《电子工程师手册》学习资料（英文版）ch101 Robotics

0.0 FIGURE 101.8 Articulated robot work envelope FIGURE 101.9 The SCARA configuration. Source: T. Owen, Assembly with Robots, Englewood Cliffs, N J. Prentice-Hall 985. With permission. speeds are possible. The articulated arm is good for tasks involving multiple insertions, complex motions, and varied tool orientations. The versatility of this configuration makes it applicable to a variety of tasks, so the user has fewer limitations on the use of the robot. However, the same features that give this robot its advantages lead to certain disadvantages. The geometry is complex, and the resulting kinematic equations are quite intricate. Straight-line motion is difficult to coordinate. Control is generally more difficult than for other geometries with associated increase in cost. Here again, arm resolution is not fixed throughout the workspace. Additionally, ne dynamics of an articulated arm vary widely throughout the workspace, so that performance will vary over the workspace for a fixed controller. In spite of these disadvantages, the articulated arm has been applied to a wide variety of research and industrial tasks, including spray painting, clean room tasks, machine loading, and parts-finishing tasks SCARA Configuration The SCARA( Selectively Compliant Assembly Robot Arm) configuration consists of two revolute joints and a linear joint(RRP), as shown in Fig. 101.9. This configuration is significantly different from the spherical figuration, since the axes for all joints are always vertical. In addition to the first three degrees of freedom (DOF), the SCARa robot will often include an additional rotation about the last vertical link to aid in orientation of parts. The work envelope of the SCARA robot is illustrated in Fig. 101.10. The SCARA configuration is the ewest of the configurations discussed here, and was developed by Professor Hiroshi Makino of Yamanashi University, Japan. e 2000 by CRC Press LLC

© 2000 by CRC Press LLC speeds are possible. The articulated arm is good for tasks involving multiple insertions, complex motions, and varied tool orientations. The versatility of this configuration makes it applicable to a variety of tasks, so the user has fewer limitations on the use of the robot. However, the same features that give this robot its advantages lead to certain disadvantages. The geometry is complex, and the resulting kinematic equations are quite intricate. Straight-line motion is difficult to coordinate. Control is generally more difficult than for other geometries, with associated increase in cost. Here again, arm resolution is not fixed throughout the workspace. Additionally, the dynamics of an articulated arm vary widely throughout the workspace, so that performance will vary over the workspace for a fixed controller. In spite of these disadvantages, the articulated arm has been applied to a wide variety of research and industrial tasks, including spray painting, clean room tasks, machine loading, and parts-finishing tasks. SCARA Configuration The SCARA (Selectively Compliant Assembly Robot Arm) configuration consists of two revolute joints and a linear joint (RRP), as shown in Fig. 101.9. This configuration is significantly different from the spherical configuration, since the axes for all joints are always vertical. In addition to the first three degrees of freedom (DOF), the SCARA robot will often include an additional rotation about the last vertical link to aid in orientation of parts. The work envelope of the SCARA robot is illustrated in Fig. 101.10. The SCARA configuration is the newest of the configurations discussed here, and was developed by Professor Hiroshi Makino of Yamanashi University, Japan. FIGURE 101.8 Articulated robot work envelope. FIGURE 101.9 The SCARA configuration. (Source: T. Owen, Assembly with Robots, Englewood Cliffs, N.J.: Prentice-Hall, 1985. With permission.) Xmax Ymin Ymax Z max Z min = 0.0 Xmin 0˚

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 equiva￾lent 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 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 corre￾sponding reduction in repeatability and accuracy. Other robot configurations can be mounted on gantry systems, thus gaining many of the advan￾tages 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 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 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 nonde￾structive 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 pro￾grammed subroutines. 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

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 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 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 compu￾tational 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: Wiley￾Interscience, 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: 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 occasionally publishes an issue devoted to robotic systems. The home page for the IEEE Robotics and Auto￾mation 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/~robot￾ics/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 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 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