Engineering based robot optimization methodology

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ScienceDirect IFAC PapersOnLine 52-27 (2019) 305–310

Engineering based robot optimization Engineering based robot optimization Engineering based robot optimization Engineering methodology based robot optimization methodology methodology methodology ∗ ∗

ˇ ∗ Arnold J´ ∗ ˇ Martin Svejda a ger ∗ ∗ Martin Svejda Arnold J´ a ger ˇ ∗ ∗ Martin Svejda J´ a ger ∗ ∗ ˇ ∗ Arnold ∗ Martin Svejda Arnold J´ a ger Martin Svejda Arnold J´ a ger ∗ ∗ ˇ Martin Svejda Arnold J´ a ger ∗ ∗ University of West Bohemia, NTIS Research Centre, Pilsen, Czech Czech ∗ University of West Bohemia, NTIS Research Centre, Pilsen, ∗ ∗ University of West Bohemia, NTIS Research Centre, Pilsen, Czech ∗ West Bohemia, NTIS Research Centre, Pilsen, Czech Republic of (e-mail: [email protected], [email protected]). ∗ University Republic (e-mail: [email protected], [email protected]). University West Bohemia, NTIS Research Centre, Pilsen, Czech Republic (e-mail: [email protected], [email protected]). Republic of (e-mail: [email protected], [email protected]). Republic (e-mail: [email protected], [email protected]). Abstract: The The paper paper deals deals with with the the engineering engineering based based methodology methodology for for optimal optimal design design of of Abstract: Abstract: The paper deals with the engineering based methodology for optimal design of Abstract: The paper deals with the engineering based methodology for optimal design of non-standard robotic architectures. Two layer algorithm is presented for the optimization non-standard robotic Two layer algorithm presented for optimization of Abstract: The paperarchitectures. deals with the engineering based is methodology forthe optimal design of non-standard robotic architectures. Two layer algorithm is presented for the optimization non-standard robotic architectures. Two layer algorithm is presented for the optimization of robot kinematic parameters. The first layer includes mathematical optimization of the simplified non-standard robotic architectures. Two layer algorithm is presented for the optimization of robot kinematic parameters. The first firstTwo layerlayer includes mathematical optimization of the simplified simplified non-standard robotic architectures. algorithm is presented for the optimization of robot kinematic parameters. The layer includes mathematical optimization of the robot kinematic parameters. The first layer includes mathematical optimization of the simplified dynamic model model of of the the robot robot resulting resulting in in aa priori priori estimation estimation of of the the kinematic kinematic parameters. parameters. A A dynamic robot kinematic parameters. The first layer includes mathematical optimization of the simplified dynamic model of the robot resulting in a priori estimation of the kinematic parameters. A dynamic model offunction the robot in force/torque a priori estimation of theis A general objective objective function for resulting robot joint joint force/torque minimization iskinematic taken into intoparameters. account. The The general for robot minimization taken account. dynamic model offunction the robot resulting in force/torque a priori estimation of theis kinematic parameters. A general objective for robot joint minimization taken into account. The general objective function for robot joint force/torque minimization is taken into account. The second layer provides an iterative approach which makes possible to adjust the kinematic second provides an iterative approach which makes possible adjust kinematic general layer objective function for robot joint force/torque minimization isto taken intothe account. The second layer provides an iterative approach which makes possible to adjust the kinematic second layer provides an iterative approach which makes possible to adjust the kinematic parameters according to unmodeled unmodeled engineering requirements. Thetoproposed proposed optimization second layer provides iterative which makes adjust kinematic parameters to engineering The optimization second layeraccording provides an an iterative approach approach whichrequirements. makes possible possible adjust the the kinematic parameters according to unmodeled engineering requirements. The proposed optimization parameters according to the unmodeled requirements. Theto proposed optimization approach is is illustrated illustrated on the example engineering of 55 aa DoF DoF robot robot for industrial industrial degreasing machine. approach on example of for degreasing machine. parameters according to unmodeled engineering requirements. The proposed optimization approach is illustrated on the example of 5 a DoF robot for industrial degreasing machine. approach is illustrated on the example of 5 a DoF robot for industrial degreasing machine. approach is illustrated on Federation the example of 5 a DoF robotHosting for industrial degreasing machine. © 2019, IFAC (International ofrobot; Automatic Control) by Elsevier Ltd. All rights reserved. Keywords: parametric optimization; non-standard application Keywords: parametric optimization; robot; non-standard non-standard application Keywords: parametric optimization; robot; application Keywords: parametric optimization; robot; non-standard application Keywords: parametric optimization; robot; non-standard application 1. INTRODUCTION INTRODUCTION at one one end end that that can be be individually individually fired fired pneumatically pneumatically 1. at 1. INTRODUCTION INTRODUCTION at one one end end that that can can be individually fired pneumatically 1. at can be be with individually fired coming pneumatically andone steered robotically, with sensor input input coming from aa 1. INTRODUCTION at end that can individually fired pneumatically and steered robotically, sensor from 1. INTRODUCTION at one end that can be with individually fired coming pneumatically and steered robotically, with sensor input input coming from aa and steered robotically, sensor from grid steered of machine machine vision cameras. cameras. Theinput E-series robot [17]a and robotically, with sensor coming from grid of vision The E-series robot [17] and steered robotically, with sensor input coming from grid of machine vision cameras. The E-series robot [17]a The field of robotics covers wide range of robot archigrid of machine vision cameras. The E-series robot [17] The field of robotics covers wide range of robot archisystem produced by Agrobot Agrobot robotic harvesters consists of grid of machine vision cameras. The E-series robot [17] system produced by robotic harvesters consists of The field of robotics covers wide range of robot archigrid of machine vision cameras. The E-series robot [17] system produced by Agrobot robotic harvesters consists of The field of robotics covers wide range of robot architectures from simple robots (planar, SCARA) through system produced by Agrobot robotic harvesters consists of The field of robotics covers wide range of robot architectures from simple robots (planar, SCARA) through up 24 robotic arms working wirelessly as a team and it is system produced by Agrobot robotic harvesters consists of 24 robotic arms working wirelessly as team and it is The fieldfrom of robotics range of robotthrough archi- up tectures from simple covers robots wide (planar, SCARA) through system produced by working Agrobotwirelessly robotic harvesters up 24 robotic robotic arms working wirelessly as aaa team teamconsists and it it of is tectures simple robots (planar, SCARA) mainstream of robotics (standard 6-axis industrial robot up 24 arms as and is tectures from simple robots (planar, SCARA) through mainstream of robotics (standard 6-axis industrial robot designed for fast picking of strawberries including ripeness up 24 robotic arms working wirelessly as a team and it is designed for fast picking of strawberries including ripeness tectures from (planar, SCARA) through mainstream of simple roboticsrobots (standard 6-axis industrial robot designed up 24 robotic arms working wirelessly asincluding a team and it is for fast fast picking of strawberries strawberries including ripeness mainstream of robotics (standard 6-axis industrial robot with spherical wrist) to complex architectures for for picking of ripeness mainstream of robotics 6-axis industrial with spherical wrist) to complex robotic robotic architectures for designed identification. Two tactical light resp. resp. heavy heavy surveillance designed for fast picking of strawberries including ripeness identification. Two tactical light surveillance mainstream of wrist) robotics (standard 6-axis architectures industrial robot robot with spherical wrist) to (standard complex robotic architectures for designed for fast picking of strawberries including ripeness identification. Two tactical light resp. heavy surveillance with spherical to complex robotic for special application. While the common industrial robots of identification. Two tactical light heavy surveillance with wrist) to robotic architectures special application. While the common industrial robots of robots (Bulldog (Bulldog resp. Mastiff) [18]resp. represent the military Two tactical light heavy surveillance robots resp. Mastiff) [18] represent the military with spherical spherical wrist) to complex complex robotic architectures for special application. While the common common industrial robotsfor of identification. identification. Two tactical light resp. heavy the surveillance robots (Bulldog resp. Mastiff) [18]resp. represent the military special application. While the industrial robots of world-leading manufacturers (KUKA, Fanuc, ABB, etc.) robots (Bulldog resp. Mastiff) [18] represent military special application. While the common industrial robots of world-leading manufacturers (KUKA, Fanuc, ABB, etc.) robot. Each of them is equipped with a 4 DoF robotic robots (Bulldog resp. Mastiff) [18] represent the military Each of them is equipped with aa 44 DoF robotic special application. While the (KUKA, common industrial robots of robot. world-leading manufacturers (KUKA, Fanuc, ABB, ABB, etc.) robots Each (Bulldog resp. Mastiff) [18] with represent the military robot. Each of them is equipped with DoF robotic world-leading manufacturers Fanuc, etc.) have undergone a long development and their kinematic robot. of them is equipped a 4 DoF robotic world-leading manufacturers (KUKA, Fanuc, ABB, etc.) have undergone a long development and their kinematic arm with 2 optional axes. Medical robots are often based robot. Each of them is equipped with a 4 DoF robotic arm with 2 optional axes. Medical robots are often based world-leading manufacturers (KUKA,and Fanuc, etc.) arm have undergone long development development and theirABB, kinematic robot. Each of themaxes. is equipped 4 DoF with optional axes. Medical with robotsa are are oftenrobotic based have undergone aaa long their kinematic architecture as well as actuators design and control sysarm with 222arms optional Medical often have undergone long development and their kinematic architecture as well as actuators design and control syson special special arms architectures. Therobots best-known Da based Vinci arm with optional axes. Medical robots are often based on architectures. The best-known Da Vinci have undergone a long development and their kinematic architecture as well as actuators design and control sysarmspecial with 2arms optional axes. Medical are often on special arms architectures. Therobots best-known Da based Vinci architecture as well as actuators design and control systems are well optimized, there are specific applications on architectures. Vinci architecture as well as actuators design and control systems are well optimized, there are specific applications Surgical System [21] comprises comprisesThe threebest-known articulatedDa arms in on special arms architectures. The best-known Da Vinci Surgical System [21] three articulated arms in architecture as well as actuators design and control systems are well optimized, there are specific applications on specialSystem arms architectures. Vinci Surgical System [21] comprises comprisesThe threebest-known articulatedDa arms in tems are well optimized, there are specific applications where their use is complicated or completely inadequate Surgical [21] three articulated arms in tems are well optimized, there are specific applications where their use is complicated or completely inadequate the first generation and four in the second generation. The Surgical System [21] comprises three articulated arms in the first generation generation and four in in the the second generation. The tems are well there or specific applications where their useoptimized, is complicated complicated orarecompletely completely inadequate the Surgical System [21] comprises three articulated armsThe in first and four second generation. where their use is inadequate for many reasons, e.g. large footprint, robust and heavy the first generation and four in the second where their use complicated or for many reasons, e.g. large footprint, robust and heavy Siemens ARTIS pheno pheno [8] enables enables quick generation. and precise preciseThe Xfirst generation and four in the second generation. The Siemens ARTIS [8] quick and Xwhere their use is is e.g. complicated or completely completely inadequate for many reasons, e.g. large footprint, footprint, robust inadequate and heavy heavy the the first generation and four in the second generation. The Siemens ARTIS pheno [8] enables quick and precise Xfor many reasons, large robust and mechanical construction, insufficient/excessive number of Siemens ARTIS pheno [8] enables precise Xfor e.g. footprint, heavy mechanical construction, insufficient/excessive number of ray investigations investigations of blood blood vessels quick using aand C-shaped XARTIS [8] precise ray of vessels using C-shaped Xfor many many reasons, reasons, e.g. large large footprint, robust robust and and heavy mechanical construction, insufficient/excessive number of Siemens Siemens ARTIS pheno pheno [8] enables enables quick and precise Xray investigations of blood blood vessels quick using aaaand C-shaped Xmechanical construction, insufficient/excessive number of degrees of freedom (DoFs), protection or unsuitable meray investigations of vessels using C-shaped mechanical construction, insufficient/excessive number of degrees of freedom (DoFs), protection or unsuitable meray arm which automatically moves across the patient of using aa C-shaped Xarm which automatically moves across the patient mechanical construction, insufficient/excessive numbermeof ray degrees of freedom freedom (DoFs), protection or or unsuitable unsuitable meinvestigations of blood blood vessels vessels using C-shaped Xray investigations arm which which automatically automatically moves across the patient patient degrees of (DoFs), protection chanical arrangement. All these reasons lead to the need ray moves across the degrees freedom protection unsuitable mechanical arrangement. All these reasons lead to the need and arm it is is based based on customization of standard standard serial robot arm which automatically moves across the patient and it on customization of serial robot degrees of ofarrangement. freedom (DoFs), (DoFs), protection orlead unsuitable me- ray chanical arrangement. All these these reasonsor lead to the the need need ray arm which automatically moves across the patient and it is based on customization of standard serial robot chanical All reasons to for research and development of new robot architectures. and it is based on customization of standard serial robot chanical arrangement. All these reasons lead to the need for research and development of new robot architectures. architecture. Preoperative planning for the multi-arm multi-arm suron of standard serial architecture. Preoperative planning for the surchanical arrangement. All these reasons lead to the need and for research and development development of new new robot architectures. and it it is is based based on customization customization of for standard serial robot robot architecture. Preoperative planning for the multi-arm multi-arm surfor research and of robot architectures. architecture. Preoperative the surfor research and development of new robot architectures. gical robot robot cooperation cooperation isplanning presented in [31]. The kinekinearchitecture. Preoperative planning for the multi-arm surgical is presented in [31]. The for research and development of new robot architectures. Special robot architectures can achieve considerably exarchitecture. Preoperativeis for in the[31]. multi-arm surSpecial robot architectures can achieve considerably exgical robot cooperation cooperation isplanning presented in [31]. The kinekinepresented The Special robot robot architectures architectures can can achieve achieve considerably considerably exex- gical matic robot control of of the the 6 DoF DoF general general articulated robotic arm Special gical presented in The matic control articulated robotic arm tended functional properties when compared to Special robot architectures achieve considerably exgical robot robot cooperation isgeneral presented in [31]. [31].robotic The kinekinetended functional propertiescan when compared to convenconvenmatic controlcooperation of the the 666 DoF DoFis general articulated robotic arm matic control of articulated arm Special robot architectures can achieve considerably extended functional properties when compared to convenfor minimally-invasive minimally-invasive operations is discussedrobotic in [7]. [7]. The The tended functional properties when compared toemployed convenmatic control general articulated for operations is discussed in tional industrial or mobile robots. They are often tended functional when compared convenmatic control of of the the 66 DoF DoF general is articulated robotic arm tional industrial or mobile robots. They are often employed for minimally-invasive operations is discussed in [7]. arm The minimally-invasive operations discussed in [7]. The tendedindustrial functional properties when compared toemployed conven- for tional industrial or properties mobile robots. robots. They are often oftento employed group of the robots of non-standard kinematic architectional or mobile They are for minimally-invasive operations is discussed in [7]. The group of the robots of non-standard kinematic architecin specific handling and pick and place applications. The tional industrial or robots. often for minimally-invasive is discussed [7]. The in specific handling and pick and place applications. The group of the the robots robots of of operations non-standard kinematicin architecarchitecof non-standard kinematic tional industrial or mobile mobile robots. They are often employed employed in specific handling and pick pick andThey placeare applications. The group tures form form therobots inspection robot for for Non Non Destructive Testin specific handling and and place applications. The group of the of non-standard kinematic architectures the inspection robot Destructive Testother cases are devoted to the robotic structures for nonin specific handling and pick and place applications. The group of the robots of non-standard kinematic architecother cases are devoted to the robotic structures for nontures form the inspection robot for Non Destructive Testform the inspection robot for Non Destructive Testin specific and to pick placestructures applications. The tures other caseshandling are devoted devoted to theand robotic structures for nonnoning (NDT) applications [10]. VENDY robot for circumother cases are the robotic for tures form the inspection robot for Non Destructive Testing (NDT) applications [10]. VENDY robot for circumcircumstandard applications where robot kinematics have to be other are to robotic structures for nontures(NDT) form the inspection[10]. robotVENDY for Non robot Destructive Teststandard applications where robot kinematics have to be ing (NDT) applications [10]. VENDY robot for applications for circumother cases cases are devoted devotedwhere to the therobot robotic structures forto nonstandard applications where robot kinematics have to be ing ferential pipe welds testing testing [24] or more morerobot complex robotic standard applications kinematics have be ing (NDT) applications [10]. VENDY for circumferential pipe welds [24] or complex robotic completely different to meet specific application requirestandard applications where robot kinematics have to be ing (NDT) applications [10]. VENDY robot for circumcompletely different to meet specific application requireferential pipe welds testing [24] or more complex robotic ferential pipe welds testing [24] or more complex robotic standard applications where robot kinematics have to be completely different to meet specific application requiresystem SAVA SAVA [25; 30] 30] for elbow elbow and branch weld testing testing completely different to meet specific application requireferential pipe testing [24] more complex system [25; for and branch weld ments, e.g. inspection robots. The following examples show completely different meet specific application requireferentialSAVA pipe welds welds testing [24] or or more complex robotic ments, e.g. inspection robots. The following examples show system SAVA [25; 30] 30] for elbow elbow and branch weld robotic testing [25; for and branch completely different to to meet The specific application requirements, e.g. inspection inspection robots. The following examples show system were completely completely designed and optimized. Theweld latesttesting NDT ments, e.g. robots. following examples show system SAVA [25; 30] for elbow and branch weld testing were designed and optimized. The latest NDT the special robot architectures falling in different fields ments, e.g. inspection robots. The following examples show system SAVA [25; 30] for and elbow and branch the special robot architectures falling in different fields were completely designed and optimized. Theweld latesttesting NDT completely designed optimized. The latest NDT ments, e.g. inspection robots. Thefalling following show were the special robot architectures architectures falling in examples different fields fields multi-redundant robot ROBIN with up to 13 DoF was the special robot in different were completely designed and optimized. The latest NDT multi-redundant robot ROBIN ROBIN with up up to to 13 13 DoF DoFNDT was of robotics. The known Rover designed by the the special architectures falling different were completely designed and optimized. of robotics. The well well known Mars Mars Roverin designed byfields the multi-redundant multi-redundant robot with was robot ROBIN with up The to areas. 13latest DoF was therobotics. special robot robot architectures falling indesigned differentby fields of robotics. The well known Mars Rover designed by the introduced for inspections in very restricted areas. Virtual of The well known Mars Rover the multi-redundant robot ROBIN with up to 13 DoF was introduced for inspections in very restricted Virtual NASA Jet Propulsion Laboratory is equipped with of robotics. The well known Mars Rover designed by the multi-redundant robot ROBIN with up to 13 DoF was NASA Jet Propulsion Laboratory is equipped with introduced for inspections in very restricted areas. Virtual introduced for inspections in very restricted areas. Virtual of robotics. The well known Mars Rover designed by the NASA Jet Propulsion Propulsion Laboratory is equipped equipped with simulation model model and control control algorithm design is reported reported NASA Jet Laboratory is with the introduced for inspections in very restricted areas. Virtual simulation and algorithm design is 2.1 meter long robot arm [11; 23] designed for more chalNASA Jet Propulsion Laboratory is equipped with the introduced for inspections in very restricted areas. Virtual 2.1 meter long robot arm [11; 23] designed for more chalsimulation model and control algorithm design is reported control algorithm design is reported NASA Jetlong Propulsion Laboratory is equipped withchalthe simulation 2.1 meter long robot arm arm [11; 23] 23] designed designed for more more chalin [29; [29; 2]. 2]. model and 2.1 meter robot [11; for simulation in lenging research mission. Mobile robot arm with teaching 2.1 long arm [11; designed more chalsimulation model and and control control algorithm algorithm design design is is reported reported lenging research mission. Mobile robot arm with teaching in [29; 2]. 2]. model [29; 2.1 meter meter long robot robot arm Mobile [11; 23] 23]robot designed for more chal- in lenging research mission. Mobile robot arm for with teaching lenging research mission. arm with teaching in [29; 2]. fantom device which mimics robotic arm kinematics and lenging research mission. Mobile robot arm with teaching in [29; 2]. fantom device which mimics robotic arm kinematics and Unfortunately, introducing the the non-standard non-standard and and useruserUnfortunately, introducing lenging research mission. Mobile robot arm with teaching fantom device which mimics robotic arm kinematics and Unfortunately, introducing introducing the the non-standard non-standard and and useruserfantom device which mimics robotic arm kinematics and is used for controlling the arm is presented in [3]. The Unfortunately, fantom device which mimics robotic arm kinematics and is used for controlling the arm is presented in [3]. The defined robot robot architectures architectures brings the necessity necessityand of strucstrucUnfortunately, introducing the non-standard userdefined brings the of fantom device which mimics robotic arm kinematics and is used for controlling the arm is presented in [3]. The Unfortunately, introducing brings the non-standard userdefined robot architectures architectures brings the necessity necessityand of strucis used for controlling the arm is presented in [3]. The interesting field of robotics represent agriculture robots. defined robot the of strucis controlling the is in The interesting field of robotics represent agriculture robots. tural/parametric optimization which results in of well debrings the necessity structural/parametric optimization which results in well deis used used for for field controlling the arm arm is presented presented in [3]. [3]. The defined interesting field of robotics robotics represent agriculture robots. defined robot robot architectures architectures brings the results necessity of structural/parametric optimization which results in well deinteresting of represent agriculture robots. The unmanned ground vehicle equipped with 8 DoF coltural/parametric optimization which in well deinteresting field of robotics represent agriculture robots. The unmanned ground vehicle equipped with 8 DoF colsigned, technically feasible and easy-controllable robots. tural/parametric optimization which results in well designed, technically feasible and easy-controllable robots. interesting field ground of robotics represent agriculture robots. The unmanned ground vehicle equipped with 88 DoF DoF col- signed, tural/parametric results in well detechnicallyoptimization feasible and andwhich easy-controllable robots. The unmanned vehicle equipped with collaborative robot arm that permits to work in unstructured signed, technically feasible easy-controllable robots. The vehicle equipped 88 DoF laborative robot arm that permits to work in unstructured Many general general methods for unconstrained unconstrained and constrained constrained technically feasible and easy-controllable robots. Many methods for and The unmanned unmanned ground vehicle equipped with DoF colcol- signed, laborative robot ground arm that that permits to work workwith in unstructured unstructured signed, technically feasible and easy-controllable robots. Many general methods for unconstrained and constrained laborative robot arm permits to in environments is shown in [15]. Efficient harvesting system Many generalhave methods unconstrained laborative arm permits to in environments is shown in [15]. Efficient harvesting system optimization have beenfor presented [20; 14; 14;and 16]constrained which can can methods unconstrained optimization been presented [20; 16] which laborative robot robot arm that that permits to work work in unstructured unstructured environments is shown shown in [15]. [15]. Efficient harvesting system Many Many general generalhave methods for unconstrained and constrained optimization have beenfor presented [20; 14; 14;and 16]constrained which can can environments is in Efficient system [1] made by Energid company can pick aaharvesting fruit every 22 to 33 optimization been presented [20; 16] which environments is shown in [15]. Efficient harvesting system [1] made by Energid company can pick fruit every to be used for robot parametric optimization problem [26] optimization have been presented [20; 14; 16] which can be used for for robot robot parametric optimization problem [26] environments is shown in [15]. can Efficient [1] made by by Energid Energid company can pick aaharvesting fruit every everysystem to 33 be optimization have been presented [20; 14; 16] which [26] can used parametric optimization problem [26] [1] made company pick fruit 22tools to seconds. The system uses flexible tubes with removal be used for robot parametric optimization problem [1] by can pick fruit every to seconds. The system uses flexible tubes with removal tools used for robot parametric optimization problem [26] [1] made made The by Energid Energid company cantubes pick aawith fruitremoval every 22tools to 33 be seconds. The system company uses flexible flexible tubes with removal tools be used for robot parametric optimization problem [26] seconds. system uses seconds. The system uses flexible tubes removal seconds. system flexible Federation tubes with with removal tools tools 2405-8963 The © 2019, IFAC uses (International of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2019.12.678

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Martin Švejda et al. / IFAC PapersOnLine 52-27 (2019) 305–310

leading to dexterity optimization, joint force/velocity minimization, singularities and obstacles overcoming, etc. 2. ROBOT OPTIMAL DESIGN METHODOLOGY On the other hand many, of optimization methods mentioned above are strictly dependent on the clear definition of the optimization problem which comprises unique objective function, constraints and robot workspace or trajectory where the robot is to be optimized. These requirements are often not fully satisfactory because of some condition arising from other restrictions which are difficult to model or can not be modeled at all, e.g. machining limitations, robot cabling and packaging, limitation resulting from mechanical design of product family (motors, gears, sensors), etc. These restrictions make impossible to use blindly the mathematical optimization background and assume we get the desired optimal robot design which is ready for manufacturing, control and use in a satisfactory manner. Therefore, the paper presents the methodology for optimal robot kinematic design which combines the general optimization algorithms as well as iterative re-design process based on real manufacturing requirements. The proposed methodology is supported by the following steps: Initial mathematical optimization based on the virtual simulation model: The first phase of the proposed methodology which serves for initial optimization of the kinematic parameters of the robot. The simplified virtual simulation model of the robot is derived, workspace and trajectory of the end-effector is generated and the objective function is defined. The optimal kinematic parameters of the robot are found through a chosen optimization algorithm. Iterative parameters redesign to meet other unmodeled requirements: An iterative process where the initial robot kinematic parameters are integrated into the CAD model of the robot and the 3D Kinematic Parameters Dependent CAD (KPDCAD) model is obtained containing real links and joints dimensions, shapes, materials and actuators specification. The dynamic parameters (mass, center of gravity and inertia tensor) are obtained for each robot kinematic pairs (joints and the following arm) via appropriate decomposition of KPDCAD model (commonly available feature in CAD/CAM software). The iterative process is summarized as follows: (1) Adjust the robot kinematic parameters according to expert’s (e.g. a construction designer) requests to fulfil the real limitations. (2) Use KPDCAD model to generate robot dynamic model. (3) Define and evaluate the objective function (not necessarily the same as in the initial mathematical optimization). (4) Verify the results, if expert’s requests are fulfilled and objective function values are acceptable stop the iterations and continue, else go to (1). (5) The optimal robot parameters are derived and the robot design is acceptable for the following manufacturing processes - final CAD/CAM documentation is generated.

The proposed methodology is demonstrated on the design of 5 DoF serial robot of special architecture, see Fig. 1, which is used for the spray nozzle positioning inside the cleaning chamber of the industrial degreasing machine. The design of the robot under consideration follows the previous developed serial-parallel robot AGEBOT [22; 5] (AGgressive Environment roBOT) for positioning of the technological part inside the cleaning chamber. L2

Base

interior of cleaning chamber L3 q1

Link 1

q2

Link 2

q3

Link 3

L1

q4 q5

L4

Spray nozzle L5

Link 4

Fig. 1. Illustrative example of the robot architecture 2.1 Initial mathematical optimization The joint resp. end-effector (spray nozzle) coordinates of the robot are defined as T T resp. X = [x y z α β] , (1) Q = [q1 q2 q3 q4 q5 ] where [x y z] is the position of the spray nozzle center point and α resp. β are consecutive rotations about x resp. y axis representing the spray direction n T

n = [sin(β) − cos(β) sin(α) cos(β) cos(α)] . The robot kinematic parameters ξ represent the link lengths (2) ξ = [L1 L2 L3 L4 L5 ] . The inverse kinematics for position is derived for a new introduced robot as follows: q1 = atan2 (Sq1 , Cq1 ) , (3)   2 2 2 ±k2 k1 (k2 + k1 ) ± k12 (k22 + k12 ) Sq1 = , Cq = , 1 (k22 + k12 ) k1 k22 + k12 T

T

[k1 k2 k3 ] = [x y z] − L5 n, q3 = atan2 (Sq3 , Cq3 ) , (4)  l12 + l22 − L23 − L24 , Cq3 = ± 1 − Sq32 , Sq3 = 2L3 L4     Sq1 k2 − L2 + k1 Cq1 l1 l2 = k3 − L1 , l3 Sq1 k1 − Cq1 k2



Martin Švejda et al. / IFAC PapersOnLine 52-27 (2019) 305–310

q2 = atan2 (Sq2 , Cq2 ) , L4 Sq3 l2 + L3 l2 + l1 L4 Cq3 , Sq2 = L24 + 2L4 L3 Sq3 + L23 −l2 L4 Cq3 + l1 L4 Sq3 + l1 L3 , Cq2 = L24 + 2L4 L3 Sq3 + L23

(5)

q5 = atan2 (Sq5 , Cq5 ) ,  Sq5 = −m3 , Cq5 = ± m21 + m22 ,     Cq1 Cq23 Sq1 Cq23 Sq23 m1 m2 = Sq1 −Cq1 0 n, Cq1 Sq23 Sq1 Sq23 −Cq23 m3 Sq23 = sin(q2 + q3 ), Cq23 = cos(q2 + q3 ),

(6)

(7)

q4 = atan2 (Sq4 , Cq4 ) , m2 m1 Sq4 = , Cq4 = . Cq5 Cq5

(8)

The forward kinematics for position as well as velocity and acceleration dependency between joint and end-effector coordinates and dynamic model can be computed generally for serial robots [19] through Denavit-Hartenberg notation [4]. The dynamic model of the robot is ¨ + C(Q, Q) ˙ Q ˙ + G(Q) = τ F M (Q)Q (9) where M , C, G are appropriate dynamic matrices/vectors, τ resp. F are joint resp. end-effector external forces/torques and J (Q) is the kinematic Jacobian which maps the joint velocity to translation resp. angular velocity of the endeffector coordinate system. The simplified ”rod” model of

307

Fig. 3. Robot workspace with the end-effector acceleration definition It was proven that the maximum 2-norm joint forces/ torques for the end-effector to be at the position X (corresponding joint position Q) and moving from the steady state in any direction with maximum acceleration amax is given as:   ¨ + G(Q), τ  ≤ σmax M (Q) · J −1 (Q) · X   −1 τ max = σmax M (Q) · J (Q) · amax + G(Q), (11) where σmax () is the maximal singular value of the matrix. Note, that the constant amax represents a weighting factor between the static optimization (amax = 0) and dynamic optimization (amax >> 0, the influence of the gravity is almost neglected, e.g. in high speed applications). The initial optimization is defined as follows:   min J(X, ξ) , ξ  = argmax ξ

Motor i

Joint i+1

Link i

Fig. 2. Simplified robot link the robot link is shown in Fig. 2 and the dynamic parameters of i-th link dependent on the kinematic parameters (link length) are expressed:  T 2   

π d i ρ Li 2 00 2 π d i 2 ρ L i + 8 Mi

,

1/32 π di 4 ρ Li

Ii =  4

4

ρ (Li 3 di 2 π ρ+3/4 π di 4 ρ Li +16 Mi Li 2 +3 Mi di 2 )di 2 Li π 192 π di 2 ρ Li +768 Mi ρ (Li 3 di 2 π ρ+3/4 π di 4 ρ Li +16 Mi Li 2 +3 Mi di 2 )di 2 Li π 192 π di 2 ρ Li +768 Mi



 , 

(10) where mi is a mass, T i is a center of gravity, I i is an inertia tensor of the ith-link of length Li , diameter di and density ρ. The motor is modeled as an added mass Mi at the beginning of the link. The optimization criterion is based on a measure published in [27]. Let’s assume that the robot is supposed to move ˙ = 0 ⇒ Q ˙ = 0) in any from the steady state (X direction in the required workspace with a maximum required acceleration, see Fig. 3, ¨ = amax . max X X∈Xopt

(12)

1 , (13) Jpen + τ max where J is an objective function, X is the position of the end-effector from a required robot workspace X opt and Jpen is so-called penalty function which makes possible to integrate equality/inequality constraints in a simple and effective way [20] and transform the constrained optimization problem to an unconstrained one. The penalty function is assumed to limit the range of the optimized robot kinematic parameters. J(X, ξ) =

Joint i

mi = 1/4 π di 2 ρ Li + Mi , T i = −

X∈X opt

The optimization problem (12) was solved in Matlab through simplex search method fminsearch [12]. Resolving the optimization problem (12), we get the optimal robot kinematic parameters ξ  which ensure that the 2-norm joint forces/torques of the robot over the workspace which have to be applied to reach the maximum end-effector acceleration amax in any direction (from steady-state) will be minimized. Therefore, the initial robot kinematic parameters estimation supported by the mathematical background is found. 2.2 Iterative parameters redesign The CAD model of the robot including the desired endeffector trajectory as an restriction of the robot workspace is depicted in Fig. 4. The trajectory was designed in SolidWorks as a point cloud and exported to Excel sheet. The coincidence points were interpolated by the line segments with polynomial blending (Matlab), see Fig. 5, and the feedrate for demanded velocity profile (bang-bang accelera-

Martin Švejda et al. / IFAC PapersOnLine 52-27 (2019) 305–310

308

tion profile with max. velocity Vmax and max. acceleration Amax , see Fig. 6) along the trajectory was computed with regards to velocity limitation of the robot joints (feedrate correction), for more details see [28].

1

distance

0.5

velocity acceleration

0

−0.5

0

1

2

3

4

5

t [s]

Fig. 6. Trajectory feed profile

Fig. 4. CAD model of the robot and exported coincidence points

Fig. 7. CAD model decomposition    1 4 2 ¯ . Vmax = Amax Tend − Tend − 2 Amax

Interpolated orientation (slerp with poly blend) Interpolated translation (line segments with poly blend)

Coincide points (including spry nozzle direction)

Z Y X

(14)

Inverse kinematics and inverse dynamic model were used for evaluating joint velocity, acceleration and torque for the planed end-effector trajectory parametrized by the takt time. 3. RESULTS AND CONCLUSION

Fig. 5. Coincidence points interpolation The KPDCAD model respecting the real structural design of the robot joints and links was decomposed, see Fig. 7, and the real dynamic parameters (generally different from the simplified ”rod” dynamic model (10) mentioned above) were exported (CAD software routine). The resulting dynamic model of the robot was used for the following verification dependent on the new objective function which took into account the engineering requirements. The takt time Tend was chosen as an independent variable and the joint velocity, acceleration and torque represented the outputs of the new objective function. Therefore the velocity profile with respect to max. acceleration Amax and takt time Tend results in a new velocity, see Fig. 6:

The initial robot kinematic parameters obtained from the mathematical optimization: (15) ξ  = [0.55 0.232 0.389 0.283 0.1] [m]. The following CAD modelling of the robot and the iterative process of adjusting the kinematic parameters to fulfil the engineering requirements (especially cabling and links collision limitation) result in the final robot kinematic parameters: ξ = [0.7 0.232 0.239 0.4136 0.471] [m]. (16) The Fig. 8 illustrates the resulting takt time Tend depending on the required one. The reduction can be shown at the beginning of the graph where the max. robot joint velocity limitation (feedrate correction) leads to slowing

Martin Švejda et al. / IFAC PapersOnLine 52-27 (2019) 305–310

The proposed methodology for engineering optimization was used for rapid prototyping of several other robots of non-standard architectures which have been developed at the NTIS research centre for key industrial partners. Despite the fact that the methodology does not provide generic fully automated tool for robot optimization, its main advantages can be summarized as follows: • A priori robot parameters estimation is supported by the model based design approach (simplified dynamic model, general objective function). • Unmodeled engineering requirements are taken into account based on iterative parameters adjustment supported by the robot CAD model.

Max. joint velocity [rad/s]

down of the end-efector along the planned trajectory. The Fig. 9 shows the maximum joint velocity, acceleration and torque depending on the resulting takt time. This dynamical study allows to verify the correct dimensioning of the robot actuators with respect to the minimum takt time.

309

Max. joint acceleration [rad/s2]



Resulting takt time [s]

Max. joint velocity [Nm]

Moreover the following control system design tasks which have to be taken into account for non-standard robot architectures are also addressed to NTIS research centre and some of them can be found in [9; 6; 13].

Resulting takt time [s]

Fig. 9. Maximum joint velocity, acceleration and torque [3] Required takt time [s]

Fig. 8. Resulting robot takt time ACKNOWLEDGEMENTS This work was supported by the project InteCom No. CZ.02.1.01/0.0/0.0/17 048/0007267 of the Czech Ministry of Education, Youth and Sports and the Technology Agency of the Czech Republic under Competence Centre CIDAM (Center for Intelligent Drives and Advanced Machine Control) No. TE02000103.

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