Plural robotic drive.

BACKGROUND OF THE INVENTION

0001This invention relates to speed control in a robot and, more particularly, to a transfer of power among plural motors diving a common joint of the robot to equalize travel of the motors.

0002Robots are being employed with increasing frequency for positioning a large variety of loads in industrial processes. Both speed and precision are desirable qualities in robotic tasks, the speed enabling more efficient operation and the precision enabling the robots to perform operations requiring highly precise movements.

0003Robots are composed of one or more members which are movable relative to a frame of reference. A member may translate, pivot or rotate relative to another of the members. Some form of prime mover, such as an electric motor, is associated with each member for providing the movement. Each movable member, including its prime mover, is frequently referred to as a joint irrespective of the type of motion which the member may undergo. A load to be positioned by the robot is held by an end effector, or gripper, extending from one of the joints.

0004A situation of particular interest is the case of a robot wherein a joint translates sideways as in a robot structured with joints arranged in a cartesian coordinate system. For example, a joint disposed along the X-axis may be supported by a joint which translates along the Y-axis. The X-axis joint, in turn, may support a Z-axis joint which terminates in a gripper for carrying a load. For precise positioning of the load, it is desireable that both ends of the X-axis joint move in synchronism.

0005A problem arises in that such synchronism has been attained by a massive interconnecting structure which minimizes bending of the X- axis joint. The use of such heavy structure is inefficient in energy consumption and increases the cost of the robot. Also, the increased weight of the joint necessitates a larger drive motor. Larger electric motors in joints are disadvantageous because of slower response times which militate against desireable rapid precise movements of a robot.

0006One attempt to solve the foregoing problem is the use of two electric motors, one at each end of the X-axis joint. Such a configuration can be obtained by the use of two Y-axis joints disposed at opposite ends of the X-axis joint, and supporting the X-axis joint. The two motors are advantageous in that they are smaller and have faster response times than the foregoing larger motor. However, the dynamic loading of the two motors varies during a translation of the Z-axis joint along the X-axis joint. A problem still remains in that presently available motor control systems do not compensate for changing dynamic inertial loads to provide adequate synchronism between the two motors. As a result bending of the X-axis joint may occur with a possible binding in the drives and bearings of the two Y-axis joints.

SUMMARY OF THE INVENTION

0007The foregoing problem is overcome and other advantages are provided in a multiple-axis robot wherein a load-­bearing member, disposed along the X-axis of a cartesian coordinate system, is supported at its ends by a pair of Y-axis joints of the robot. The joints connect with the ends of the load-bearing member, and provide for translation of the load-bearing member. In accordance with the invention, each of the Y-axis joints includes a linear variable-reluctance stepping motor, and a position sensing device which provides position data along a path of travel of the joint. The sensing device includes a glass grid and, along with interpolation circuitry, provides position data which is accurate to a small fraction, smaller by some orders of magnitude, than a spacing between magnetic pole pieces of the motor to attain high positional accuracy in the joint. The robot has motor-control circuitry comprising a feedback control loop coupled to respective ones of the position sensing devices for driving the motor of each Y-axis joint with great precision.

0008In accordance with a further feature of the invention, the motor-control circuitry of the robot includes a cross-coupled control loop between the motors of the two joints. The cross-coupled loop acts as a power distribution circuit which can shift power between the Y-axis joints so as to advance or retard the progress of one joint relative to the other joint, thereby to maintain synchronism in travel of the joints along their respective paths. The cross-coupled loop is responsive to a difference in the positions sensed by the sensing devices of the Y-axis joints, and to a difference in velocities of the joints. The velocities are obtained by differentiation of position data reported by the sensing devices. By use of both position and velocity data of each joint, the power can be shifted accurately between joints so as to correctly compensate for any difference of travel along their respective paths.

0009In a preferred embodiment of the invention, the load-­bearing member is formed as a joint disposed along the X-axis. The robot comprises further a joint disposed along the Z-axis and carried by the X axis joint, the Z-axis joint being translatable along the X-axis by the X-axis joint. The Z-axis terminates in a gripper which is rotatably mounted to the Z-axis. The gripper is operative for holding a load. This provides four degrees for freedom, namely, the three axes of the coordinate system and the rotation of the gripper.

0010Measurement of position is done at each of the Y-axis joints. The use of the two Y-axis joints inhibits bending of the X-axis load-bearing member as compared to previous use of only a single cantilevered joint. Thereby, the actual location of the load agrees with the measured position to a much higher degree of accuracy than has been obtained heretofore.

0011The precise synchronism attained by the invention in the operation of the two Y-axis joints allows for a substantial reduction in the weight of the X-axis load-­bearing member while maintaining correct alignment of the ends of the load-bearing member. The reduction in weight in the mechanical coupling in combination with the electrical coupling of the Y-axis joints, raises the apparent resonant frequency of the structure and allows for a faster response to attenuate any mechanical transient motions. This improves accuracy in positioning the load. The cross-coupled loop provides point by point tracking of the Y-axis joints in prescribed paths of travel whereby the Y-axis joints cooperate in the movement of the X-axis joint and the load. The cross-coupled loop compensates for differences in inertial loading of the Y-axis joints due to a shifting of position of the Z-axis joint and the load along the X axis. Also the foregoing reduction in weight provides for a more economical operation of the robot.

0012An additional feature of the invention enables the stepping motors of the two Y-axis joints to be operated synchronously at higher speeds by injection of additional lead phase angle as compared to the nominal amount of phase angle present at lower speeds. The phase angle is the apparent position of the magnetic field impressed by an armature of a motor relative to the position of an array of teeth of a stator of the motor. The angle is leading in the direction of motion of the armature along the stator. Shifting of phase angle introduces a shift in motor drive force. In order to insure that such a change in motor drive force does not upset the balance in the driving of the opposite ends of the X-axis load-bearing member by the two Y-axis joints, the circuitry of the invention delays the injection of a phase change until both motors have passed into a different speed range, and then alters the phase angle simultaneously in both of the motors.

BRIEF DESCRIPTION OF THE DRAWINGS

0013The aforementioned aspects and other features of the invention are explained in the following description, taken in connection with the accompanying drawing wherein: <ul id="ul0001" list-style="none"><li>Fig. lA is a perspective view of a multiple axis robot of the invention wherein two joints of the robot move a common load-bearing member along a path designated by a pair of side rails;</li><li>Fig. lB is a simplifed isometric view of the robot of Fig. lA;</li><li>Fig. 2A is an enlarged isometric view of a stator bar of a linear motor and position sensing apparatus, shown partially diagrammatically, of a Y-axis joint of the robot of Fig. lA;</li><li>Fig. 2b is a diagrammatic view of the linear motor taken along the line 2B-2B in Fig. 1B showing a stator bar and an armature housing of the motor;</li><li>Fig. 3 is an electrical schematic diagram of circuitry of the invention including feedback and cross-coupling circuits for the robot of Fig. l;</li><li>Fig. 4 is a block diagram of a differentiator of Fig. 3.</li><li>Fig. 5 is a block diagram of a position command unit of Fig. 3;</li><li>Fig. 6 is a graph of a set of input position signals for the unit of Fig. 3;</li><li>Fig. 7 is a graph of a set of interpolated positions between positions of the signals of Fig. 6;</li><li>Fig. 8 is a block diagram of a gain command unit of Fig. 3; and</li><li>Fig. 9 is a graph of velocities of robot joints and an injection of lead phase angle to motors of the joints for demonstrating the operation, including hysteresis, of a lead angle generator of Fig. 8.</li></ul>

DETAILED DESCRIPTION

0014With reference to Figs. lA, lB, 2A, and 2B, there is shown a multiple axis robot 20 having motorized drives for positioning a load 22 along X, Y, and Z axes of a cartesian coordinate system 24. The robot 20 comprises a joint 26 disposed horizontally in the X direction, two joints 28 and 30 arranged in parallel and disposed horizontally in the Y direction, a joint 32 disposed in the Z direction, and a gripper 34 extending from a lower end of the joint 32. The joints 28 and 30 are also identifed by Yl and Y2, respectively. The load 22 is held by the gripper 34, the latter being carried by the joint 32. The joint 32 is carried by the joint 26, and is operative for moving the gripper 34 vertically relative to the joint 26. The joint 26 imparts translational motion in the X direction to the joint 32 and the gripper 34. The joint 26, in turn, serves as a load bearing member and is connected at one end to the joint 28, and at the opposite end to the joint 30. The joints 28 and 30 are operative to impart translational motion to the joint 26 along with the joint 32 and the gripper 34 in the Y direction.

0015In accordance with the invention, the joints 28 and 30 are operated in synchronism for transporting the joint 26, the synchronous operation preventing the introduction of any bending forces between the joints 28 and 30 and the joint 26, which forces might jam the movements of the joints 28 and 30. The synchronous operation is accomplished by feedback and cross-coupled loops, as will be described subsequently, which connect with the motorized drives of the joints 28 and 30.

0016The motorized drives comprise electric motors, more specifically, variable-reluctance linear stepping motors 36A and 36B, respectively, in the joints 28 and 30. The steps in such a motor permit positional control of each of the joints 28 and 30 wherein movement of the joints 28 and 30 can be synchronized to a resolution finer than the step distance of the motor along an entire path of travel. The motors 36A-B comprise, respectively, stator bars 38A-B and armature housings 40A-B which ride upon the respective bars 38A-­ B. The bars 38A and 38B also serve as outer arms of a fixed frame 42 of the robot 20, and may be mounted by legs 44 upon a base 46. The X-axis joint 26 similarly comprises a linear stepping motor 48 having a stator bar 50 with an armature housing 52 riding thereon for imparting translation to the Z-axis joint 32. The joint 32 comprises a well-known lead screw assembly 54 for raising and lowering the gripper 34. The gripper 34 includes a rotary drive 56 to impart rotation of the gripper 34 and the load 22 relative to the joint 32.

0017In a preferred embodiment of the invention, the robot 20 carries a payload of approximately 2 kg (5 pounds), the joints of the X and Z axes weigh 11 kg (30lbs) and the armature housings 40A-B of the Yl and Y2 joints each weigh 1.5 kg (4lbs). The ratio of payload weight to weight of the robot is approximately l4%, this being a significant improvement over presently available ratios of approximately 4%.

0018Figs. 2A-B show details in the construction of the motor 36A. This description of the motor 36A applies also to the motor 36B which has the same construction as the motor 36A. As shown in Fig. 2A, the stator bar 38A of the motor 36A comprises upper and lower steel rails 58 and 60, each of which is provided with a smooth bearing surface for receiving bearings (not shown) of the armature housing 40A, by which bearings the housing 40A rides upon the rails 58 and 60. In a preferred embodiment of the invention, the housings 40A-B each have a length of 7.62 cm. The rails 58 and 60 stiffen the bar 38A for supporting the weight of the joints 26 and 32 and the load 22, while providing torsional strength to resist twisting. The cross section of the lower rail 60 is broadened for increased torsional strength, thereby to improve accuracy in positioning the load 22. The bearings are spring loaded, preferrably to insure precise alignment of the housing 40A with the bar 38A.

0019It is noted that the bar 38A serves the dual purposes of supporting joints of the robot 20 while also serving as a component of the motor 36A. The rails 58 and 60 are spaced apart by a set of silicon iron laminations which are pinned to the rails 58 and 60, and are also bonded to each other and to the rails to provide strength to the bar 38A. Each of the laminations is configured with a tooth and valley construction defining a set of teeth 62 for the motor 36A. The teeth 62 are arranged along the bar 38A, in a preferred embodiment of the invention, with a pitch of 0.254 cm. The width of a tooth is equal to the width of a valley, namely, 0.127 cm. The laminated construction of the bar 38A reduces the flow of eddy currents, and the attendant power loss, induced by magnetic fields in the composite structure of iron and steel.

0020In Fig. 2B the diagrammatic view is useful in explaining the operation of motor 36A. The armature housing 40A comprises a toothed structure (Fig. 2A), which is similar to the toothed structure of bar 38A and which defines a set of magnetic poles 64, only three of which are shown by way of example. Since the motor 36A is a variable reluctance motor, there are no permanent magnets in the motor, all magnetic fields are produced by electrical energization of coils 66 disposed about respective ones of the poles 64. The coils 66 are electrically activated with current supplied by a drive circuit 68 (shown in Figs. l and 3) which provides the function of commutation for successively activating the poles 64 to develop magnetic forces between the poles 64 and individual ones of the teeth 62. The spacing between the poles 64 differs from that of the teeth 62 so as to permit emplacement of the poles 64 at positions which are optimal for applying electromagnetic forces during successive positions of the armature housing 40A for urging the armature housing 40A along the stator bar 38A.

0021The motor 36A further comprises a magnetoresistive detector 70A, of well-known form, which senses the presence of individual ones of the teeth 62 as they approach the poles 64 during movement of the armature housing 40A along the stator bar 38A. A corresponding detector 70B (Fig. l) is provided within the motor 36B. Output signals of the detector 70A activate the drive circuit 68 to provide the commutating function in accordance with the positions of the teeth 62 relative to the armature housing 40A, and in accordance with the required direction of force to be exerted by the joint 28 for positioning the load 22 (Fig. l).

0022Figs. l and 2A also show position sensors 72A, 72B, and 72C included within respective ones of the joints 28, 30 and 26 for signaling the drive circuit 68 as to the positions of the respective joints 28, 30 and 26. The sensors 72A-C are of similar construction. A detailed view of the sensor 72A is shown in Fig. 2A; it is understood that the description of the sensor 72A applies also to the sensors 72B and 72C. Additional position sensors, not shown, are incorporated within the Z-axis joint 32 and the rotary drive 56 of the gripper 34 for signaling their respective positions.

0023The sensor 72A comprises a grid 74 enclosed within a protective case 76 and positioned by struts (not shown in Fig. 2A) in parallel relation to the stator bar 38A. A holder 78 extends from the armature housing 40A and has two legs 80A and 80B which envelope a portion of the grid 74. The holder 78 passes though a groove 82 with a rubber seal 84 which excludes ambient light and dirt outside the case 76 from the interior of the case 76, while permitting the holder 78 to pass back and forth along the grid upon movement of the armature housing 40A along the stator bar 38A. The material from which the grid 74 is fabricated is transparent and also has a coefficient of thermal expansion which is equal to that of the steel in the rails 58 and 60, a suitable material being Vicore glass. The leg 80A holds a lamp 86 for illuminating distance marks 88 on the grid 74. The leg 80B holds a pair of detectors 90 and 92 of light of the lamp 86, the detectors 90 and 92 being positioned for viewing the marks 88. The detectors 90 and 92 output electric signals indicating the presence and absence of a mark 88, and are spaced apart by one-quarter of the distance between successive marks 88 to provide for inphase and quadrature detection of the marks 88.

0024Preferably, the marks 88 are of equal widths, the width being equal to the spacing between successive ones of the marks 88. This arrangement provides that, during movement of the armature housing 40A, the inphase and quadrature signals of the detectors 90 and 92 have sine waveforms which are interpolated and converted to square waves which are then suitable for processing by digital circuitry of the drive circuit 68. As will be disclosed below with reference to Fig. 3, such circuitry includes well-known logic units 94 and counters 96 responsive to the times of occurrence of the detector signals to determine the locations of the armature housings 40A-B, and also to determine whether the armature housings 40A-B are progressing in a forward or reverse direction along the respective stator bars 38A-B. The circuitry 94 allows interpolation between the grid marks 88 to resolve distance increments and to position a joint to an accuracy of two micrometer (79 millionths of an inch).

0025The drive circuit 68 (Figs.l and 3) provides electronic activation of all the joints 26, 28, 30 and 32, as well as the gripper 34. Connection of the drive circuit 68 to the joints 26 and 32, and to the gripper 34 has been deleted from the figures to facilitate a presentation of the invention. The drive circuit 68 connects with the motors 36A-B via lines 98A-B, respectively, for imparting current command signals to the motors 36A-B. The drive circuit 68 receives position data form the sensors 72A-B via lines l00A-B, respectively, and the tooth-pole spacing in the motors 36A-B from the magnetoresistive detectors 70A-B via lines l02A-B, respectively.

0026In accordance with a feature of the invention, the use of the two joints 28 and 30 instead of a single joint for positioning the load 22 along the Y axis permits a significant reduction in weight of the positioning system 20. By driving the load-bearing member, namely the joint 26, from both ends by the joints 28 and 30, bending stresses in the load-bearing member can be avoided so as to negate the need for a massive rigid structure as would be required if only one joint were employed for positioning the load-bearing member along the Y axis. However, in order to take advantage of the light weight structure, it is necessary for both of the joints 28 and 30 to track each other precisely as they advance along their respective bars 38A-B. Such precise tracking prevents a bending of the load-bearing member, which bending may induce unduly high forces on the bearings with possible development of a binding of the bearings.

0027The accurate positioning and tracking of the joints 28 and 30 is accomplished, in accordance with the invention, by the foregoing construction of the linear motor which introduces displacement without the use of any gearing and backlash associated therewith. The drive circuit 68 includes individual feedback control loops, as will be described below, for energizing the linear motors 36A-B so as to provide for accurate movement of the joints 28 and 30 along their respective bars 38A-B.

0028In addition, the invention provides for improved tracking of the positions of the joints 28 and 30 by a cross coupling of signals between the two feedback loops which activate the motors 36A-B. The cross coupling includes signals obtained from positional errors of each loop plus position rate of change, or velocity, of each loop. The cross coupling raises the apparent resonant frequency of the structure of the robot 20, an effect which tends to overcome any mechanical vibrations which might otherwise be present in the structure and, thereby improves the position tracking between the two joints 28 and 30.

0029As will be described with reference to Fig. 3, the cross-coupled signals are introduced at summing points in the feedback control loops. The signals are algebraically summed, with positive and negative signs, so as to accomplish a distribution of power between the two loops such that more power is applied to a lagging joint and a retarding force is applied to a leading joint, depending on the position errors and velocities of the joints. This allows the lagging joint to catch up with the leading joint so as to insure proper tracking of their respective positions. Such adjustment in the relative positions of the two joints 28 and 30 supplements the position control provided to the joints individually by the feedback loops ll6 and ll8.

0030In the use of the robot 20, the position of the load 22 may be varied along the X axis such that, at times, the load 22 may be near the bar 38A while, at other times, the load 22 may be near the bar 38B. When the load 22 is positioned at equal distance between the two bars 38A-B, the joints 28 and 30 must exert equal driving forces to accelerate and decelerate the load 22 during a displacement thereof in the Y direction. However, when the load 22 is positioned at unequal distances between the bars 38A-B, different forces must be exerted by the joints 28 and 30 during such acceleration and deceleration of the load 22. As a result, the dynamic loading of the joints 28 and 30 is dependent on the position of the load 22 in the X dimension. Due to such differences in dynamic loading, the individual feedback loops may experience different positioning errors in the control of the respective joints 28 and 30. However, the cross coupling of the invention compensates for such differences in dynamic loading so as to provide for the necessary accuracy in tracking between the joints 28 and 30 so as to insure that no excessive bending stresses develop within the X-axis joint 26.

0031With reference to Fig. 3, there is provided a description of the drive circuit 68 and its interconnection with the joints 28 and 30. In the preferred embodiment of the invention, the drive circuit 68 is implemented by a digital computer which provides the various functions of signal processing such as summing, scaling, integration and differentiation of position data signals received from the sensors 72A-B. In order to facilitate an explanation of the operation of the drive circuit 68, Fig. 3 shows discrete components as are present in analog circuits, it being understood that each component represents a specific function to be performed by the computer. Thus, Fig. 3 serves as a logic flow chart for the operation of the computer, and also shows how the circuit 68 could be constructed in analog form. It is noted that the digital form of the circuit 68 is preferred in order to avoid drift.

0032Output digital drive signals of the circuit 68 for the motor 36A-B are converted by converters l04 to analog signals which are coupled via power amplifiers l06 to the motors 36A-B. Current from the amplifiers l06 is steered via coil selectors l08 to the requisite coils 66 for driving the motors 36A-B in a desired direction.

0033The mechanical interconnection of the two joints 28 and 30 is represented by a dashed line ll4. The drive circuit 68 comprises two of the aforementioned feedback loops of which a first loop ll6 connects via the lines 98A, l00A and l02A respectively to the motor 36A, the position sensor 72A, and the tooth detector 70A. The second loop ll8 connects via the lines 98B, l00B and l02B to the motor 36B, the sensor 72B, and the tooth detector 70B. Mechanical connections between the motor 36A, the detector 70A and the sensor 72A is indicated by dashed line l20. Mechanical interconnection between the motor 36B, the detector 70B and the sensor 72B is indicated by dashed line l22.

0034Each of the feed back loops ll6 and ll8 comprises, in addition to its respective motor and sensor, a summer l24, an integration unit l26, a summer l28, an amplifier l30, a differentiator l32, a linearizing unit l34, and an amplifier l36, these components being in addition to the aforementioned logic unit 94, counter 96, digital-to-analog converter l04 and power amplifier l06. A clock l40 provides clock pulses, via terminal C, to components of the loops ll6 and ll8, such as the differentiator l32, for operating these components to process successive samples of position data. Such position data includes both input position commands, and present joint positions reported by the sensors 72A-B, as will be described below. The clock pulses appear periodically at intervals of 2 milliseconds, which interval is the spacing between successive samples of input position applied to the summers l24. The clock l40 participates in all operations of the robot 20 to synchronize the transmission and reading of samples of data among the components of the foregoing circuitry of the robot 20.

0035In accordance with a feature of the invention, the drive circuit 68 includes cross-coupling circuitry l42 connected between the two loops ll6 and ll8 which implements a distribution of power between the two loops ll6 and ll8 such that a lagging joint receives an increased amount of power while a leading joint receives a decreased amount of power. For example, in the event that the joint 28 were lagging behind the joint 30, the cross-coupling circuitry l42 would activate the loop ll6 to increase the flow of power to the motor 36A while decreasing the flow of power to the motor 36B. Such shifting of power brings the two joints into registration with each other with reference to the coordinate system 24 (Fig. l). The cross-coupling circuitry l42 comprises two summers l44 and l46, and two amplifiers l48 and l50.

0036Also included within the drive circuit 68 are a position command unit l52A which inputs desired joint positions to the summers l24 of the loops ll6 and ll8, and a gain command unit l52B which provides gain factors to amplifiers of the loops ll6 and ll8 via terminals Al, A2, A3 and Bl, B2, B3, respectively. The gain command unit l52B also provides a lead-angle command to the Y-axis motors 36A-B as will be described below. Each of the integration units l26 comprises an integrator l54, an amplifier l56 whose output is summed with the integrator l54, and a switch l58 serially connected with the integrator l54. The switches l58 are operated by signals from the gain command unit l52B at terminals A4 and B4.

0037With reference also to Figure 4 there is shown the construction of the differentiator l32 of the first loop ll6. Each of the differentiators l32 have the same construction. Accordingly, this description applies also to the differentiator l32 of the loop ll8. In the first loop ll6, the differentiator l32 receives an input signal on line l60 from the counter 96, and outputs a signal on line l62. In the second loop ll8, the differentiator l32 receives an input signal on line l64 from the counter 96 and outputs a signal on line l66. The differentiator l32 comprises a register l68, four weighting units l70, and a summer l72. Samples of input position data on line l60 are clocked into the register l68 by clock pulses at terminal C. The weighting units l70 interconnect respective cells of the register l68 to input ports of the summer l72. The weighting units l70 provide four weighting factors shown as Wl, W2, W3 and W4. The most recent sample is multiplied by the factor Wl, and the oldest sample is multiplied by the factor W4. Alternate ones of the weighting samples are applied to positive and negative ones of the input ports of the summer l72 as indicated in the figure. Suitable weighting factors are the following. Wl = ll, W2 = l8, W3 = 9 and W4 = 2. The summer l72 forms differences between the weighted samples, the combination of these differences being outputted as the derivative of the input position signal. Thus, the output signal of the summer l72 is the velocity of the joint 28.

0038In operation, the drive circuit 68 of Figure 3 energizes the two motors 36A and 36B of the joints 28 and 30. While the two loops ll6 and ll8 are provided for activation of the motors 36A and 36B, respectively, it is to be understood that the two loops do not operate independently because of electrical and mechanical coupling between the two loops. Electrical coupling is provided by the cross-coupling circuitry l42 while the mechanical coupling of line ll4 is provided by the connection of the load-bearing member of the joint 26 (Figure l) with the joints 28 and 30. Signals induced within the loops ll6 and ll8 by virtue of the foregoing coupling are smaller than those which would be present in each of the loops ll6 and ll8 if the loops could be operated independently of each other. Accordingly, the operation may be described by initially considering each of the loops ll6 and ll8 to have independent operation after which the effects of cross-coupling may be considered.

0039The positions of the joints 28 and 30, as sensed by the sensors 72A-B are outputted as counts by the counters 96. The operation is the same for both of the sensors 72A-B so that only the operation of the sensor 72A need be described, the description applying also to the sensor 72B. The counter 96 counts pulses of the signal outputted by the logic unit 94 which receives its input from sensor 72A via lines l00A (Fig. 2A). The counter 96 is initialized at a reference point of convenience on the bar 38A. The count of the counter 96 represents displacement of the housing 40A from the reference point. The counter 96 counts up or down as commanded by the logic unit 94, an upward counting indicating forward movement of the housing 40A while a downward counting indicates a reverse movement of the housing 40A. The output count of the counter 96 is a digitally formatted signal suitable for use by the driver circuit 68. The logic unit 94 outputs an up/down command to a control terminal of the counter 96 based on the time of occurrence of the inphase signal relative to the quadrature signal of the detectors 90 and 92.

0040In the operation of the first loop ll6 by itself, the command unit l52A provides a position signal to the positive input terminal of the summer l24 while the present position derived from sensor 72A, is applied to the negative input terminal of the summer l24 along line l60. The difference between these two signals is outputted by the summer l24 via line l74 to the integration unit l26. The integration unit l26 operates in either of two modes, a terminal-phase mode in which both the integrator l54 and the amplifier l56 are employed, and a high-speed mode wherein the integrator l54 is disconnected by the switch l58.

0041The differentiator l32 outputs a velocity signal via the amplifier l30 to a negative input terminal of the summer l28. An output signal of the integration unit l26 is applied to a positive input terminal of the summer l28. The velocity signal serves as a damping signal for controlling stability of the loop ll6. The summer l28 forms the difference between the signals of the integration unit l26 and the differentiator l32, and applies the difference to the joint 28, via the series combination of the linearizing unit l34, the amplifier l36, the converter l04, the power amplifier l06, and the coil selector l08.

0042The linearizing unit l34 may comprise a square-root circuit as is represented by the square-root sign shown in the figure. As is well known, the driving force provided by a motor, such as the motor 36A, is proportional to the square of the current which drives the motor. The linearizing unit l34 compensates for the squaring relationship by obtaining the square root of the absolute value of the drive signal (output of summer l28) so as to linearize the operation of the first feed back loop ll6.

0043The foregoing current-squared relationship and the corresponding square-rooting function approximations to the motor characteristics permit an adequate amount of linearizing to be accomplished. However, it is noted that additional non-linear considerations may arise during certain optional modes of operation of the motor 36A. For example, high speed operation of the motor 36A, is accomplished by advancement or skipping of certain phases in the sequence of coil energizations. Such phase skip, when employed, is done concurrently with the two Y-axis joints 28, and 30, and is synchronized between the two joints by lead angle control from the command unit l52B as will be described below. The phase skip is employed because the electrical time-constants of the coil circuits do not permit as rapid an energization of the coils as would be required for the high speed operation. The advancement of the phase of energization of the coils in the sequence of energization partially circumvents the limitations of the time constants so as to provide a further increase in the speed of the motor 36A.

0044The output signal of the linearizing unit l34 is applied to the amplifier l36 to be scaled to an appropriate magnitude for driving the motor 36A. The signal outputted by the summer l28 is in digital format and include a sign bit which is applied directly to the selector l08, the sign bit indicating whether the motor 36A is to generate force in the forward or the reverse direction. The signal outputted by the amplifier l36 is applied to the converter l04 for conversion to an analog value of current which is applied by the power amplifier l06 and the coil selector l08 to the motor 36A.

0045During a movement of the load 22 from one position along the Y-axis to another position along the Y-axis, the velocity imparted to the load 22, as well as to the x-axis stator bar 50, has a profile similar to that of a trapezoid in which the speed increases approximately linearly from zero to a maximum value under substantially constant acceleration, the speed then continuing at the constant value until the terminal phase in which the load 22 approaches closely to the desired position. Thereupon, the speed decreases substantially linearly with time to a value of zero. There may be some overshoot beyond the desired position in which case the Y-axis joints 28 and 30 reverse direction to bring the load 22 to the desired position.

0046The command unit l52A outputs a succession of updated position signals periodically at intervals of two milliseconds to the summer l24. During the interval of constant speed, the steady flow of position signals in combination with the negative feedback of the velocity signal of the differentiator l32 provide a substantially constant drive signal to the motor 36A.

0047The loop ll6 functions as a feedback loop with respect to position control of the joint 28 in response to each of the succession of updated signals. Loop stability is attained in accordance with, well-known practice for computer-controlled feedback loops. Thus, the data sampling rate and the inherent drift resistance of a computer controlled loop enhances the loop stability. Also, if desired, a well-known lead-lag filter (not shown) can be incorporated within the amplifier l36 to provide desirable values of phase and gain margins in accordance with well-knownfeedback control.

0048The foregoing description of the loop ll6 applies also to the loop ll8. The operation of these loops is modified by the cross-coupling circuitry l42 in the following manner.

0049In the cross-coupling circuitry l42, the summer l44 connects with the output terminals of the two summers l24 to receive the positional error signals on the lines l74 and l76. The summer l44 subtracts the signal on line l76 from the signal on line l74 and outputs their difference via the amplifier l48 to each of the summers l28. The difference signal is applied to a positive input terminal of the summer l28 in the first loop ll6, and to a negative input terminal of the summer l28 in the second loop ll8.

0050The summer l46 of the cross-coupling circuitry l42 connects with output terminals of the two differentiators l32 for receiving velocity signals from each of the loops ll6 and ll8. The summer l46 subtracts the velocity signal of the loop ll8 from the velocity signal of the loop ll6, and applies their difference via the amplifier l50 to both of the summers l28. The amplifier l50 applies the difference signal to a negative input terminal of the summer l28 in the first loop ll6, and to a positive input terminal of the summer l28 in the second loop ll8.

0051The operation of the cross-coupling circuitry l42 may be demonstrated for the case wherein the joints 28 and 30 are advancing in the Y direction towards a target position. If the joint 28 were to be lagging behind the joint 30, then the positional error of the first loop on line l74 would be greater than the position error of the second loop on line l76. The summer l44 would then output a net positive correction signal to the two summers l28. In the first loop ll6, the correction signal is applied to a positive input terminal of the summer l28, this providing an increased current on line 98A which increases the speed of the motor 36A. The correction signal is also applied to a negative input terminal of the summer l28 of the second loop ll8 resulting in a decrease in the output current on line 98B resulting in a decrease in the speed of the motor 36B. The lagging joint 28 thereby increases its speed while the leading joint 30 thereby decreases its speed.

0052Similarly, it is readily seen that, by way of example, if the joint 28 is traveling at a greater speed than the joint 30, the summer l46 outputs a positive correction signal which is applied to a negative input terminal of a summer l28 in the first loop ll6, and to a positive input terminal of the summer l28 in the second loop ll8. This results in a decrease of the current on line 98A and an increase in the current on line 98B for a decrease in the speed of the joint 28 and an increase in the speed of the joint 30.

0053A further example is a situation occurring near the end of a movement of the joints 28 and 30, as the joints 28 and 30 are approaching their final positions. In this situation, one of the joints may actually be ahead of a desired intermediate goal outputted by the position command unit l52A while the other joint is behind the desired intermediate goal. The cross coupling of the two loops ll6 and ll8 by the summer l44 causes the leading joint to give up power to the trailing joint to allow the trailing joint to catch up to the leading joint. In addition, the effect of the cross coupling may introduce a retarding force, opposite to the direction of travel, to the leading joint dependent on the magnitudes of signals in the loops ll6 and ll8 as compared to the magnitude of a cross-coupling signal. Thereby, the operation of the cross-coupling circuitry l42 tends to equalize the positions of the two joints 28 and 30, and also tends to equalize the velocities of the two joints 28 and 30.

0054It is further noted that, due to the mechanical interconnection of the two joints 28 and 30 by the stator bar 50, the presence of a mechanical vibration in the joint 28 would be mechanically coupled to the joint 30 and, similarly, a mechanical vibration appearing on the joint 30 would be mechanically coupled to the joint 28. As a result, the stability of either of the feedback loops ll6 and ll8 is dependent, not only the inertia of the corresponding ones of the joints 28 and 30, but is also dependent on the inertia of the other one of the two joints, and the mechanical stiffness of the interconnection provided by the joint 26, as well as on the inertia and position of the load 22 and the joint 32 in the X dimension. The electrical operation of the cross-­coupling circuitry l42 dampens mechanical vibration occurring between joints 28 and 30 and raises the apparent mechanical resonant frequency by electromagnetically stiffening the structure. It is also noted that the use of two Y-axis joints reduces bending in the X-axis stator bar 50 from that which would occur if only one Y-axis joint were employed. The reduced bending insures that the actual position of the load 22 agrees with that reported by the sensors 72A-B.

0055In the construction of the robot 20, the loop gains are adjusted by first stabilizing each of the loops ll6 and ll8 individually, and then introducing a higher-­order stabilization by activation of the cross-coupling circuitry l42. In the absence of the cross-coupling circuitry l42, a maximum dynamic differential displacement of 76 <i>y</i>m may occur between the joints 28 and 30. Upon activation of the cross-coupling circuitry l42, the differential displacement between the two joints is reduced to less than 12.7 <i>y</i>m for an improvement by a factor of at least 6.

0056The gains of the amplifiers l56, l30, and l36 are to be selected experimentally to provide the desired scale factors for operation of the drive circuit 68 in accordance with the physical sizes and weights of the components of the robot 20. By way of example in the construction of the preferred embodiment of the invention, the gain factor inputted at terminal Al to the amplifier l56 has a value of 3072 during the high speed operation of the motors 36A and 36B, and a value of 2048 during the terminal phase. The gain factor inputted at terminal A2 to each of the amplifiers l30 has a value of 3584 during the high speed operation of the motors 36A and 36B, and a value of 3072 during the terminal phase. The gains of the amplifiers l48 and l50 are fixed at 5l2 and 448, respectively during both the high speed operation and the terminal phase.

0057The foregoing values are significant with respect to the ratios of the gains. With respect to the gain applied to positional error via the amplifier l56, there is a drop in value of approximately 2/3 between the high speed operation and the terminal phase. A smaller change in gain is implemented with respect to the velocity damping at the amplifier l30 in each of the loops ll6 and ll8. The ratio of the position-error gain of amplifier l56 to the differential position-error gain of amplifier l48 is approximately 6:l for the high operation and 4:l for the terminal phase. In the case of the velocity damping and differential velocity-gain terms of the amplifiers l30 and l50, the ratios are approximately 8:l in the case of high speed operation and 7:l in the terminal phase.

0058The foregoing gain ratios show that the value of gain employed in the portions of the cross-coupling circuitry l42 for differential position and differential velocity are substantially smaller than the corresponding gains employed in the positional error and velocity damping in each of the loops ll6 and ll8. This relationship allows each of the loops ll6 and ll8 to be operated in accordance with well-­known principles of servomechanisms and feedback control. The contribution of the cross-coupling circuitry l42, being relatively small compared to those of the positional error and velocity damping terms, permits a correction to be applied to each of the loops ll6 and ll8 for improved accuracy in their performance without introducing excessive complexity to the overall operation of the system 20. The equalization of position and velocity between the joints 28 and 30 by the cross-coupling circuitry l42 increases the positioning accuracy of the load 22, and also removes any excess bending and stresses within the joint 26 which would otherwise develop, thereby permitting smooth operation of the bearings joints 28 and 30.

0059With reference now to Figs. 5-7, the position command unit l52A comprises a host computer l78 and an interpolator l80. A desired movement of the load 22 (Fig. l) along the Y-axis by the joints 28 and 30 is defined in the host computer l78 by a start point and an end point as depicted in a graph l82 of Fig. 6. The graph l82 shows distance of travel along the Y-axis as a function of time. The movement is implemented at the host computer l78 by establishing a sequence of intermediate position goals l84 which are applied as input signals to the interpolator l80. The intermediate position goals l84 are spaced apart along the time axis of the graph l82 by increments of 20 milliseconds. The interpolator l80 then divides the foregoing intervals by ten to provide a set of finely-­spaced position goals l86 set between the intermediate goals l84. The goals l86 are spaced apart along the time axis at increments of 2 milliseconds, as is shown in a graph l88 in Fig. 7. The graph l88 also shows distance versus time, and is a magnified view of a portion of the graph l82. The finely-spaced position goals are outputted as a sequence of signal samples by the interpolator l80 via line l90 to the summers l24 (Fig. 3).

0060The slope of the graph l82 represents the velocity at which the joints 28 and 30 must travel between the start point and the end point. By increasing the number of intermediate position goals l84, between the same start point and end point, while keeping the update rate at 2 msec, the host computer reduces the velocity. A decrease in the number of position goals l84 results in an increased velocity. A sufficient number of intermediate goals l84 is selected by the host computer l78 to insure that the acceleration and velocity requirement is within the capability of the robot 20. The slope of the graph l82 and the velocity are not constant, but vary from a low values near the start and the end points to higher values at the mid-­portion of the path of travel. A corresponding variation in velocity occurs with respect to the finely-spaced goals l86 of the graph l88. This results in the aforementioned trapeziodal velocity profile, which profile is depicted in a graph l82A of Fig. 6, wherein the speed increases approximately linearly form zero to a maximum value, continues at the maximum value until the terminal phase, and then decreases substantially linearly with time to a value of zero.

0061As may be appreciated from viewing both the graphs l82 and l88, the Yl and Y2 joints 28 and 30 move the load 22 along a prescribed path wherein the feedback loops ll6 and ll8 operate in response to an incremental motion plan as set forth by the finely-spaced goals l86. The finely-spaced goals l86 enable the loops ll6 and ll8 to update the position of the load 22 sequentially with the occurrence of each goal while maintaining relatively small positional errors for each of the joints 28 and 30. The positional error of each of the joints 28 and 30 is to be kept small enough such that the differential positional error of the cross-­coupling circuitry l42 is a significant percentage of the total error. This insures that the differential effect is maintained above any background noise for optimum benefit of the cross-coupling circuitry l42.

0062Fig. 8 shows a block diagram of the gain command unit l52B of Fig. 3, the gain command unit l52B comprising a gain selector l92 for use in control of the Yl joint 28, a gain selector l94 for use in control of the Y2 joint 30, and a lead angle generatorl96 for use in control of both of the joints 28 and 30. The gain selectors l92 and l94 have the same construction; accordingly, only the gain selector l92 will be described in detail, it being understood that the description applies also to the gain selector l94. The gain selector l92 receives input position-error and velocity signals on lines l74 and l62, and outputs gain control signals at terminals Al, A2, A3 and a switch control signal at terminal A4. Similarly, the gain selector l94 receives input position-error and velocity signals on lines l76 and l66, and outputs gain control signals at terminals Bl, B2, B3 and a switch control signal at terminal B4. The lead angle generator l96 receives the foregoing input velocity signals on lines l62 and l66, and outputs a lead-angle magnitude command signal on line l98 to each of the coil selectors l08. The sign of the velocity signal provides the motion direction input to coil selector l08.

0063The gain selector l92 comprises memories 200, 202 and 204, a multiplier 206, and a switch 208. In operation, the memory 202 outputs the gain control signals at terminals Al and A2 to the corresponding terminals of the amplifiers l56 and l30 (Fig. 3) in response to receipt of an address on line 2l0 from the memory 200. A graph 2l2, shown within the block of the memory 200, depicts the operation of the memory 200. In the graph 2l2, velocity is plotted along the vertical axis, and positional error is plotted along the horizontal axis. A central rectangle or window 2l4 encloses a region representing a condition of operation of the Yl joint 28 wherein both the positional error and the velocity of the joint have relatively small values, these values being less than 0,5 mm and 25 mm per second, respectively, in the preferred embodiment of the invention. Such speeds within the window 2l4 are much smaller than, for example, the speed of 30,5 cm per second at which a phase advance is to be made in the operation of the Y-axis motors 36A-B (as well as in the X-axis motor 48). The small value of velocity, within the window 2l4, is represented in the graph l82A (Fig. 6) by circles 2l6.

0064The memory 200 is addressed by the signals on lines l74 and l62, the addressing selecting points in the graph 2l2. In response to an addressing of points within the window 2l4, the memory 200 directs the memory 202 to output two gain control signals at the terminals Al and A2 for control of gain in the amplifiers l56 and l30, respectively, (Fig. 3). The memory 202 also outputs a gain control signal on line 2l8 to the multiplier 206 and the switch 208 for control of the amplifier l36. The memory 200 also operates the switch 208 to place it in the position shown (Fig. 8) for coupling the gain control signal from line 2l8 to terminal A3, and operates the switch l58 (Fig. 3) via terminal A4 to activate the integrator l54.

0065In response to an addressing of points outside the window 2l4, the memory 200 directs the memory 202 to output the high-speed gain control signals via terminals Al and A2 to the amplifiers l56 and l30. The switch l58 is opened to disconnect the integrator l54, and to place the switch 208 in the alternate position for coupling an output terminal of the multiplier 206 to terminal A3. Also, a high-speed gain control signal is outputted by the memory 202 on line 2l8.

0066The memory 204 is addressed by the velocity signal on line l62, and outputs a gain correction factor via line 220 to the multiplier 206. A graph 222, shown within the block of the memory 204, depicts a variation in the gain control factor as a function of velocity, which variation is stored in the memory 204. The gain control factor varies from a value of 0.25 at low speed to a value of l.0 at high speed to compensate for reduced gain of the motors 36A-B at higher velocities. A dip in the graph 222 is located at 224 to reflect the increased motor gain which occurs upon an advancement in the lead phase angle at speed of 30.5 cm per second. The multiplier 206 multiplies the gain factor on line 2l8 by the variable gain correction term on line 220, and outputs the product via the switch 208 to terminal A3. The memory 204 has no effect on the operation of the joints 28 and 30 at the low velocities and positional errors within the window 2l4 because the multiplier 206 is disconnected from terminal A3 by the switch 208. It is only for larger values of velocity and positional errors falling outside the window 2l4 that the switch 208 connects the multiplier 206 to terminal A3. The opposite situation applies to the above-noted operation of the integrator l54, namely, the switch l58 is operated by the signal on line 2l0 from the memory 200 to connect the integrator l54 during the presence of velocity and positional error signals within the window 2l4 and to disconnect the integrator l54 for larger values of velocity and positional error signals falling outside the window 2l4.

0067The lead angle generator l96 comprises three comparators 226, 228 and 230, two memories 232 and 234, and a gate 236. The comparators 226 and 228 each have one input terminal connected respectively to the velocity signals on lines l66 and l62, and a second input terminal which receives a reference signal outputted by the memory 234. The comparator 230 has two input terminals coupled respectively to output terminals of the comparators 226 and 228. The output of AND gate 230 to addresses both of the memories 232 and 234. The memory 232 is responsive to a one bit address of the output signal of the comparator 226 to provide either of two lead angles via line l98 to adjust the phase relationship between the armature currents and the teeth locations of the motors 36A-B. The adjustment of the phase is accomplished at the coil selectors l08.

0068With reference also to Fig. 2B, the phase angle and the lead angle are further explained as follows. In the construction of the motors 36A-B, three sets of coils 66 are provided. The coils in each set are wired in series (not shown) for simultaneous excitation and are considered to be phases. For example, if the phases are identified by the letters A, B and C, a successive excitation of the sets of coils is accomplished in half steps by commutation as follows: A, AB, B, BC, C, CA and back to A. A phase advance in the direction of motion of, for example, one step, creates a force which urges the armature housing 40A or 40B in the direction of motion, while a phase shift in the opposite direction exerts a retarding force to slow the movement of the housing 40A or 40B.

0069In operation, the adjustment of the lead angle is in accordance with speed of operation of the joints 28 and 30 and follows a hysteresis pattern as may be understood with reference to Figs. 8 &amp; 9. The reference signal outputted by the memory 234 is initially set at a value of 30.5 cm per second. The lead angle outputted by the memory 232 is initially set at l/2 steps, wherein a step is equal to l/3 distance between centers of adjacent teeth 62 (Figs. 2B). As the velocities of the joints 28 and 30 increase past the value of the reference signal, the comparators 226 and 228 output logic-l signals. The AND gate 230 outputs a logic-l signal if and only if both input signals are one. When both of the comparators 226 and 228 are outputting logic-l signals, the AND gate 230 passes a logic-l signal to address inputs of memories 232 and 234. Thereupon, the memory 232 outputs a lead angle of l step, and the memory 234 outputs a reference velocity of 25.4 cm per second.

0070During a subsequent slowing of the motors 36A-B, the comparators 228 and 226 output logic-0 signals when the velocities of the respective joints 28 and 30 drop below 25.4 cm per second, this being the value of the reference signal. When either of the comparators 226 or 228 are outputting logic-0, the AND gate 230 then outputs a logic-0 signal to address the memories 232 and 234. Thereupon, both of the memories 232 and 234 revert to outputting their original signals, the memory 232 outputting a lead angle of l/2 step, and the memory 234 outputting a reference of l2 inches per second. During a subsequent increase in the velocities of the joints 28 and 30, the foregoing procedure repeats. The two joint velocities are shown in the upper traces of the graph of Fig. 9, while the value of the lead angle is plotted in the lower trace of the graph.

0071The following inventive features are noted. Hysteresis is present in that there is a difference of 2 inches per second between the trigger speeds for a change in lead angle, depending on whether the joint velocities are increasing or decreasing. Also, no transition in lead angle takes place unless joints 28 and 30 have shifted to a new speed range. This prevents any unnecessary transitions in lead angle in the event that the joint velocities are maintained in the vicinity of a transition speed. Furthermore, the changes in lead angle are made simultaneously in both of the joints 28 and 30 to maintain complete synchronism in their respective movements.

0072Also shown in Fig. 8 is a block diagram of one of the coil selectors l08 and its connections to the magnetoresistive tooth detector 70A and the armature housing 40A of the motor 36A in the joint 28, and to the lead angle generator l96. The other one of the coil selectors l08 is similarly connected to the corresponding components (not shown in Fig. 8) of the joint 30. Since both of the coil selectors l08 are of the same construction, only one of them is to be described, it being understood that the description applies to both of the coil selectors l08. The coil selector l08 comprises a digitizer 238, commutation logic and a commutation switch 242.

0073In operation, the tooth detector 70A comprises a set of three magnetoresistive sensors (not shown) held by the armature housing 40A in a straight line parallel to the line to teeth 62 (Fig. 2 A) of the stator bar 38A and spaced apart from each other by spacings of one-third the periodicity of the teeth 62. Thereby, the tooth detector 70A outputs a well-known three-phase analog signal of which the components are spaced apart electrically by l20 degrees. The three components give the relative mechanical position between the poles 64 and the teeth 62 unambiguously. The digitizer 238 comprises well-known analog-to digital converters and logic (not shown) for converting the components of the analog signal of the detector 70A to digital format, and for extracting the mechanical phase angle in digital format.

0074The digitally formatted phase angle of the digitizer 238 is processed with the magnitude of the lead angle on line l98, and direction of force control and direction of motion signals (see Fig. 3 and Fig. 8) by the commutation logic 240. The direction of motion is derived from the sign of the velocity signal (obtained from block l32) and is used to determine the direction in which the "lead angle" is to be applied. The direction of force is not to be confused with the direction of motion. The direction of force can be opposite to the direction of motion as is the case when a retarding force is required to slow the motor. The direction of force is obtained from the sign bit of the output signal of the summer l28 (Fig. 3) in the loop ll6 of the Yl joint. Motor current from the amplifier l06 of the loop ll6 is coupled via the commutation switch 242 to the requisite set or sets of the coils 66 of the motor 36A. The commutation switch 242 operates in response to the output of commutation logic 240 to energize the requisite coils 66 of the motor 36A. As the armature housing 40A advances along the stator bar 38A, the digitally formatted mechanical phase angle changes in accordance with the changing position of the poles 64, upon which the coils 66 are wound, relative to the position of the teeth 62. The motors 36A-B can be operated at still higher speeds with the injection of larger amounts of lead angle to the commutation logic 240. This can be accomplished by use of a further lead angle generator (not shown) with the comparators and memories thereof being set at higher values of velocities for outputting an additional increment in phase angle to the commutation logic 240.

0075The foregoing physical arrangement of the robot 20 with the pair of joints 28 and 30 carrying the transversely positioned joint 26 provides for a substantial reduction in overall weight of the moving components of the robot without a reduction in the load-carrying capacity of the robot. This physical arrangement of the robot increases positional accuracy by reducing bending of the transverse joint 26 which carries the load, the increased positional accuracy being maintained even with a shifting in position of the load along the joint 26. While individual feedback loops ll6 and ll8 are employed for driving each of the joints 28 and 30 to each of a sequence of closely spaced positional goals, the use of cross coupling circuitry injects an additional component to the loop error signals based on differences in positional error and velocity for more precise synchronization of the joints 28 and 30. Also, the synchronized injection of lead phase angle to the excitation of the joint motors 36A and 36B enables the motors to operate at higher speeds while retaining synchronism during the lead angle injection.