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Hybrid Position/Force Control of Manipulators1 Hybrid Position/Force Control of 1 M. H. Raibert Manipulators 2 A new conceptually simple approach to controlling compliant motions of a robot J.J. Craig manipulator is presented. The "hybrid" technique described combines force and torque information with positional data to satisfy simultaneous position and force Jet Propulsion Laboratory, trajectory constraints specified in a convenient task related coordinate system. California Institute of Technology Analysis, simulation, and experiments are used to evaluate the controller's ability to Pasadena, Calif. 91103 execute trajectories using feedback from a force sensing wrist and from position sensors found in the manipulator joints. The results show that the method achieves stable, accurate control of force and position trajectories for a variety of test conditions. Introduction Precise control of manipulators in the face of uncertainties fluence control. Since small variations in relative position and variations in their environments is a prerequisite to generate large contact forces when parts of moderate stiffness feasible application of robot manipulators to complex interact, knowledge and control of these forces can lead to a handling and assembly problems in industry and space. An tremendous increase in efective positional accuracy. important step toward achieving such control can be taken by A number of methods for obtaining force information providing manipulator hands with sensors that provide in­ exist: motor currents may be measured or programmed, [6, formation about the progress of interactions with the en­ 11], motor output torques may be measured [7], and wrist or vironment. Though recent advances in robotics technology hand mounted sensors may be used [9, 12]. The first two of have led to the application of computer controlled these techniques are limited by the accuracy and availability manipulators to industrial handling and simple assembly of manipulator models that compensate for the complicated operations, advances in the use of hand sensors have been inertial, frictional, and gravitational effects that influence very slow to appear. Therefore manual dexterity remains force measurements. The dynamic range of force information quite low and continues to limit application opportunities and obtained at the joints may also be restricted when large growth. gravitational terms exist, even for the static case. The slow progress is due partly to a lack of rugged, reliable Though wrist-mounted force sensors pose challenging sensors of sufficient precision and versatility. But perhaps problems in mechanical design, eletronics, communications, more important is the lack of adequate controller ar­ and reliability, they are more sensitive and easier to use than chitectures and computing techniques needed to take ad­ joint sensors. Since the mass between a manipulator's wrist vantage of such sensory information, where it available. Such and its fingers is small and there are no articulations, a force- techniques are just now being developed. sensor mounted there requires only minor corrections for The use of manipulators for assembly tasks requires that dynamic effects and has a larger potential dynamic range. For the precision with which parts are positioned with respect to these reasons this paper concentrates on use of a hand sensor. one another be quite high—higher in fact than that available In any case, the basic control formulation given here could from joint-mounted position sensors attached to imperfectly easily be adapted for use with the other force measurement rigid manipulators driven by imperfectly meshed gears. schemes mentioned. Manipulators of greater precision can be achieved only at the The goal here is to present a conceptually simple method expense of size, weight, and cost. The ability to measure and for controlling both the position of a manipulator and the control contact forces generated at the hand, however, offers contact forces generated at the hand that does not suffer from a low cost alternative for extending effective precision. Since the approximate nature of previous schemes [6]. We also relative measurements are used, absolute errors in the position present the results of experiments that explore use of the of the manipulator and manipulated objects no longer in- hybrid technique in conjunction with data provided by a wrist-mounted force sensor. Note that the method we propose here does not prescribe This paper presents the results of one phase of research carried out at the Jet particular feedback control laws for the regulation of errors. Propulsion Laboratory, California Institute of Technology, under Contract Rather it suggests a control architecture within which such No. NAS-7-100, sponsored by the National Aeronautics and Space Ad­ laws can be applied. ministration. Author is now a graduate student at Stanford University. Contributed by the Dynamic Systems and Control Divison for publication in Background the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received at ASME Headquarters, February 25, 1981. The approach taken here is based on a theory of compliant 126/Vol. 102, JUNE 1981 Transactions of the ASME Copyright © 1981 by ASME Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/ on 04/06/2015 Terms of Use: http://asme.org/terms 3 force and position manipulator control that has its roots in IING CRANK NATURAL CONSTRAINTS V . 0 L = 0 the work of Whitney [5, 12], and Paul and Shimano [6, 10], x ' and that was recently formalized by Mason [4]. The following f* »x-o Tro briefly describes Mason's theoretical framework that sup­ Ux = o a; = 0 ports, and is supported by the present work. C y Every manipulation task can be broken down into **--ff" ARTIFICIAL CONSTRAINTS XV v = 0 f elemental components that are defined by a particular set of y x"° contacting surfaces. With each elemental component is 'tSr^^ "z *"l f„-0 associated a set of constraints, called the natural constraints, 7=0 that result from the particular mechanical and geometric r„ - 0 characteristics of the task configuration. For instance, a hand in contact with a stationary rigid surface is not free to move through that surface (position constraint), and, if the surface TURNING SCREWDRIVER NATURAL CONSTRAINTS - 0 f 0 is frictionless, it is not free to apply arbitrary forces tangent to 7 - 0 the surface (force constraint). Figure 1 shows two task f = 0 - „ -0« configurations for which compliant control is useful along ' 7=0 with the associated natural constraints. z ARTIFICIAL CONSTRAINTS In general, for each task configuration a generalized 0 f - 0 surface can be defined in a constraint space having N degrees x p - PITCH P»2 r -0 of freedom, with position constraints along the normals to OF SCREW m*z a2 T.. " 0 this surface and force constraints along the tangents. These two types of constraint, force and position, partition the degrees of freedom of possible hand motions into two or­ thogonal sets that must be controlled according to different Fig. 1 Examples of force control tasks showing the constraint frame criteria. |C|, natural constraints, and artificial constraints. In these examples T Additional constraints, called artificial constraints, are [vx,Vy,vz, uxuy, uz] is the hand's velocity vector, 3 translational and 3 T introduced in accordance with these criteria to specify desired angular components, given in [C\. [fx, fy, 1Z, TX> ry, TZ] is the force motions or force patterns in the task configuration. That is, vector acting on the hand, 3 forces and 3 torques, also given in [ C |. The each time the user specifies a desired trajectory in either a's are constants, (a) Turning a crank at a constant rate, u1. (b) Turning position or force, an artificial constraint is defined. These a screw with constant rate, «2. Note that screw is frictionless. constraints also occur along the tangents and normals to the generalized surface, but, unlike natural constraints, artificial Reference [4] gives more details and examples of this for­ force constraints are specified along surface normals, and malism. artificial position constraints along tangents - consistency Note that the coordinate system within which constraints with the natural constraints is preserved. (See Fig. 1.) and trajectories are specified is not that of the joints of the manipulator, nor necessarily that of the manipulator hand or 3 In this paper "position" implies "position and orientation" and "force" sensor. It is an N degree of freedom Cartesian system defined implies "force and torque." with respect to the task geometry. Takase [11] first introduced Nomenclature B friction acting at manipulator joint (C) the constraint coordinate system X, Y,Z = Cartesian direction F force vector specifying 3 translational a = constant and 3 rotational degrees of freedom r = force compensator transfer function [H] coordinate system fixed in hand yj/ = position compensator transfer func­ [J] Jacobian matrix tion stiffness constant K A = kinematic function of manipulator position servo gains [Kpp\,[Kpi\,[Kpd\ Q = inverse kinematic function force servo gains [K/rUK/,] o) = rotational velocity link offset in manipulator I T = actuator forces and torques mass of manipulator link M T = torque N number of Cartesian degrees of freedom Subscripts manipulator position in joint coor­ c = Coulomb friction dinates d = desired rotation matrix which rotates from e = error {H)to{C} / = force S compliance selection vector ff = feed-forward [Ss] compliance selection matrix [S] p = position force transformation from [H] to r = reaction surface [C] 5 = static friction v = translational velocity w = wrist w = wrist sensor deflection due to forces at x,y,z = cartesian directions hand Preceding Superscripts X = position vector specifying 3 trans­ lational and 3 rotational degrees of C = quantity measured in (C) freedom H = quantity measured in [H] Journal of Dynamic Systems, Measurement, and Control JUNE 1981, Vol. 102/127 Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/ on 04/06/2015 Terms of Use: http://asme.org/terms specification of constraints in a Cartesian system, and Paul COORDINATE has called this system the constraint frame, (C) [6].
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