Rapid Evaluation of Reconfigurable Robots Anatomies Using Computational Intelligence

Rapid Evaluation of Reconfigurable Robots Anatomies Using Computational Intelligence Harry Valsamos1, Vassilis Moulianitis2, and Nikos Aspragathos1 1 Mechanical and Aeronautics Engineering Dept. University of Patras, 26500, Rio, Achaia, Greece 2 Dept. of Product and Systems Design Engineering, University of Aegean, 84100, Ermoupolis, Syros, Greece balsamos@mech.upatras.gr, moulianitis@syros.aegean.gr, asprag@mevh.upatras.gr Abstract. Designing a reconfigurable manufacturing robotic workcell is a complex and resource demanding procedure. In this work a multi criteria index is introduced, allowing the designer to evaluate the various anatomies achieved by a reconfigurable manipulator, and to define the area in the manipulator’s configuration space where a task can be accomplished with good performance under the selected performance measure. An adaptive neuro-fuzzy inference system is trained, in order to rapidly produce the index value for arbitrary anatomies achieved by the manipulator. The system is tested using a case study reconfigurable manipulator, and the derived results determined by the system after its training are presented and compared to the actual index value for calculated for the relevant anatomy. Keywords: Reconfigurable robots, ANFIS, Anatomy selection. 1 Introduction The design of robotic manufacturing workcells has been under constant research due to the rapidly increasing usage of robotic systems in the manufacturing industry. In the design stage, the engineer has to address several key issues such as the matching of a robot type to a given task, the optimal positioning of the task in the robot’s workspace for the robot to present the best performance, the sequencing of the task(s) to achieve shorter cycle time etc. These considerations are task oriented, resulting in the design of a single purpose robotic workcell with optimal performance. Several approaches and methods are proposed in the relative literature addressing the problems of robotic workcell design [1,2,3,4]. In the last decades, as the reconfiguration paradigm was identified as a key feature for the enhancement of the manufacturing productivity [5] by allowing the rapid adaptation, reconfigurable robots have increasingly attracted the interest of researchers [6,7]. The design of a robotic workcell including reconfigurable robots is a far more challenging task than the design of the corresponding one composed of fixed anatomy R. Setchi et al. (Eds.): KES 2010, Part II, LNAI 6277, pp. 341–350, 2010. © Springer-Verlag Berlin Heidelberg 2010 342 H. Valsamos, V. Moulianitis, and N. Aspragathos robots. Firstly, the design under the assumption that a single task or a variety of similar ones should be addressed by the workcell is not applicable since the main advantage of a reconfigurable system is its ability to address a wider range of different tasks by altering its anatomy and software. Therefore, the first and foremost problem to be considered is the determination of the optimal anatomy for a given task. This particular problem was addressed in the literature and several interesting methods were proposed [8,11,12]. For both the optimal anatomy and task planning, these procedures are extremely time consuming and require significant amounts of computational power, due the sharp increase in the search space. This happens because for each emerging anatomy, the manipulator presents a different workspace both in terms of volume and shape but most importantly in terms of the variation of robot performance. An engineering tool is required to evaluate an emerging anatomy in terms of performance for the particular task, such as manipulability measure, MVR etc, and then the determination of the configuration space area where the performance of the manipulator is “good”. Since the evaluation of the anatomy is time consuming an adaptive neuro-fuzzy inference system (ANFIS) is trained towards the rapid calculation of the performance measure. ANFIS has been used in various applications including engineering [8], medicine [9], economics etc. In the present paper a robotic performance measure is proposed allowing the evaluation of emerging anatomies of a reconfigurable manipulator based on manipulability. A neuro-fuzzy inference system is presented, allowing the rapid determination of the proposed measure for each emerging anatomy, as a means to its rapid calculation, allowing its rapid implementation to optimal design processes. An example for a six DOF reconfigurable robot manipulator is presented showing the advantages of this procedure and concluding remarks are closing this paper. 2 The Proposed Global Kinematic Measure A local robotic kinematic measure y depends on the particular manipulator configuration θ, given by a non linear function: y = f (θ) . Where θ = [θ , θ , ..., θ 1 2 ] T n (1) is a vector of joint variables. Since most kinematic measures are local, efforts have been made to derive global indices characterizing the manipulators performance in the whole volume of its workspace [13] or for a given task [14,15]. Such measures are very commonly used in the relative literature presenting methods and tools for the optimal design and planning of manipulator tasks. The procedure usually met in such optimization problems for fixed anatomy robotic systems today requires the determination of an area in the manipulator’s workspace where if a task is placed the robot shows the best possible performance [16]. Typically this is achieved by computing a global index in terms that characterize the manipulator’s performance for the given task, requiring the subsequent recalculation of the index for a different task. Such a procedure is time and computational resources demanding. Rapid Evaluation of Reconfigurable Robots Anatomies 343 The design and operation of reconfigurable robots present a far greater challenge. Their changeable anatomy results in the different workspaces for a given reconfigurable structure presenting different performance behavior in each one. For a reconfigurable robot, the variation of its anatomy has to be taken into account in the formulation of the measure function, since the m anatomical parameters θ = [θ , ..., θ p p1 ] T pm directly affect its value; therefore the measure is given as: y = f (θ p , θ) . (2) For each anatomy denoted by θp, the determined values of y create a hyper-surface in the n-dimensional configuration space. Figure 1 represents the curve that the values of y represent in the configuration space for a system of 1 d.o.f. Fig. 1. The curve constructed by the values of θ for a 1 d.o.f. mechanism In order to derive the introduced global measure for evaluating the current anatomy θp of the manipulator, the following indices are defined, as illustrated in fig. 1: • The overall mean value of the measure achieved by the robot in its configuration space for the current anatomy, y • The mean value of the m highest values achieved by the robot in its configuration space, ymax , given by: (3) m ymax = ∑y i =1 i max . m 344 H. Valsamos, V. Moulianitis, and N. Aspragathos Where the number of m is determined by the designer and the highest values are determined by simply sorting all available values of y in the configuration space • The distance δ ymax between y and ymax , is given by: δ ymax = ymax − y . • from (4) The factor δ y is the distance of the highest value of y recorded ymax These three indexes can be used to structure a multi criteria measure to evaluate the behavior of the current anatomy of the robot in its configuration space for the selected measure y. The overall mean value provides the starting point of the anatomy’s overall performance. A good anatomy should have a higher value than others achieved by the reconfigurable manipulator. The distance δ ymax provides an insight of the configuration space area where the current anatomy will present a “good” performance if the task is placed within. The largest the area, the bigger the number of configurations contained therein meaning that the anatomy presents larger areas in its workspace where it can perform tasks with good performance. However, there is always the danger that the anatomy may present a few very high values while the others are closer to y . This could cause the value of δ ymax to become rather high, but the number of configurations contained within it to be rather low, due to the sharp increase the extremely high values cause to ymax . In order to amend this situation from such an anatomy a high evaluation score, a limiting factor is introduced. A low value of this index implies that the highest values appear in a more balanced way around ymax , which in turn implies that the area denoted by δ ymax , contains a larger number of configurations, while a high value implies the opposite. The proposed measure is therefore structured by y , δ ymax and δ y . A “good” anatomy is one that achieved high values for the first tow criteria and a low value for the last one, in comparison to other anatomies achieved by the reconfigurable system. 3 The ANFIS System for the Rapid Calculation of the Measure 3.1 Score Calculation In order to take into account the interaction among the three criteria and to favor the anatomies that present the above requirements the discrete Choquet integral [17] is used as the measurement of score which is a generalization of the weighted i arithmetic mean [17]. Assuming an anatomy θ p with a profile of criteria i C i = { x1i , x2i , x3i } = { y i , δ ymax , δ y i } the Choquet integral is defined as: Rapid Evaluation of Reconfigurable Robots Anatomies ( ) ( ) Cu ( θ p ) := ∑ x ij ⎡u A ( C j ) − u A ( C j +1 ) ⎤ . ⎣ ⎦ j =1 n 345 (5) u ∈ FC , FC denotes the set of all fuzzy measures on C which is the set of the three criteria, and u is a monotonic set function on C defined as: where, u : 2 C → [0,1] with u (∅ ) = 0 ( ⋅) and u (C ) = 1 . indicates a permutation of C which is the set of criteria such that A ( C j ) = {C j ,..., Cn } , A ( Cn +1 ) = ∅ . (6) x j ≤ ... ≤ xn , Since there are three criteria six (6) fuzzy measures must be defined. The order of the criteria presented in this paper shows the importance of them. So, u ({C1} ) = u ({ y } ) has the highest value of the fuzzy measures that correspond to the subsets with cardinality one. The fuzzy measures of these subsets must satisfy the following: u ({C1} ) < u ({C2 } ) < u ({C3 } ) In order to favor the anatomies that present high values for (7) y and δ ymax and low value for δ y the fuzzy measures that correspond to the subsets with cardinality two must satisfy the following: u ({C1} ) + u ({C3 } ) < u ({C1 , C3 } ) (8) u ({C1} ) + u ({C2 } ) > u ({C1 , C2 } ) u ({C2 } ) + u ({C3 } ) < u ({C2 , C3 } ) In addition, all fuzzy measures must fulfill the following constraints: ( ) ∀ i, j = 1, 2,3 and i ≠ j 0 < u ({C } ) < u ({C , C } ) < 1 0 < u ({Ci } ) < u {Ci , C j } < 1 j i (9) j So far, the complexity of the procedure to find the best anatomy is increased and is time consuming. In order to lower the time of this procedure an adaptive neuro-fuzzy inference system is trained to produce the score rapidly according to the pseudojoints angles. 3.2 System Training The proposed approach uses a set of k random anatomies θ p and mj (j=1…k) random configurations θ for the jth anatomy in order to produce training data set for an adaptive 346 H. Valsamos, V. Moulianitis, and N. Aspragathos neuro-fuzzy inference system (FIS). The Sugeno-type system has as inputs the anatomical parameters θ p that postulate the anatomy and rapidly derives the index of the current anatomy. Every input of the FIS system has three triangular fuzzy sets defined nθ p in [-π/2, π/2] while the outputs ( 3 ,where nθ p is the number of anatomical parame- ters) of the system are constant numbers. In fig. 3 the mean error for a hundred epochs for training a system using 4096 samples of anatomies and 200 random samples of configurations for each anatomy. Set of random configurations θ Index calculation ( Cu y ( θ p , θ ) Set of random anatomies θ p New Index Cu ( θ p new ) Training Data ( )⎤⎦ set ⎡θ p , Cu θ p ) ⎣ New anatomy ANFIS θp new Fig. 2. Training Data Set derivation and fuzzy inference system generation 0.15 0.14 Error 0.13 0.12 0.11 0.1 0.09 0 20 40 60 80 100 Epochs 120 140 160 180 Fig. 3. Training error for two hundred epochs 200 Rapid Evaluation of Reconfigurable Robots Anatomies 347 4 Case Study In order to validate the correct operation of the ANFIS for the rapid determination of the measure for emerging anatomies achieved by a reconfigurable manipulator, an arbitrary 6 d.o.f. reconfigurable robot was structured using three active joints, rigid links, six pseudo joints and a spherical joint, representing the usual structure of most industrial manipulators today where the axes of rotation of the last three joints intersect and a given point. Such an arrangement is favored due to the fact that an analytical solution to the inverse kinematics can be obtained. The reference manipulator is illustrated in fig. 4. Fig. 4. The case study 6 d.o.f. reconfigurable manipulator The robot’s reconfiguration to a new anatomy is achieved by the resetting of the pseudo joints to a new angle. Pseudo joints [18,19] are passive connector modules that when placed in a modular reconfigurable robot’s lattice allow the rapid reconfiguration of its anatomy to a new one, without dismantling it. They allow the manipulator to achieve anatomies that are currently not favored in robotic design, i.e. presenting angles formed by consecutive joint axes different to the standard 00 or 900 of current fixed anatomy robot manipulators. The angle of the pseudo joints for this work varies within the range of [-900,+900]. The particular set up of the robots structure, i.e. the sequence and orientation of pseudo joints, links and active joints was chosen so that the manipulator would be able to achieve a wide range of different anatomies which would include both anatomies that are “in line” with current practice in manipulator design as well as anatomies that are not favored by current practice. The kinematic measure selected for this case study is the well known Yoshikawa’s manipulability index, given by: w (θ p , θ) = J (θ p , θ) ⋅ J T (θ , θ) p (10) 348 H. Valsamos, V. Moulianitis, and N. Aspragathos Where, θp is the vector whose elements are the pseudo joints setting representing the current anatomy of the reconfigurable system and θ is the vector whose elements are the joint coordinates for the current configuration (posture) of the robot as its end effector reaches a point in its workspace. Yoshikawa proposed the well known manipulability index as a measure of the ability of a manipulator to move its end effector in its workspace in terms of speed and also as a measure of how far the current position of the end effector lies from a singular configuration of the robot [20]. In order to train the system 2000 random samples of anatomies and 200 random samples of configurations per anatomy were derived. Using the 200 configurations the w , δ wmax (in a window of the 10 highest values) and δ wmax values is calculated for every anatomy providing the training sets. In order to calculate the score according to formula (5) for every anatomy the fuzzy measures are defined according to formulas (7), (8), (9) and are shown in Table 1. Using these training sets the adaptive neuro-fuzzy inference system is trained and tested using 30 random samples. Table 2, presents the actual training data. The results are shown in fig 5. Table 1. Definition of the fuzzy measures for the case study Set {C1} {C2 } {C3 } {C1 , C2 } {C1 , C3} {C2 , C3 } Fuzzy Measure 0.4 0.35 0.3 0.7 0.8 0.75 Table 2. Actual training data. (Pseudo joint settings (anatomy) in degrees) Θp1 Θp2 Θp3 Θp4 Θp5 Θp6 90 90 90 30 30 30 30 90 90 90 30 90 30 90 30 90 30 90 90 90 90 90 90 90 30 30 30 90 90 30 30 30 90 90 30 30 90 30 30 90 90 30 30 90 90 90 90 90 90 90 90 90 90 90 Index value 0.1144 0.2033 1.4880 0.8455 0.3916 0.1415 0.5211 0.6054 0.7904 Rapid Evaluation of Reconfigurable Robots Anatomies 349 3 Trained Results Calculated Results Evaluation Score 2.5 2 1.5 1 0.5 0 0 5 10 15 Samples 20 25 30 Fig. 5. Comparison between the results of the trained FIS system and the calculated ones In this example all scores are calculated in 1.42 sec using the trained system while they need 147.79 sec using equation (5). The time needed to calculate the score depends on the number of configuration samples used, while the score estimation by the FIS is independent. The mean (absolute) error of results comparing the trained system results and the calculated results was -0.038 (0.2426) presenting an acceptable performance of the trained system. 5 Conclusions A multi criterion index is proposed to address the problem of evaluating different anatomies emerging through the reconfiguration of a robotic system, at the early stages of the reconfigurable workcell design. The index allows the end user to evaluate the various anatomies based on their respective overall kinematic performance therefore assisting the choice of the most suited anatomy to the task. Additionally, the index also allows the determination of “good performance” area in the manipulator’s configuration space, where if the task is placed the selected anatomy will exhibit good kinematic performance. This helps to reduce the search space for latter parts of the workcell design process such as placing the task in the optimal location in the manipulator’s workspace and scheduling it. In order to reduce the required time and complexity for determining the index value for all possible anatomies, an ANFIS system is created and trained using a smaller number of samples. After the system training, it produces the index values for all possible anatomies achieved by the manipulator. The use of the system allows for a steep decrease in the overall computational time and load required in order to obtain the results for each new anatomy, severely improving the design process performance. 350 H. Valsamos, V. Moulianitis, and N. Aspragathos References 1. Petiot, J., Chedmail, P., Hascoet, J.: Contribution to the Scheduling of Trajectories in Robotics. Robotics and Computer Integrated Manufacturing 14, 237–251 (1998) 2. Zacharia, P.T., Aspragathos, N.A.: Optimal Robot Task Scheduling based on Genetic Algorithms. Robotics and Computer – Integrated Manufacturing 21(1), 67–79 (2005) 3. Dissanayake, M., Gal, J.: Workstation planning for Redundant Manipulators. Int. J. 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