacles upon detection while taking into account a global goal direction. While such algorithms have frequently proven effective, they often encounter situations in which the goal configuration becomes unreachable by the robot despite the availability of a traversable path. More commonly, reactive fuzzy navigation may suffer from “shortsighted” behavior wherein the angle to the final goal influences all steering decisions in unison with local sensor data. Situations then arise in which short range sensors may not detect obstacles between the current configuration of the robot and the goal. In these cases, a path may be selected that is less desirable than others available. Figure 3 compares the results of shortsighted behavior to an end-to-end path plan. Through purely reactive short-range fuzzy control, the robot attempts to move in the direction of the goal at point B when obstacle 2 is still out of its perceptive range. The undesirable path ABCDEG is the result. Clearly, with the benefit of long-range planning, path AJKG would be seen as more desirable.

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