Carl D. Crane

A Smart Kinestatic Interactive Platform (SKIP)

This paper describes a unique parallel mechanism named the Smart Kinestatic Interactive Platform (SKIP) which was granted a U.S. patent in January 1993. Briefly, this mechanism consists of a platform connected to a base via six legs. The invention, which has a specialized geometry. lends its& to a wide range of commercial applications each of which has a potential market. This device, together with a new theory for the simultaneous control of contact forces and motion, provides a firm foundation for a family of commercial products. A SKIP device is currently being developed by the University of Florida and Rockwell International 4; on behalf of NASA, Kennedy Space Center. This device will be applied specifically to NASAs ground support operations with the objective of increasing efficiency while reducing cost. Specifically, the platform will be used to present a workpiece to a two axis milling machine. In this way, the workpiece will be positioned and oriented with six degrees of freedom relative to the milling tml. This feature, coupled with the ability to perform force control constitutes a new technology which will assist in the reduction of the cost of ground operations at the Kennedy Space Center. Technical Descrip!ion of SKIP A platform or parallel mechanism is defined as any mechanical device that has six legs that connect a moving platform to a base. This kind of mechanism possesses the desirable characteristics of high accuracy, high payload-to-weight ratio, and good static stability. To apply Kinestatic Control to these mechanisms it is necessary to first obtain accurate compliance models. These models can be readily determined for parallel mechanisms, provided that the position and orientation of the moving platform is known relative to the base. Therefore, the key and central task is to determine the position and orientation of the moving platform relative to the base L,- This paper is declared a work of the U S . Government and is not subject to copyright protection in the United States. given the sensed lengths of the six legs. This task is referred to as the forward kinematic analysis for the system, and for these kinds of mechanisms the simplest solution involves solving an eighth degree polynomial in a single variable. The geometrically simplest parallel mechanism has the structure of an octahedron, and it is designated as a 3-3 platform since there are three connecting points on the base and three on the moving platform. The double connection points shown in Figure 1 produce a very simple geometry. However, there is a very serious mechanical disadvantage. It is not possible to design the necessary concentric ball and socket joints at each of the double connection points without mechanical interference. It is preferable to separate the double connection points and in this way to overcome the mechanical design problem. In general, as double connecting points are separated, the complexity of the forward kinematic analysis for the platform increases. It should be noted that there are multiple solutions. This means that there are multiple closures of the mechanism and that there exist a number of different ways it can be assembled. Each assembly yields a different position and orientation of the platform while possessing the same set of six leg lengths. It is, of course, pcssible to perform numerical iterations (an optimization using six independent variables) to obtain the position and orientation of the platform. However, t is well known that such iterative solutions have a tendency to jump from one closure to another. From a practical viewpoint, this is undesirable. It is far more desirable to derive a single polynomial in a single variable, the solution of which yields all possible locations of the moving top platform. The desired solution can then be extracted tom this finite set of all solutions. Such a solution is said to be in closed-form. 3-3 Platform 6-3 Platform 6-6 Platform Special 6-6 Platform Figure 1: Parallel Mechanisms It was only recently that the closed-form forward analysis for the geometrically simplest 3 3 platform was solved by Griffis and Duffy [I]. Briefly, an eighth degree polynomial solution was derived, and this has been extended to a 6 3 platform (Stewarts original platform). It would be desirable to perform the forward analysis f a a general 6-6 device, however this is unrealistic. The closed form equation will be at least a 40th degree polynomial, which has been obtained for a similar device of lesser complexity [2], and this is computationally impractical for real time control. Griffis and Duffy have invented platforms which provide the benefits of both the 3 3 and general 6-6 platforms. These platforms, which have been patented by the University of Florida, allow for the simple analysis of the 3-3 with an eighth degree polynomial, and allow for the mechanical benefits of the general 6-6 by eliminating mechanical interference. As previously stated, the necessity for a simplified closed-form forward kinematic analysis (specialized geometry) manifests itself whenever the mechanism is to control force and position simultaneously. The requirements of specialized geometry and good mechanical design (no mechanical interference) is satisfied by the platforms that have been patented by the University of Florida. It is the union of the theory of Kinestatic Control and these platforms that yields the SKIP concept. ,. bJ Histow of SKIP Development The first parallel mechanism was the Stewart Platform (see Figure 1, the 63 device) which is used in existing flight simulators. These simulators are currently produced by Link Corp. (U.S.A.) and Redifussion Corp. (U.K.). Flight simulators consist of a platform upon which the pilot rides. The platform is connected to a base by six legs. (Each leg is a SPS kinematic chain where S represents a ball and socket joint and P designates a sliding or prismatic joint which is actuated.) The pilot controls the pitch, yaw, and roll of the platform using a joystick. The analysis required to control the motion of the platform through space is relatively simple. Given successive positions and orientations of the platform, it is required to determine sets of leg lengths. This is the so called reverse kinematic analysis and for each location of the platform, there is a unique solution. This technology is well established and has evolved over a period of some twenty five years since 0. Stewart published a paper on such devices in 1965 [3]. It is common practice to call all platforms Stewart platforms. However, Stewarts specific design is illustrated in Figure 1, where it is designated as a 6-3 platform. (It can be seen that there are .-v three connecting points on the platform, and six connecting points on the base.) Two new platforms have been invented by Grifris and Duffy, and a US patent has been allowed to the University of Florida. A prototype of one of these platforms has been built (see Figure 2) at the Center for Intelligent Machines and Robdics at the University of Florida The problem of controlling force and motion of the platform has been the subject of an NSF contract (cePls J. Duffy and C. Crane) entitled A Geometrical and Experimental Investigation of Simultaneous Force and Motion Control of Robot Manipulators. This contract was awarded in December 1988 and n was completed in December 1991. Briefly, the task of controlling force and motion of the platform was accomplished by introducing compliance into the legs. A new theory called Kjnestatic Control has been successfully developed and most importantly, this has not been a paper study. This novel theory has been verified experimentally in the University of Florida Center for Intelligent Machines and Robotics laboratory. Contact forcedtorques between the robd end effector and the environment have been reduced to specified levels and wen been nullified completely whilst simultaneousiy controlling the end effector motion. Two prize winning papers (Best Paper award by the American Society of Mechanical Engineers (Sept 90) and a nomination for Best Paper by the International Federation for the Theory of Machines and Mechanism (July 90)) have been published on the theory [4], [5J. This new theory constitutes the basis for the control of the prototype platformknd effector which will be designed under this proposed effort. The introduction of compliance info the legs of platforms that have a simple forward analysis enables one to control forces and motions simultaneously. Such a platform is classified as a Smart Kinestatic Interactive Plztform (SKIP).