《电子工程师手册》学习资料（英文版）ch101 Robotics.pdf_大学文库

10l Robotics Cartesian Configuration . C Ty A. Lasky Configuration. Articulated Configurati Configuration. Gantry Configuratio 101.2 Dynamics and Control Independent Joint Control of the Robot. Dynamic Models iversity of California, Dav omputed Torque Methods. Adaptive Control. Resolved R Lal tummala Motion Control. Compliant Motion. Flexible Manipulators Justification. Implementation Strategies. Applications in Nicholas G. Drey Manufacturing. Emerging Iss 101.1 Robot Configuration Ty A. Lasky and Tien C. hsia Configuration is a fundamental classification for industrial robots. Configuration refers to the geometry of the robot manipulator, i.e., the manner in which the links of the manipulator are connected at each joint. The Robotic Industries Association(RIA) defines a robot as a manipulator designed to move material, parts, tools, or specialized devices, through variable programmed motions for the perfo rmance or a riety of tasks. With this finition, attention here is focused on industrial manipulator arms, typically mounted on a fixed pedestal base. Mobile robots and hard automation [ e.g., Computer Numerical Control( CNC)machines] are excluded The emphasis here is on serial-chain manipulator arms, which consist of a serial chain of linkages, where each link is connected to exactly two other links, with the exception of the first and last, which are connected to only one other link. Additionally, the first three links, called the major linkages, are focused on, with only a brief mention of the last three links, or wrist joints, also called the minor linkages Robot configuration is an important consideration in the selection of a manipulator. Configuration refers to the way the manipulator links are connected at each joint. Each link will be connected to the subsequent link by either a linear(sliding or prismatic) joint, which can be abbreviated with a P, or a revolute (or rotary) int,abbreviated with an R. Using this notation, a robot with three revolute joints would be abbreviated as RRR, while one with a rotary joint followed by two linear (prismatic) joints would be denoted RPP. Each configuration type is well suited to certain types of tasks and ill suited to others. Some configurations are more versatile than others. In addition to the geometrical considerations, robot configuration affects the structural stiffness of the robot, which may be an important consideration. Also, configuration impacts the complexity the forward and inverse kinematics, which are the mappings between the robot actuator (joint)space, and the Cartesian position and orientation of the robot end-effector, or tool. There are six major robot configurations commonly used in industry. Details for each configuration are presented in subsequent subsections. The simplest configuration is the Cartesian robot, which consists of three rthogonal, linear joints(PPP), so that the robot moves in the x, y and z directions in the joint space. The c 2000 by CRC Press LLC

© 2000 by CRC Press LLC 101 Robotics 101.1 Robot Configuration Cartesian Configuration • Cylindrical Configuration • Spherical Configuration • Articulated Configuration • SCARA Configuration • Gantry Configuration • Additional Information 101.2 Dynamics and Control Independent Joint Control of the Robot • Dynamic Models • Computed Torque Methods • Adaptive Control • Resolved Motion Control • Compliant Motion • Flexible Manipulators 101.3 Applications Justification • Implementation Strategies • Applications in Manufacturing • Emerging Issues 101.1 Robot Configuration Ty A. Lasky and Tien C. Hsia Configuration is a fundamental classification for industrial robots. Configuration refers to the geometry of the robot manipulator, i.e., the manner in which the links of the manipulator are connected at each joint. The Robotic Industries Association (RIA) defines a robot as a manipulator designed to move material, parts, tools, or specialized devices, through variable programmed motions for the performance of a variety of tasks. With this definition, attention here is focused on industrial manipulator arms, typically mounted on a fixed pedestal base. Mobile robots and hard automation [e.g., Computer Numerical Control (CNC) machines] are excluded. The emphasis here is on serial-chain manipulator arms, which consist of a serial chain of linkages, where each link is connected to exactly two other links, with the exception of the first and last, which are connected to only one other link. Additionally, the first three links, called the major linkages, are focused on, with only a brief mention of the last three links, or wrist joints, also called the minor linkages. Robot configuration is an important consideration in the selection of a manipulator. Configuration refers to the way the manipulator links are connected at each joint. Each link will be connected to the subsequent link by either a linear (sliding or prismatic) joint, which can be abbreviated with a P, or a revolute (or rotary) joint, abbreviated with an R. Using this notation, a robot with three revolute joints would be abbreviated as RRR, while one with a rotary joint followed by two linear (prismatic) joints would be denoted RPP. Each configuration type is well suited to certain types of tasks and ill suited to others. Some configurations are more versatile than others. In addition to the geometrical considerations, robot configuration affects the structural stiffness of the robot, which may be an important consideration. Also, configuration impacts the complexity of the forward and inverse kinematics, which are the mappings between the robot actuator (joint) space, and the Cartesian position and orientation of the robot end-effector, or tool. There are six major robot configurations commonly used in industry. Details for each configuration are presented in subsequent subsections. The simplest configuration is the Cartesian robot, which consists of three orthogonal, linear joints (PPP), so that the robot moves in the x, y, and z directions in the joint space. The Ty A. Lasky University of California, Davis Tien C. Hsia University of California, Davis R. Lal Tummala Michigan State University Nicholas G. Odrey Lehigh University

cylindrical configuration consists of one revolute and two linear TABLE 101.1 Robot Arm Geometry Usage coordinate system. The spherical configuration consists of two rev Percent of Use olute joints and one linear joint(RRP), so that the robot moves in Cartesian a spherical, or polar, coordinate system. The articulated(arm-and elbow) configuration consists of three revolute joints(RRR), giving Articulated 85025 the robot a somewhat human-like range of motion. The SCARA SCARA (Selectively Compliant Assembly Robot Arm) configuration con- sists of two revolute joints and one linear joint(RRP), arranged in York: Elsevier, 1988. With permission. different fashion than the spherical configuration. It may also be equipped with a revolute joint on the final sliding link. The gantry configuration is essentially a Cartesian configuration, with the robot mounted on an overhead track system. One can also mount other robot config urations on an overhead gantry system to give the robot an extended workspace, as well as free up valuable factory floor space. The percentage usage of the first five configuration types is listed in Table 101.1. This table does not include gantry robots, which are assumed to be included in the Cartesian category. Additionally, this information is from 1988, and does not accurately represent current usage In general, robots with a rotary base have a speed advantage. However, they have more variation in resolution and dynamics compared to Cartesian robots. This can lead to inferior performance if a fixed controller is used over the robot's entire workspace. Cartesian Configuration The Cartesian configuration consists of three orthogonal, axes, abbreviated as PPP, as shown in Fig. 101.1. Thus, the space of the robot corresponds directly with the standard right handed Cartesian xyz-coordinate system, yielding the simplest possible kinematic equations. The work envelope of the Carte sian robot is shown in Fig. 101.2. The work envelope encloses all the points that can be reached by the robot arm or the mounting point for the end-effector or tool. The area reachable by an end effector or tool is not considered part of the work envelope interaction with other machines, parts, or processes must take of a robot is assumed to be equivalent to the work envelope. There are several advantages to this configuration. As noted above, the robot is kinematically simple, since motion on each Cartesian axis corresponds to motion of a single actuator. This eases the programming of linear motions. In particular, it is easy to do a straight vertical motion, the most common motion in assembly tasks. The Cartesian geometry also yields a constant FIGURE 101.1 The Cartesian configuration arm resolution throughout the workspace; i.e., for any config ( Source: T. Owen, Assembly with Robots, Engle ration, the resolution for each axis corresponds directly to the wood Cliffs, N. Prentice-Hall, 1985. with per- resolution for that joint. The simple geometry of the Cartesian robot leads to correspondingly simple manipulator dynamics. The disadvantages of this configuration include inability to reach objects on the floor or points invisible from the base of the robot, and slow speed of operation in the horizontal plane compared to robots with a rotary base. Additionally, the Cartesian configuration requires a large operating volume for a relatively small workspace. Cartesian robots are used for several applications. As noted above, they are well suited for assembly opera- tions, as they easily perform vertical straight-line insertions. Because of the ease of straight-line motions, they are also well suited to machine loading and unloading. They are also used in clean room tasks c 2000 by CRC Press LLC

© 2000 by CRC Press LLC cylindrical configuration consists of one revolute and two linear joints (RPP), so that the robot joints correspond to a cylindrical coordinate system. The spherical configuration consists of two revolute joints and one linear joint (RRP), so that the robot moves in a spherical, or polar, coordinate system. The articulated (arm-andelbow) configuration consists of three revolute joints (RRR), giving the robot a somewhat human-like range of motion. The SCARA (Selectively Compliant Assembly Robot Arm) configuration consists of two revolute joints and one linear joint (RRP), arranged in a different fashion than the spherical configuration. It may also be equipped with a revolute joint on the final sliding link. The gantry configuration is essentially a Cartesian configuration, with the robot mounted on an overhead track system. One can also mount other robot configurations on an overhead gantry system to give the robot an extended workspace, as well as free up valuable factory floor space. The percentage usage of the first five configuration types is listed in Table 101.1. This table does not include gantry robots, which are assumed to be included in the Cartesian category. Additionally, this information is from 1988, and does not accurately represent current usage. In general,robots with a rotary base have a speed advantage. However, they have more variation in resolution and dynamics compared to Cartesian robots. This can lead to inferior performance if a fixed controller is used over the robot’s entire workspace. Cartesian Configuration The Cartesian configuration consists of three orthogonal, linear axes, abbreviated as PPP, as shown in Fig. 101.1. Thus, the joint space of the robot corresponds directly with the standard righthanded Cartesian xyz-coordinate system, yielding the simplest possible kinematic equations. The work envelope of the Cartesian robot is shown in Fig. 101.2. The work envelope encloses all the points that can be reached by the robot arm or the mounting point for the end-effector or tool. The area reachable by an end effector or tool is not considered part of the work envelope. All interaction with other machines, parts, or processes must take place within this volume [Critchlow, 1985]. Here, the workspace of a robot is assumed to be equivalent to the work envelope. There are several advantages to this configuration. As noted above, the robot is kinematically simple, since motion on each Cartesian axis corresponds to motion of a single actuator. This eases the programming of linear motions. In particular, it is easy to do a straight vertical motion, the most common motion in assembly tasks. The Cartesian geometry also yields a constant arm resolution throughout the workspace; i.e., for any configuration, the resolution for each axis corresponds directly to the resolution for that joint. The simple geometry of the Cartesian robot leads to correspondingly simple manipulator dynamics. The disadvantages of this configuration include inability to reach objects on the floor or points invisible from the base of the robot, and slow speed of operation in the horizontal plane compared to robots with a rotary base.Additionally, the Cartesian configuration requires a large operating volume for a relatively small workspace. Cartesian robots are used for several applications. As noted above, they are well suited for assembly operations, as they easily perform vertical straight-line insertions. Because of the ease of straight-line motions, they are also well suited to machine loading and unloading. They are also used in clean room tasks. FIGURE 101.1 The Cartesian configuration. (Source: T. Owen, Assembly with Robots, Englewood Cliffs, N.J.: Prentice-Hall, 1985. With permission.) TABLE 101.1 Robot Arm Geometry Usage Arm Geometry Percent of Use Cartesian 18 Cylindrical 15 Spherical 10 Articulated 42 SCARA 15 Source: V. D. Hunt, Robotics Sourcebook, New York: Elsevier, 1988. With permission

Plan view Horizontal OOOO Vertical Work Envelope Envelope Elevation FIGURE 101. 10 SCARA robot work envelope This configuration has many advantages and is quite popular in industry. The configuration was designed pecifically for assembly tasks [Truman, 1990], so has distinct advantages when applied in this area. Because of the vertical orientation of the joints, gravity does not affect the dynamics of the first two joints. In fact, for these joints, the actuators can be shut off and the arm will not fall, even without the application of brakes. As the name SCARA implies, this allows compliance in the horizontal directions to be selectively varied; therefore, ne robot can comply to horizontal forces. Horizontal compliance is important for vertical assembly operations Because of the vertical linear joint, straight-line vertical motions are simple. Also, SCARA robots typically have high positional repeatability. The revolute joints allow high-speed motion. On the negative side, the resolution of the arm is not constant throughout the workspace, and the kinematic equations are relatively complex. In addition, the vertical motion of the SCARa configuration is typically quite limited. While the SCARA robot can reach around objects, it cannot reach over them in the same manner as an articulated arm. Gantry Configuration The gantry configuration is geometrically equiva ent to the Cartesian configuration, but is sus pended from an overhead crane and typically can be moved over a large workspace. It consists of three linear joints(PPP), and is illustrated in Fig. 101. 11. In terms of work envelope, it will have a rectangular volume that sweeps out most of the inner area of the gantry system, with a height lim- ited by the length of the vertical mast, and the headroom above the gantry system. One consid eration in the selection of a gantry robot is the type of vertical linkage employed in the z axis. A monomast design is more rigid, yielding tighter olerances for repeatability and accuracy, but requires significant headroom above the gantry to have a large range of z axis motion. On the other hand, a telescoping linkage will require signifi cantly less headroom but is less rigid, with corre sponding reduction in repeatability and accuracy her robot configurations can be mounted on FIGURE 101.11 The gantry configuration. Source: T Owen, ry systems, thus gaining many of the advan- Assembly with Robots, Englewood Cliffs, N J: Prentice-Hall, 1985. of this geometr With permission. c 2000 by CRC Press LLC

© 2000 by CRC Press LLC This configuration has many advantages and is quite popular in industry. The configuration was designed specifically for assembly tasks [Truman, 1990], so has distinct advantages when applied in this area. Because of the vertical orientation of the joints, gravity does not affect the dynamics of the first two joints. In fact, for these joints, the actuators can be shut off and the arm will not fall, even without the application of brakes. As the name SCARA implies, this allows compliance in the horizontal directions to be selectively varied; therefore, the robot can comply to horizontal forces. Horizontal compliance is important for vertical assembly operations. Because of the vertical linear joint, straight-line vertical motions are simple. Also, SCARA robots typically have high positional repeatability. The revolute joints allow high-speed motion. On the negative side, the resolution of the arm is not constant throughout the workspace, and the kinematic equations are relatively complex. In addition, the vertical motion of the SCARA configuration is typically quite limited. While the SCARA robot can reach around objects, it cannot reach over them in the same manner as an articulated arm. Gantry Configuration The gantry configuration is geometrically equivalent to the Cartesian configuration, but is suspended from an overhead crane and typically can be moved over a large workspace. It consists of three linear joints (PPP), and is illustrated in Fig. 101.11. In terms of work envelope, it will have a rectangular volume that sweeps out most of the inner area of the gantry system, with a height limited by the length of the vertical mast, and the headroom above the gantry system. One consideration in the selection of a gantry robot is the type of vertical linkage employed in the z axis. A monomast design is more rigid, yielding tighter tolerances for repeatability and accuracy, but requires significant headroom above the gantry to have a large range of z axis motion. On the other hand, a telescoping linkage will require signifi- cantly less headroom but is less rigid, with corresponding reduction in repeatability and accuracy. Other robot configurations can be mounted on gantry systems, thus gaining many of the advantages of this geometry. FIGURE 101.10 SCARA robot work envelope. Horizontal Reach Work Envelope Swing Horizontal Stroke Horizontal Reach Plan View Elevation Work Envelope Vertical Stroke Vertical Reach FIGURE 101.11 The gantry configuration. (Source: T. Owen, Assembly with Robots, Englewood Cliffs, N.J.: Prentice-Hall, 1985. With permission.)

Gantry robots have many advantageous properties. They are geometrically simple, like the Cartesian robot, with the corresponding kinematic and dynamic simplicity. For the same reasons, the gantry robot has a constant arm resolution throughout the workspace. The gantry robot has better dynamics than the pedestal-mounted artesian robot, as its links are not cantilevered. One major advantage over revolute-base robots is that its dynamics vary much less over the workspace. This leads to less vibration and more even performance than typical pedestal-mounted robots in full extension Gantry robots are much stiffer than other robot configura tions,although they are still much less stiff than Numerical Control(NC)machines. The gantry robot can straddle a workstation, or several workstations for a large system, so that one gantry robot can perform the work of several pedestal-mounted robots. As with the Cartesian robot, the gantry robot's simple geometry is similar to that of an NC machine, so technicians will be more familiar with the system and require less training time. Also, there is no need for special path or trajectory computations. A gantry robot can be programmee directly from a Computer-Aided Design( CAD)system with the appropriate interface, and straight-line motions are particularly simple to program. Large gantry robots have a very high payload capacity. Small, table-top systems can achieve linear speeds of up to 40 in. s(1.025 m/s), with a payload capacity of 5.0 lb(. 26 kg) making them suitable for assembly operations. However, most gantry robot systems are not as precise as other configurations, such as the SCARA configuration. Additionally, it is sometimes more difficult to apply a gantry robot to an existing workstation, as the workpieces must be brought into the gantry's work envelope, which may be harder to do than for a pedestal-mounted manipulator. Gantry robots can be applied in many areas. They are used in the nuclear power industry to load and unload reactor fuel rods. Gantry robots are also applied to materials-handling tasks, such as parts transfer, machine ading, palletizing, materials transport, and some assembly applications. In addition, gantry robots are used for process applications such as welding, painting, drilling, routing, cutting, milling, inspection, and nonde The gantry robot configuration is the fastest-growing segment of the robotics industry. While gantry robots accounted for less than 5% of the units shipped in 1985, they are projected to account for about 30% of the robots by the end of the 1990s. One reason for this is summed up in Long [1990], which contains much more information on gantry robots in general Currently gantry robot cells are being set up which allow manufacturers to place a sheet of material in the gantry's work envelope and begin automatic cutting, trimming, drilling, milling, assembly and finishing operations which completely manufacture a part or subassembly using quick-change tools and pro- Additional Information The above six configurations are the main types currently used in industry. However, there are other configu rations used in either research or specialized applications. Some of these configurations have found limited application in industry and may become more prevalent in the future. All the above configurations are serial-chain manipulators. An alternative to this common approach is the parallel configuration, known as the Stewart platform [Waldron, 1990]. This manipulator consists of two platforms connected by three prismatic linkages. This arrangement yields the full six DOF motion(three position, three orientation) that can be achieved with a six-axis serial configuration but has a comparably very high stiffness. It is used as a motion simulator for pilot training and virtual reality applications. The negative aspects of this configuration are its relatively restricted motion capability and geometric complexity. The above configurations are restricted to a single manipulator arm. There are tasks that are either difficult or impossible to perform with a single arm. with this realization, there has been significant interest in the use of multiple arms to perform coordinated tasks[Bonitz and Hsia, 1996]. Possible applications include carrying loads that exceed the capacity of a single robot, and assembling objects without special fixturing. Multiple arms are particularly useful in zero-gravity environments. While there are significant advantages to the use of multiple robots, the complexity, in terms of kinematics, dynamics, and control, is quite high. However, the use of multiple robots is opening new areas of application for robots. e 2000 by CRC Press LLC

© 2000 by CRC Press LLC Gantry robots have many advantageous properties. They are geometrically simple, like the Cartesian robot, with the corresponding kinematic and dynamic simplicity. For the same reasons, the gantry robot has a constant arm resolution throughout the workspace. The gantry robot has better dynamics than the pedestal-mounted Cartesian robot, as its links are not cantilevered. One major advantage over revolute-base robots is that its dynamics vary much less over the workspace. This leads to less vibration and more even performance than typical pedestal-mounted robots in full extension. Gantry robots are much stiffer than other robot configurations, although they are still much less stiff than Numerical Control (NC) machines. The gantry robot can straddle a workstation, or several workstations for a large system, so that one gantry robot can perform the work of several pedestal-mounted robots. As with the Cartesian robot, the gantry robot’s simple geometry is similar to that of an NC machine, so technicians will be more familiar with the system and require less training time. Also, there is no need for special path or trajectory computations. A gantry robot can be programmed directly from a Computer-Aided Design (CAD) system with the appropriate interface, and straight-line motions are particularly simple to program. Large gantry robots have a very high payload capacity. Small, table-top systems can achieve linear speeds of up to 40 in./s (1.025 m/s), with a payload capacity of 5.0 lb (2.26 kg), making them suitable for assembly operations. However, most gantry robot systems are not as precise as other configurations, such as the SCARA configuration. Additionally, it is sometimes more difficult to apply a gantry robot to an existing workstation, as the workpieces must be brought into the gantry’s work envelope, which may be harder to do than for a pedestal-mounted manipulator. Gantry robots can be applied in many areas. They are used in the nuclear power industry to load and unload reactor fuel rods. Gantry robots are also applied to materials-handling tasks, such as parts transfer, machine loading, palletizing, materials transport, and some assembly applications. In addition, gantry robots are used for process applications such as welding, painting, drilling, routing, cutting, milling, inspection, and nondestructive testing. The gantry robot configuration is the fastest-growing segment of the robotics industry. While gantry robots accounted for less than 5% of the units shipped in 1985, they are projected to account for about 30% of the robots by the end of the 1990s. One reason for this is summed up in Long [1990], which contains much more information on gantry robots in general: Currently gantry robot cells are being set up which allow manufacturers to place a sheet of material in the gantry’s work envelope and begin automatic cutting, trimming, drilling, milling, assembly and finishing operations which completely manufacture a part or subassembly using quick-change tools and programmed subroutines. Additional Information The above six configurations are the main types currently used in industry. However, there are other configurations used in either research or specialized applications. Some of these configurations have found limited application in industry and may become more prevalent in the future. All the above configurations are serial-chain manipulators. An alternative to this common approach is the parallel configuration, known as the Stewart platform [Waldron, 1990]. This manipulator consists of two platforms connected by three prismatic linkages. This arrangement yields the full six DOF motion (three position, three orientation) that can be achieved with a six-axis serial configuration but has a comparably very high stiffness. It is used as a motion simulator for pilot training and virtual reality applications. The negative aspects of this configuration are its relatively restricted motion capability and geometric complexity. The above configurations are restricted to a single manipulator arm. There are tasks that are either difficult or impossible to perform with a single arm. With this realization, there has been significant interest in the use of multiple arms to perform coordinated tasks [Bonitz and Hsia, 1996]. Possible applications include carrying loads that exceed the capacity of a single robot, and assembling objects without special fixturing. Multiple arms are particularly useful in zero-gravity environments. While there are significant advantages to the use of multiple robots, the complexity, in terms of kinematics, dynamics, and control, is quite high. However, the use of multiple robots is opening new areas of application for robots

Typical industrial robots have six or fewer DOF. With six DOF, the robot can, within its work reach arbitrary positions and orientations. At the edge of the work envelope, a six-DOF robot can att one orientation. To increase the geometric dexterity of the manipulator, it is useful to consider rob more than six DOF, i.e., redundant robots. These robots are highly dexterous and can use the extra DOF in many ways: avoidance obstacle, joint torque minimization, kinematic singularity(points where the manipulator cannot move in certain directions) avoidance, bracing strategies where part of the arm is braced against a structure,which raises the lowest structural resonant frequency of the arm, etc. while the redundant manip- ulator configuration has many desirable properties, the geometric complexity has limited their application in industry. For any of the six standard robot configurations, the orientation capability of the major linkages is severel limited. Thus, it is critical to provide additional joints, known as the minor linkages, to provide the capability of varied orientations for a given position. Most robots include a three-DOF revolute joint wrist that is connected to the last link of the major linkages. The three revolute axes will be orthogonal and will usually intersect in common point, known as the wrist center point. Then, the kinematic equations of the manipulator can be partitioned into locating the Cartesian position of the wrist center point and then determining the orientation of a Cartesian frame fixed to the wrist axes Conclusions Each of the six standard configurations has specific advantages and disadvantages. When choosing a manipulator for a task, the properties of the manipulator geometry are one of the most important considerations. If the manipulator will be used for a wide variety of tasks, one may need to trade off performance for any given task for the flexibility that will allow the manipulator to work for the various tasks. In such a case, a more flexible geometry should be considered. The future of robotics will be interesting. With the steady increase in compu tional capabilities, the more complex geometries, including redundant and multiple robots, are beginning to see increased applications in industry. Defining Terms Degrees of freedom: The number of degrees of freedom(DOF)of a manipulator is the number of independent position variables that must be specified in order to locate all parts of the bulator. For a typical industrial manipulator, the number of joints equals the number of doF. Kinematics: The kinematics of the manipulator refers to the geometric properties of the manipulator. Forward kinematics is the computation of the Cartesian position and orientation of the robot end-effector given coordinates. Inverse kinematics is the comp Cartesian position and orientation of the end-effector. The inverse kinematic computation may not be possible in closed form, may have no solution, or may have multiple solutions. Redundant manipulator: A redundant manipulator contains more than six DOF. Singularity: A singularity is a location in the workspace of the manipulator at which the robot loses one or more DOF in Cartesian space, 1. e, there is some direction(or directions) in Cartesian space along which it is impossible to move the robot end-effector no matter which robot joints are moved. Related Topic 101.2 Dynamics and Control References R.G. Bonitz and T.C. Hsia,"Internal force-based impedance control for cooperating manipulators, " IEEE Transactions on robotics and Automation, Feb. 1996 J.J. Craig, Introduction to Robotics: Mechanics and Control, Reading, Mass. Addison-Wesley, 1986 A J. Critchlow, Introduction to robotics, New York: Macmillan, 1985 c 2000 by CRC Press LLC

© 2000 by CRC Press LLC Typical industrial robots have six or fewer DOF. With six DOF, the robot can, within its work envelope, reach arbitrary positions and orientations. At the edge of the work envelope, a six-DOF robot can attain only one orientation. To increase the geometric dexterity of the manipulator, it is useful to consider robots with more than six DOF, i.e., redundant robots. These robots are highly dexterous and can use the extra DOF in many ways: avoidance obstacle, joint torque minimization, kinematic singularity (points where the manipulator cannot move in certain directions) avoidance, bracing strategies where part of the arm is braced against a structure, which raises the lowest structural resonant frequency of the arm, etc. While the redundant manipulator configuration has many desirable properties, the geometric complexity has limited their application in industry. For any of the six standard robot configurations, the orientation capability of the major linkages is severely limited. Thus, it is critical to provide additional joints, known as the minor linkages, to provide the capability of varied orientations for a given position.Most robots include a three-DOF revolute joint wrist that is connected to the last link of the major linkages. The three revolute axes will be orthogonal and will usually intersect in a common point, known as the wrist center point. Then, the kinematic equations of the manipulator can be partitioned into locating the Cartesian position of the wrist center point and then determining the orientation of a Cartesian frame fixed to the wrist axes. Conclusions Each of the six standard configurations has specific advantages and disadvantages.When choosing a manipulator for a task, the properties of the manipulator geometry are one of the most important considerations. If the manipulator will be used for a wide variety of tasks, one may need to trade off performance for any given task for the flexibility that will allow the manipulator to work for the various tasks. In such a case, a more flexible geometry should be considered. The future of robotics will be interesting. With the steady increase in computational capabilities, the more complex geometries, including redundant and multiple robots, are beginning to see increased applications in industry. Defining Terms Degrees of freedom: The number of degrees of freedom (DOF) of a manipulator is the number of independent position variables that must be specified in order to locate all parts of the manipulator. For a typical industrial manipulator, the number of joints equals the number of DOF. Kinematics: The kinematics of the manipulator refers to the geometric properties of the manipulator. Forward kinematics is the computation of the Cartesian position and orientation of the robot end-effector given the set of joint coordinates. Inverse kinematics is the computation of the joint coordinates given the Cartesian position and orientation of the end-effector. The inverse kinematic computation may not be possible in closed form, may have no solution, or may have multiple solutions. Redundant manipulator: A redundant manipulator contains more than six DOF. Singularity: A singularity is a location in the workspace of the manipulator at which the robot loses one or more DOF in Cartesian space, i.e., there is some direction (or directions) in Cartesian space along which it is impossible to move the robot end-effector no matter which robot joints are moved. Related Topic 101.2 Dynamics and Control References R.G. Bonitz and T.C. Hsia, “Internal force-based impedance control for cooperating manipulators,” IEEE Transactions on Robotics and Automation, Feb. 1996. J.J. Craig, Introduction to Robotics: Mechanics and Control, Reading, Mass.: Addison-Wesley, 1986. A. J. Critchlow, Introduction to Robotics, New York: Macmillan, 1985

E. Long, "Gantry robots, in Concise International Encyclopedia of Robotics, R. C. Dorf, Ed, New York: Wiley R. Truman, " Component assembly onto printed circuit boards, " in Concise International Encyclopedia of Robotics, R. C. Dorf, Ed, New York: Wiley-Interscience, 1990 K J. Waldron, "Arm design, in Concise International Encyclopedia of Robotics, R. C. Dorf, Ed, New York: Wiley Interscience, 1990 Further Information The journal IEEE Transactions on Robotics and Automation is a valuable source for a wide variety of robotics research topics, occasionally including new robot configurations. Additionally, IEEE's Control Systems Magazine ccasionally publishes an issue devoted to robotic systems. The home page for the IEEE Robotics and Auto mationSocietycanbefoundat"http://www.acim.usi.edu/ras/ Another journal that often has robotics-related articles is the ASME Journal of dynamic Systems, Measurement and Control An additional source of robotics information is The Proceedings of the IEEE International Conference on Robotics and Automation. This conference is held annually. UsefulsourcesontheWorldwideWebincludetheRoboticsInternetResourcespagelocatedat"http://piglet.cs umass.edu:4321/robotics.html,andRoboticsResourceslocatedat"http://www.eg.bucknell.edu/-robot ics/rirchtml. Consult your system administrator for information on this web access 101.2 Dynamics and Control r. Lal tummala The primary purpose of the robot control system is to issue commands to joint actuators to faithfully execute a planned trajectory in the tool space. This may involve position control when the manipulator is following a trajectory through free space or a combination of position and force control if the manipulator is to react continuously to contact forces at the tool or end-effector Control systems can operate either in open loop or closed loop In open-loop systems, the output has no effect on the input On the other hand, closed-loop systems continuously sense the output and make appropriate adjustments to the input in order to keep the output at the desired level. The majority of the current industrial robots use the independent joint control method and close the loop around the joints of the robot. The desired joint positions corresponding to a tool trajectory are either taught by using a teach box or generated by solving an inverse kinematics problem. The independent joint control nethod, however, is effective only at low speeds. As the speeds increase, the coupling effects between the joints increase and warrant the inclusion of these effects in the controller development. Advanced controller devel opment and implementation based on full dynamics is one of the active areas of current research. New advances in sensor technology, faster computers, advanced robots such as direct drive arms and industrial competition provide new opportunities and motivation for accelerating the development and implementation of advanced controllers for robots in the near future Independent Joint Control of the Robot The independent joint control method assumes that a single joint of a robot is moving while all the other joints are fixed. A typical joint position control system is shown in Fig. 101. 12, where the actuator used is a dc servomotor[ Luh, 1983]. In general, any one or a combination of electric motors and hydraulic or pneumatic e the joint through the desired positions. These motors may be connected directly to the joint or indirectly through gears, chains, cables, or lead screws. The desired joint positions that are inputs to the position loops are obtained from the trajectory planner. The actual position of the joint is obtained by using a position sensor, such as a potentiometer or an optical encoder. An amplifier is used for increasing the system gain, denoted by K The velocity feedback K, is used to reinforce the effect of back emf for controlling e 2000 by CRC Press LLC

© 2000 by CRC Press LLC E. Long, “Gantry robots,” in Concise International Encyclopedia of Robotics, R. C. Dorf, Ed., New York: WileyInterscience, 1990. R. Truman,“Component assembly onto printed circuit boards,” in Concise International Encyclopedia of Robotics, R. C. Dorf, Ed., New York: Wiley-Interscience, 1990. K. J. Waldron, “Arm design,” in Concise International Encyclopedia of Robotics, R. C. Dorf, Ed., New York: WileyInterscience, 1990. Further Information The journal IEEE Transactions on Robotics and Automation is a valuable source for a wide variety of robotics research topics, occasionally including new robot configurations. Additionally, IEEE’s Control Systems Magazine occasionally publishes an issue devoted to robotic systems. The home page for the IEEE Robotics and Automation Society can be found at “http://www.acim.usi.edu/RAS/”. Another journal that often has robotics-related articles is the ASME Journal of Dynamic Systems, Measurement and Control. An additional source of robotics information is The Proceedings of the IEEE International Conference on Robotics and Automation. This conference is held annually. Useful sources on the World Wide Web include the Robotics Internet Resources page, located at “http://piglet.cs. umass.edu:4321/robotics.html”, and Robotics Resources, located at “http://www.eg.bucknell.edu/~robotics/rirc.html”. Consult your system administrator for information on this web access. 101.2 Dynamics and Control R. Lal Tummala The primary purpose of the robot control system is to issue commands to joint actuators to faithfully execute a planned trajectory in the tool space. This may involve position control when the manipulator is following a trajectory through free space or a combination of position and force control if the manipulator is to react continuously to contact forces at the tool or end-effector. Control systems can operate either in open loop or closed loop. In open-loop systems, the output has no effect on the input. On the other hand, closed-loop systems continuously sense the output and make appropriate adjustments to the input in order to keep the output at the desired level. The majority of the current industrial robots use the independent joint control method and close the loop around the joints of the robot. The desired joint positions corresponding to a tool trajectory are either taught by using a teach box or generated by solving an inverse kinematics problem. The independent joint control method, however, is effective only at low speeds. As the speeds increase, the coupling effects between the joints increase and warrant the inclusion of these effects in the controller development. Advanced controller development and implementation based on full dynamics is one of the active areas of current research. New advances in sensor technology, faster computers, advanced robots such as direct drive arms and industrial competition provide new opportunities and motivation for accelerating the development and implementation of advanced controllers for robots in the near future. Independent Joint Control of the Robot The independent joint control method assumes that a single joint of a robot is moving while all the other joints are fixed. A typical joint position control system is shown in Fig. 101.12, where the actuator used is a dc servomotor [Luh, 1983]. In general, any one or a combination of electric motors and hydraulic or pneumatic pistons can be used to move the joint through the desired positions. These motors may be connected directly to the joint or indirectly through gears, chains, cables, or lead screws. The desired joint positions that are inputs to the position loops are obtained from the trajectory planner. The actual position of the joint is obtained by using a position sensor, such as a potentiometer or an optical encoder. An amplifier is used for increasing the system gain, denoted by Ka. The velocity feedback Kv is used to reinforce the effect of back emf for controlling