開發紀錄:雲台機構設計文獻回顧——量測與控制之外,雲台本身怎麼設計

這是 LocalPapa Notes 開發紀錄系列的第二十篇。第十八篇整理了怎麼量測 LOS 抖動,第十九篇接著整理了量出頻率響應之後控制端可以怎麼優化。兩篇文章都有一個共同的預設——雲台已經存在。這篇往回補一塊:雲台本身、機構層面,是怎麼被設計出來的。

兩篇沒被引用過的奠基性文獻

馬達選型計算機的方法論一路引用 Hilkert 2008,但這篇論文其實有一篇同一期刊、同一期刊號的姊妹論文,這次才找到:

Masten, M. K. (2008). Inertially Stabilized Platforms for Optical Imaging Systems. IEEE Control Systems Magazine, 28(1), 47–64. 跟 Hilkert 那篇刊在同一期(vol. 28, no. 1),角度互補——Hilkert 講的是「怎麼選馬達、怎麼設計控制迴路」的方法論,Masten 這篇專門講光學成像系統整體穩定平台的架構設計。兩篇合起來才是完整的慣性穩定平台(ISP)入門讀物,只引用一篇等於只看了一半。

另一篇是機構架構選型的關鍵文獻:Kennedy, P. J., & Kennedy, R. L. (2003). Direct versus Indirect Line of Sight (LOS) Stabilization. IEEE Transactions on Control Systems Technology, 11(1), 3–15. 這篇比較兩種穩定迴路架構——直接量測(陀螺儀直接裝在酬載上,量的就是 LOS 本身)跟間接量測(陀螺儀裝在雲台框架上,再用運動學關係反推 LOS),分析兩者各自的擾動耦合機制。161 次以上引用,是後續幾乎所有雲台控制論文在講架構選擇時的必引來源——這其實是整個雲台設計裡最早該做的決策之一:感測器裝哪裡,直接決定了後面控制迴路能做到什麼精度。

機構本身:為什麼幾乎都是直驅無框馬達

多篇產業技術文章(CubeMars、Sierramotion、Automation International)的論述一致:雲台幾乎全部採直驅無框力矩馬達(frameless direct-drive),不用齒輪減速。原因很直接——就算是很小的齒隙(backlash),或有槽馬達本身的齒槽扭矩(cogging torque),都會嚴重破壞指向精度。無框馬達少了鐵芯開槽,齒槽扭矩趨近於零,配合高解析度編碼器可以做到微米級的平滑精度。

這解釋了馬達選型計算機裡預設假設的物理原因——為什麼從一開始就是按無框直驅馬達的扭力/電流關係去建模,而不是齒輪減速後的等效扭力。也解釋了為什麼知識庫裡特別強調馬達扭矩密度(peak torque / weight)——直驅架構下,馬達本身的扭矩就是最終輸出扭矩,沒有齒輪比可以放大,選型的容錯空間比齒輪系統小得多。

配平機構:解耦不是比喻,是真實發生的數學關係

前兩篇文章已經花了不少篇幅講配平的重要性,這次找到的文獻把這件事講得更精確:

  • Simple Design of A Gravity-Independent Mass Balance
  • Multi-axis center of mass balancing system for an optical gimbal assembly guided by inertial measurement(美國專利)
  • Stable imagery from a gimbal mounted camera using mass balance(Raptor Scientific 技術文件)

這批文獻的共同結論:當雲台配平良好時,方位角與俯仰角的運動方程式會解耦(decouple)——每一軸的角速度只取決於施加在該軸上的淨扭矩,不再受另一軸運動狀態的影響。這句話幾乎是馬達選型計算機知識庫裡「配平優先於選型」條目的教科書版本,只是這次有了明確的數學語言:配平不只是「減少重力扭矩」這麼簡單,沒配平時兩軸的運動方程式裡會多出交叉耦合項(cross-coupling terms),意味著調 Pitch 軸的控制器會連帶影響 Yaw 軸的行為,兩軸沒辦法獨立設計、獨立調參——這對控制系統設計是災難性的複雜度暴增。

配平沒做好時,這個交叉耦合的物理機制被另一組文獻講得更具體:Research on the Cross-Coupling of a Two Axes Gimbal System with Dynamic Unbalance 指出這是動態不平衡(dynamic unbalance)造成的——不只是靜態重心偏移,酬載本身的慣量張量若不是對角矩陣(也就是主慣量軸沒有對齊轉軸),旋轉時也會產生耦合扭矩。這比前兩篇文章討論的靜態配平更進一步:即使靜態配平做對了(重心在轉軸上),慣量張量沒對齊一樣會在動態時產生耦合。

動力學建模:為什麼傳統方法在雙軸雲台上會卡關

Modeling and Control of a Two-Axis Stabilized Gimbal Based on Kane Method(2024)指出一個實務上的建模痛點:用傳統的 Newton-Euler 法或 Lagrange 法對雙軸雲台建立動力學模型時,前者要處理鉸鏈約束力(constraint forces)的分析,後者雖然能避開約束力分析,但要解二階微分方程,計算效率偏低。這篇論文改用 Kane 法——用廣義座標直接寫出廣義速度、偏轉速度與角速度,再分析廣義主動力與慣性力——換來的是模型結構更簡單、計算效率更高。

這篇論文本身不影響馬達選型計算機目前的公式(計算機用的是簡化的簡諧振動加速度峰值估算,不是完整動力學模型),但它說明了一件事:計算機的公式是刻意簡化過的設計階段估算,不是精確的動力學模型——如果要做精確的控制器設計(尤其牽涉到軸間耦合的補償),遲早要走到 Kane 法或 Lagrange 法這個層級,計算機給的只是「選多大馬達」這個問題的答案,不是「怎麼把控制器調到最佳」的答案。

感測器與電子系統:雲台的另一半

前兩篇文章都聚焦在扭力/電流/控制演算法,這批文獻補上了機構之外、電子系統這一半:

  • 感測融合:多篇文獻一致指出雲台標準配置是陀螺儀加速度計的資料經 Kalman 濾波互補濾波器(complementary filter)融合後送進 PID 迴路。互補濾波器運算量遠低於 Kalman,在資源有限的嵌入式雲台控制器上更常見;Kalman 濾波器理論上更精確,但需要對感測器雜訊模型有更準確的先驗假設。
  • 集電環(slip ring):雲台的 Yaw 軸要無限旋轉,電源與訊號沒辦法用軟排線直接接過去,得靠集電環在旋轉部件與固定部件之間維持連續電接觸。小型雲台通道數落在 6–18(訊號與電源合併),大型雲台可以到約 100 通道;金對金接觸點是低雜訊、高可靠度的標準做法。這塊完全不影響馬達選型計算機的扭力計算,但如果要從零組裝一顆雲台,這是機構設計裡繞不開的一部分——尤其 Yaw 軸如果不做無限旋轉集電環,整個雲台的迴轉範圍就會被線材長度綁死。

被動隔振:跟主動控制是互補,不是取代

上一篇文章整理的 ADRC、滑模控制、摩擦補償,全部都是主動抗擾手段——用感測器量到擾動、算出補償量、驅動馬達去抵消。這次找到的文獻補上了另一半:

  • Passive Isolator Design and Vibration Damping of EO/IR Gimbal Used in UAVs(2023)
  • The Design and Validation of a Satellite Camera Vibration Isolation Platform Supported by Multi-Strut Damping Rods(2025)

被動隔振(彈簧-阻尼系統、橡膠墊、多支柱阻尼桿)跟主動控制不是二選一,而是分工:被動隔振先把高頻振動能量濾掉一部分(彈簧-阻尼系統對高頻振動的衰減效果好、不需要供電、不會因為控制器設計不良而放大擾動),主動控制再處理被動隔振濾不掉的低頻殘留擾動(被動隔振對低頻效果差,且低頻正是主動控制迴路頻寬能覆蓋的範圍)。實務上兩者常常一起用,各自負責自己擅長的頻段——這跟上一篇文章提到的「用 PSD 分析區分是伺服頻寬不夠還是結構共振被踢到」是同一個邏輯的機構端版本:先搞清楚問題在哪個頻段,再決定用被動還是主動的手段去處理。

這三篇合起來:一個完整的系列

  • 雲台 LOS 光學量測系統怎麼架:怎麼量 LOS 抖動——自準直儀、雷射 PSD、目標板攝影機三種架構
  • 雲台 LOS 優化文獻回顧:量到頻率響應之後,控制端怎麼優化——ADRC、滑模控制、摩擦補償、結構最佳化、強化學習
  • 本篇:機構本身怎麼設計——直驅選型、配平機構、動力學建模、感測器與集電環、被動隔振

前兩篇都預設「雲台已經存在」;這篇回答的是「雲台本身怎麼從零設計出來」。三篇合起來,剛好是從機構設計、到量測驗證、到控制優化的完整閉環——跟馬達選型計算機本身「先算需求、再選馬達、再量測驗證、再回頭優化」的設計哲學一致,只是這次把「機構本身怎麼設計」這一塊,用文獻把背後的物理原因講清楚。

參考文獻

  • Masten, M. K. (2008). Inertially Stabilized Platforms for Optical Imaging Systems. IEEE Control Systems Magazine, 28(1), 47–64.
  • Kennedy, P. J., & Kennedy, R. L. (2003). Direct versus Indirect Line of Sight (LOS) Stabilization. IEEE Transactions on Control Systems Technology, 11(1), 3–15. 連結
  • Hilkert, J. M. (2008). Inertially Stabilized Platform Technology: Concepts and Principles. IEEE Control Systems Magazine, 28(1), 26–46.
  • Modeling and Control of a Two-Axis Stabilized Gimbal Based on Kane Method. (2024). PMC. 連結
  • Research on the Cross-Coupling of a Two Axes Gimbal System with Dynamic Unbalance. 連結
  • Passive Isolator Design and Vibration Damping of EO/IR Gimbal Used in UAVs. (2023). International Journal of Aviation Science and Technology. 連結
  • The Design and Validation of a Satellite Camera Vibration Isolation Platform Supported by Multi-Strut Damping Rods. (2025). Coatings. DOI: 10.3390/coatings16030278

上一篇:雲台 LOS 優化文獻回顧。想試算馬達規格?雲台馬達選型計算機。想追蹤系列後續?把 LocalPapa Notes 加入書籤吧。

Dev Log: A Literature Review of Gimbal Mechanical Design — Beyond Measurement and Control, How the Gimbal Itself Gets Designed

This is the twentieth post in the LocalPapa Notes dev-log series. Post eighteen covered how to measure LOS jitter, and post nineteen followed up on what the control side can do once you have a measured frequency response. Both posts shared an assumption — the gimbal already exists. This one goes back and fills in the piece before that: how the gimbal itself, at the mechanical level, actually gets designed.

Two foundational papers this series hadn't cited

The motor sizing calculator's methodology has cited Hilkert 2008 throughout, but that paper turns out to have a companion paper in the same journal issue that this series hadn't picked up until now:

Masten, M. K. (2008). Inertially Stabilized Platforms for Optical Imaging Systems. IEEE Control Systems Magazine, 28(1), 47–64. Published in the same issue as Hilkert's paper (vol. 28, no. 1), with a complementary angle — Hilkert covers the methodology of motor selection and control-loop design; Masten covers the overall architecture of stabilized platforms for optical imaging systems specifically. Together they're the actual complete primer on inertially stabilized platform (ISP) design; citing only one is reading half the picture.

The other is the key reference for mechanical architecture selection: Kennedy, P. J., & Kennedy, R. L. (2003). Direct versus Indirect Line of Sight (LOS) Stabilization. IEEE Transactions on Control Systems Technology, 11(1), 3–15. This paper compares two stabilization-loop architectures — direct sensing (the gyroscope is mounted directly on the payload, measuring LOS itself) versus indirect sensing (the gyroscope sits on the gimbal frame, and LOS is inferred through kinematic relationships) — and analyzes how disturbances couple into the LOS in each case. With 161+ citations, it's become the standard reference nearly every subsequent gimbal control paper cites when discussing architecture choice. This is arguably one of the earliest decisions in the entire gimbal design process — where the sensor physically goes directly caps what precision the control loop downstream can ever achieve.

The mechanism itself: why it's nearly always a direct-drive frameless motor

Several industry technical articles (CubeMars, Sierramotion, Automation International) agree on the same point: gimbals are almost universally built around frameless direct-drive torque motors, with no gear reduction. The reason is direct — even a small amount of backlash, or the cogging torque inherent to a slotted motor, is enough to badly degrade pointing precision. Frameless motors, lacking a slotted iron core, have cogging torque approaching zero, and paired with a high-resolution encoder can achieve micron-level smooth precision.

This explains the physical reasoning behind an assumption the motor sizing calculator has made from the start — why it models torque/current relationships for a frameless direct-drive motor rather than the equivalent torque after gear reduction. It also explains why the knowledge base specifically emphasizes torque density (peak torque / weight): in a direct-drive architecture, the motor's own torque IS the final output torque — there's no gear ratio to amplify it — so the margin for error in sizing is much smaller than in a geared system.

The balancing mechanism: decoupling isn't a metaphor, it's a real mathematical relationship

The previous two posts already spent considerable space on why balancing matters. This literature sharpens that into something more precise:

  • Simple Design of A Gravity-Independent Mass Balance
  • Multi-axis center of mass balancing system for an optical gimbal assembly guided by inertial measurement (US patent)
  • Stable imagery from a gimbal mounted camera using mass balance (Raptor Scientific technical note)

The shared conclusion across this literature: when a gimbal is properly balanced, the azimuth and elevation equations of motion decouple — each axis's angular rate depends only on the net torque applied to that axis, no longer influenced by the other axis's motion state. This is almost the textbook version of the "balance before sizing" entry in the motor calculator's knowledge base, just now with precise mathematical language attached: balancing isn't merely "reducing gravity torque" — without it, the equations of motion for the two axes pick up cross-coupling terms, meaning tuning the Pitch axis controller inadvertently affects Yaw axis behavior, and the two axes can no longer be designed or tuned independently. For control system design, that's a catastrophic jump in complexity.

The physical mechanism behind that cross-coupling, when balancing falls short, gets spelled out more concretely in another paper: Research on the Cross-Coupling of a Two Axes Gimbal System with Dynamic Unbalance points to dynamic unbalance — not just static center-of-mass offset, but the fact that if the payload's inertia tensor isn't diagonal (i.e., its principal axes of inertia aren't aligned with the rotation axes), rotation itself generates coupling torque. This goes a step further than the static balancing the previous posts discussed: even if static balancing is done correctly (center of mass on the rotation axis), a misaligned inertia tensor will still produce coupling under dynamic motion.

Dynamics modeling: why classical methods get stuck on two-axis gimbals

Modeling and Control of a Two-Axis Stabilized Gimbal Based on Kane Method (2024) points to a real modeling pain point: building a dynamic model for a two-axis gimbal with classical Newton-Euler or Lagrangian mechanics runs into trouble — the former requires analyzing constraint forces at the hinges, and while the latter sidesteps constraint-force analysis, it requires solving second-order differential equations, which is computationally inefficient. This paper instead uses the Kane method — deriving generalized velocities, deflection velocities, and angular velocities directly from generalized coordinates, then analyzing generalized active and inertial forces — trading in a simpler model structure and higher computational efficiency.

This paper doesn't affect the motor sizing calculator's current formulas (the calculator uses a simplified simple-harmonic-motion peak-acceleration estimate, not a full dynamic model), but it illustrates something: the calculator's formulas are a deliberately simplified design-stage estimate, not a precise dynamic model. If precise controller design is needed — especially anything involving compensating for cross-axis coupling — the work eventually has to reach the level of Kane's method or Lagrangian mechanics. The calculator only answers "how big a motor," not "how to tune the controller optimally."

Sensors and electronics: the other half of the gimbal

The previous two posts both focused on torque, current, and control algorithms. This literature fills in the other half — the electronics beyond the mechanism:

  • Sensor fusion: multiple sources agree the standard gimbal configuration fuses gyroscope and accelerometer data through a Kalman filter or a complementary filter before feeding it into the PID loop. Complementary filters carry far less computational load than Kalman filters, making them more common on resource-constrained embedded gimbal controllers; Kalman filters are theoretically more accurate but require more accurate prior assumptions about the sensor noise model.
  • Slip rings: a gimbal's Yaw axis needs to rotate without limit, so power and signal can't be routed through a simple flex cable — a slip ring is needed to maintain continuous electrical contact between the rotating and stationary parts. Small gimbals typically run 6–18 channels (signal and power combined); large gimbals can reach around 100 channels. Gold-to-gold contacts are the standard for low noise and high reliability. None of this affects the torque calculations in the motor sizing calculator, but it's an unavoidable part of mechanical design if you're building a gimbal from scratch — especially since, without an unlimited-rotation slip ring on the Yaw axis, the gimbal's entire slew range ends up bounded by cable length.

Passive isolation: complements active control, doesn't replace it

The ADRC, sliding-mode control, and friction compensation covered in the previous post are all active disturbance-rejection measures — sense the disturbance, compute a compensation, drive the motor to cancel it. This literature fills in the other half:

  • Passive Isolator Design and Vibration Damping of EO/IR Gimbal Used in UAVs (2023)
  • The Design and Validation of a Satellite Camera Vibration Isolation Platform Supported by Multi-Strut Damping Rods (2025)

Passive isolation (spring-damper systems, rubber mounts, multi-strut damping rods) and active control aren't an either/or choice — they divide labor. Passive isolation first filters out a portion of the high-frequency vibration energy (spring-damper systems are effective at attenuating high-frequency vibration, need no power, and can't be made worse by poor controller design), while active control then handles the low-frequency residual that passive isolation can't reach (passive isolation is poor at low frequencies, and low frequency is exactly the band an active control loop's bandwidth can cover). In practice the two are often combined, each handling the frequency band it's good at — the same logic as "use PSD analysis to tell insufficient servo bandwidth from an excited structural resonance" from the previous post, just applied on the mechanical side: figure out which frequency band the problem is in first, then decide whether a passive or active tool is the right fix.

All three posts together: a complete series

  • How to Build an Optical LOS Measurement Rig: how to measure LOS jitter — autocollimator, laser + PSD, and target-board + camera architectures
  • A Literature Review of Gimbal LOS Optimization: once you have a measured frequency response, what the control side can do — ADRC, sliding-mode control, friction compensation, structural optimization, reinforcement learning
  • This post: how the mechanism itself gets designed — direct-drive motor selection, the balancing mechanism, dynamics modeling, sensors and slip rings, passive isolation

The first two both assumed "the gimbal already exists"; this one answers "how does the gimbal get designed from scratch." Together, the three form a complete loop from mechanical design, through measurement verification, to control optimization — matching the motor sizing calculator's own design philosophy of "compute the requirement first, size the motor, verify by measurement, then optimize" — just with the literature now filling in the physical reasoning behind the mechanical design piece.

References

  • Masten, M. K. (2008). Inertially Stabilized Platforms for Optical Imaging Systems. IEEE Control Systems Magazine, 28(1), 47–64.
  • Kennedy, P. J., & Kennedy, R. L. (2003). Direct versus Indirect Line of Sight (LOS) Stabilization. IEEE Transactions on Control Systems Technology, 11(1), 3–15. Link
  • Hilkert, J. M. (2008). Inertially Stabilized Platform Technology: Concepts and Principles. IEEE Control Systems Magazine, 28(1), 26–46.
  • Modeling and Control of a Two-Axis Stabilized Gimbal Based on Kane Method. (2024). PMC. Link
  • Research on the Cross-Coupling of a Two Axes Gimbal System with Dynamic Unbalance. Link
  • Passive Isolator Design and Vibration Damping of EO/IR Gimbal Used in UAVs. (2023). International Journal of Aviation Science and Technology. Link
  • The Design and Validation of a Satellite Camera Vibration Isolation Platform Supported by Multi-Strut Damping Rods. (2025). Coatings. DOI: 10.3390/coatings16030278

Previous post: A Literature Review of Gimbal LOS Optimization. Want to size a motor? Gimbal Motor Sizing Calculator. Want to follow the rest of the series? Bookmark LocalPapa Notes.

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