United States Patent 4 826 392 NASA

United States Patent 4 826 392 Nasa-Free PDF

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U S Patent May 2 1989 Sheet 1 of 4 4 826 392,U S Patent May 2 1989 Sheet 2 of 4 4 826 392. U S Patent May 2 1989 Sheet 3 of 4 4 826 392,ENVIRONMENT. U S Patent May 2 1989 Sheet 4 of 4 4 826 392, not consider the case of interaction of the object with an. METHOD AND APPARATUS FOR HYBRID environment, POSITION FORCE CONTROL OF MULTI ARM Fujii and Kurono introduce the concept of virtual. COOPERATING ROBOTS reference A unified equation is suggested in their. 5 method which depending on the programmer can, BACKGROUND OF THE INVENTION result in force position or masterhlave bilateral con.
trol Force control in this method is realized by specify. 1 Origin of the Invention ing an offset beyond the motion limit As such the force. The iWnti0n described herein was made in the per is controlled though the position loop without using a. formance Of work under a NASA Ontract and is 10 force sensor which results in an inaccurate force con. ject to the Provisions of public Law 96 517 35 UsC trol No compensation for the coupling between the. 202 in which the contractor has elected to retain title joints is performed. 2 Field of the Invention Alford and Belyen also present a masterhlave type. This invention relates to the field of automated con cooperation where two arms are position controlled. trol systems and more Particularly to robotic arm con 15 One arm is position servoed according to a preplanned. trol including control loops for Controlling two Or trajectory The second arm s desired trajectory is modi. more robot arms fied in real time based on the actual position of the first. 3 Description of the Prior Art arm master arm An example is provided for the case. Dual or multi arm robots add extra dimensions to of two arms moving in harmony but not holding a com. robotic applications Such robots are known today and 20 mon object It cannot be concluded from this example. will be highly developed in the future Many tasks can that the method will succeed when a closed loop kine. be performed wih the use of two or more robot arms matic link is formed by grasping a rigid object. that would be impossibleto perform using a single robot M T Mason in his report entitled Compliance and. arm The numerous different applications for cooperat Force Control for Computer Controlled Manipula. ing arms may be grouped into two categories 25 tors IEEE Transactions on Systems Man and Cyber. In the fvst category all robot arms are in rigid contact netics SMC 11 June 1981 pp 418 432 also considered. with an object The object may or may not be in contact the problem of multiple effectors and obtained natural. with an environment In the first category case the constraints for each effector such that there would be. is either the transfer of large objects or a combination of no conflict using multiple effectors on the Same rigid. transfer and force torque exertion by the object on an 30 object The theory developed by Mason on compliance. environment using two or cooperating arms ne and force control of robots is relevant to this invention. second category comprises those assembly tasks where Mason s theory considers an ideal domain in which the. each arm is holdmg a separate object tu second manipulator is the ideal effector represented as a point. category case de the first case the robot arms do in the position and force subspaces Artificial and natu. not forma complete closed link neproblem 35 ral constraints are defined for an ideal point mass and a. solved by this invention deals with the case frictionless environment The artificial constraints are. which fmds widespread use in many practical applica used to specify the desired motion and forcehorque in. tions such as handling parts assembly and a non conflicting manner in the ideal physical world. disassembly Raibert and Craig in their reported work entitled. A literature review of multi arm robotics indicates 40 Hybrid Position Force Control of Manipulators. that the reported has dealt mostly with Journal Of Dynamics SYstemsv Measurement and. Control June 1981 utilized Mason s theory and devel. masterhlave architecture The literature does not teach. oped the so called Position Force Control, Or suggest the problem by the method and technique In this method force and torque information. apparatus of this invention The extension of developed 45 is combined with position d a b to achieve the desired. theories in the areas of kinematics dynamics and con position and force torque in a task related. trol for sing1e rob0tS to the Of, This invention presents a novel extension to the hy. bots however is far from trivial drid control techniques discussed above and utilizes the. Previous work in robots for exmpley is basic position and force torque concepts developed by. reported in 50 Mason Raibert and Craig This invention is basically. A Ishid T 9 Force control in Coordination Of different from Mason Raibert and Craig in that two or. Two Arms Proceedings of the 5th International Confir arrps are controlled in a closed kinematic loop. ence on Artijicial Intelligence pp 717 722 August 1977. B Fujii S and Kurono S Coordinated Computer SUMMARY OF THE INVENTION. Control of a Pair of Manipulators Fourth World Con 55 AS noted above the prior art concentrated on a mas. greuon the n e o V OfMachinesandMeChanhs Univer ter slave approach wherein for example a master arm. SitY of Newcastle upon TWe SePt 8 12 1975 and c pulls and the slave simply follows without contributing. Alford c 0 and Belyen S M Coordinated Control to the task invention departs from that conven. of T W O Robot AMB Proceedings of the International tional approach by providing a system free from any. Conference on Robotics Atlanta Ga Mar 13 15 1984 60 master or slave arm Instead two or more robot arms. Ishida considers a two arm transport system where each share in applying a scaled amount of force in order. one arm is position controlled while the second arm to move an object being controlled by the two or more. follows the first one by way of compliance The move robot arms to a desired position and orientation The. ments are restricted to either parallel or rotational mo novel architecture of this invention provides hybrid. tions and the degree of cooperation in this method is 65 position force control of robots having a plurality of. not very clear In other words it is not explicit whether cooperating arms wherein each arm is controlled such. or not to what degree each arm carries the burden of that the burden of actuation is shared between the arms. transporting the object Also this Ishida method does in a non conflicting way as they control the position of. and force upon a designated point on a mutually held. Single degree of freedom, object This invention is applicable whether or not the. controlled object is in contact with a rigid external Two separate ideal cases will be considered 1 A. environment The position control loops of this inven single point mass 20 FIG 2 rigidly attached to two. tion are based upon each manipulator s Cartesian space 5 single degree of freedom actuators 25 30 e g DC mo. dynamic equations In the position control subspace a tors or hydraulic actuators In this case we will assume. feature of this invention allows the robot arms to exert that the motion of the point mass 20 is not resisted by. additional forces torques to achieve compression ten any external force 2 The same mass 20 and actuators. sion or torsion in the object without affecting the exe 25 30 of the first case with the exception that the point. cution of motion trajectories In the force control sub 10 mass 20 FIG 5 is in Contact with an external obstacle. space the total force tWue magnitude square is mini 19 21 such that the point mass 20 is not free to move. mized while realizing the net desired forcehorque on 1 point M free to move. the environment FIG 2 shows a schematic drawing for this configura. BRIEF DESCRIPTION OF THE DRAWINGS tion where mass 20 is free to move F1 and F2 represent. l5 the total force acting on the point mass 20 and the com. FIG 1is a schematic drawing of a multi arm cooper bined inertia ofthe moving parts ofthe actuators2530. ating robot affecting a single object If the desired motion x of the point mass is specified. FIG 2 is a schematic diagram Of a two actuator SYS by d t then each of the servo systems can be con. tem trolled to induce this motion on the mass The block. FIG 3 is a schematic diagram of a Servo 2o diagram of FIG 3 shows a Servo control system for the. trol loop for a two actuator single degree of freedom combined system In FIG 3 the total mass is a combina. system tion of the mass 20 of the object to be moved and the. FIG 4 is a schematic block diagram of a Position moveable mass of the actuators 25 and 30 That total. force controlled point mass using two linear actuators m where m M1 M M2 and Mi9 with i 1 2. depicts a constrained useful in under 25 are the effective task space masses of the actuators and. standing the development of equations explaining this is the of the point mass. invention The total force applied on the equivalent mass is f. FIG 6 depicts selection of F1 and F2 for a bar and is which is given by. useful in understanding the development of equations. explaining this invention 30 f F1 F2 1,FIG 7 is force control block diagram of a con. strained mass using two actuators N1 and N2 are real positive numbers with N1 N2 1. FIG 8 is a block diagram schematic of a position neequation of motionof this system is given by. control loop for arm i, FIG 9 is a schematic block diagram of a force con 35 m i f V I.
trol loop for arm i d i Kpl fKpZ xd X 2,FIG 10 is a schematic block diagram of a position. force hybrid control for a multi arm cooperating robot by defining e xd x and noting that N1 N2 1 we. DETAILED DESCRIPTION OF THE 40,DRAWINGS m e K i Kvz i Kpi Kp2 e 0 3. Consider the schematic drawing of FIG 1 where n, robot arms 1 2 3 n are shown gripping a single rigid As shown in FIG 3 we are concerned about position. object 5 In this analysis we will assume that the contact ing the mass 20 which includes moving the total mass. between each of the grippers at the ends of the arms and 45 m When we want something to move the control loop. the object 5 is rigid The main difference between this must specify distance velocity and acceleration Ac. case and that of a single arm is that additional natural cordingly the input signal to the control loop input. constraints are introduced due to the fact that all the terminal 50 is the term mjid which is the total mass. grippers must be connected firmly to a rigid object times the desired acceleration G The values for scalers. This means that the a f m s can exert forces or torques on 50 51 52 that is the values of N1 and N2 may be any. each other without the object contacting an external predetermined amounts depending upon the value of. environment The arms must also move and apply the load to be shared For example in FIG 2 if the mass. forces in harmony in order to induce the desired motion 20 is divided in half as shown by the dashed vertical. to the object line it may be desired to have actuator 25 push 50 and. The problem posed by a multi arm robot is more 55 actuator 30 pull 50 This is by no means limiting since. clearly understood if we reduce the workspace to a the scaler values may be any shared amount as desired. single degree of freedom d 0 f The results can then for the situation The scalers are connected in feed for. be generalized to the full six d 0 f position orientation ward loops 53 54 which feed the scaled amount to. case summation points 55 and 60 for each actuator A second. The main ideas behind the present invention will first 60 input term to the servo loop is the desired distance xd. be discussed in connection with FIG 2 for a very sim for the object to be moved That second term is applied. ple case i e a point mass 20 which is either free to via input lead 40 A summing junction 41 is connected. move along a straight line one degree of freedom or to input terminal 40 and receives a feedbacksignal from. can exert a force in that direction In either case it is a distance sensor 42. assumed that the point mass 20 is being controlled by 65 Sensor 42 as is well known converts the actual. two linear actuators 25 30 The solutions obtained for movement x into an electrical signal that is applied at. these simple cases will then be generalized for a multi terminal 43 to the summation junction 41 An error. arm robotic system signal e is developed at summation junction 41 and that. error signal is applied to inputs of two controllers 43 44. one each for each actuator The controllers 43 44 may. x Sensors such as sensor 42 are to be understood in 10. FIGS 4 and 7 through 10 which figures show a dot Q Fl2 F22 7. connected at the output in the feedback loop for sim. plicity purposes which results in a unique solution given by. The gains k shown in the equations for the PD con,F1 F2 Fd 2 8. trollers can be selected easily to obtain a critically 15. damped system having a closed kinematic loop With The criterion of equation 7 assures that we select. this design in the ideal case where we have perfect one solution out of infinite many solutions with the. trackingy the Only force that is being exerted On the property that the sum of the length of the force vectors. point mass is that which is required to achieve the de 2o is minimized On the other hand if we were applying. United States Patent I91 Hayati ill Patent Number 4 826 392 POSITION FORCE CONTROL OF MULTI ARM COOPERATING ROBOTS BACKGROUND OF THE INVENTION 1 Origin of the Invention The iWnti0n described herein was made in the per ject to the Provisions of public Law 96 517 35 UsC is controlled though the position loop without using a trol No compensation for the coupling between the formance Of

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