Neuro-fuzzy Control of a Robotic Arm

This paper first presents a discussion of the reasoning and method for combining neural networks and fuzzy logic. The problem of moving a robotic arm in the presence of an obstacle is discussed. Several neuro-fuzzy controllers are trained using sample data obtained from a human’s control of a robotic arm. Their performance is quantified and compared. It is shown that the definition of the fuzzy membership functions plays a significant role in the ability of the neuro-fuzzy controller to learn and generalize. Possible directions for future work are suggested. NEURO-FUZZY SYSTEMS Recently, the combination of neural networks and fuzzy logic has received attention. Neural networks bring into this union the ability to learn, but also require an excessive number of iterations for training of complex systems. Fuzzy logic offers a system model based on membership functions and a rule base, but require an explicit stating of the IF/THEN rules. Several methods for combining neural networks and fuzzy logic have been studied (Khan, 1993) (Lin and Song, 1994) (Nauck, et. al., 1993). In this paper, the authors implement the inference stage of a fuzzy system using a neural network (Challoo, et. al., 1994) (Keller, et. al., 1992). Figure 1 illustrates the system architecture for the described combination of neural networks and fuzzy logic. By replacing the rule base of a fuzzy system with a trainable neural network, complex input-output relationships can be achieved which can not be easily specified by Fuzzifier Neural Network Rule Base Defuzzifier Inputs Crisp Outputs Crisp membership values membership values Figure 1. A fuzzy system with neural network rule base W. Kelly, R. Challoo, et. al, “Neuro-fuzzy Control of a Robotic Arm”, Proceedings of the Artificial Neural Networks In Engineering Conference , St. Louis, MO, November 10-13, 1996, pp. 837-842. 838 IF/THEN rules. With fuzzification and defuzzification stages augmenting a neural network, significant improvements in the training time, in the ability to generalize, and in the ability to find minimizing weights can be realized. Furthermore, the fuzzy membership functions give the designer more control over the neural network inputs and outputs. THE ROBOTIC ARM PROBLEM For robots to become effectively used in a wide range of applications, they must gain the ability to work in unpredictable environments. This paper addresses the problem of planning the trajectory of a three-link robotic arm in the presence of an obstacle. The arm operates in two dimensions in an environment containing a randomly placed obstacle and goal. The starting position of the arm is arbitrary as well. For the purpose of designing the control system, the positions of the obstacle and goal and the joint angles of the arm are assumed to be available from position feedback sensors in the arm. The arm is modeled as a three-link planar manipulator, as shown in Figure 2. The model is strictly geometric. That is, the dynamics of moving a finite mass arm are not considered for the purpose of this study. The controller will determine a series of joint angles, Θ(t), that move the end effector from a given starting position (xs, ys) to a desired final position (xg, yg) without colliding with the obstacle at (xo, yo). Previous approaches to this problem using fuzzy logic have focused on choosing the joint angles of redundant manipulators given a desired path (Kim and Lee, 1993) (Xu, et. al., 1993) (Wang, et. al., 1994) or specifying criteria for choosing those joint angles using fuzzy rules (Palm, 1992). Unlike these approaches, this work uses a fuzzy controller that learns the strategy for moving the arm to the goal position without touching the obstacle. That strategy is learned by observing a human’s control of the arm. The goal must be assumed to lie within the possible reach of the end-effector and the obstacle must be assumed to lie outside the path of the first link. The problem can be summarized as follows: Given a robotic arm with: • the current joint angles, Θ(0), • an obstacle position, (xo, yo), and • a desired position, or goal, (xg, yg); Find a trajectory, Θ(t), such that: • the end-effector reaches the goal, • the arm does not touch the obstacle, and • the calculations can be performed in real-time with current hardware. W. Kelly, R. Challoo, et. al, “Neuro-fuzzy Control of a Robotic Arm”, Proceedings of the Artificial Neural Networks In Engineering Conference , St. Louis, MO, November 10-13, 1996, pp. 837-842. 839 STATE REPRESENTATION One of the primary considerations in the design of the neuro-fuzzy controller is the representation of the state of the system. The ability of the final neuro-fuzzy controller to generalize a solution from training data depends largely on the data representation scheme. The controller must be provided with the joint angles and the locations of the obstacle and goal. There are actually several ways to provide information about the locations of the goal and obstacle. Providing Cartesian or polar coordinates of the two objects would result in seven, independent inputs. This scheme, however, would require that the controller repeatedly learn the same strategy for similar configurations of the endeffector, goal and obstacle if that configuration happened to occur in a different Cartesian region. If, on the other hand, the location of the goal and obstacle are represented by their relative distance to the end-effector, then strategies can be generalized for similar configurations regardless of where they occur in Cartesian space. Table 1 and Table 2 list the inputs and outputs that were chosen to represent the system. NEURO-FUZZY SOLUTION As with most systems involving neural networks, training samples were required which demonstrated the desired input-output relationship. The samples were obtained by cycling through a series of goal and obstacle positions on a simulation of obstacle