| [Newport](https://www.newport.com/search/?q1=hexapod%3Arelevance%3Acompatibility%3AMETRIC%3AisObsolete%3Afalse%3A-excludeCountries%3AFR%3AnpCategory%3Ahexapods&ajax&text=hexapod) | USA |
| [Symetrie](https://symetrie.fr/en/hexapods-en/positioning-hexapods/) | France |
| [CSA Engineering](https://www.csaengineering.com/products-services/hexapod-positioning-systems/hexapod-models.html) | USA |
| [Aerotech](https://www.aerotech.com/product-catalog/hexapods.aspx) | USA |
{{<figuresrc="/ox-hugo/stewart_ht_uw.jpg"caption="<span class=\"figure-number\">Figure 16: </span>Hood Technology Corporation (HT) and the University of Washington (UW) have designed and tested a unique hexapod design for spaceborne interferometry missions <&thayer02_six_axis_vibrat_isolat_system>">}}
{{<figuresrc="/ox-hugo/stewart_czech.jpg"caption="<span class=\"figure-number\">Figure 25: </span>Stewart platform from Brno University (Czech) <&brezina08_ni_labview_matlab_simmec_stewar_platf_desig>">}}
From (<ahref="#citeproc_bib_item_30">Hauge and Campbell 2004</a>):
> Elastomer flexures, rather than steel, reduce lateral stiffness and improve passive performance at payload resonance (damping) and at frequencies greater than 100 Hz.
| [Figure 26](#figure--fig:stewart-dong07) | (<ahref="#citeproc_bib_item_20">Dong, Sun, and Du 2008</a>), (<ahref="#citeproc_bib_item_21">Dong, Sun, and Du 2007</a>) |
| | (<ahref="#citeproc_bib_item_39">Kim and Cho 2009</a>) |
| | (<ahref="#citeproc_bib_item_79">Yun and Li 2010</a>) |
From (<ahref="#citeproc_bib_item_30">Hauge and Campbell 2004</a>):
> In general, force sensors such as load cells, work well to measure vibration, but have difficulty with cross-axis dynamics.
> Inertial sensors, on the other hand, do not have this cross-axis limitation, but are usually more sensitive to payload and base dynamics and are more difficult to control due to the non-collocated nature of the sensor and actuator.
> Force sensors typically work well because they are not as sensitive to payload and base dynamics, but are limited in performance by a low-frequency zero pair resulting from the cross-axial stiffness.
> This zero pair has confused many researchers because it is very sensitive, occasionally becoming non-minimum phase.
> The zero pair is the current limitation in performance using load cell sensors.
#### Integral Force Feedback {#integral-force-feedback}
| University | Actuators | Sensors | Control | Main Object | Link to bibliography |
| JPL | Magnetostrictive | Force (collocated), Accelerometers | Two layers: Decentralized IFF, Robust Adaptive Control | Two layer control for active damping and vibration isolation | (<ahref="#citeproc_bib_item_27">Geng et al. 1995</a>) |
| JPL | Voice Coil | Force (collocated) | Decentralized IFF | Decentralized force feedback to reduce the transmissibility | (<ahref="#citeproc_bib_item_60">Spanos, Rahman, and Blackwood 1995</a>), (<ahref="#citeproc_bib_item_59">Rahman, Spanos, and Laskin 1998</a>) |
| Washinton | Voice Coil | Force, LVDT, Geophones | LQG, Force + geophones for vibration, LVDT for pointing | Centralized control is no better than decentralized. Geophone + Force MISO control is good | (<ahref="#citeproc_bib_item_65">Thayer and Vagners 1998</a>), (<ahref="#citeproc_bib_item_66">Thayer et al. 2002</a>) |
| Wyoming | Voice Coil | Force | Centralized (cartesian) IFF | Difficult to decouple in practice | (<ahref="#citeproc_bib_item_53">O’Brien et al. 1998</a>) |
| Wyoming | Voice Coil | Force | IFF, centralized (decouple) + decentralized (coupled) | Specific geometry: decoupled force plant. Better perf with centralized IFF | (<ahref="#citeproc_bib_item_44">McInroy 1999</a>), (<ahref="#citeproc_bib_item_47">McInroy, O’Brien, and Neat 1999</a>), (<ahref="#citeproc_bib_item_46">McInroy and Hamann 2000</a>) |
| Brussels | APA | Piezo force sensor | Decentralized IFF | | (<ahref="#citeproc_bib_item_2">Abu Hanieh, Horodinca, and Preumont 2002</a>) |
| Brussels | Voice Coil | Force Sensor | Decentralized IFF | Effect of flexible joints | (<ahref="#citeproc_bib_item_56">Preumont et al. 2007</a>) |
| Shangai | Piezoelectric | Force Sensor + Accelerometer | Vibration isolation, HAC-LAC (IFF + FxLMS) | Dynamic Model + Vibration Control | (<ahref="#citeproc_bib_item_74">Wang et al. 2016</a>) |
| China | | | Decentralized IFF | Design cubic configuration to have same modal frequencies: optimal damping of all modes | (<ahref="#citeproc_bib_item_78">Yang et al. 2017</a>) |
| Washinton | Voice Coil | Force | Decentralized IFF | Comparison of force sensor and inertial sensors. Issue on non-minimum phase zero | (<ahref="#citeproc_bib_item_30">Hauge and Campbell 2004</a>) |
| China | Piezoelectric | Force, Position | Vibration isolation, Model-Based, Modal control: 6x PI controllers | Stiffness of flexible joints is compensated using feedback, then the system is decoupled in the modal space | (<ahref="#citeproc_bib_item_77">Yang et al. 2019</a>) |
#### Sky-Hood Damping {#sky-hood-damping}
| University | Actuators | Sensors | Control | Main Object | Link to bibliography |
| Wyoming | Voice Coil | Accelerometer (collocated), ext. Rx/Ry sensors | Cartesian acceleration feedback (isolation) + 2DoF pointing control (external sensor) | Decoupling, both vibration + pointing control | (<ahref="#citeproc_bib_item_43">Li, Hamann, and McInroy 2001</a>) |
| China | Voice Coil | Geophone + Eddy Current (Struts, collocated) | Decentralized (Sky Hook) + Centralized (modal) Control | | (<ahref="#citeproc_bib_item_58">Pu et al. 2011</a>) |
| China | Voice Coil | Accelerometer in each leg | Centralized Vibration Control, PI, Skyhook | | (<ahref="#citeproc_bib_item_1">Abbas and Hai 2014</a>) |
| Einhoven | Voice Coil | 6dof Accelerometers on mobile and fixed platforms | Self learning feedforward (FIR), Centralized MIMO feedback (sky hood damping) | | (<ahref="#citeproc_bib_item_6">Beijen et al. 2018</a>) |
| Harbin (China) | Voice Coil | Accelerometer in each leg | Decentralized vibration control | Vibration Control with VCM and Decentralized control | (<ahref="#citeproc_bib_item_63">Tang, Cao, and Yu 2018</a>) |
| Washinton | Voice Coil | Geophones | Decentralized Inertial Feedback | Centralized control is no better than decentralized. Geophone + Force MISO control is good | (<ahref="#citeproc_bib_item_66">Thayer et al. 2002</a>) |
| Washinton | Voice Coil | Geophones | Decentralized Sky Hood Damping | Comparison of force sensor and inertial sensors | (<ahref="#citeproc_bib_item_30">Hauge and Campbell 2004</a>) |
| Harbin (China) | Voice Coil | Accelerometers | MIMO H-Infinity, active damping | Model + active damping with flexible hinges | (<ahref="#citeproc_bib_item_37">Jiao et al. 2018</a>) |
#### Vibration Control of Narrowband Disturbances {#vibration-control-of-narrowband-disturbances}
| University | Actuators | Sensors | Control | Main Object | Link to bibliography |
| Washinton | Voice Coil | Force, LVDT, Geophones | LQG, Force + geophones for vibration, LVDT for pointing | FEM => State Space | Centralized control is no better than decentralized. Geophone + Force MISO control is good | (<ahref="#citeproc_bib_item_65">Thayer and Vagners 1998</a>), (<ahref="#citeproc_bib_item_66">Thayer et al. 2002</a>) |
| Wyoming | Voice Coil | Force, LVDT | IFF, centralized (decouple) + decentralized (coupled) | Lumped | Specific geometry: decoupled force plant. Better perf with centralized IFF | (<ahref="#citeproc_bib_item_44">McInroy 1999</a>), (<ahref="#citeproc_bib_item_47">McInroy, O’Brien, and Neat 1999</a>), (<ahref="#citeproc_bib_item_46">McInroy and Hamann 2000</a>) |
| Seoul | Hydraulic | LVDT | Decentralized (strut) vs Centralized (cartesian) | | | (<ahref="#citeproc_bib_item_38">Kim, Kang, and Lee 2000</a>) |
| Wyoming | Voice Coil | Accelerometer (collocated), ext. Rx/Ry sensors | Cartesian acceleration feedback (isolation) + 2DoF pointing control (external sensor) | Analytical equations | Decoupling, both vibration + pointing control | (<ahref="#citeproc_bib_item_43">Li, Hamann, and McInroy 2001</a>) |
| Japan | APA | Eddy current displacement | Decentralized (struts) PI + LPF control | | | (<ahref="#citeproc_bib_item_24">Furutani, Suzuki, and Kudoh 2004</a>) |
| China | Voice Coil | Geophone + Eddy Current (Struts, collocated) | Decentralized (Sky Hook) + Centralized (modal) Control | | | (<ahref="#citeproc_bib_item_58">Pu et al. 2011</a>) |
| China | Piezoelectric | Leg length | Tracking control, ADRC, State observer | Analytical | Use of ADRC for tracking control of cubic hexapod | (<ahref="#citeproc_bib_item_49">Min, Huang, and Su 2019</a>) |
| China | Piezoelectric | Force, Position | Vibration isolation, Model-Based, Modal control: 6x PI controllers | Solid/Flexible | Stiffness of flexible joints is compensated using feedback, then the system is decoupled in the modal space | (<ahref="#citeproc_bib_item_77">Yang et al. 2019</a>) |
From: (<ahref="#citeproc_bib_item_77">Yang et al. 2019</a>):
> On the other hand, the traditional modal decoupled control strategy cannot deal with the flexible Stewart platform governed by Eq. (34) because it is impossible to achieve simultaneous diagonalization of the mass, damping and stiffness matrices.
> To make the six-DOF system decoupled into six single-DOF isolators, we design a new controller based on the leg’s force and position feedback.
> The idea is to synthesize the control force that can compensate the parasitic bending and torsional torques of the flexible joints and simultaneously achieve diagonalization of the matrices M, C and K.
| Washinton | Voice Coil | Force and Inertial | LQG, Decentralized, Sensor Fusion | Combine force/inertial sensors. Comparison of force sensor and inertial sensors. Issue on non-minimum phase zero | (<ahref="#citeproc_bib_item_30">Hauge and Campbell 2004</a>) |
| Netherlands | Voice Coil | | Sensor Fusion, Two Sensor Control | | (<ahref="#citeproc_bib_item_70">Tjepkema 2012</a>) |
#### HAC-LAC {#hac-lac}
| University | Actuators | Sensors | Control | Main Object | Link to bibliography |
| JPL | Magnetostrictive | Force (collocated), Accelerometers | Two layers: Decentralized IFF, Robust Adaptive Control | Two layer control for active damping and vibration isolation | (<ahref="#citeproc_bib_item_27">Geng et al. 1995</a>) |
| Shangai | Piezoelectric | Force Sensor + Accelerometer | Vibration isolation, HAC-LAC (IFF + FxLMS) | Dynamic Model + Vibration Control | (<ahref="#citeproc_bib_item_74">Wang et al. 2016</a>) |
| Wyoming | Voice Coil | Accelerometer (collocated), ext. Rx/Ry sensors | Cartesian acceleration feedback (isolation) + 2DoF pointing control (external sensor) | Decoupling, both vibration + pointing control | (<ahref="#citeproc_bib_item_43">Li, Hamann, and McInroy 2001</a>) |
| China | Voice Coil | Geophone + Eddy Current (Struts, collocated) | Decentralized (Sky Hook) + Centralized (modal) Control | | (<ahref="#citeproc_bib_item_58">Pu et al. 2011</a>) |
| China | Voice Coil | Force sensors (strus) + accelerometer (cartesian) | Decentralized Force Feedback + Centralized H2 control based on accelerometers | | (<ahref="#citeproc_bib_item_75">Xie, Wang, and Zhang 2017</a>) |
#### Sensor Fusion {#sensor-fusion}
| University | Actuators | Sensors | Control | Main Object | Link to bibliography |
| Netherlands | Voice Coil | Force (HF) and Inertial (LF) | Sensor Fusion, Two Sensor Control | | (<ahref="#citeproc_bib_item_70">Tjepkema 2012</a>), (<ahref="#citeproc_bib_item_71">Tjepkema, van Dijk, and Soemers 2012</a>) |
| Washinton | Voice Coil | Force (HF) and Inertial (LF) | LQG, Decentralized, Sensor Fusion | Combine force/inertial sensors. Comparison of force sensor and inertial sensors. Issue on non-minimum phase zero | (<ahref="#citeproc_bib_item_30">Hauge and Campbell 2004</a>) |
#### Other Strategies {#other-strategies}
| University | Actuators | Sensors | Control | Main Object | Link to bibliography |
| China | Piezoelectric | Force, Position | Vibration isolation, Model-Based, Modal control: 6x PI controllers | Stiffness of flexible joints is compensated using feedback, then the system is decoupled in the modal space | (<ahref="#citeproc_bib_item_77">Yang et al. 2019</a>) |
| Washinton | Voice Coil | Force, LVDT, Geophones | LQG, Force + geophones for vibration, LVDT for pointing | Centralized control is no better than decentralized. Geophone + Force MISO control is good | (<ahref="#citeproc_bib_item_65">Thayer and Vagners 1998</a>), (<ahref="#citeproc_bib_item_66">Thayer et al. 2002</a>) |
| Wyoming | Voice Coil | Force | IFF, centralized (decouple) + decentralized (coupled) | Specific geometry: decoupled force plant. Better perf with centralized IFF | (<ahref="#citeproc_bib_item_44">McInroy 1999</a>), (<ahref="#citeproc_bib_item_47">McInroy, O’Brien, and Neat 1999</a>), (<ahref="#citeproc_bib_item_46">McInroy and Hamann 2000</a>) |
- Jacobian decoupling: in the cartesian frame or in the frame of the struts
- Modal decoupling
- SVD decoupling
Identify Jacobian for better decoupling: (<ahref="#citeproc_bib_item_13">Cheng, Ren, and Dai 2004</a>), (<ahref="#citeproc_bib_item_28">Gexue et al. 2004</a>).
| Japan | APA | Eddy current displacement | Decentralized (struts) PI + LPF control | (<ahref="#citeproc_bib_item_24">Furutani, Suzuki, and Kudoh 2004</a>) |
| China | Voice Coil | Accelerometer in each leg | Centralized Vibration Control, PI, Skyhook | (<ahref="#citeproc_bib_item_1">Abbas and Hai 2014</a>) |
#### Modal Decoupling {#modal-decoupling}
| China | Voice Coil | Geophone + Eddy Current (Struts, collocated) | Decentralized (Sky Hook) + Centralized (modal) Control | (<ahref="#citeproc_bib_item_58">Pu et al. 2011</a>) |
| China | Piezoelectric | Force, Position | Vibration isolation, Model-Based, Modal control: 6x PI controllers | (<ahref="#citeproc_bib_item_77">Yang et al. 2019</a>) |
#### Multivariable Control {#multivariable-control}
From (<ahref="#citeproc_bib_item_66">Thayer et al. 2002</a>):
> Experimental closed-loopcontrol results using the hexapod have shown that controllers designed using a decentralized single-strut design work well when compared to full multivariable methodologies.
| China | PZT | Geophone (struts) | H-Infinity and mu-synthesis | (<ahref="#citeproc_bib_item_40">Lei and Benli 2008</a>) |
| China | Voice Coil | Force sensors (strus) + accelerometer (cartesian) | Decentralized Force Feedback + Centralized H2 control based on accelerometers | (<ahref="#citeproc_bib_item_75">Xie, Wang, and Zhang 2017</a>) |
| Harbin (China) | Voice Coil | Accelerometers | MIMO H-Infinity, active damping | (<ahref="#citeproc_bib_item_37">Jiao et al. 2018</a>) |
### Long Stroke Stewart Platforms {#long-stroke-stewart-platforms}
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