Fundamentals and Design Issues

A robot manipulator is fundamentally a collection of links connected to each other by joints, typically with an end effector (designed to contact the environment in some useful fashion) connected to the mechanism. A typical arrangement is to have the links connected serially by the joints in an open-chain fashion. Each joint provides one or more degree of freedom to the mechanism.

 

Manipulator designs are typically characterized by the number of independent degrees of freedom in the mechanism, the types of joints providing the degrees of freedom, and the geometry of the links connecting the joints. The degrees of freedom can be revolute (relative rotational motion θ between joints) or prismatic (relative linear motion d between joints). A joint may have more than one degree of freedom. Most industrial robots have a total of six independent degrees of freedom. In addition, most current robots have essentially rigid links (we will focus on rigid-link robots throughout this section).

Robots are also characterized by the type of actuators employed. Typically manipulators have hydraulic or electric actuation. In some cases where high precision is not important, pneumatic actuators are used.

 A number of successful manipulator designs have emerged, each with a different arrangement of joints and links. Some “elbow” designs, such as the PUMA robots and the SPAR Remote Manipulator System, have a fairly anthropomorphic structure, with revolute joints arranged into “shoulder,” “elbow,” and “wrist” sections. A mix of revolute and prismatic joints has been adopted in the Stanford Manipulator and the SCARA types of arms. Other arms, such as those produced by IBM, feature prismatic joints for the “shoulder,” with a spherical wrist attached. In this case, the prismatic joints are essentially used as positioning devices, with the wrist used for fine motions.

The above designs have six or fewer degrees of freedom. More recent manipulators, such as those of the Robotics Research Corporation series of arms, feature seven or more degrees of freedom. These arms are termed kinematically redundant, which is a useful feature as we will see later .

Key factors that influence the design of a manipulator are the tractability of its geometric (kinematic) analysis and the size and location of its workspace. The workspace of a manipulator can be defined as the set of points that are reachable by the manipulator (with fixed base). Both shape and total volume are important. Manipulator designs such as the SCARA are useful for manufacturing since they have a simple semicylindrical connected volume for their workspace (Spong and Vidyasagar, 1989), which facilitates workcell design. Elbow manipulators tend to have a wider volume of workspace, however the workspace is often more difficult to characterize. The kinematic design of a manipulator can tailor the workspace to some extent to the operational requirements of the robot.

In addition, if a manipulator can be designed so that it has a simplified kinematic analysis, many planning and control functions will in turn be greatly simplified. For example, robots with spherical wrists tend to have much simpler inverse kinematics than those without this feature. Simplification of the kinematic analysis required for a robot can significantly enhance the real-time motion planning and control performance of the robot system. For the rest of this section, we will concentrate on the kinematics of manipulators.

 For the purposes of analysis, a set of joint variables (which may contain both revolute and prismatic variables), are augmented into a vector q, which uniquely defines the geometric state, or configuration of the robot. However, task description for manipulators is most naturally expressed in terms of a different set of task coordinates. These can be the position and orientation of the robot end effector, or of a special task frame, and are denoted here by Y. Thus Y most naturally represents the performance of a task, and q most naturally represents the mechanism used to perform the task. Each of the coordinate systems q and Y contains information critical to the understanding of the overall status of the manipulator. Much of the kinematic analysis of robots therefore centers on transformations between the various sets of coordinates of interest.

Manipulator Kinematics

The study of manipulator kinematics at the position (geometric) level separates naturally into two subproblems: (1) finding the position/orientation of the end effector, or task, frame, given the angles and/or displacements of the joints (Forward Kinematics); and (2) finding possible angles/displacements of the joints given the position/orientation of the end effector, or task, frame  (Inverse Kinematics). At the  velocity level, the Manipulator Jacobian  relates joint  velocities to end effector  velocities and is important in motion planning and for identifying Singularities. In the case of Redundant Manipulators, the Jacobian is particularly crucial in planning and controlling robot motions. We will explore each of these issues in turn in the following subsections.