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On generating the motion of industrial robot manipulatorsK. Kaltsoukalas, S. Makris, G. Chryssolourisn,1Laboratory for Manufacturing Systems and Automation, University of Patras, Greecea r t i c l e i n f oArticle history:Received 17 October 2013Received in revised form19 September 2014Accepted 8 October 2014Available online 29 October 2014Keywords:Path planningIndustrial robot motionGrid searcha b s t r a c tIn this study, an intelligent search algorithm is proposed to define the path that leads to the desiredposition and orientation of an industrial robots manipulator end effector. The search algorithm graduallyapproaches the desired configuration by selecting and evaluating a number of alternative robotsconfigurations. A grid of the robots alternative configurations is constructed using a set of parameterswhich are reducing the search space to minimize the computational time. In the evaluation of thealternatives, multiple criteria are used in order for the different requirements to be fulfilled. Thealternative configurations are generated with emphasis being given to the robots joints that mainlyaffect the position of the end effector. Grid resolution and size parameters are set on the basis of thedesired output. High resolution is used for a smooth path and lower for a rough estimation, by providingonly a number of the intermediate points to the goal position. The path derived is a series of robotconfigurations. This method provides an inexperienced robot programmer with flexibility to generateautomatically a robotic path that would fulfill the desired criteria without having to record intermediatepoints to the goal position.& 2014 Elsevier Ltd. All rights reserved.1. IntroductionIn the recent years, there is an increasing need for flexiblemanufacturing systems, capable of adapting to different marketdemands and product-mix changes 1. The dynamic environmentin production requires an increasing number of reconfigurationson assembly manufacturing resources 3. In automated assemblysystems such as robots, the flexibility is normally restricted due tothe high programming effort required in order for robot trajec-tories to adjust to different assembly cell layouts. Experiencedrobot programmers have to spend considerable time in order tooptimize the robotic paths for each specific application by usingconventional programming methods. A method that is widelyused is programming by demonstration, where the intermediatepoints to the goal position are recorded by sequentially movingthe robot to each position using the teach pendant. The robotsfinal path is generated by connecting the recorded points via arobot controller, which tries to pass through all the points bytaking into consideration the dynamic constraints of the robot. Therobots final trajectory is highly dependent on the points recordedand the experience of the respective programmer, who has carriedthis out. Automatic path planning for robotics poses the questionas to how a robot can move from its initial to the final position andhas been investigated during the last decades mainly focusing onpath planning for collision avoidance.One of the techniques for motion planning is the construction ofapproximate models by sampling their configuration space. Over thelast few years, there has been a lot of work carried out for theimprovement of sampling based motion planning algorithms. It ishard to define a single criterion that can classify all planners indistinct categories. The classical separation is between roadmap-based planners and tree-based planners 4.The probabilistic road-map path planning was introduced in 5 as a new method ofcomputing collision-free paths for robots. The method proceeds intwo phases: those of learning and query. In the learning phase, aprobabilistic roadmap is constructed by generating the robotsrandom free configurations and connecting them using a simplemotion planner, also known as a local planner. Different approacheshave been used to address a variety of problems. In 6, two differentmethods for constructing and querying roadmaps are suggested forthe motion planning of deformable objects. Another two deforma-tion techniques that can be applied to the resulting path are alsopresented. The obstacle probabilistic roadmap method is introducedinto 7, where several strategies for node generation are describedand multi-stage connection strategies are proposed for cluttered3-dimensional workspaces. In 8, a randomized planner is describedfor planning CF-compliant motion between two arbitrary polyhedralsolids, by extending the probabilistic roadmap paradigm for plan-ning collision-free motion to the space of contact configurations. Thekey to this approach is a novel sampling strategy of generatingrandom CF-compliant configurations.Contents lists available at ScienceDirectjournal homepage: /locate/rcimRobotics and Computer-Integrated Manufacturing/10.1016/j.rcim.2014.10.0020736-5845/& 2014 Elsevier Ltd. All rights reserved.nCorresponding author.E-mail address: xrisollms.mech.upatras.gr (G. Chryssolouris).1Tel.: 30 2610 997262.Robotics and Computer-Integrated Manufacturing 32 (2015) 6571The concept of Rapidly-exploring the Random Tree is introducedin 9. The basic idea is that an initial sample (the starting config-uration) is the root of the tree and newly produced samples are thenconnected to the samples already existing in the tree. In 10, twoRapidly-exploring Random trees (RRTs) were rooted at the start andduring the goal configurations. Each one of the trees explores thespace around it and also advances towards each other through theuse of a simple greedy heuristics. Although it was originallydesigned that motions be planned for a human arm (modeled as a7-DOF kinematic chain), in the automatic graphic animation ofcollision-free grasping and manipulation tasks, the algorithm hasbeen applied to a variety of path planning problems. Tree-basedplanners have proven to be a good framework for dealing with real-time planning and re-planning problems. In 11, a re-planningalgorithm is presented for repairing Rapidly-exploring RandomTrees when changes are made to the configuration space. Insteadof abandoning the current RRT, the algorithm efficiently removesonly the newly-invalid parts and maintains the rest. Dynamicobstacle avoidance has been investigated for the mobile robotsfound in industrial environments in 12. However, industrialmanipulators are typically programmed to execute predefined paths.The two main categories of robotic programming methods are thoseof online programming and offline programming.In 13, an online path planning and programming supportsystem is proposed for the transformation of the users interactioninto a simplified task that generates acceptable trajectories,applicable to industrial robot programming. In 14, a novelapproach to robot programming using an Augmented Realityenvironment was proposed, offering flexibility and adaptabilityto different environments when an on-site robot programmingapproach was desired. The path planning methodology included abeam search algorithm to generate paths. In 15, there is a similarstudy, where the user is able to perform operations, namely via-points selection and modification, in order for a smooth andcollision-free path to be achieved. An on-line robot motionplanning approach that is based upon pre-computing the globalconfiguration space (C-space) connectivity is proposed. In 16, themotion planner consists of an off-line stage and an on-line stageand the collision-free path is searched in this C-space by using theA*algorithm under a multi-resolution strategy.In this study, an intelligent search algorithm is proposed todefine an industrial robot manipulators path that leads to thedesired position and orientation of the end effector. A maximumnumber of alternative configurations are selected and evaluated ineach step until the desired configuration is approached within apredefined error. The alternative configurations are generated in aclever way giving emphasis to the joint angles that mainly affectthe robots position in the workspace. In the configuration space,there is a grid constructed to derive the robots alternative config-urations. A set of clever parameters are used to reduce the searchspace and increase the performance of the algorithm. In theevaluation of the alternatives, multiple criteria that would enhancethe algorithms flexibility to extend are used, in order for thedifferent requirements, namely the shortest path, to be fulfilled.2. ApproachFor an industrial robot manipulator (usually six degrees offreedom), the path planning problem is described via threehierarchical levels as shown in Fig. 1. For a given starting and goalposition, the requested paths include the robots intermediateconfigurations, where each configuration is a set of six jointparameters.2.1. Grid search of the alternative configurationFor an industrial robot manipulator with n degrees of freedom(n-DoF), the alternative configurations are defined from a set of njoint angles. If the possible values of each joint angle are equal to2k1, with resolution d(Fig. 2), the number of alternativeconfigurations is given by the following equation:Number of alternative configurations N 2k1n1For each joint angle that can be incremented, a dnresolutionhas to be selected.The number of alternative configurations increases for a robotwith higher degrees of freedom and a larger grid (k) size. For thisreason, the following parameters are used for the reduction of thealternative configurations, where a multi-criteria evaluation willbe carried out as follows:?Decision Horizon (DH): This parameter is taking values from oneto n (DoF of the robot). Starting from the base of the robot, DHFig. 1. Hierarchical levels for path planning problem (6 DOFs robot).K. Kaltsoukalas et al. / Robotics and Computer-Integrated Manufacturing 32 (2015) 657166parameter defines the degrees of freedom which are taken inconsideration while constructing the grid of the alternativeconfigurations. For joint angles, in the decision horizon, a grid iscreated as shown in Fig. 2. For the remaining joints, outside thedecision horizon, only a number of samples are randomly takenin order to have complete alternative robot configurations. Therobots joints are separated into those that mainly affect therobots movement in the workspace (position of the end effector)and those that mainly affect the orientation of the end effector.When only the target position has to be reached and theorientation of the end effector is ignored this parameter couldbe reduced for better performance and less computational time.?Maximum number of alternatives (MNA): A maximum number ofalternatives from the grid in the decision horizon are randomlyselected for evaluation. If MNA4N then automatically theparameter MNAN.?Sample Rate (SR): A sample rate is defined as the number ofsamples taken from the joints, outside the decision horizon, inorder to form the robots complete alternative configurations.When the orientation of the end effector is considered, SRparameter should be increased in order to generate morealternative configurations which affect the orientation of theend effector.For an industrial manipulator with 6 DOF (n6, Fig. 3), even fork1 and d101 for each degree of freedom, the number ofalternative configurations is given by Eq. (1): (Figs. 46)N 36 729 Alternative neighbor configurations of robotBy setting DH3, only the first three degrees of freedom aretaken into consideration whilst the number of the alternativeconfiguration on the grid drops down toNDH 3 33 27 Alternative configurations for DH 3The maximum number of alternatives in the decision horizon isdefined as follows:MNArNThe probability of getting the alternative configuration closer tothe desired position is given by the following equation:pDH;MNA MNAN2From 1 and 2pDH; MNA MNA2k1DH3Therefore, in the example with the 6 DOFs robot where, thenumber of the alternative configurations was found to be N27(for DH3)If MNA20, the probability of getting the alternative config-uration that is closer to the desired position is given by Eq.(2)Fig. 2. Available joint angles for each degree of freedom in the DH.Fig. 3. COMAU Smart5 Six, 6 DOF, Industrial Manipulator.Fig. 4. Alternative configurations using MNA3, DH3 and SR2 parameters for 6 DOFs.K. Kaltsoukalas et al. / Robotics and Computer-Integrated Manufacturing 32 (2015) 657167Probability to get the best alternative configuration in DH,P(DH3, MNA20) 20=27 74%Consequently, for exhaustive search in DH (P1), MNAN27Giving sample rate (SR)2 for each alternative in the decisionhorizon, two samples are taken from the rest of the joints; thus,the number of complete alternative configurations becomesN completeMNA 27; SR 2 MNAnSR 27 ? 2 54 complete alternativesIn general, the number of complete alternative configurationsfor the predefined MNA and SR parameters is given by thefollowing equation:Number of complete alternative configurationsMNA;SR;Ncomplete MNAnSR4The proposed algorithm does not have to search the entire work-space of the robot. During each iteration, only a maximum numberof neighbor configurations are evaluated. Calculation time for acomplete target path depends on the distance of the starting pointto the target. Calculation time also increases when more inter-mediate points are requested for a smoother path that betterfulfills the desired criteria.2.2. Evaluation of the alternative configurationsMultiple criteria are used for the evaluation of the alternativeconfigurations. A decision matrix is built as shown in the followingtable. In the context of this study, two criteria have been taken intoconsideration, those of the distance due to translation and the distancedue to rotation from the target position and the robots orientation.Despite the fact that the proposed algorithm could also be used justfor the definition of the joint parameters for a given position andorientation of the robots end effector (inverse kinematics), the mainpurpose of this study is to plan the robots path, which better fulfillsthe multiple criteria defined by the user. The search algorithm is easilyextensible for more criteria. (Tables 1 and 2)The utility for each of the alternatives is calculated as theweighted sum of the distance due to translation and to orientation.Ui WtjjXi?XjjWrfqi;q5where Xi?X, is the Euclidean distance of the end effector from thetarget position and fqi;qtarget is the distance due to rotation(orientation of the target configuration).The weight factors Wtand Wrare selected from the user inorder to give emphasis to the desired criterion. If the user is onlyinterested in the position of the end effector, the factors Wt1 andWr0 should be used.The metric of the distance between rotations is the Norm of theDifference of Quaternions, described in detail in 17.fqi;qtarget min fjjqi?qtargetjj;jjqiqtargetjjg6where, J J denotes the Euclidean norm (or 2-norm) and q theorientation of the end effector, expressed in quaternions. Themetric gives values in the range 0;ffiffiffi2p?.The alternative configuration with the smaller utility function isselected at each decision point.Path search algorithmInput: Target position (X Y Z), target orientation (Euler anglesZYZ”), DH, MNA, SR, (k, d: grid size & resolution)Output: Target configuration (123 n) & the sequenceof the intermediate configurations (path)1. The Grid parameters k & dare defined.2. The DH is defined. DH1/number of the robots DOF.3. The Grid is constructed for DH. Alternatives are generated.4. The MNA is selected in order to enable a configuration near thetarget.5. The SR is defined. Random samples are taken from the jointsafter the DH.6. A decision matrix is built; MNAnSR complete alternatives areevaluated. The alternative configuration that provides thesmaller value of the utility function is selected.7. The resolution and the size of the grid are redefined.8. Steps 17 are repeated until there is an alternative configura-tion that provides the target position and target orientationwithin the pre-defined distance error.2.3. Industrial manipulator motion generationThe proposed algorithm calculates the robots sequential,intermediate configurations in order to approach the target posi-tion while fulfilling the predefined criteria for the path. Everyconfiguration of the robot is within its joint limits. The robotcontroller uses the derived path in order to generate the motion ofthe industrial manipulator, taking into consideration the dynamicconstraints of the robot.3. ImplementationThe proposed algorithm has been implemented in Matlab withthe use of the Robotics Toolbox 18. The flowchart of thealgorithm is presented in the following figure.Fig. 5. Industrial robot motion generation.Table 1Evaluation of the alternatives according to the distance criteria.AlternativeConfigurationsNormalized criteriaUtility valueDistance dueto translationDistance dueto rotationUi W1Ci1 W2Ci2(where W1and W2the criteria weights)Alternative 1C11C12U1Alternative 2C21C22U2Alternative 3C31C32U3AlternativemMNAnSRCm1Cm2UmK. Kaltsoukalas et al. / Robotics and Computer-Integrated Manufacturing 32 (2015) 6571684. ResultsIn Figs. 7 and 8, it is observed that the grid size and resolutionparameters (k, d) have a great influence on the smoothness ofthe path towards the desired position. Lower values of theseparameters lead to better paths, however, the computational timeis increased.4.1. Search algorithm parameters correlationIn order for the correlation among the search parameters MNA,DH and SR to be examined, a set of experiments was designedusing the Taguchi method with the objective of process timeminimization. The initial values of the grid parameters wereselected to be k5 and d0.1 rad (E61).4.1.1. Taguchi design of experimentsThe effect of the search parameters DH, MNA, and SR will beexamined so as for the process time required for finding the pathto be minimized to the target position. Four levels are selected foreach parameter. The proposed set of experiments, according to theTaguchi method, is given in L16 table.L16 table:Fig. 7. Grid resolution effect on the on the path (a) d0.01 rad and (b) d0.1 rad.Fig. 6. Flowchart of the proposed algorithm.Table 2Set of experiments for 4 levels of the parameters DH, MNA, and SR.Exp. no.DHMNASRTime (Sec)122510.60225020.57327531.124210041.82532540.72635030.91737520.918310011.17942520.551045010.911147542.1612410031.601352531.291455042.841557510.4816510022.01K. Kaltsoukalas et al. / Robotics and Computer-Integrated Manufacturing 32 (2015) 657169. Analysis of means (ANOM)?From Figs. 9 and 10, it is observed that the target position of theend effector is better approached for DH3 (first three degreesof freedom of the robot). The higher values of MNA and SR aresufficient only when the orientation is taken into consideration.In order for both the target position and orientation of the endeffector to be approached, the best results (lowest computingtime) are given for DH3, MNA25 and SR2.?The interaction among the parameters DH, MNA and SR andtheir effect on the computing time is presented in Fig. 11. It isconfirmed that for lower DH values sufficient SR has to beconsider whilst for higher DH values the SR value should beminimum for less computing time.Fig. 8. Grid size effect on the path (a) path generated for k1 and (b) path generated for k5.Fig. 9. DH, MNA and SR vs. processing time (target position).Fig. 10. DH, MNA and SR vs. processing time (target position and orientation).Fig. 11. Interaction of DH with SR (target position).K. Kaltsoukalas et al. / Robotics and Computer-Integrated Manufacturing 32 (2015) 6571705. ConclusionsIn this study, an intelligent search algorithm is proposed todefine the path that leads to the desired position and orientation ofthe end effector of an industrial robot manipulator. The gridparameters as well as the search algorithm parameters DH, MNA,SR are proven to be drastically reducing the processing time. Asregards the problem of approaching the target position, it is shownthat the best results are obtained when the first three joints of therobot have been considered (DH3). This is consistent with theinitial assumption that the first three degrees of the robots freedom(joints) are responsible for the end effectors position. For the rest ofthe joints, only a few samples are sufficient in order for the pathtowards the target position to be determined. When the orientationof the end effector is considered, a higher sample rate for the jointangles, outside the decision horizon, should be used. The criteriaconsidered for the calculation of the distance from the targetposition and orientation through weight factors, are predefined bythe user. The path is sent to the robot controller, where the motionprogram of the industrial manipulator is generated. The algorithmis extensible to the use of more criteria in the future. Free collisionpaths will be addressed in a future study via a collision detectionmodule integrated into the algorithm.AcknowledgmentsThis study has received funding by the project X-act/FoF-ICT-314355, funded by the European Commission under the 7thFramework Program.References1 Chryssolouris G. Manufacturing Systems Theory and Practice. 2nd ed. .New York: Springer-Verlag; 2006.2 Mourtzis D, Alexopoulos K, Chryssolouris G. Flexibility consideration in thedesign of manufacturing systems: an industrial case study. CIRP J Manuf SciTechnol 2012;5(4):27683.3 Karl F, Reinhart G, Zaeh MF. Strategic planning of reconfigurations on manufac-turing resources. Procedia CIRP Internet. 2012 Jan cited 14.10.14; 3: 60813.Available from: /retrieve/pii/S2212827112002764.4 Tsianos
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