Richard P. Paul

Kinematic control equations for simple manipulators

The basis for all advanced manipulator control is a relationship between the cartesian coordinates of the end-effector and the manipulator joint coordinates. A direct method for assigning link coordinate systems and obtaining the end effector position, and Jacobian, in terms of joint coordinates is reviewed. Techniques for obtaining the solution to these equations for kinematically simple manipulators, which includes all commercially available manipulators, is presented. Finally the inverse Jacobian is developed from the solution.

Kinematics of Robot Wrists

Robots for use in assembly and other interactive tasks must be able to respond to both forces and velocity com mands within their workspace. By considering a general six-joint robot we show that all such robots are limited in their ability to respond in orientation to feedback commands. We also show that it is simple to predict, if not to avoid, these regions of degeneracy in which the manipulator loses a degree of freedom.

Manipulator Cartesian Path Control

In describing the motion of a manipulator we are concerned with the position to which the hand moves, as well as the path it traverses. Paths made up of straight line segments connected together by smooth transitions with controlled acceleration are proposed. Segments end points may be defined in various fixed and moving Cartesian coordinate systems. The evaluation rate of the straight line motion is analyzed and an interpolation scheme described.

On homogeneous transforms, quaternions, and computational efficiency

Three-dimensional modeling of rotations and translations in robot kinematics is most commonly performed using homogeneous transforms. An alternate approach, using quaternion-vector pairs as spatial operators, is compared with homogeneous transforms in terms of computational efficiency and storage economy. The conclusion drawn is that quaternion-vector pairs are as efficient as, more compact than, and more elegant than their matrix counterparts. A robust algorithm for converting rotational matrices into equivalent unit quaternions is described, and an efficient quaternion-based inverse kinematics solution for the Puma 560 robot arm is presented. >

Planning for dexterous manipulation with sliding contacts

Dexterous manipulation refers to the skillful execution of object reorienting and repositioning maneuvers, especially when performed within the grasp of an articulated mechani cal hand. In this paper we study the problem of gaining a secure and enveloping grasp of a two-dimensional object by exploiting sliding at the contacts between the object and the hand. This is done in two steps:first, choosing an initial grasp with which the object can be manipulated away from the support, and second, continuously altering the grasp so that envelopment is achieved. The plans generated by our technique could be executed with only position control. How ever, it would be prudent to incorporate contact force sensing to prevent damage during unexpected events. The main contributions of this paper are the derivation of liftability regions of a planar object for use in manipulation planning; the use of the lifting phase plane in manipulation planning; and the derivation of the quasi-static forward object motion problem, which provides a basis for general three- dimensional manipulation planning with rolling and/or sliding contacts.

Teleprogramming: toward delay-invariant remote manipulation

This paper addresses the problem of teleoperation in the presence of communication delays. Delays occur with earth-based teleoperation in space and with surface-based teleoperation undersea using untethered submersibles and acoustic communication links. The delay in obtaining position and force feedback from the remote slave arms makes direct teleoperation infeasible. We are proposing a control methodology, called teleprogramming, which draws on the experience in the development of supervisory control techniques and robotics over the last three decades and introduces a number of new ideas in operator-model interaction as well as the nature and content of the information being sent to the slave robot. A teleprogramming system allows the operator to kinesthetically, as well as visually, interact with a graphic simulation of the remote environment and to interactively, online teleprogram the remote manipulator through a sequence of elementary robot instructions. A key feature and contribution of this work is the fact that these instructions are generated automatically, in real time, based on the operators interaction with the simulated environment. The slave robot executes these commands delayed in time and, should an error occur, allows the operator to specify the necessary corrective actions and continue with the task. We will in this paper introduce the overall teleprogramming control concept, describe its main components, and report on the preliminary results using our experimental teleprogramming system.

Manipulator compliance based on joint torque control

The application of robot manipulators to batch manufacturing product assembly requires the control and monitoring of both robot force and position. A good force sensing technique is imperative to increase the robots capabilities in this area. A fast reliable force servo system based on the proper sensing technique is also needed to increase the speed of robot operations. This paper analyzes currently existing force sensing techniques concluding that a joint torque sensing technique will results the best performance in a force servo system. A new, simple, high again, wide bandwidth torque servo system using a joint torque sensor system has been developed and has been verified by using a single joint manipulator. An accurate method of selecting the force servo joints to provide compliance has also been developed. Finally, a complete and consistent algorithm for performing compliance is presented.

Problems and research issues associated with the hybrid control of force and displacement

The hybrid control of force and position is basic to the science of robotics but is only poorly understood. Before much progress can be made in robotics, this problem needs to be solved in a robust manner. However, the use of hybrid control implies the existence of a model of the environment, not an exact model (as the function of hybrid control is to accommodate these errors), but a model appropriate for planning and reasoning. The monitored forces in position control are interpreted in terms of a model of the task as are the monitored displacements in force control. The reaction forces of the task of writing are far different from those of hammering. The programming of actions in such a modeled world becomes more complicated and systems of task level programming need to be developed. Sensor based robotics, of which force sensing is the most basic, implies an entirely new level of technology. Indeed, robot force sensors, no matter how compliant they may be, must be protected from accidental collisions. This implies other sensors to monitor task execution and again the use of a world model. This new level of technology is the task level, in which task actions are specified, not the actions of individual sensors and manipulators.

A joint torque sensing technique for robots with harmonic drives

The authors propose a joint torque sensing technique making use of the existing structural elasticity of robots. The technique provides joint torque sensing without reducing the stiffness of the robot or changing the mechanical structure of the joints. The elasticity of the flexsplines of the harmonic drives is utilized to measure the joint torque. The flexsplines are flexible thin cups, made from steel, in the harmonic drives that are driven by the wave generators. A finite-element analysis of the flexsplines shows that a special configuration of strain gauges, mounted on the flexspline, has to be employed to eliminate errors in sensor information due to rotation of the wave generator. Characteristics of the torque sensor are examined experimentally. The linearity and the dynamic response are almost the same as those of a conventional sensing technique. For a one-link robot arm, both theoretical and experimental investigations support the validity of the sensing technique. >

An investigation of frictionless enveloping grasping in the plane

Grasping by a two-dimensional hand composed of a palm and two hinged fingers is studied. The mathematics of fric tionless grasping is presented and used in the development of a planner/simulator. The simulator computes the motion of the object using an active constraint set method and assuming exact knowledge of the physical properties of the polygonal object, hand, and support. Grasping is divided into three phases. During the first phase, the initial grasping configura tion is found. In the second phase, the object is manipulated away from the support, bringing it into contact with the palm. In the last phase, the grip is adjusted to minimize the contact forces acting on the object.