Information Sciences 145 (2002) 113–126 www.elsevier.com/locate/ins
Generation of efficient adjustment strategies for a fuzzy-neuro force controller using genetic algorithms – application to robot force control in an unknown environment Kazuo Kiguchi a
a,*
, Keigo Watanabe a, Toshio Fukuda
b
Department of Advanced Systems Control Engineering, Saga University, 1 Honjomachi, Saga-shi, Saga 840-8502, Japan b Center of Cooperative Research in Advanced Science and Technology, Nagoya University, 1 Furo-cho, Chikusa-ku, Nagoya 464-3603, Japan Received 4 July 2001; received in revised form 8 October 2001; accepted 28 November 2001
Abstract This paper presents an effective generation method of adjustment strategies for a fuzzy-neuro force controller (FNFC) of a robot manipulator in an unknown environment. In this method, strategies to adjust the FNFC in accordance with the environment dynamics are automatically generated in off-line manner using genetic algorithms (GA). The generated strategies are stored in a neural network and used for adjusting the FNFC in on-line. Therefore, the FNFC is automatically adjusted in accordance with the unknown dynamics of an environment using the generated strategies which are stored in the neural network. Fuzzy fitness evaluation method is proposed for the effective evolution of the neural network in the GA process. The effectiveness of the generated adjustment strategies of the FNFC has been evaluated by computer simulation with a 3DOF robot manipulator model. Ó 2002 Elsevier Science Inc. All rights reserved. Keywords: Robot manipulator; Force control; Unknown environment; Soft computing
*
Corresponding author. Tel.: +81-952-28-8702; fax: +81-952-28-8587. E-mail address:
[email protected] (K. Kiguchi).
0020-0255/02/$ - see front matter Ó 2002 Elsevier Science Inc. All rights reserved. PII: S 0 0 2 0 - 0 2 5 5 ( 0 2 ) 0 0 2 2 6 - 8
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1. Introduction Force control is one of the most important and fundamental tasks of robot manipulators in order to carry out sophisticated tasks. It has not been realized for practical use, however, since the dynamics of the environment affects the dynamics of the whole system, although it has been studied for many years [1– 4]. One of the main problems of force control is the difficulty in obtaining the dynamic properties of every environment. In the case when the dynamics of an environment is unknown or uncertain, a robot controller has to adapt itself to the dynamics of the environment. Furthermore, since the desired force is often given as step signals, fast adaptation is expected to avoid accidental damage of both the robot manipulator and the environment. Recently, soft computing techniques (fuzzy reasoning, neural networks, and genetic algorithms (GA)) are playing important roles in robotics. They have been applied for robot force control in unknown environments [3–16]. In the case when dynamic properties of the environment is unknown, i.e., when material properties of the environment is unknown, the robot force controller has to compensate for unknown dynamics of the environment by adaptation or iterative learning. Adaptive type neuro force controllers [5–9] are effective force controllers for unknown environment. Tokita et al. [5] applied off-line trained neural networks to adjust the gains of PID controller according to the hardness of the environment. This type of neuro force controller is known as an indirect type force controller. Yabuta and Yamada [6] introduced a direct type adaptive neuro force controller, in which a neural network is directly used as a controller, for a 1DOF robot. Kiguchi and Necsulescu [7] applied this type of adaptive neuro controller for hybrid position/force control of multi-DOF robot manipulator in Cartesian coordinate system. In these methods, uncertain/ unknown dynamics of the robot and the environment, modeling error, friction, and external disturbances can be compensated for by the effect of neural networks. Recently, in order to improve the ability of adaptation to unknown environment, visco-elastic neurons (damping neurons) which has visco-elastic characteristics in themselves were proposed and applied to this type of neuro force controller [8]. Jung and Hsia [9] proposed an adaptive neuro controller based on torque-based impedance control and position-based impedance control. In their torque-based method, the output of the neural network is added to the output of impedance controller in order to compensate for uncertain/unknown dynamics of the robot and the environment. In the position-based method, the output of the neural networks is used to modify the reference trajectory. Disadvantage of these adaptive neuro force controllers is possibility of undesired oscillation or unexpected overdamped/underdamped responses. Undesired oscillation or unexpected overdamped/underdamped responses might occur until the controller adapts to the environment dynamics. Neural networks are powerful tools not only for adaptation, but also for
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iterative learning. Cohen and Flash [10] adjusted impedance parameters using the neural networks that are obtained by iterative learning to represent the stiffness and viscosity matrices. Tsuji et al. [11] extended this method to regulate the desired impedance through learning of neural networks. In their method, the neural networks for position and velocity control are trained using iterative learning during free motion, and then the neural network for force control is trained during contact motion to realize a smooth transition from free to contact motion. However, these methods are applicable only when iterative learning is allowed before practical operation. It is known that a fuzzy-neuro force controller (FNFC), a combination of a fuzzy force controller and a neuro force controller, is one of the most effective controllers for hybrid position/force control in unknown environments [12– 14,16]. Human knowledge can be reflected in control rules and learning/adaptation ability can be obtained by applying the FNFC. The FNFC is the same as the trained neuro force controller using human linguistic control rules which are obtained through experience as teaching data, and does not require actual prelearning. When the dynamic properties of the unknown environment are extremely different from the initially estimated ones, however, undesired oscillation or unexpected overdamped/underdamped responses might occur until the controller adapts to the environment dynamics even with the FNFC. In order to cope with this problem, we have proposed the on-line controller adjustment methods, which adjust the controller inputs immediately by multiplying certain amount of coefficients in accordance with the dynamics of the environment [12,13]. This method is very effective for the robot controller to deal with unknown environments using the limited number of control rules, since it is impossible to prepare certain control rules for every environment. Actually, this method seems similar to what human does. Human being does not have every control rules for every situation, but moderately adjusts the existing control rules in accordance with the situation. Therefore, it is important to incorporate this human strategy into the control law of the robot manipulator. However, there is difficulty in obtaining the effective adjustment strategy of the control rules practically. This paper presents the generation method of the adjustment strategy of the FNFC. The generated adjustment strategy is stored in a neural network and used for adjustment of the FNFC in on-line manner in accordance with the environment dynamics. In the proposed method, the force control rules are immediately adjusted based on the strategy stored in the neural network, which is evolved by GA [17], according to the properties of the environment. In the other words, the human-like adjustment strategy of the FNFC is automatically generated by GA in order to make the FNFC immediately adapt to the environment. Once the FNFC is roughly adjusted in accordance with the environment dynamics, uncertain/unknown dynamics of the robot and the environment, modeling error, friction, and external disturbances can be compensated for by the effect of its own adaptation/learning ability.
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In the evaluation process in GA, the adjustment strategy (individual) which results in the least accumulated control error in every environment is usually the best strategy (individual). In the case of force control, however, overshooting error is much worse than undershooting error, since the overshooting error might cause damage of the robot manipulator or the environment. Consequently, the adjustment strategy of the FNFC has to be designed to avoid the overshooting. In order to generate the effective adjustment strategy of the FNFC by GA, fuzzy fitness evaluation method is proposed in this paper. The effectiveness of the generated adjustment strategies of the FNFC has been evaluated by computer simulation with a 3DOF planar robot manipulator model.
2. Robot manipulators The dynamic properties of environments have to be known in order to control contact force with conventional control techniques since the dynamics of the environment affects the dynamics of the whole system. The dynamic equation of a 3DOF planar robot manipulator (see Fig. 1) is written by MðqÞ€ q þ hðq; q_ Þ þ Fjc sgnðq_ Þ ¼ s J T f ;
ð1Þ
where M is inertia matrix, h denotes Coriolis and centrifugal components, Fjc is Coulomb friction of the robot manipulator joint, s is output torque, J is Jacobian, f is the applied force to the environment, and q is an angular vector. The acceleration of the end-effector of the robot manipulator in the Cartesian coordinate system is written as: €x ¼ J € q þ J_ q_ ;
ð2Þ
where x is a position vector in the Cartesian coordinate system.
Fig. 1. 3DOF planar robot manipulator.
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Fig. 2. Block-diagram of the system.
Using the selection matrix S, which selects the direction for force control and that for position control, and the Eqs. (1) and (2), the equation of the hybrid control is written as: s ¼ MðqÞJ 1 ½ðI SÞux J_ q_ þ hðq; q_ Þ þ Fjc sgnðq_ Þ þ J T fd þ J T Suf ; ð3Þ where up is the position control command and uf is the force control command. In this equation, however, the dynamics of the environment is not taken into account. In the case when the property of the environment is softer than that of initially estimated environment, time delay tend to occur. In the case when the property of the environment is harder than that of initially estimated environment, undesired oscillation and overshooting tend to occur. Consequently, the dynamics of the environment must be compensated for by adjusting the force control command uf . The block-diagram of the system is depicted in Fig. 2. In this study, the force control command uf is the output of the proposed FNFC.
3. Fuzzy-neuro force controllers (FNFCs) In order to realize precise force control with a robot manipulator in an environment whose material properties are unknown or uncertain, the controller must have the adaptation ability to the environment dynamics. A FNFC, a combination of a fuzzy force controller and a neuro force controller, is one of the most effective controllers for force control in an unknown environment. The FNFC is designed based on human expert linguistic control rules and adjusted on-line to adapt to an unknown environment and compensate for modeling errors, friction, and external disturbances at the task level. As far as the dynamic property of the unknown environment is similar to that of initially estimated one, the desired force can be generated without problem by the FNFC.
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Fig. 3. Architecture of the fuzzy-neuro force controller.
In this study, the FNFC consists of five layers (Input Layer, Fuzzifier Layer, Rule Layer, Defuzzifier Layer, and Output Layer) expressing the fuzzy IFTHENPcontrol process. The architecture of the FNFC is depicted in Fig. 3 Here, means sum of the inputs and P means the multiplication of the inputs to each neuron. Input variables to the controller are the error between the desired force and the measured force and the momentum of the robot manipulator in the direction of force control. Five kinds of fuzzy linguistic variables (PB: Positive Big, PS: Positive Small, ZO: Zero, NS: Negative Small, and NB: Negative Big) are defined for each input variable, and 17 fuzzy IF-THEN control rules are prepared based on human expert linguistic control rules. The degree of fitness to each fuzzy linguistic variable is calculated in the fuzzifier layer using the sigmoidal function, which is written as Eq. (4), and the Gaussian function, which is written as Eq. (6). 1 ; 1 þ eus
ð4Þ
us ðxÞ ¼ wo þ wi x;
ð5Þ
fs ðus Þ ¼
2
fG ðuG Þ ¼ euG ; uG ðxÞ ¼
wo þ x ; wi
where wo is a threshold value and wi is a weight.
ð6Þ ð7Þ
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The output from the controller is the force command for the robot manipulator in the task space. The adaptation/learning (adjustment of every weight value) of the FNFC is carried out using the back-propagation learning algorithm at every sampling period. In this study, the input variables of the FNFC are also adjusted in on-line manner based on the generated adjustment strategy.
4. Adjustment of FNFCs In this study, the force control rules are adjusted by the generated adjustment strategy, which is stored in the neural network, according to the properties of an environment. We have proposed the on-line controller adjustment methods [12,13] in which the controller input scale coefficients are adjusted in accordance with the relation between the deformation of the environment and the reaction force in order to make the controller adapt immediately to the environment. In this study, the adjustment of the FNFC is carried out by multiplying the input variable by the scale coefficients (KE and KMO ) generated by the input adjustment neural network (IANN). This operation makes the shape of membership function change as shown in Fig. 4. Consequently, the control rules can be adjusted by this operation. In this study, the adjustment strategy is generated using GA and stored in the IANN. The architecture of the IANN is depicted in Fig. 5. The IANN consists of three layers. Surface displacement distance, displacement velocity, displacement acceleration of the environment, and reaction force from the environment are used for input information of the IANN. The IANN outputs the scale coefficients (KE and KMO ) for the FNFC input variables. Thus, the adjustment strategy of the FNFC is designed to output appropriate scale coefficients for the FNFC input variables based on the surface displacement distance, displacement velocity, displacement acceleration of the environment, and the reaction force from the environment. The scale coefficients for each input variable is generated according to the adjustment strategy stored in the IANN. The GA is applied to design the optimal adjustment strategy of the FNFC. Here, design of the adjustment strategy means design of weights in the IANN. In our previous study [12,13], the adjustment strategy of the FNFC is designed by human operators based on their experience and knowledge. However, there was difficulty in finding the proper adjustment strategy practically. In this study, the adjustment strategy of the FNFC is automatically generated by GA. Once the FNFC is roughly adjusted in accordance with the environment dynamics based on the generated adjustment strategy, uncertain/unknown dynamics of the robot and the environment, modeling error, friction, and external disturbances can be compensated for by the effect of its own adaptation/learning ability.
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Fig. 4. Change of membership function.
Fig. 5. Architecture of the input adjustment neural network.
5. Genetic algorithms with fuzzy fitness evaluation The GA has been applied to obtain the adjustment strategy of the FNFC automatically in the IANN. The operating process of GA is depicted in Fig. 6.
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Fig. 6. Operating process of GA.
Each individual represents the weights of the IANN (i.e., the FNFC adjustment strategy) in this process. Therefore, the best individual means the weights of the IANN that generates the best input scale coefficients (i.e., the best adjustment strategy). Ten individuals are prepared in one generation in this study. Force control simulation in five kinds of environments is performed in the evaluation process of GA. The accumulated force control error in all prepared environments in the simulation indicates the fitness of the IANN. Therefore, the IANN which results in the least accumulated force control error in all prepared environments is the most optimal one in this method. In this evaluation process, the force control simulation is performed in one of the prepared environments, then it is performed in another prepared environment until it is performed in all prepared environments. The adaptation of the FNFCs to the unknown dynamics of each environment is carried out with the back-propagation learning algorithm at each sampling period during each simulation. The evaluation function for the controller adaptation is written as:
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1 Ea ¼ ðfd f Þ2 ; 2
ð8Þ
where fd is the desired force and f is the generated force. In the case of force control, overshooting error is much worse than undershooting error. The overshooting error might cause damage of the robot manipulator or the environment. In order to avoid undesired overshooting, the fuzzy evaluation is proposed in this study. In this method, fuzzy reasoning has been applied to evaluate a degree of influence of each force error. Consequently, a much larger weight is given to the overshooting error and a smaller weight is given when the measured force is not reached to the desired force yet and the error is decreasing. The equation of the fitness function is written as: EGP ¼ WGP jfd f j;
ð9Þ
where WGP is the fuzzy controlled weight for error. The best three individuals in the population are selected as offspring in the next generation without any genetic operation. The other offspring in the next generation are generated with the crossover operation and the mutation operation. In this study, the roulette wheel selection method is applied for selection of individuals.
6. Simulation The force control simulation has been performed with a 3DOF planar robot manipulator model (see Fig. 1) using the generated IANN in five kinds of environments which are different from those used in force control simulation process in GA. The modeling error and joint friction of the robot manipulator is taken into account in the simulation. The desired force is the combination of step signals, which change between 20 and 10 N every 2 s. The sampling time in the simulation is set to be 1 ms. The force control simulation without the IANN has also been performed for comparison. The dynamics model of environments used in the simulation is written as: f ¼ Me€xe þ Be x_ e þ Ke xe ;
ð10Þ
where xe is the displacement of the environment surface, and Me ; Be , and Ke denote the coefficients of equivalent mass, damping, and spring of the environment, respectively. The properties of the environments used in the simulation are shown in Table 1. The initial IF-THEN control rules of the FNFC are designed to be the best performance in the medium environment The optimal adjustment strategy of the FNFC (the optimal weights of the IANN) is generated through the GA operation process explained in the
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Table 1 Property of the prepared environments Environment Environment Environment Environment Environment
1 2 3 4 5
Mass (N sec2 =m)
Damping (N sec/m)
Spring (N/m)
0.002 0.02 0.08 0.12 1.2
1.2 12 80 100 400
8:0 103 8:0 104 1:5 105 4:0 105 1:8 106
Section 5. The mutation rate in the GA reproduction process is 1/80. The adjustment strategy (individual in GA) has been evolved 1000 generation. The simulation results with and without the IANN in the softest, medium, and hardest environment are shown in Figs. 7–9, respectively. Figs. 7 and 8 show the effectiveness of adaptation/learning ability of the FNFC in the softest and medium environment, although a little time delay occurred in the softest environment in simulation without the IANN. When the dynamic properties of the environment are extremely different from the initially estimated ones, however, undesired oscillation and unexpected overshooting occur until the controller adapts to the environment dynamics even with the FNFC as shown in Fig. 9. However, if the FNFC is moderately and immediately adjusted based on the adjustment strategy according to the environment dynamics, the undesired overshooting and the undesired oscillation are eliminated as shown in
Fig. 7. Force control simulation results in the softest environment.
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Fig. 8. Force control simulation results in the medium environment.
Fig. 9. Force control simulation results in the hardest environment.
Fig. 9. These simulation results show the effectiveness of the generated adjustment strategy of the FNFC.
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7. Conclusions The generation method of the human-like adjustment strategy of FNFC has been proposed. In this method, the force control rules are automatically adjusted in on-line manner using the neural network, which is evolved off-line by GA, according to the properties of an environment. The fuzzy fitness evaluation method has been also proposed for effective evolution of the neural network, which stores the adjustment strategy of the FNFC, in the GA process. The effectiveness of the proposed force control method has been verified by simulation with a 3DOF planar robot manipulator model.
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