FUNDAMENTAIS OF ROBOTICSAnalysis and Control

FUNDAMENTAIS OF ROBOTICS Analysis and Control

7Robotic ManipulationThe term robot can convey many different meanings in the mind of the reader, de- pending on the context. In the treatment presented here, a robot will be taken to mean an industrial robot, also called a robotic manipulator or a robotic arm. An ex- ample of an industrial robot is shown in Fig. 1-1. This is an articulated robotic arm and is roughly similar to a human arm. It can be modeled as a chain of rigid links interconnected by flexible joints. The links correspond to such features of the human anatomy as the chest, upper arm, and forearm, while the joints correspond to the shoulder, elbow, and wrist. At the end of a robotic arm is an end-effector, also called a tool, gripper, or hand. The tool often has two or more fingers that open and cise.To further characterize industrial robots, we begin by examining the role they play in automation in general. This is followed by a discussion of robot classifica- tions using a number of criteria including: drive technologies, work envelope ge- ometries, and motion control methods. A brief summary of the most common appli- cations of robots is then presented; this is followed by an examination of robot design specifications. Chap. 1 concludes with a discussion of the use of notation and a summary of the notational conventions adopted in the remainder of the text.1-1 AUTOMATION AND ROBOTSMass-production assembly lines were first introduced at the beginning of the twenti- eth century (1905) by the Ford Motor Company. Over the ensuing decades, special- ized machines have been designed and developed for high-volume production of me- chanical and electrical parts. However, when each yearly production cycle ends and new models of the parts are to be introduced, the specialized machines have to be shut down and the hardware retooled for the next generation of models. Since peri- odic modification of the production hardware is required, this type of automation is1

7Robotic ManipulationThe term robot can convey many different meanings in the mind of the reader, de- pending on the context. In the treatment presented here, a robot will be taken to mean an industrial robot, also called a robotic manipulator or a robotic arm. An ex- ample of an industrial robot is shown in Fig. 1-1. This is an articulated robotic arm and is roughly similar to a human arm. It can be modeled as a chain of rigid links interconnected by flexible joints. The links correspond to such features of the human anatomy as the chest, upper arm, and forearm, while the joints correspond to the shoulder, elbow, and wrist. At the end of a robotic arm is an end-effector, also called a tool, gripper, or hand. The tool often has two or more fingers that open and cise.To further characterize industrial robots, we begin by examining the role they play in automation in general. This is followed by a discussion of robot classifica- tions using a number of criteria including: drive technologies, work envelope ge- ometries, and motion control methods. A brief summary of the most common appli- cations of robots is then presented; this is followed by an examination of robot design specifications. Chap. 1 concludes with a discussion of the use of notation and a summary of the notational conventions adopted in the remainder of the text.1-1 AUTOMATION AND ROBOTSMass-production assembly lines were first introduced at the beginning of the twenti- eth century (1905) by the Ford Motor Company. Over the ensuing decades, special- ized machines have been designed and developed for high-volume production of me- chanical and electrical parts. However, when each yearly production cycle ends and new models of the parts are to be introduced, the specialized machines have to be shut down and the hardware retooled for the next generation of models. Since peri- odic modification of the production hardware is required, this type of automation is1

referred to as hard automation. Here the machines and processes are often very efficient, but they have limited flexibility.More recently, the auto industry and other industries have introduced more flexible forms of automation in the manufacturing cycle. Programmable mechanical manipulators are now being used to perform such tasks as spot welding, spray paint- ing, material handiing, and component assembly. Since computer-controlled mechanical manipulators can be easily converted through software to do a variety of7%\

Figure 1-1 An industrial robot. (Courtesy of Intelledex, Inc., Corvallis, OR.)tasks, they are referred to as examples of soft automation. A qualitative comparison of the cost effectiveness of manual labor, hard automation, and soft automation as a function of the production volume (Dorf, 1983) is summarized in Fig. 1-2.It is evident that for very low production volumes, such as those occurring in small batch processing, manual labor is the most cost-effective. As the production volume increases, there comes a point V\ where robots become more cost-effective than manual labor. As the production volume increases still further, it eventually reaches a point Vi where hard automation surpasses both manual labor and robots in cost-effectiveness. The curves in Fig. 1-2 are representative of general qualitative trends, with the exact data dependent upon the characteristics of the unit being pro- duced. As robots become more sophisticated and less expensive, the range of pro-2Robotic Manipulation Chap. 1

referred to as hard automation. Here the machines and processes are often very efficient, but they have limited flexibility.More recently, the auto industry and other industries have introduced more flexible forms of automation in the manufacturing cycle. Programmable mechanical manipulators are now being used to perform such tasks as spot welding, spray paint- ing, material handiing, and component assembly. Since computer-controlled mechanical manipulators can be easily converted through software to do a variety of

Figure 1-1 An industrial robot. (Courtesy of Intelledex, Inc., Corvallis, OR.)tasks, they are referred to as examples of soft automation. A qualitative comparison of the cost effectiveness of manual labor, hard automation, and soft automation as a function of the production volume (Dorf, 1983) is summarized in Fig. 1-2.It is evident that for very low production volumes, such as those occurring in small batch processing, manual labor is the most cost-effective. As the production volume increases, there comes a point v\ where robots become more cost-effective than manual labor. As the production volume increases still further, it eventually reaches a point vi where hard automation surpasses both manual labor and robots in cost-effectiveness. The curves in Fig. 1-2 are representative of general qualitative trends, with the exact data dependent upon the characteristics of the unit being pro- duced. As robots become more sophisticated and less expensive, the range of pro-2Robotic Manipularon Chap. 1

Unit cost\

Production volumeFigure 1-2 Relative cost-efectivenessof soft automation.duction volumes [ui, U2] over which they are cost-effective contines to expand at both ends of the production spectrum.In order to more clearly distinguish soft automation from hard automation, it is useful to introduce a specific definition of a robot. A number of definitions have been proposed over the years. However, as robotic technology contines to evolve, any definition proposed may need to be refined and updated before long. For the purpose of the material presented in this text, the following definition is used:Definition 1-1-1: Robot. A robot is a software-controllable mechanical de- vice that uses sensors to guide one or more end-effectors through programmed mo- tions in a workspace in order to maniplate physical objects.Contrary to popular notions about robots in the Science fiction literature (see, for instance, Asimov, 1950), todays industrial robots are not androids built to im- personate humans. Indeed, most are not even capable of self-locomotion. However, many of todays robots are anthropomorphic in the sense that they are patterned af- ter the human arm. Consequently, industrial robots are often referred to as robotic arms or, more generally, as robotic manipulators.1-2 ROBOT CLASSIFICATIONIn order to refine the general notion of a robotic manipulator, it is helpful to classify manipulators according to various criteria such as drive technologies, work envelope geometries, and motion control methods.1- 2-1 Drive TechnologiesOne of the most fundamental classification schemes is based upon the source of power used to drive the joints of the robot. The two most popular drive technologies are electric and hydrauic. Most robotic manipulators today use electric drives in the form of either DC servomotors or DC stepper motors. However, when high-speedSee. 1-2 Robot Classification3

manipulation of substantial loads is required, such as in molten Steel handiing or auto body part handiing, hydraulic-drive robots are preferred. One serious drawback of hydraulic-drive robots lies in their lack of cleanliness, a characteristic that is im- portant for many assembly applications.Both electric-drive robots and hydraulic-drive robots often use pneumatic tools or end-effectors, particularly when the only gripping action required is a simple open-close type of operation. An important characteristic of air-activated tools is that they exhibit built-in compliance in grasping objects, since air is a compressible fluid. This is in contrast to sensorless rigid mechanical grippers, which can easily damage a delicate object by squeezing too hard.1- 2-2 Work-Envelope GeometriesThe end-effector, or tool, of a robotic manipulator is typically mounted on a flange or pate secured to the wrist of the robot. The gross work envelope of a robot is defined as the locus of points in three-dimensional space that can be reached by the wrist. We will refer to the axes of the first three joints of a robot as the major axes. Roughly speaking, it is the major axes that are used to determine the position of the wrist. The axes of the remaining joints, the minor axes, are used to establish the ori- entation of the tool. As a consequence, the geometry of the work envelope is deter- mined by the sequence of joints used for the first three axes. Six types of robot joints are possible (Fu et al., 1987). However, only two basic types are commonly used in industrial robots, and they are listed in Table 1-1.TABLE 1-1 TYPES OF ROBOT JOINTSTypeNotationSymbolDescription

RevoluteRRotary motion about an axis

PrismaticPLinear motion along an axis

Revolute joints (R) exhibit rotary motion about an axis. They are the most common type of joint. The next most common type is a prismatic joint (P), which exhibits sliding or linear motion along an axis. The particular combination of revolute and prismatic joints for the three major axes determines the geometry of the work envelope, as summarized in Table 1-2. The list in Table 1-2 is not exhaustive, since there are eight possibilities, but it is representative of the vast majority of com- mercially available robots. As far as analysis of the motion of the arm is concerned, prismatic joints tend to be simpler than revolute joints. Therefore the last column in Table 1-2, which specifies the total number of revolute joints for the three major axes, is a rough indication of the complexity of the arm.For the simplest robot listed in Table 1-2, the three major axes are all prismatic; the resulting notation for this configuration is PPP. This is characteristic of a Cartesian-coordinate robot, also called a rectangular-coordnate robot. An example4Robotic Manipulation Chap. 1

TABLE 1-2 ROBOT WORK ENVELOPES BASED ON MAJOR AXESRobotAxis 1Axis 2Axis 3Total revolute

CartesianPPP0

CylindricalRPP1

SphericalRRP2

SCARARRP2Jbt

ArticulatedRRR3

P = prismatic, R = revolute.of a Cartesian-coordinate robot is shown in Fig. 1-3. Note that the three sliding joints correspond to moving the wrist up and down, in and out, and back and forth. It is evident that the work envelope or work volume that this configuraron generales is a rectangular box. When a Cartesian-coordinate robot is mounted from above in a rectangular frame, it is referred to as a gantry robot.

Figure 1-3 Cartesian robot.If the first joint of a Cartesian-coordinate robot is replaced with a revolute joint (to form the configuration RPP), this produces a cylindrical-coordnate robot. An example of a cylindrical-coordinate robot is shown in Fig. 1-4. The revolute joint swings the arm back and forth about a vertical base axis. The prismatic joints then move the wrist up and down along the vertical axis and in and out along a radial axis. Since there will be some minimum radial position, the work envelope gen- erated by this joint configuration is the volume between two vertical concentric cylinders.

Figure 1-4 Cylindrical robot.Sec. 1-2Robot Classification5

If the second joint of a cyndrical-coordinate robot is replaced with a revolute joint (so that the configuration is then RRP), this produces a spherical-coordinate robot. An example of a spherical-coordinate robot is shown in Fig. 1-5. Here the first revolute joint swings the arm back and forth about a vertical base axis, while the second revolute joint pitches the arm up and down about a horizontal shoulder axis. The prismatic joint moves the wrist radially in and out. The work envelope generated in this case is the volume between two concentric spheres. The spheres are typically truncated from above, below, and behind by limits on the ranges of travel of the joints.

Figure 1-5 Spherical robot.Like a spherical-coordinate robot, a SCARA robot (Selective Compliance As- sembly Robot Arm) also has two revolute joints and one prismatic joint (in the configuration RRP) to position the wrist. However, for a SCARA robot the axes of all three joints are vertical, as shown in Fig. 1-6. The first revolute joint swings the arm back and forth about a base axis that can also be thought of as a vertical shoulder axis. The second revolute joint swings the forearm back and forth about a vertical elbow axis. Thus the two revolute joints control motion in a horizontal plae. The vertical component of the motion is provided by the third joint, a prismatic joint which slides the wrist up and down. The shape of a horizontal cross section of the work envelope of a SCARA robot can be quite complex, depending upon the limits on the ranges of travel for the first two axes.LnJ1 about the kth unit vector of the fixed coordinate frame F, then premultiply R and /?*()-4. If there are more fundamental rotations to be performed, go to step [2]; else, stop. The resulting composite rotation matrix R maps mobile M coordinates into fixed F coordinates.36Direct Kinematics: The Arm Equation Chap. 2

Thus composite rotation matrices are built up in steps starting with the identity matrix which corresponds to no rotation at all. Rotations of frame M about the unit vectors of frame F are represented by premultiplication (multiplication on the left) by the appropriate fundamental rotation matrix. Similarly, rotations of frame M about one of its own unit vectors are represented by postmultiplication (multiplication on the right) by the appropriate fundamental rotation matrix.Since a convention has been adopted for the order of the yaw, pitch, and roll operations, a general expression for the composite yaw-pitch-roll transformation matrix can be obtained. Suppose that the yaw-pitch-roll angles are represented by a vector 0 in R3. For notational convenience, let S* = sin 0* and C* = eos 0*. We then have the following result, which summarizes the composite yaw-pitch-roll tool transformation:Proposition 2-3-1: Yaw-Pitch-Roll Transformation. Let YRP (0) represent the composite rotation matrix obtained by rotating a mobile coordinate frame M = {m \ m2, m3} first about unit vector /' with a yaw of 0i, then about the unit vector f2 with a pitch of 02, and finally about unit vector/3 with a roll of 03. The resulting composite yaw-pitch-roll matrix YPR (0) maps M coordinates into F coordinates and is given by:YPR (0) =C2C3 S1S2C3 C,S3 C1S2C3 + Si S3C2S3 S1S2S3 4* C1C3 C1S2S3 ~ S1C3S2SiC2CiC2Proof. This is verified by simply applying Algorithm 2-3-1 and using the expressions for the three fundamental rotation matrices. Using the notational shorthand C* = eos dk and S* = sin 0* and Algorithm 2-3-1, we have:YPR (0) = R3(03)/?2(02)Rl(0l)C3s3oc3s3o-s3c3o-s3c3oo01001c2os2c2o-s2s2oc2s,s2c,S1C2"100"

0Ci-Si

0SiCiJ

C1S2-Sic,c2C2C3 S1S2C3 C1S3 C1S2C3 + Si s3 C2S3 S1S2S3 + C,C3 C1S2S3 S1C3 S2SiC2C1C2Example 2-3-2: Yaw-Pitch-RoIISuppose we rotate the tool in Fig. 2-8 about the fixed axes starting with a yaw of tt/2, followed by a pitch of -7t/2 and, finally, a roll of tt/2. What is the resulting composite rotation matrix?Sea 2-3 Rotations37

Solution Applying Prop. 2-3-1:~}r2Ir 7r

\2/ !^ 2

~o0r

010

100

Suppose the point p at the tool tip has mobile coordinates [p]M [0, 0, 0.6]r. Find [p]F following the yaw-pitch-roll transformation.Solution Using Prop. 2-3-1:IpY = RIpY4ioo 0

0-100

l 0 0__0.6_

= [0.6, 0, OfExercise 2-3-1: Yaw-Pitch-Roll. Verify that Example 2-3-2 is correct by sketching the tool position and the coordinate frames after each fundamental rotation is performed.Exercise 2-3-2: Roll-Pitch-Yaw. An alternative way to define the yaw- pitch-roll transformation is to perform the rotations about unit vectors of the mobile frame M and in the reverse order: roll, pitch, yaw. This tends to be easier to visual- ize, particularly when the angles are arbitrary. Show that the resulting composite rotation matrix RPY (0), is the same as in Prop. 2-3-1. Is the route taken by the tool the same?Exercise 2-3-3: Fundamental Rotations. Verify that the general yaw-pitch- roll transformation YPR (0) includes the three fundamental rotations {R\, R2, Ri} as special cases.A general rotation of a mobile frame M with respect to a fixed frame F can al- ways be decomposed into a sequence of three fundamental rotations as in Prop.2- 3-1. It is also possible to represent a general rotation as a single rotation by an angle about an arbitrary unit vector u as shown in Fig. 2-9. This is called the equiv- alent angle-axis representation. For notational convenience, let C = eos S(f> = sin