Active Vertical Stabilization Mechanism for Lightweight Handheld Cameras

Transcription

1 Active Vetical Stabilization Mechanism fo ightweight Handheld Cameas Ali Utku Pehlivan Disney Reseach os Angeles Günte Niemeye Disney Reseach os Angeles Abstact Camea technology is continuously impoving and high quality cameas ae now available unde one pound of weight. This enables novel and innovative uses, fo example at the end of a long boom pole. Unfotunately lighte cameas used in such ways ae moe susceptible to vetical distubances and the bouncing associated with walking esulting in shaking and distotion. We intoduce a miniatuized active stabilization mechanism that attenuates such distubances and keeps the camea steady. Feedback contol effectively emulates the stabilizing inetial dynamics associated with highe weights without the penalty of highe weight. The system uses only acceleomete eadings and avoids pue integation and associated numeical dift issues. We design, analyze, build, and test the mechanism to show appopiate pefomance. Figue : A lightweight camea on a 3dof active gimbal and boom is susceptible to vetical distubances.. Intoduction Camea opeatos ae always tying to captue new and unique camea pespectives. To facilitate thei effots, we ecently placed a small fom facto camea at the end of an eight foot hand-held boom pole []. The system, seen in Fig., includes an active thee degee of feedom (3 dof) gimbal to stabilize the camea oientation. Unfotunately, the camea emains susceptible to vetical tanslation distubances, caused mostly by walking and exaspeated by the boom length. It is ou objective to stabilize against such distubances. Mechanical stabilization systems fo potable cameas have been commecially available since the 970s. age camea inetias and even added weights mechanically filte out any distubances. A widely known example, Steadicam, tansfes the heavy weight diectly to the opeato s body [, 3]. The mechanism utilizes stategically placed spings fo the gavity compensation ove a lage ange of motion and adds a camea gimbal beyond the stabilization. In ou application, the boom s flexibility and fee movement equie the stabilization mechanism to be miniatuized and located at the tip of the boom. A puely passive appoach is not applicable fo two main easons. Fist, the camea weight has to be at least an ode of magnitude smalle, substantially educing the efficacy of passive inetial stabilization. Second, the mechanism s ange of motion is much smalle than the possible vetical movements. So the system needs to include some estoing stiffness to keep the camea in the tavel ange. A puely passive stiffness, togethe with the low mass, would aises the passive filteing s cutoff fequency and again deceases efficacy. Finally, attached to a moving boom, a vetical efeence is not natually available. In this wok, we develop an active miniatuized stabilization mechanism, aimed to be integated within an active gimbal. Effectively, the system ceates the dynamics of a lage camea inetia without the penalty of weight needed to be caied. We ae able to avoid pue integation of the acceleomete signal and any as-

2 sociated numeical dift, achieving height stabilization without a diect height measuement. The pape fist states the design specifications in tems of desied attenuation of vetical distubances. It then pesents the mechanical stuctue of a possible extended gimbal and analyzes the equied passive gavity compensation elements. It also deives the active contolle and acceleomete usage. A final expeimental evaluation is followed by a bief discussion and concluding emaks. (a). Design Specifications The developed mechanism acts as a low pass filte, isolating the camea fom unintended movements in the vetical diection. To specify the necessay attenuation, we examine both the expected distubances as well as the necessay smoothness. To chaacteize possible distubances, we obseved two unexpeienced opeatos holding a fully extended boom and walking at a comfotable speed. Both opeatos held the boom in thee diffeent oientations (vetically, hoizontally, and at appoximately 45 ), walked fowads, backwads, and sideways, and epeated each scenaio thee times fo 7 tests each. An OptiTack optical motion captue system ecoded the boom tip s motion, with example tajectoies shown in Fig. (b). Based on a powe spectal density analysis of the tip motion, we see the lagest powe in the ange Hz (Fig. (a)). To find the matching signal amplitude, we integated the total powe in this fequency ange coesponding to the signal vaiance, σ. And given a faily peiodic distubance, we estimate the aveage signal s amplitude as σ. This compomises between the smalle σ amplitude a pue sinusoid would exhibit and the 3σ amplitude a totally andom signal might geneate [4]. The esulting distubance amplitudes acoss holding cases and subjects ae pesented in Table. Oveall, we expect the vetical distubances to show amplitudes up to 0.03m within the fequency ange of 0.5-Hz. To define the desied stabilization smoothness, we visually compaed photos taken fom diffeent heights. In paticula, as the camea moves vetically the foegound shifts elative to the backgound. The just noticeable diffeence places a bound on acceptable height vaiations. In ou tests, sampled in Fig. 3, we placed a lamp as foegound m fom the camea. A mm displacement was not noticeable, while a 5mm displacement was clealy noticeable. As the pespective change can be appoximated by tanslating the foegound, it is not supising that a mm shift at a m distance is unnoticeable. (b) Figue : Chaacteization of expected distubances (a) Powe spectal density and (b) Sample tajectoies of the boom tip vetical movements. Table : Distubance amplitudes acoss subjects and holding cases. Subject Vetical Diagonal Hoizontal S 0.07m 0.06m 0.03m S 0.03m 0.04m 0.0m Consequently, we desie the stabilization mechanism to attenuate the vetical distubances by a facto 0 o moe, fom m to unde 3mm (ideally mm) within the 0.5-Hz fequency ange. 3. Integated Gimbal Stuctue The miniatuized active stabilization mechanism is intended to be used within a gimbal stuctue. Hee we eview a poposed integated gimbal to gain insight into the development of the stabilization mechanism. The integated active gimbal combines the active miniatuized stabilization with oll-pitch joints and a pan-tilt platfom into a 5 dof mechanism (Fig. 4). All degees of feedom ae necessay to povide a vetical efeence to the stabilization. Assume the boom may be olled and held at any angle. Numbeed outwad fom the boom to the camea, the axes and povide oll and pitch joints such that axis 3 is always vetical. Axis

3 (a) (b) (c) Figue 3: Sample camea images showing: (a) the base image, (b) a mm shift, (c) a 5mm shift. Fo illustative puposes, the shifted images ae dakened and ovelaid with computed diffeences in yellow. The actual compaisons wee pefomed altenately viewing images in the same location, simulating a video steam. 3 and 5 togethe then function as pan and tilt to oient the camea while keeping it level. And axis 4, using a leveam to the camea, impats and stabilizes vetical movements. While theoetically edundant to contol camea oientation and vetical displacement, the kinematic stuctue isolated in Fig. 4(a) offes seveal key benefits. Fist, once the camea s cente of mass is pefectly aligned with the axes 3 and 5, hence only axis 4 sees any gavitational loads. Second, as axis 3 povides a vetical efeence, the gavity load on axis 4 can be offset by a passive compensation as descibed below. Togethe this elaxes the stength needs, size, and ultimately weight of all actuatos. Futhemoe, sandwiching the stabilization inside the pan-tilt platfom allows the tilt axis 5 to actively counte tilt vaiations impated by the axis 4. We can avoid the typical paallelogam aangements employed to isolate vetical stabilization fom oientation. This again educes size, weight, numbe of moving pats, and thus fiction of the design. Finally, the edundancy helps avoid singula positions o gimbal lock duing nomal opeations. The boom and camea can independently point in any diection, with the possible exception of exact vetical oientations. Dynamically, to ensue smooth motions we aim to decease fiction on all axes as much as possible by employing bushless diect dive actuatos. Without gavity loading, the expected toques ae quite small and we taget actuatos with a 0.Nm continuous toque limit. 3 (a) (b) Figue 4: The poposed integated active gimbal: (a) the kinematic stuctue, and (b) a compute aided design (CAD) model. Note the CAD model does not yet include a 5th axis. 4 5

4 In this study we focus on the active vetical stabilization mechanism built aound axis 4. We emembe, howeve, that the design is intended to fit inside the integated active gimbal. 4. Gavity Compensation Mechanism d To suppot the oveall stabilization and educe the equied actuato toques, we implement a passive gavity compensation mechanism. This mechanism should balance as much of the load s weight as possible while intoducing as little fiction and added complexity as necessay. The final tilt actuato otates the camea about its cente of mass, so fo the pupose of this mechanism design we can conside the load to be a point mass m on a leve am moving ±45 about a hoizontal nominal oientation. In the following deivation, all angles ae measued clockwise elative to this hoizontal oientation. Pefect gavitational compensation can be ealized using a counte-balance mass with no added fiction and vey little complexity [5]. Unfotunately the added weight is pohibitive in this application and we focus on sping-based designs. Pefect sping compensation equies anchoing an ideal sping above the leveam s pivot point, as shown in Fig. 5. To confim the esult, conside the potential enegies of gavity and the sping E gav = mg sin(θ) () E sping = k = k ( d + d cos(θ + 90 ) ) () The changes in enegy exactly balance if d = mg k which can easily be fine-tuned with a slightly vaiable ancho point. Unfotunately exact compensation equies an ideal zeo fee-length sping fo which the stoed enegy and toque each zeo at exactly zeo length. Such spings ae extemely had to manufactue and not pactical. Thus many gavity compensation designs use cable and pulley systems o linkages to hide the sping s est length and mimic the above layout [6]. These geneally add fiction, complexity, and weight. We theefoe taget appoximate compensation designs, shifting the sping ancho point and possibly combining two spings. Without moving pats, we can minimize fiction and weight while optimizing the compensation. Conside conventional spings with a est o fee length 0. Ancho the spings a distance d fom the (3) Figue 5: Idealized passive gavity compensation. pivot point and an angle β fom hoizontal, as shown in Fig. 6. Fist evaluate a single sping, depicted in ed. Fom tigonomety, the sping length is = d + d cos(θ β) (4) whee we ecall angles to be measued clockwise fom hoizontal. The effective leveam o distance to the pivot point is h = d 4 (d + ) (5) d sin(θ β) = so that the compensation toque is τ(d,β) = k 0 θ d sin(θ β) (6) Using the paametes of the physical system (=0.075m, m=0.895kg, k=0n/m, 0 =0.05m) we achieve the minimal maximum eo to balance gavity acoss the ±45 wokspace fo d=0.6m and β= 0. The esultant compensation is gaphed in Fig. 7(a) with a maximum eo of 0.077Nm o.7% of the maximum gavity toque. Fo efeence, the actuatos can delive 0.Nm allowing the active contolle to account fo the esidual eos. Notice that the sping takes a length of 0.49m at the nominal position. This leads to a design somewhat lage than desied as it expands the size of the suounding gimbal. A stiffe sping could ceate a moe compact layout, at the expense of inceased sensitivity and likely lage eos in pactice. To futhe impove the compensation we conside the use of a second, coective sping. Optimizing a dual-sping configuation fo minimal maximum eo, we see two even lage spings

5 d d β β m Figue 6: Appoximate Sping-Based Gavity Compensation. Ancho Point Nominal Sping Maximum Distance Angle ength Eo Single Sping 0.6m m 0.077Nm Dual Sping 0.55m m Eo-Optimized 0.070m 0.50m 0.007Nm Dual Sping 0.00m m Size-Optimized 0.055m m 0.084Nm Table : Gavity Compensation Design Paametes. The sping s ancho point as well as length at the nominal leve location convey a sense of the design s size. The maximum toque eo descibes the compensation quality. counteacting each othe. The paametes ae collected in Table. The esultant compensation is impoved with a maximum eo of 0.007Nm, as seen in Fig. 7(b). In pactice howeve, the lage size inceases oveall dimensions and weight. A moe compact design is achieved when esticting β = 90, that is attaching the pimay sping above the pivot point. The fist (pimay) sping leaves a lage eo which the second sping is able to coect. The esultant design is smalle than the single-sping solution, while achieving an equally good compensation, shown in Fig. 7(c). This was implemented and used in the demonstation system. 5. Active Vetical Stabilization In theoy, if the camea wee pefectly suspended, its inetia would keep it stationay egadless of the base o boom movements. Howeve, given all impefections and the elatively low inetia, we need to implement an active stabilization to einfoce the natual dynamics. As such, the following contolle ceates an atificially lage inetia and ejects foces due to impefections in the gavity compensation, fiction, wiing and othe distubances. In addition, as the boom can move vetically ove seveal metes, the camea must gadually e-equilibate and follow the boom s low-speed vetical movements. Sensing of the vetical movements with espect to gound is challenging at best. ida, ultasound, o pessue sensos can be confused by thei suoundings and give false eadings. Acceleometes ae insensitive to the envionment but obtaining position via double integation involves significant challenges [7], such as exteme sensitivity to DC offset, which leads up to measuement dift. Fotunately, the following scheme enables acceleomete feedback without pue integation. Conside the vetical stabilization joint shown in Fig. 8 with x = x base x cam (7) If we desie the dynamics of a lage inetia m d as well as a low e-equilibating stiffness K d and damping B d m d ẍ cam = B d (ẋ base ẋ cam ) + K d (x base x cam ) (8) we should asset the filteing tansfe function X cam B d s + K d = X base m d s = ξ ω ns + ωn + B d s + K d s + ξ ω n s + ωn (9) Geate stabilization with a lage desied inetia and a softe vitual sping implies a lowe cutoff fequency. The coesponding deflection x would obey s X base X = s + ξ ω n s + ωn = s X cam ξ ω n s + ω n (0) We see the desied dynamics (8) elate the deflection diectly to acceleation. We place an acceleomete on the base side of the actuato to leveage the geate filteing and inheently povide a contol signal fom the obseved distubance. Fom a = ẍ base we compute a desied deflection X d A = H(s) = s + ξ ω n s + ω n and a desied joint angle θ d = sin x d x d () () Using a popotional+deivative joint contolle, the actual camea dynamics ae govened by mẍ cam = b( ẋ ẋ d ) + k( x x d ) + F dist (3)

6 (a) Single Sping (b) Dual Sping Eo-Optimized (c) Dual Sping Size-Optimized Figue 7: Gavity Compensation Toques ove the wokspace. x base θ x cam Figue 8: Vetical Stabilization Joint (with the gavity compensation mechanism not shown). whee the actual mass m is subject to the effective contolle gains b and k as well as foce distubances F dist. Substituting () we find the closed-loop dynamics bs + k ξ ω n s + ωn X cam = ms + bs + k s + ξ ω n s + ωn + ms + bs + k F dist X base (4) High contolle gains eject any distubances while the low vitual stiff and high desied mass independently set ω n to filte the unintended vetical movements. 6. Acceleomete Noise/Bownian Motion The contolle s filteing stuctue () avoids pue integation of the acceleomete and povides toleance to senso offsets. Unfotunately acceleometes also contain andom senso noise which, whethe integated o filteed, esults in Bownian movements of the camea. In essence, the acceleomete signal-to-noise atio detemines how well small base movements can be ejected vesus how much Bownian motion is injected. Assume the acceleomete noise has a powe spectal density S a (ω) vesus fequency ω = π f. The vaiance of the acceleomete signal, being the squae of the standad deviation σ a and the expected value of a(t), can be econstucted fom σ a = E[a(t) ] = π S a (ω) dω (5) Meanwhile, when passed though the linea timeinvaiant (TI) system H( jω) given in (), the powe spectal density is shaped by S x (ω) = H( jω) S a (ω) (6) We can thus pedict the vaiance of the vetical deflection due to acceleomete noise as σ x = E[ x(t) ] = π H( jω) S a (ω) dω (7) Fo white acceleomete noise with a constant S a σ x = S a π and substituting ν = ω/ω n we find σ x = S a π = S a π ω 3 n (ωn ω ) dω (8) + (ξ ω n ω) ν 4 + (4ξ )ν + dν π ξ = S a 4ξ ωn 3 ω 3 n (9) The standad deviation of the joint deflection Sa σ x = (0) ω n ξ ωn is theefoe both popotional to the standad deviation of the aw acceleomete signal as well as moe than invesely popotional to the desied natual fequency. In Fig. 9 we take aw acceleomete eadings while the system is at est and compute the Bownian motion esulting fom () fo vaying fequencies. This clealy shows the stong dependence on cutoff fequency. 7. Evaluation of the Mechanism We evaluated the stabilization chaacteistics of the implemented system in a benchtop expeiment. Duing

7 Figue 9: Bownian motion in the vetical deflection. Standad deviations ae 5.9mm,.mm and 0.mm fo the cutoff fequencies 0.Hz, 0.5Hz abd Hz, espectively. the expeiment the base of the stabilization mechanism moved on a linea slide, diven by a bushed DC actuato. The setup is shown in Fig.. The linea slide was excited with a 0.03 m peak to peak swept-sine wave with the fequency changing fom 0.0 Hz to 3 Hz in 60 seconds. The motion of both the base and the camea wee sensed via an OptiTack optical motion captue system at a fequency of 0 Hz. The magnitude esponse of the system was ceated using the tfestimate function in MATAB, and is plotted in Fig.. The stabilization mechanism deceases in the magnitude by 3 to 30 fold in the 0.5- Hz ange. 8. Discussion and Conclusion We pesented the development of an active miniatuized stabilization mechanism. Unlike mechanical stabilization fo potable cameas, which use lage camea inetias to attenuate distubances, ou system achieves stabilization within a smalle dimension and fo cameas at least an ode of magnitude lighte. It combines a passive gavity compensation, optimized within the available space, with an active contolle. The contolle ejects any impefections in the gavity compensation, fiction, o othe foces while ceating the dynamics of a low vitual stiffness and high desied mass to filte the unintended vetical movements. Fo sensing, we employed only an acceleomete, avoiding pue integation of its signal and any associated numeical dift. Pactically, the noise in the acceleomete foces the tade off in the selection of the cut off fequency. To eject moe distubances and keep the camea stationay, we wish to educe the cutoff fequency. But this inceases the andom Bownian motion caused by acceleomete noise. To achieve the desied distubance ejection we taget filteing at o below 0.Hz. This (a) (b) Figue 0: Expeimental setup showing: () the camea, () a camea mounted acceleomete, (3) and (0) gavity compensation spings, (4) the bushless DC diect dive actuato, (5) the dive electonics and base acceleomete, (6) the vetical linea slide, (7) slide dive electonics, (8) powe supply, and (9) slide dive actuato Figue : The expeimental tansfe function estimate shows a 3 to 30 fold attenuation in the 0.5- Hz ange.

8 causes up to ±0mm of Bownian motion with ou acceleomete showing 400µg/ Hz noise. Fotunately, the latest geneation acceleometes educe noise nealy an ode of magnitude to 50µg/ Hz. We thus believe the newest sensos have eached the sweet spot necessay fo pactical opeation. We also note that the gavity compensation was optimized fo ou available sping stiffness k. Fom (3) we see stiffe spings could povide a moe compact design. But such designs become moe sensitive to toleances and compensation eos gow moe apidly at the wokspace extemes. Also, the design dimensions ae moe fundamentally dictated by the distubance amplitudes. So we find the appoximate design ules ( 3)distubance amplitude () k mg () Finally, we pesented the active contolle with a linea vitual stiffness K d. In pactice fast vetical movements could dive the system past the available wokspace. A nonlinea stiffening gain would help pevent impact into joint limits and ceate an appopiate amplitude-dependent filte cutoff. Oveall we ae excited that camea and senso technology has eached the theshold of enabling this miniatuized stabilization. We look fowad to seeing these light weight and flexible systems slowly eplace thei heavy pedecessos and disupt the industy. Refeences [] V. Robets and K. Salte, Countebalanced monopod jib fo cameas, Patent, Aug. 9, 06, U.S. Patent 9,4,4. [] G. W. Bown, Equipment fo use with hand held motion pictue cameas, Patent, Ap., 977, U.S. Patent 4,07,68. [3] S. Feaa, Steadicam: Techniques and aesthetics. CRC Pess, 03. [4] S. W. Smith et al., The scientist and enginee s guide to digital signal pocessing. Califonia Technical Pub. San Diego, 997. [5] J. P. Whitney and J. K. Hodgins, A passively safe and gavity-countebalanced anthopomophic obot am, in 04 IEEE Intenational Confeence on Robotics and Automation (ICRA). IEEE, 04, pp [6] J.. Hede, Enegy-fee systems. theoy, conception and design of statically balanced sping mechanisms, Ph.D. dissetation, Delft Univesity of Technology, 00. [7] O. Celik, H. B. Gilbet, and M. K. O Malley, Dynamic displacement sensing, system identification, and contol of a speake-based tendon vibato via acceleometes, IEEE/ASME Tansactions on Mechatonics, vol. 8, no., pp. 8 87, 03.