Development of a Hexapod Laser-based Metrology System for Finer Optical Beam Pointing Control

Transcription

1 nd AIAA International Communications Satellite Sstems Conference & Ehibit Ma 004, Montere, California AIAA Development of a Heapod Laser-based Metrolog Sstem for Finer Optical Beam Pointing Control Hong-Jen Chen *, Ed J. Hospodar, Jr., and Brij N. Agrawal Naval Postgraduate School, Montere, California Free-Space Optical Communications requires stable and precise pointing on spacecraft to maintain optimal operating condition. One technolog to achieve high precision pointing and steering for imaging or laser communication paload in the presence of vibrations is to make use of a Stewart platform with active struts. At the Spacecraft Research and Design Center (SRDC) of Naval Postgraduate School (NPS), a heapod with voice coil actuators is equipped with in line accelerometers to perform the tasks of vibration isolation. For the tasks of pointing for optical paload, we adopted the approach of eternal measurement sstem, which provides directl the position and orientation information of the heapod top platform. A laser metrolog sstem, composed of three pairs of laser diodes and detectors, is design and fabricated at NPS. In this paper we document its development process, which includes the design, analsis, inspection and preliminar calibration effort. I. Introduction ree-space Optical Communications requires stable, high-precision laser pointing on spacecraft to maintain F optimal operating condition. Acquisition, tracking and pointing technologies for future spacecraft, such as a bifocal rela mirror spacecraft, is currentl under investigation at the Spacecraft Research and Design Center (SRDC) of Naval Postgraduate School (NPS). One technolog to achieve high precision pointing and steering for imaging or laser communication paload in the presence of vibrations is the use of a Stewart platform with active struts. A heapod at SRDC, provided b CSA Engineering, Inc. 1, is constructed based on an arrangement of si selfsupporting electromagnetic voice coil actuators with in-line accelerometers enabling the control of high frequenc vibrations. For the operation of steering and pointing, feedback of the position and orientation of the top platform is necessar. There are basicall two approaches to obtain such measurement: installing si identical displacement sensors in-line with the struts and constructing an eternal metrolog sstem that measures the motion of the top plate directl. We adopt the later approach because there is limited space in the struts for installation of additional sensors and it will change the current heapod configuration greatl if the former approach is taken. Previousl at our center, we implemented the eternal measurement approach with Edd current position sensors, as also shown in Fig. 1. It makes use of a set of three Edd current sensors to determine the tip and tilt angle for pointing, whereas the other motion variables, including the rotation about the vertical ais of smmetr, are assumed to be zero. Pointing eperiments using this measurement sstem has been done with reasonable results,3,4. However, it is observed that the sensors can easil be influenced b environment magnetic noise and the Pleiglas posts of the setup are not rigid enough to keep awa from the influence of vibrating disturbances. In addition, control without monitoring all degrees of freedom of the top plate motion raises certain questions such as whether there is a degrading or even destabilizing effect from other degrees of freedom to the tip and tilt pointing performance. Therefore the laser-based metrolog sstem (LMS) 5, which is the subject of this paper, is developed. Currentl the LMS has been designed and fabricated, and a precision calibration device is being developed in order to calibrate both its absolute and relative accurac. In the following sections we first introduce the heapod with the Edd current sensor sstem, then eplain the design, equations of measurement, inspection, and initial calibration effort during the past few months at our center. * National Research Council Research Associate, Department of Mechanical and Astronautical Engineering, MAE/Cn, AIAA Member Major USAF, Department of Mechanical and Astronautical Engineering, MAE/Ho Distinguished Professor and Director, Spacecraft Research and Design Center, Department of Mechanical and Astronautical Engineering, MAE/Ag, AIAA Associate Fellow. 1 This material is declared a work of the U.S. Government and is not subject to copright protection in the United States.

2 II. The NPS Heapod with the Edd Current Measurement Sstem The heapod at NPS, shown in Fig. 1, was designed and constructed b CSA Engineering, Inc. As a 6-DOF manipulator, it is capable of delivering a significant range of motion in all si degrees of rigid bod motion: ±5.7 mm of aial/position travel, ±0 mm of lateral motion, ±.5 degree of tip-tilt motion and ±10 degrees of twist. It can be outfitted with a variet of sensors for the investigation of vibration isolation, vibration suppression, and pointing and tracking applications. Each one of the si struts, composed of an actuator and a sensor, is connected to the base plate and paload platform using metal fleure joints. The actuator is a Motran AXF-70 self-supporting electromagnetic voice coil actuator. An in-line bracket holds and aligns an accelerometer along each of the strut ais. This design results in a self-contained unit for vibration isolation and suppression tasks. To perform pointing and tracking tasks, an eternal measurement Figure 1. NPS Heapod with Edd Current Measurement Sstem. device is constructed in-house at NPS to provide feedback of the tip and tilt motion of the top plate. The sensing devices are the Kaman Instrumentation s Multi-Purpose Variable Impedance transducer measuring sstems (KD- 300) non-contact linear proimit measuring sstem. The sstem used si Kaman tpe 8C sensors and was designed for sensing the motion of the paload platform with respect to metallic targets fied on the base plate and the si sensors were arranged on the paload platform. The entire Edd current metrolog subsstem (ECMS) allows a maimum possible range of ±1.5 degrees and it is capable of providing a theoretical resolution of degrees in tip and tilt motion if it is free from noise. In practice, due to noise contamination, it is not possible to achieve that resolution. The detecting range is reduced due to the limitation of the configuration of the entire assembl and the limited range of 1.7 mm of the Edd current sensors. The set of three sensors are calibrated using Pleiglas spacers of known thickness: the are firml pressed to align the sensor spacing between the top platform and the sensor targets and to adjust the linearit of the KD-300. III. The Laser-based Metrolog Sstem for the Heapod As indicated before, the Edd current measurement sstem does not provides the full measurement of the heapods pose, i.e. both the position and the orientation. It is subject to environment magnetic noise and vibrating disturbance. These are the main reasons we seek for another metrolog sstem that could be free from all these shortcomings. A sstem composing of laser diodes and position detectors mounted on rigid metallic posts is then selected for implementation. A. The Design The design concept of the measurement sstem is shown in Fig. and its final assembl on the heapod is shown in Fig. 3. Basicall the metrolog sstem is composed of two subsstems: the laser source subsstem and the sensor subsstem. Both the set of three lasers and the set of three position sensing detectors () have their three nominal aes coincide with those of the other set, with the following properties satisfied: all aes are co-plane, passing through the center on heapod s vertical ais of smmetr, and are 10 degrees apart as shown in Fig Figure. Design of the laser metrolog sstem. Figure 3. NPS Heapod with the laser metrolog sstem.

3 This configuration has the following advantages for our heapod: 1) Compact and nonsingular: capable of providing si independent readings for determination of both the position and orientation of the 6 DOF top plate motion (analsis given in net section), ) Allows the space underneath the top plate to be used for the mounting base of the target posts, 3) Modular, providing simplicit in design and fabrication of the two subsstems: the laser source subsstem and the target detector subsstem. B. The Sensor Subsstem The sensor subsstem includes the 's, the mounts, the support structure, and the amplifier. The, shown in Fig. 4, is a dual-lateral position sensor that provides vertical and horizontal measurements of the incident laser light spot. The support structure, shown in Fig. 5, holds the 's and its mounts (Fig. 6) level and vertical at 10 degrees separation. This allows the three lasers to point directl at the three 's when the heapod top plate is at its home position. The support structure is attached to the heapod bottom plate. The amplifier is located off the heapod and is connected to the 's b cables. f g Figure 4. Position sensing detector () from On-Trak Photonics Figure 5. Sensor subsstem s Support structure, including base clinder and bottom boomerang. Figure 6. Laser source subsstem, including diode lasers, mounts, and top boomerang. Figure 7. Laser source subsstem, including diode lasers, mounts, and top boomerang. C. The Design The laser source subsstem, shown in Fig. 7, includes the diode lasers, the fied mounts, and the top boomerang. The diode lasers are the source of light energ to be detected on the s. Each laser is housed in a fied mount, and the mount uses precision pins to attach itself precisel on an equilateral triangular plate separated b 10 degrees the top plate optical boomerang. The boomerang provides a flat surface to keep the laser mounts in a plane and has pin holes to mount the laser-mount assembl precisel with a 10-degree angular separation. The entire laser source is then attached to the Pleiglas plate on top of the heapod. D. The Advantage With the s mounted in front of the three diode lasers at 8 inches from the center, the corresponding best possible range and resolution for tip-and-tilt motion are.8 degrees and degrees, respectivel. In addition to the improvement in detecting resolution, the laser metrolog sstem offers several more advantages: 1) Better structural rigidit and accurac: the structure is entirel made of aluminum instead of the more fleible Pleiglas material, with the accurac of ±

4 ) Less influence from environment noise: the measurement sstem will eperience less vibration from disturbance and less light contamination under controlled dark environment. 3) Less possible damage during heapod operation: being non-proimit sensors and placed at a larger distance than the heapod s lateral translation limit, there won t be an possible impact on the sstem due to ecessive relative motion as in the case of the Edd current measurement sstem. IV. Input-Output Relations for the Laser Metrolog Sstem A. Coordinate Sstems for the metrolog sstem and the heapod base frame The moving and fied coordinate sstems of the laser metrolog are illustrated in Fig. 8. The fied coordinate sstem, defined b the set of z aes, is fied on the base of the heapod where the sensor sstem is attached with its - plane aligned with the three normal aes of the s and its origin o coincided with the intersecting point of those three aes. The moving coordinate sstem, defined b the set of uvw aes, is attached to the top moving platform of the heapod with its u-v plane aligned with the three beams (central aes) of the diode lasers and its origin coincident with the intersecting point of those three aes. When the heapod is resting at its home position, the moving and fied coordinate sstems coincide with each other and the three aes of the laser source and sensor subsstems also coincide with each other. Because of the eisting posts of the Edd current measurement sstem, the new laser metrolog sstem cannot be mounted with its and aes aligned with the horizontal aes of smmetr of the heapod, which are the global X and Y aes attached to the base plate of the heapod. Therefore, the laser metrolog sstem is mounted with a counterclockwise rotation of 17 degrees about the heapod s vertical ais of smmetr, which is both the z ais for the z sstem and the Z ais for the global XYZ sstem. B. Input-Output relations between the two coordinate frames of the laser metrolog sstem Considering the motion of the moving uvw frame with respect to the fied z frame of the laser metrolog sstem, we ma appl the law of superposition in getting the vertical (f) and horizontal (g) readings from the s (as shown in Fig. 4) due to each individual degree of freedom. This is justified b the fact that both translation and rotation of the heapod top plate are ver small under normal operating condition: the range of rotation must be within the.8 degrees region limited b size of the s and the translation is nearl zero since we alwas do the heapod pointing gimbaled about the origin. A nice consequence of appling the small angle approimation is that the relation between the f and g readings and the motion of the heapod top plate can be epressed in the form a 6 b 6 matri, and the input-output relation for the laser metrolog sstem (i.e. the solution for the position and orientation of the top plate from the f and g readings of the ) can be obtained b simpl inverting that matri. 1. Tip and tilt motions (θ and θ ) and vertical translation (z) Figure 9 illustrates the contribution to the f readings due to the tip and tilt motions. The location center of an given is at (e i, e i ) on the plane. Acknowledging that translation in z direction has direct contribution equall to all f readings on, and appling small angle approimation, f = e θ e θ +z, i = 1,,3 (1) i i i. Rotation about vertical ais (θ z ) Figure 10 illustrates the contribution to the g readings due to the pure rotation of the top plate about z ais (θ z ). Appling small angle approimation, it is obvious that g = eθ, i = 1,,3 () i i z z, w, Z o, o Y, v X, u Figure 8. Moving (uvw) and fied (z) coordinate sstems for the laser metrolog sstem 4

5 θ O e Side View e θ e e Side View e tan(θ ) θ e e tan(θ ) θ θ θ e Figure 9. Contribution to the f readings due to small tip and tilt top plate motion g 3 g θ e z e 3 Y O e 1 g 1 X Figure 10. Contribution to the g readings from pure rotation about z ais O e α e e +g Figure 11. Contribution to the g readings from from translation of top plate along ais 3. Translations of top plate in the plane (, ) Figures 11 and 1 illustrate the contribution to the g readings due to the translations of heapod top plate along the and aes b the amount of and, respectivel. Appling small angle approimation, and given that cos(α i ) = e i / e i and sin(α i ) = e i / e i it is obvious that O α e e e +g Figure 1. Contribution to the g readings from translation of top plate along ais ei ei gi = ( ), i = 1,,3 ei ei (3) 4. Input-output relation of the laser metrolog sstem Putting equations (1), () and (3) in matri form, e1 e e e 0 f e3 e3 0 f e1 e 1 f e 3 1 z = e1 e 1 g1 θ e e g e θ e e g θ 3 z e3 e e3 e3 e3 (4) 5

6 Denoting the 6 b 6 matri in equation (3) as L, it is a nonsingular matri for the configuration of the laser metrolog sstem illustrated in Fig. or 8. Therefore the transformation matri, M, relating the vector of readings q = (f 1, f, f 3, g 1, g, g 3 ) to the pose vector r = (,, z, θ, θ, θ z ) is simpl the inverse matri of t he 6 b 6 matri in equation (3), i.e., r Mq M L -1 =, where = (5) 5. Epressing the pose of the heapod in the global coordinate sstem As mentioned earlier, there is rotation of α = -17 degrees from the XYZ frame to z frame. As the command is given in Cartesian coordinates in the XYZ frames, the output of the laser metrolog sstem, i.e. the pose of the heapod, should be epressed in this frame for control. The relation between the two coordinate sstem is X cosα sinα Y sinα cosα Z z = θ X cosα sinα 0θ θ Y sinα cosα 0θ θ Z θ z (6) Note that the transformation matrices between the position sub-vectors and the orientation sub-vectors in equation (6) are identical due to small angle approimation. V. Inspection and calibration of the laser metrolog sstem Once the laser metrolog sstem has been fabricated, the parts and subsstems must be inspected to obtain detailed as-built knowledge in the vertical and horizontal planes of the metrolog sstem. The idea is to verif how well the entire sstem has been made to match the original design. As described in the Section IIIA, for both the three aes of the laser beams and the three normal aes to the detecting surfaces should both satisf the following conditions as closel as possible: 1) the three aes are on the same plane ) the three aes are intersecting at the same point on heapod s vertical ais of smmetr at home position 3) the three aes are equall separated b 10 degree on the plane the all reside in The information obtained during inspection will be instructive to the later calibration process. As a matter of fact when calibration tools are not readil available, sstem inspected to match design well should give a reasonable performance. In the following, we describe how the components and subassemblies were inspected for the laser metrolog sstem. The aggregate of the as-built deviations in the vertical plane are put in appendi A as eample of the verification results along with some eplanation. A. Inspection of the sensor subsstem The approach is to build up from the PPH bottom plate to the point where the 's are attached. As shown in Fig. 13, the substructures of sensor subsstem starting from the base, include the base clinder, the bottom optical boomerang, the mounts and the s. The first sub-structure to go through verification is the assembl of the base clinder and the bottom optical boomerang, shown in Fig. 14. The assembl is placed inspected on a granite table using a precision height meter accurate to ". The meter was slid along the entire working surfaces to determine the height and parallelism between the top and bottom of the whole assembl. The mounts were then added on top of the bottom boomerang and Mount Diode Laser Bottom Boomerang 6 Laser Mount Top Boomerang PPH base plate Base Clinder Struts Figure 13. Vertical build-up of the metrolog sstem on the heapod

7 the process is repeated. It was discovered that the top of mount no. 1 is lower than that of the other two on the assembl. 1 Twisting Tipping Figure 13. Inspection of base clinder Figure 14. Possible rotational error of and bottom boomerang on granite table the - mount or laser- laser with precision height meter. mount combinations. Since the measurement of the clinder and boomerang assembl showed practicall no rotational errors at all. The overall rotational errors about all aes, i.e., twisting, rotating, and tipping errors, are determined b inspecting the and mount combination. It is discovered that the back cover of each is not flush with the working surface. The projects below the working surface b 0.001" for 1 and b 0.00" for and 3, causing the to lean forward toward the lasers (tipping). The lean angle and its effect on the origin and detecting aes are calculated b using the errors and the dimensions of the. The same procedure is also carried out for investigating the twisting and rotational errors. The twisting angle all are found to be level to However, set 1 of and mount was found to have a noticeable rotational error of degree, therefore the vertical and horizontal location of the center of 1 will be moved b the amounts of each. B. Inspection of the laser source subsstem Inspection procedure similar to that in the previous section was also carried out for the laser source subsstem. The top boomerang was discovered to be made nearl perfect in height and parallelism. After inspecting the three laser-laser mount assemblies, we discovered that all the center beams are about perfectl parallel with the design aes, i.e., there are practicall no twisting and tipping angular errors introduced b the assemblies. However, shifts of aes do eist: the amount in height of the aes awa from designed value could be as much as and the amount to sidewas could be as much as 0.00, which will lead to error in angular accurac of about degree if not compensated after future calibration. The most significant quantit to inspect for the entire subsstem is perhaps the side angle of each laser beam that directl relates to the accurac of the 10 degree separation configuration. As sets of two precision pins and pinholes are used in joining the laser mount Rotating Figure 14. Inspection of laser source assembl on granite table with precision height meter. assembl onto the top boomerang, the location of the pinhole sets determines the final accurac of both the shift of twist angular error of the beams. Our inspection result shows that the pinholes on the three laser mounts are all made with nearl perfect accurac in the twisting angle, but the have about of shift sidewas. Determination of the shift and the twist errors of the pinhole sets is actuall the most complicated inspection process. Due to the lack of identical pin pairs at the workshops at NPS, mismatch pair of pin and pinhole pairs were used in inspection. The clearance (roughl to 0.00 ) and misalignment between the pin and pinhole aes then generates uncertainties in measuring the eact distance between pinholes. Therefore the eact information on the twisting angle and the shifting distance of the aes cannot be obtained either. Through trails, however, it is believed that the maimum possible twist error is about degrees. VI. Conclusion An eternal laser metrolog sstem has been designed and fabricated for a heapod at NPS. The manufacture accurac of the metrolog sstem s components and subassemblies has also been inspected. The sstem possesses 7

8 several advantages over the eisting metrolog sstem whose ke components are Edd current sensors. The new sstem is less subject to mechanical and magnetic noise in the environment, and it is capable of providing the full 6 DOF measurement of the heapod top plate motion (both translation and rotation). A precision calibration sstem is currentl under development and will be used to verif and adjust the new laser metrolog sstem. Once the new metrolog sstem has been calibrated to produce accurate and precise measurement of the heapod s position and orientation, the heapod ma then be used for investing enhanced control schemes and achieving better performance in precision pointing of a paload mounted on the top platform. Appendi The difference between the design and the as-built sstem for the vertical plane are shown in Table 1. Table 1. Difference between design and as-built for the vertical plane. Vertical Estimate 1 3 item Design (inches) As-Built (inches)difference (in) As-Built (inches) difference (in) As-Built (inches)difference (in) +/- (in) Build-up to clinder+bottom boomerang mount (0,0) of detector E E subtotal Build-up to Laser Laser1 Laser Laser3 clinder+bottom boomerang verification baseplate verification spacer verification top plate groove in verification top plate CSA plate+pleiglass top boomerang top boomerang to center of laser subtotal parallelism of verif sstem cant of beam total diff of subtotals convert to mm Actual f-reading percent error Acknowledgments The authors would like to acknowledge the significant contribution made b Mr. Ja Adeff and Mr. Glenn Harrell on the design and fabrication of the laser metrolog sstem. References 1 Eric M. Flint, PHEX-1 (Tpe 1 Pointing Heapod) User Guide, CSA Engineering, Inc., 565 Leghorn Street, Mountain View, CA, Aug 000. C. G. Taranti, R. Cristi, and B. N. Agrawal, An Efficient Algorithm for Vibration Suppression to Meet Pointing Requirements of Optical Paloads, AIAA Guidance, Navigation, and Control Conference & Ehibit, 6-9 Aug 001, Montreal, Quebec, Canada 3 Ronald M. Bishop, Jr., Development of Precision Pointing Controllers with and without Vibration Suppression for the NPS Precision Pointing Heapod, Master & Engineer's Thesis, Department of Aeronautic and Astronautic Engineering, Naval Postgraduate School, Montere, CA, December H.-J. Chen, R. M. Bishop, and B. N. Agrawal, Paload Pointing and Active Vibration Isolation Using a Heapod, 003 AAS/AIAA Astrodnamics Specialist Conference, Big Sk, Montana, Aug 3-7, Edward J. Hospodar, Jr., A Laser Metrolog Sstem for Precision Pointing, Master Thesis, Department of Mechanical and Astronautical Engineering, Naval Postgraduate School, Montere, CA, December