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Kinematics,SingularityandDexterityAnalysisof PlanarParallelManipulatorsBasedonDHMethod 397 0cpbpapp 3y3x3 2 y 2 x (29) If p x and p y in equation 28 are substituted in equation 29, one can obtain after simplification 0cba 2 333 22 (30) where )abab( 12131312 , 12131312 cbcb and 13121213 caca . The equation 30 can be converted into the eight-degree polynomial using 2 t1 t2 sin and 2 2 t1 t1 cos . The roots of this polynomial are the answer of the forward kinematics problem. Once is determined, p x and p y can be found easily substituting the angle in equation 28. After having position (p x , p y ) and orientation (), the passive joint angles can be found using the equation 21 by back substitution )ld( OBcossinp , )ld( OBsincosp 2tanA ii yyxy ii xyxx i iiiiii (31) The Jacobian matrix of the 3-dof PPM shown in Figure 3 is computed as follows. 0 d d d d Q d Q d Q d Q d Q d Q d Q d Q d Q p p p Q p Q p Q p Q p Q p Q Q p Q p Q 3 2 1 3 3 2 3 1 3 3 2 2 2 1 2 3 1 2 1 1 1 y x 3 y 3 x 3 2 y 2 x 2 1 y 1 x 1 0 d d d ld00 0ld0 00ld p p 3 2 1 33 22 11 y x 333 222 111 (32) where iii yxxxi sincosOBp (33) iii xyyyi sincosOBp (34) )OBOBpp(cos )OBOBpp(sin iiiiii iiiiii yxxyyxxy yyxxyyxxi (35) The overall Jacobian matrix is obtained as 33 3 33 3 33 3 22 2 22 2 22 2 11 1 11 1 11 1 ldldld ldldld ldldld J (36) Numerical example for the inverse kinematics: The dimensions of the planar 3-dof RPR parallel manipulator are given as l 1 =10, l 2 =10, l 3 =10, OB x1 =0, OB y1 =0, OB x2 =20, OB y2 =0, OB x3 =10, OB y3 =45, M 1 M 2 =15. The position of the point P in terms of the coordinate frame {xyz} attached to the M 1 corner of the moving platform is chosen as (4, 5). The angles λ 1 , λ 2 and λ 3 are computed as 231.3402, -24.4440 and 66.3453, where 51.3402 1 and 24.4440, 2 respectively. Moreover, the lengths PM 1 , PM 2 and PM3 are determined as 6.4031, 12.0830 and 8.7233, respectively. If the position and orientation in terms of the base frame {XYZ} are given as p x =12, p y =18 and =30º, the active joint variables d 1 d 2 and d 3 can be found as 6.0617, 9.5881 and 8.3594, respectively. The passive joint variables θ 1 , θ 2 and θ 3 are found as -43.4006, -11.8615 and -176.7655, respectively by back substitution. Numerical example for the forward kinematics: The dimensions of manipulator are given as l 1 =11, l 2 =11, l 3 =11, OB x1 =0, OB y1 =0, OB x2 =10, OB y2 =0, OB x3 =5, OB y3 =32, M 1 M 2 =10. The position of the point P in terms of the coordinate frame {xyz} is chosen as (5, 2.8868). The angles λ 1 , λ 2 and λ 3 are computed as 210.0004, -30.0004 and 90, where 30 1 and 30.0004, 2 respectively. Moreover, the lengths PM 1 , PM 2 and PM 3 are determined as 8.4853, 7.8102 and 3.5616, respectively. If the active and passive joint variables are given as d 1 =8, d 2 =7.9999, d 3 =7.9999 and θ 1 =-52.1046, θ 2 =-52.105, θ 3 =-127.8937, the position and orientation of end-effector in terms of base coordinate frame {XYZ} are found as p x =19,9936 p y =14.5569 and =0.000932º, respectively. Numerical example for the Jacobian matrix and condition number: Using the dimensions of numerical example for the inverse kinematics above, the Jacobian matrix and condition number are found as 0.47340.9984-0.0564 11.52900.97860.2055 3.64890.72660.6871 J and 8.1351 (37) Numerical example for the workspace determination: The dimensions of the manipulator are given as l 1 =l 2 =l 3 =8.5, OB x1 =0, OB y1 =0, OB x2 =17, OB y2 =0, OB x3 =9, OB y3 =40, M 1 M 2 =16. The lengths of the actuated prismatic joints vary between d i (min)=0 and d i (max)=8.5, where i=1,2,3. If the position of the point P in terms of the coordinate frame {xyz} is chosen as (7, 7), the angles λ 1 , λ 2 and λ 3 are computed as 225, -37.8750 and 81.7020, where 54 1 and RobotManipulators,NewAchievements398 37.8750, 2 respectively. Moreover, the lengths PM 1 , PM 2 and PM 3 are determined as 9.8995, 11.4018 and 6.9289, respectively. The workspace is obtained as 110.6180 for =0º orientation. The red rectangle given by Figure 4 illustrates the limits of the discretized Cartesian area. Additionally, the black region shows the reachable workspaces of the manipulator. Fig. 4. The workspace of the planar 3-dof RPR parallel manipulator. Numerical example for the dexterity and singularity analysis: The Figure 5 shows the inverse dexterity of the manipulator using the same dimensions given by the example for workspace determination. The GDI of the manipulator is found as 0.00018179. As can be illustrated in Figure 5, as the inverse of the condition numbers increase the manipulator accomplish better gross motion capability like the regions represented with red color. At the same time, the diagonal line divides the workspaces of the manipulator into two regions, illustrates the singular points. The dark blue areas illustrate the non-reachable workspaces of the manipulator. Fig. 5. The inverse dexterity graph for planar 3-dof RPR parallel manipulator. 4. Conclusion In this book chapter, the forward and inverse kinematics problems of planar parallel manipulators are obtained using Denavit & Hartenberg (1955) kinematic modelling convention. Afterwards some fundamental definitions about Jacobian matrix, condition number, global dexterity index, singularity and workspace determination are provided for performing the analyses of a two-degree-of-freedom (2-dof) PPM and a 3-dof Fully Planar Parallel Manipulator. 5. References Agrawal, S. K. (1990). Workspace boundaries in-parallel manipulator systems. Int. J. Robotics Automat , Vol., 6(3), pp. 281-290 Bonev, I. A. & Ryu, J. (2001). A geometrical method for computing the constant-orientation workspace of 6-PRRS parallel manipulators . Mechanism and Machine Theory, Vol., 36 (1), pp. 1–13 Denavit, J. & Hartenberg, R. S., (1955). A kinematic notation for lower-pair mechanisms based on matrices. Journal of Applied Mechanics, Vol., 22, 1955, pp. 215–221 Fichter, E. F. (1986). A Stewart platform-based manipulator: General theory and practical consideration. Journal of Robotics Research, pp. 157-182 Gosselin C., (1990). Determination of the workspace of 6-d.o.f parallel manipulators. ASME Journal of Mechanical Design, Vol., 112, 1990, pp. 331-336 Gosselin, C. & Angeles, J. (1991). A global performance index for the kinematic optimization of robotic manipulators. Journal of Mech Design, Vol., 113, 1991, pp. 220-226 Gosselin, C. M. & Guillot, M. (1991). The synthesis of manipulators with prescribed workspace. Journal of Mechanical Design, Vol., 113, pp. 451–455 Heerah, I.; Benhabib, B.; Kang, B. & Mills, K. J. (2003). Architecture selection and singularity analysis of a three-degree-of freedom planar parallel manipulator. Journal of Intelligent and Robotic Systems, Vol., 37, 2003, pp. 355-374 Hubbard, T.; Kujath, M. R. & Fetting, H. (2001). MicroJoints, Actuators, Grippers, and Mechanisms, CCToMM Symposium on Mechanisms, Machines and Mechatronics, Montreal, Canada Kang, B.; Chu, J. & Mills, J. K. (2001). Design of high speed planar parallel manipulator and multiple simultaneous specification control, Proceedings of IEEE International Conference on Robotics and Automation, pp. 2723-2728, South Korea Kang, B. & Mills, J. K. (2001). Dynamic modeling and vibration control of high speed planar parallel manipulator, In Proceedings of IEEE/RJS International Conference on Intelligent Robots and Systems, pp. 1287-1292, Hawaii Kim, D. I.; Chung, W. K. & Youm, Y. (1997). Geometrical approach for the workspace of 6- DOF parallel manipulators, Proceedings of IEEE International Conference on Robotics and Automation , pp. 2986-2991, Albuquerque, New Mexico Merlet, J. P. (1995). Determination of the orientation workspace of parallel manipulators. Journal of Intelligent and Robotic Systems, Vol., 13, pp. 143-160 Merlet, J. P. (1996). Direct kinematics of planar parallel manipulators, Proceedings of IEEE International Conference on Robotics and Automation, Vol., 4, pp. 3744-3749 Kinematics,SingularityandDexterityAnalysisof PlanarParallelManipulatorsBasedonDHMethod 399 37.8750, 2 respectively. Moreover, the lengths PM 1 , PM 2 and PM 3 are determined as 9.8995, 11.4018 and 6.9289, respectively. The workspace is obtained as 110.6180 for =0º orientation. The red rectangle given by Figure 4 illustrates the limits of the discretized Cartesian area. Additionally, the black region shows the reachable workspaces of the manipulator. Fig. 4. The workspace of the planar 3-dof RPR parallel manipulator. Numerical example for the dexterity and singularity analysis: The Figure 5 shows the inverse dexterity of the manipulator using the same dimensions given by the example for workspace determination. The GDI of the manipulator is found as 0.00018179. As can be illustrated in Figure 5, as the inverse of the condition numbers increase the manipulator accomplish better gross motion capability like the regions represented with red color. At the same time, the diagonal line divides the workspaces of the manipulator into two regions, illustrates the singular points. The dark blue areas illustrate the non-reachable workspaces of the manipulator. Fig. 5. The inverse dexterity graph for planar 3-dof RPR parallel manipulator. 4. Conclusion In this book chapter, the forward and inverse kinematics problems of planar parallel manipulators are obtained using Denavit & Hartenberg (1955) kinematic modelling convention. Afterwards some fundamental definitions about Jacobian matrix, condition number, global dexterity index, singularity and workspace determination are provided for performing the analyses of a two-degree-of-freedom (2-dof) PPM and a 3-dof Fully Planar Parallel Manipulator. 5. References Agrawal, S. K. (1990). Workspace boundaries in-parallel manipulator systems. Int. J. Robotics Automat , Vol., 6(3), pp. 281-290 Bonev, I. A. & Ryu, J. (2001). A geometrical method for computing the constant-orientation workspace of 6-PRRS parallel manipulators . Mechanism and Machine Theory, Vol., 36 (1), pp. 1–13 Denavit, J. & Hartenberg, R. S., (1955). A kinematic notation for lower-pair mechanisms based on matrices. Journal of Applied Mechanics, Vol., 22, 1955, pp. 215–221 Fichter, E. F. (1986). A Stewart platform-based manipulator: General theory and practical consideration. Journal of Robotics Research, pp. 157-182 Gosselin C., (1990). Determination of the workspace of 6-d.o.f parallel manipulators. ASME Journal of Mechanical Design, Vol., 112, 1990, pp. 331-336 Gosselin, C. & Angeles, J. (1991). A global performance index for the kinematic optimization of robotic manipulators. Journal of Mech Design, Vol., 113, 1991, pp. 220-226 Gosselin, C. M. & Guillot, M. (1991). The synthesis of manipulators with prescribed workspace. Journal of Mechanical Design, Vol., 113, pp. 451–455 Heerah, I.; Benhabib, B.; Kang, B. & Mills, K. J. (2003). Architecture selection and singularity analysis of a three-degree-of freedom planar parallel manipulator. Journal of Intelligent and Robotic Systems, Vol., 37, 2003, pp. 355-374 Hubbard, T.; Kujath, M. R. & Fetting, H. (2001). MicroJoints, Actuators, Grippers, and Mechanisms, CCToMM Symposium on Mechanisms, Machines and Mechatronics, Montreal, Canada Kang, B.; Chu, J. & Mills, J. K. (2001). Design of high speed planar parallel manipulator and multiple simultaneous specification control, Proceedings of IEEE International Conference on Robotics and Automation, pp. 2723-2728, South Korea Kang, B. & Mills, J. K. (2001). Dynamic modeling and vibration control of high speed planar parallel manipulator, In Proceedings of IEEE/RJS International Conference on Intelligent Robots and Systems, pp. 1287-1292, Hawaii Kim, D. I.; Chung, W. K. & Youm, Y. (1997). Geometrical approach for the workspace of 6- DOF parallel manipulators, Proceedings of IEEE International Conference on Robotics and Automation , pp. 2986-2991, Albuquerque, New Mexico Merlet, J. P. (1995). Determination of the orientation workspace of parallel manipulators. Journal of Intelligent and Robotic Systems, Vol., 13, pp. 143-160 Merlet, J. P. (1996). Direct kinematics of planar parallel manipulators, Proceedings of IEEE International Conference on Robotics and Automation, Vol., 4, pp. 3744-3749 RobotManipulators,NewAchievements400 Merlet, J. P.; Gosselin, C. M. & Mouly, N. (1998). Workspaces of planar parallel manipulators. Mechanism and Machine Theory, Vol., 33, pp. 7–20 Merlet, J. P. (2000). Parallel robots, Kluwer Academic Publishers Tsai, L. W. (1999). Robot analysis: The mechanics of serial and parallel manipulators, A Wiley- Interscience Publication RobotManipulatorProbabilisticWorkspaceAppliedtoRoboticAssistance 401 RobotManipulatorProbabilisticWorkspaceAppliedtoRoboticAssistance FernandoA.AuatCheein,FernandodiSciascio,JuanMarcosToiberoandRicardoCarelli x Robot Manipulator Probabilistic Workspace Applied to Robotic Assistance Fernando A. Auat Cheein, Fernando di Sciascio, Juan Marcos Toibero and Ricardo Carelli Instituto de Automatica, National University of San Juan Argentina 1. Introduction The probabilistic modelling of a robot manipulator workspace when combined with a Human-Machine Interface (HMI) allows the extraction and learning of the spatial preferences of the user. Furthermore, the knowledge of the most accessed zones of the robot’s workspace permits the bounding of the time needed for the robot to reach a given position at its workspace. From its early beginning, the use of robot manipulators within the robotic assistance field was concerned to emulate an orthopaedic arm (Fukuda et al, 2003; Zecca et al, 2002; Lopez et al, 2009). Therefore, the robot manipulator was considered as the final actuator of the assistive system where its main goal was to imitate the movements of an arm. Depending on the user/patient capabilities, the robot manipulator was commanded by either electro- myographic or electro-encephalic signals (Ferreira et al, 2006a; 2006b; 2008). A robotic device controlled by a Muscle-Computer Interface (MCI) can be found in (Artemiadis & Kyriakopoulos, 2006; Lopez et al, 2007; Millan et al, 2004; Ferreira et al, 2006b; Lopez et al, 2009; Ferreira et al, 2008). In these works, the electro-miographic signal is acquired, processed, classified and converted to motion commands. The system is closed by a bio- feedback loop. When used with a robot manipulator, a MCI is usually connected to a set of muscles that the patient is able to move at its own will. The number of channels used by the interface increases as increases the number of the degrees of freedom (DOF) of the robot (Yatsenko et al, 2007; Lopez et al, 2009; Ferreira et al, 2008). Thus, for a single 2DOF robot manipulator are necessary three different muscles: two to govern each DOF and a third to set a sign (if the manipulator is moving to the left or to the right), for a direct control of the robot manipulator. For robotic devices controlled by Brain-Computer Interfaces (BCI’s), the situation is analogous to the MCI; the number of signals or patterns to be extracted from the EEG (electro-encephalogram) increases as increases with the number of DOF’s –or actions– to be performed by the robot. Although most applications of BCI’s are oriented to govern a mobile robot –because of its direct analogy with a motorized wheelchair (Bastos Filho et al, 2007a; Bastos Filho, 2007; Ferreira et al, 2008; Bastos Filho et al, 2007b)– some works have been published showing the implementation of a BCI to control the movements of a robot 22 RobotManipulators,NewAchievements402 manipulator (Oskoei & Hu, 2007; Farry et al, 1996; Auat Cheein et al, 2007a; Auat Cheein et al, 2007b; Auat Cheein et al, 2008). The way that the patient interacts with the interface is determined by the objective of the HMI. Thus, for a HMI connected to a robot, the proper motion of the automata serves as a bio-feedback channel to the user (Wolpaw et al, 2002 ; Ferreira et al, 2008). A more suitable way to interact with the user is by means of scan modes. The scan modes have been widely used in the recent years for assistance technology. It is not restricted only to BCI’s or MCI’s but to most of HMI. The scan mode applied to a HMI’s in robotic assistance is mainly composed by a series of icons; each icon represents an action or a place attached to the robotic task; the patient, using its biological signals, displace the scan over the several icons; once an icon is selected –also using the biological signals– the robot performs the task associated with the selected icon. This kind of interface decreases the effort of the user when generating the biological signals, relegating the control of the interface to the control of the scan. Moreover, some HMI include an automatic scan; thus the user only has to accept –or cancel if needed– an icon within the scan. Figure 1 shows a general architecture of a HMI with a scan mode incorporated. Robot Manipulator Motorized Weelchair Mobile Robot scan mode bio- feedback robotic device bio-feedback Signal Acquisition/ Digitalization user/patient Signal Processing Feature Extraction Translation Fig. 1. General architecture of a HMI. The dashed and solid blue-lines correspond to a HMI that control the robotic device in a direct way; the solid and dashed-red lines refer to a HMI with a scan mode incorporated on it. Figure 1 shows the general architecture of a HMI. When the HMI has a scan mode, the bio- feedback loop is closed by both the robot’s movements and the scan mode itself. As was stated before, the scan mode reduces the work of the HMI’s user, although it restricts the interface to a number of actions associated with the icons within the scan. In this work we show the implementation of a robot manipulator workspace scan mode applied to a HMI. Although we have used a BCI, any other HMI can be adapted to the system presented in this work. The robotic device used is a SCARA robot manipulator (Sciavicco & Siciliano, 2000). The robot’s workspace is divided into cells. Each cell has a probability value associated with it. The scan mode is run according the probability information of the cell, decreasing in that way the time needed for the robot to reach the desire cell. Once a cell is chosen by the user, the robot manipulator reaches the center of mass of the cell using a kinematic controller. Three types of scan modes are shown in this work: an uniform scan mode and two based on the probabilistic information of the workspace. The three scan modes are tested by Monte Carlo experiments. The probability-based scan modes learn the preferences of the patient by the measure of the probability of a cell in being selected by the user. The probability value of each cell at the robot’s workspace is dynamically maintained according to the patient cell’s selection. Considering that the robot’s workspace behaves as a probability density function, the Kullback-Liebler (relative entropy) measure is shown in order to establish a measure of divergence between the different scan modes. 2. Overview of the System The main objective of the HMI is that the user/patient be capable of generating a set of commands by means of his/her biological signals in order to control the robotic device used. In this work, the HMI used is a BCI but is not restricted to it. The BCI is controlled by event related potentials (ERP) acquired from the occipital lobe of the patient. Such potentials are the event related synchronization/desynchronization (ERS/ERD). The ERS/ERD potentials are measured in the alpha band (8–13 Hz) of the EEG from the occipital lobe. The BCI conform an alphabet of commands from the ERS and ERD which are then sent to a Finite State Machine (FSM). The FSM contains actions or desired behaviors of the robot to be performed if the user generates the appropriate command. The BCI was tested in a population of 25 cognitive normal volunteers and the results can be seen in (Ferreira et al, 2008). The robot manipulator is the actuator device that completes the HMI system. The robot used in this work is a SCARA type, Bosch SR-800 (see Fig. 2). In the absence of perturbations and without considering gravity effects, the dynamic of a rigid robot manipulator with n joints can be expressed as (1). )(),()( qfqqqCqqM (1) In (1), q is an n 1-array of joint angular positions; is an n 1-array of applied torques; M(q) is the n n positive definite inertia matrix; ),( qqC is an n n matrix of centripetal and Coriolis effect and )(qf is an n 1-array of friction moments. More information about the robot’s parameters can be found in (Bastos Filho et al, 2006 ; Ferreira et al, 2006c). RobotManipulatorProbabilisticWorkspaceAppliedtoRoboticAssistance 403 manipulator (Oskoei & Hu, 2007; Farry et al, 1996; Auat Cheein et al, 2007a; Auat Cheein et al, 2007b; Auat Cheein et al, 2008). The way that the patient interacts with the interface is determined by the objective of the HMI. Thus, for a HMI connected to a robot, the proper motion of the automata serves as a bio-feedback channel to the user (Wolpaw et al, 2002 ; Ferreira et al, 2008). A more suitable way to interact with the user is by means of scan modes. The scan modes have been widely used in the recent years for assistance technology. It is not restricted only to BCI’s or MCI’s but to most of HMI. The scan mode applied to a HMI’s in robotic assistance is mainly composed by a series of icons; each icon represents an action or a place attached to the robotic task; the patient, using its biological signals, displace the scan over the several icons; once an icon is selected –also using the biological signals– the robot performs the task associated with the selected icon. This kind of interface decreases the effort of the user when generating the biological signals, relegating the control of the interface to the control of the scan. Moreover, some HMI include an automatic scan; thus the user only has to accept –or cancel if needed– an icon within the scan. Figure 1 shows a general architecture of a HMI with a scan mode incorporated. Robot Manipulator Motorized Weelchair Mobile Robot scan mode bio- feedback robotic device bio-feedback Signal Acquisition/ Digitalization user/patient Signal Processing Feature Extraction Translation Fig. 1. General architecture of a HMI. The dashed and solid blue-lines correspond to a HMI that control the robotic device in a direct way; the solid and dashed-red lines refer to a HMI with a scan mode incorporated on it. Figure 1 shows the general architecture of a HMI. When the HMI has a scan mode, the bio- feedback loop is closed by both the robot’s movements and the scan mode itself. As was stated before, the scan mode reduces the work of the HMI’s user, although it restricts the interface to a number of actions associated with the icons within the scan. In this work we show the implementation of a robot manipulator workspace scan mode applied to a HMI. Although we have used a BCI, any other HMI can be adapted to the system presented in this work. The robotic device used is a SCARA robot manipulator (Sciavicco & Siciliano, 2000). The robot’s workspace is divided into cells. Each cell has a probability value associated with it. The scan mode is run according the probability information of the cell, decreasing in that way the time needed for the robot to reach the desire cell. Once a cell is chosen by the user, the robot manipulator reaches the center of mass of the cell using a kinematic controller. Three types of scan modes are shown in this work: an uniform scan mode and two based on the probabilistic information of the workspace. The three scan modes are tested by Monte Carlo experiments. The probability-based scan modes learn the preferences of the patient by the measure of the probability of a cell in being selected by the user. The probability value of each cell at the robot’s workspace is dynamically maintained according to the patient cell’s selection. Considering that the robot’s workspace behaves as a probability density function, the Kullback-Liebler (relative entropy) measure is shown in order to establish a measure of divergence between the different scan modes. 2. Overview of the System The main objective of the HMI is that the user/patient be capable of generating a set of commands by means of his/her biological signals in order to control the robotic device used. In this work, the HMI used is a BCI but is not restricted to it. The BCI is controlled by event related potentials (ERP) acquired from the occipital lobe of the patient. Such potentials are the event related synchronization/desynchronization (ERS/ERD). The ERS/ERD potentials are measured in the alpha band (8–13 Hz) of the EEG from the occipital lobe. The BCI conform an alphabet of commands from the ERS and ERD which are then sent to a Finite State Machine (FSM). The FSM contains actions or desired behaviors of the robot to be performed if the user generates the appropriate command. The BCI was tested in a population of 25 cognitive normal volunteers and the results can be seen in (Ferreira et al, 2008). The robot manipulator is the actuator device that completes the HMI system. The robot used in this work is a SCARA type, Bosch SR-800 (see Fig. 2). In the absence of perturbations and without considering gravity effects, the dynamic of a rigid robot manipulator with n joints can be expressed as (1). )(),()( qfqqqCqqM (1) In (1), q is an n 1-array of joint angular positions; is an n 1-array of applied torques; M(q) is the n n positive definite inertia matrix; ),( qqC is an n n matrix of centripetal and Coriolis effect and )(qf is an n 1-array of friction moments. More information about the robot’s parameters can be found in (Bastos Filho et al, 2006 ; Ferreira et al, 2006c). RobotManipulators,NewAchievements404 Considering that the objective of the HMI is to position the robot manipulator at a specific cell of its workspace, a kinematic controller was used (Kelly et al, 2004). Fig. 2. Robot manipulator Bosch SR-800. 3. Sequential Scan Mode The scan mode developed in this work is an automatic one. The workspace of the robot manipulator is divided into cells. As a first approach lets considerer that the cells do not have a probability value associated with them. Thus, the probability of a cell to be chosen by the patient is the same for all the cells at the robot’s workspace. Moreover, the probability of being scanned is also the same. Figure 3.a shows the cells’ distribution of the robot’s workspace. The number of cells can be increased if the application requires it. Instead of scanning cell by cell, the robot’s workspace is divided into three main zones. Then, the scan mode is first made zone by zone until one zone is selected by the user (see Fig. 3.b). Once a zone is selected, the scan is made row by row of the selected zone. If after three row-by-row scans, no row is selected, the scan returns to be executed zone-by-zone. On the other hand, if a row is selected, then the scan passes to be cell-by-cell until a cell is selected (see Fig. 3.c). The scan returns to be row-by-row if no cell is selected after three runs. Once a cell is selected, the robot is positioned at the center of mass of the cell and the scan mode begins again zone-by-zone. The three zones division of the robot manipulator’s workspace is based on the fact that a normal limbed patient grasps the elements of the environment from the right, center or left to his/her body. The final interface is presented in Fig. 4. a) b) c) Fig. 3. Sequential scan mode. a) The scan is first executed zone-by-zone until one zone is selected by the user; b) then the scan is executed row-by-row of the selected zone; c) the scan is run cell-by-cell of the selected row. RobotManipulatorProbabilisticWorkspaceAppliedtoRoboticAssistance 405 Considering that the objective of the HMI is to position the robot manipulator at a specific cell of its workspace, a kinematic controller was used (Kelly et al, 2004). Fig. 2. Robot manipulator Bosch SR-800. 3. Sequential Scan Mode The scan mode developed in this work is an automatic one. The workspace of the robot manipulator is divided into cells. As a first approach lets considerer that the cells do not have a probability value associated with them. Thus, the probability of a cell to be chosen by the patient is the same for all the cells at the robot’s workspace. Moreover, the probability of being scanned is also the same. Figure 3.a shows the cells’ distribution of the robot’s workspace. The number of cells can be increased if the application requires it. Instead of scanning cell by cell, the robot’s workspace is divided into three main zones. Then, the scan mode is first made zone by zone until one zone is selected by the user (see Fig. 3.b). Once a zone is selected, the scan is made row by row of the selected zone. If after three row-by-row scans, no row is selected, the scan returns to be executed zone-by-zone. On the other hand, if a row is selected, then the scan passes to be cell-by-cell until a cell is selected (see Fig. 3.c). The scan returns to be row-by-row if no cell is selected after three runs. Once a cell is selected, the robot is positioned at the center of mass of the cell and the scan mode begins again zone-by-zone. The three zones division of the robot manipulator’s workspace is based on the fact that a normal limbed patient grasps the elements of the environment from the right, center or left to his/her body. The final interface is presented in Fig. 4. a) b) c) Fig. 3. Sequential scan mode. a) The scan is first executed zone-by-zone until one zone is selected by the user; b) then the scan is executed row-by-row of the selected zone; c) the scan is run cell-by-cell of the selected row. [...]... reduction is drastic and the robot is easily in the safe zone This latter approach that combines soft covering and active sensing is often referred to robot skin This concept is a promising solution that could 426 Robot Manipulators, New Achievements 110 Activated skin Desactivated skin Without skin Maximum measured force (N) 100 90 80 Unified pain tolerance threshold 70 60 50 40 30 20 10 0 0 0.1 0.2 0.3 0.4... mechanism on the robot that can disconnect the endeffector if the forces applied on it are excessive Firstly, in the case of mechanisms performing horizontal motion only, the load to be carried by the robot is not limited This is also the case for the 3-DOF architectures if gravity is compen- 424 Robot Manipulators, New Achievements Fig 2 Example of a collision between a person and a suspended robot with... Considering that the scan mode of this approach is based on the probability weight of the cells of the robot s workspace, if a cell, e.g., has the highest probability value of the zone 2 at time t, and it is successively accessed, then at the instant t + k that cell might abandon the 410 Robot Manipulators, New Achievements zone 2 -because of it probability value increases- and enter to zone 1 Nevertheless,... potentially harmful contacts Ebert et al (2005); Lu et al (2005); 420 Robot Manipulators, New Achievements 2 to detect a collision by monitoring joint torques or a robot skin and quickly react to maintain the contact forces under a certain levelDe Luca et al (2006); Duchaine, Lauzier, Baril, Lacasse & Gosselin (2009); 3 to design robots that are intrinsically safe, i.e., that are physically unable to... probability value according to Table 1- remains unbounded in Fig 8.b The probability value of the cells and zones in Fig 8 is represented by the gray-bar at the top of each figure 414 Robot Manipulators, New Achievements a) b) Fig 8 Robot s workspace zones’ division after the Monte Carlo experiment a) Zones probability distribution according to the first approach of the probability scan mode b) Cells probability... -density function- and q (.) -mass function- respectively 416 Robot Manipulators, New Achievements f ( x) )dx f ( x) log( g ( x) D f || g D p||q x p ( x) log( p ( x) ) q( x) (5) (6) Considering that the set of cells is the same for both probability based scan modes approaches, equation (6) is directly applied to the pmds of the robot manipulator Thus, for the experiment shown in Fig... on EMG and EEG applied to robotic systems Journal of NeuroEngineering and Rehabilitation, 5, 1-15 Fishman, G.S (1996) Monte Carlo Concepts, Algorithms, and Applications New York, SpringerVerlag Fukuda, O ; Tsuji, T ; Kaneko, M & Otsuka, A (2003) A Human-Assisting Manipulator Teleoperated by EMG Signals and Arm Motions IEEE Trans on Robotics and Automation, 19, 210- 222, ISSN: 104 2-296X Kelly, R.; Carelli,... 0278-940X On the Design of Human-Safe Robot Manipulators 419 23 0 On the Design of Human-Safe Robot Manipulators Vincent Duchaine, Nicolas Lauzier and Clément Gosselin Department of Mechanical Engineering Université Laval Canada 1 Introduction Bringing robot manipulators in the same environment as humans seems a natural evolution in the path towards more advanced robotics This upcoming co-existence will...406 Robot Manipulators, New Achievements Fig 4 Visualization of the robot manipulator’s workspace according to the user interface 4 Probability-based Scan Mode Two probability-based scan modes have been implemented in this work A first approach... passive compliance is a promising approach However, this method also has some disadvantages First, by adding a torque limiter on each joint of a serial robot, the force threshold will depend on the configuration of the manipulator 422 Robot Manipulators, New Achievements This is because the relation between external forces and articular torques is determined by the Jacobian matrix of the manipulator, which . kinematics of planar parallel manipulators, Proceedings of IEEE International Conference on Robotics and Automation, Vol., 4, pp. 3744-3749 Robot Manipulators, New Achievements4 00 Merlet, J been published showing the implementation of a BCI to control the movements of a robot 22 Robot Manipulators, New Achievements4 02 manipulator (Oskoei & Hu, 2007; Farry et al, 1996; Auat Cheein. friction moments. More information about the robot s parameters can be found in (Bastos Filho et al, 2006 ; Ferreira et al, 2006c). Robot Manipulators, New Achievements4 04 Considering that the