Stewart Platform - Bibliography

University	Figure	Configuration	Joints	Actuators	Sensors	Application	Link to bibliography
JPL	fig:stewart_jpl	Cubic	Flexible	Voice Coil (0.5 mm)	Force (collocated)		spanos95_soft_activ_vibrat_isolat, rahman98_multiax Vibration Isolation (Space)
Washinton, JPL	fig:stewart_ht_uw	Cubic	Elastomers	Voice Coil (10 mm)	Force, LVDT, Geophones	Isolation + Pointing (Space)	thayer98_stewar, thayer02_six_axis_vibrat_isolat_system, hauge04_sensor_contr_space_based_six
Wyoming	fig:stewart_uw_gsp	Cubic (CoM=CoK)	Flexible	Voice Coil	Force		mcinroy99_dynam, mcinroy99_precis_fault_toler_point_using_stewar_platf, mcinroy00_desig_contr_flexur_joint_hexap, li01_simul_vibrat_isolat_point_contr, jafari03_orthog_gough_stewar_platf_microm
Brussels	fig:stewart_ulb_vc	Cubic	Flexible	Voice Coil	Force	Vibration Isolation	hanieh03_activ_stewar, preumont07_six_axis_singl_stage_activ
SRDC	fig:stewart_naval	Not Cubic	Ball joints	Voice Coil (10 mm)			taranti01_effic_algor_vibrat_suppr
SRDC	fig:stewart_pph	Non-Cubic	Flexible	Voice Coil	Accelerometers, External metrology: Eddy Current + optical	Pointing	chen03_payload_point_activ_vibrat_isolat
Harbin (China)	fig:stewart_tang18	Cubic	Flexible	Voice Coil	Accelerometer in each leg		chi15_desig_exper_study_vcm_based, tang18_decen_vibrat_contr_voice_coil, jiao18_dynam_model_exper_analy_stewar
Einhoven	fig:stewart_beijen	Almost cubic	Flexible	Voice Coil	Force Sensor + Accelerometer	Vibration Isolation	beijen18_self_tunin_mimo_distur_feedf, tjepkema12_activ_ph
JPL	fig:stewart_geng	Cubic (6-UPU)	Flexible	Magnetostrictive	Force (collocated), Accelerometers	Vibration Isolation	geng93_six_degree_of_freed_activ, geng94_six_degree_of_freed_activ, geng95_intel_contr_system_multip_degree
China	fig:stewart_zhang11	Non-cubic	Flexible	Magnetostrictive	Inertial		zhang11_six_dof
Brussels	fig:stewart_ulb_pz	Cubic	Flexible	Piezoelectric, Amplified	Piezo Force	Active Damping	abu02_stiff_soft_stewar_platf_activ
SRDC	fig:stewart_uqp	Cubic		Piezoelectric (50 um)	Geophone	Vibration	agrawal04_algor_activ_vibrat_isolat_spacec
Taiwan	fig:stewart_nanoscale	Cubic	Flexible	Piezoelectric (120 um)	External capacitive		ting06_desig_stewar_nanos_platf, ting13_compos_contr_desig_stewar_nanos_platf
Taiwan	fig:stewart_ting07	Non-Cubic	Flexible	Piezoelectric (160 um)	External capacitive (LION)		ting07_measur_calib_stewar_microm_system
Harbin (China)	fig:stewart_du14	6-SPS (Optimized)	Flexible	Piezoelectric	Strain Gauge		du14_piezo_actuat_high_precis_flexib
Japan	fig:stewart_furutani	Non-Cubic	Flexible	Piezoelectric (16 um)	Eddy Current Displacement Sensors	Cutting machine	furutani04_nanom_cuttin_machin_using_stewar
China	fig:stewart_yang19	6-UPS (Cubic?)	Flexible	Piezoelectric	Force, Position		yang19_dynam_model_decoup_contr_flexib
Shangai	fig:stewart_wang16	Cubic	Flexible	Piezoelectric	Force Sensor + Accelerometer		wang16_inves_activ_vibrat_isolat_stewar
Matra (France)	fig:stewart_mais	Cubic	Flexible	Piezoelectric (25 um)	Piezo force sensors	Vibration control	defendini00_techn
Japan	fig:stewart_torii	Non-Cubic	Flexible	Inchworm			torii12_small_size_self_propel_stewar_platf
Netherlands	fig:stewart_naves	Non-Cubic	Flexible	3-phase rotary motor	Rotary Encoders		&naves20_desig;&naves20_t_flex

University	Figure	Configuration	Joints	Actuators	Sensors	Link to bibliography
Japan	fig:stewart_cleary	6-UPS	Conventional	DC, gear + rack pinion	Encoder, 7um res	cleary91_protot_paral_manip
Seoul	fig:stewart_kim00	Non-Cubic	Conventional	Hydraulic	LVDT	kim00_robus_track_contr_desig_dof_paral_manip
Xidian (China)	fig:stewart_su04	Non-Cubic	Conventional	Servo Motor + Screwball	Encoder	su04_distur_rejec_high_precis_motion
Czech	fig:stewart_czech	6-UPS	Conventional	DC, Ball Screw	Absolute Linear position	brezina08_ni_labview_matlab_simmec_stewar_platf_desig, houska10_desig_implem_absol_linear_posit, brezina10_contr_desig_stewar_platf_linear_actuat

From &hauge04_sensor_contr_space_based_six:

Elastomer flexures, rather than steel, reduce lateral stiffness and improve passive performance at payload resonance (damping) and at frequencies greater than 100 Hz.

Main Object	Link to bibliography
Effect of flexures	mcinroy02_model_desig_flexur_joint_stewar

Main Object	Link to bibliography
Geometry for decoupling (CoM, CoK)	mcinroy00_desig_contr_flexur_joint_hexap
	afzali-far16_vibrat_dynam_isotr_hexap_analy_studies

Figure	Link to bibliography
fig:stewart_dong07	dong08_stiff_resear_high_precis_large, dong07_desig_precis_compl_paral_posit
	kim09_desig_model_novel_precis_micro_stage
	yun10_desig_analy_novel_redun_actuat
	gao02_necw_kinem_struc_paral_manip_desig
	horin06_singul_condit_six_degree_of

Main Object	Link to bibliography
Compute orientation	bonev01_new_approac_to_orien_works
Reachable Workspace	pernkopf06_works_analy_stewar_gough_type_paral_manip
Determination of the max. singularity free workspace	jiang09_deter_maxim_singul_free_orien
Orientation Workspace	jiang09_evaluat_repres_theor_orien_works

From &hauge04_sensor_contr_space_based_six:

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.

Here, the objective is to position the mobile platform with respect to an external metrology or internal metrology.

Control Strategy:

• Decentralized P, PI or PID
• LQR, LQG
• H-Infinity
• Two Layer

University	Actuators	Sensors	Control	Modelling	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	thayer98_stewar, thayer02_six_axis_vibrat_isolat_system
Wyoming	Voice Coil	Force, LVDT	IFF, centralized (decouple) + decentralized (coupled)	Lumped	Specific geometry: decoupled force plant. Better perf with centralized IFF	mcinroy99_dynam, mcinroy99_precis_fault_toler_point_using_stewar_platf, mcinroy00_desig_contr_flexur_joint_hexap
Seoul	Hydraulic	LVDT	Decentralized (strut) vs Centralized (cartesian)			kim00_robus_track_contr_desig_dof_paral_manip
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	li01_simul_vibrat_isolat_point_contr
Japan	APA	Eddy current displacement	Decentralized (struts) PI + LPF control			furutani04_nanom_cuttin_machin_using_stewar
China	Voice Coil	Geophone + Eddy Current (Struts, collocated)	Decentralized (Sky Hook) + Centralized (modal) Control			pu11_six_degree_of_freed_activ
Harbin (China)	PZT Piezo	Strain Gauge	Decentralized position feedback		Workspace, Stiffness analyzed	du14_piezo_actuat_high_precis_flexib
China	Piezoelectric	Leg length	Tracking control, ADRC, State observer	Analytical	Use of ADRC for tracking control of cubic hexapod	min19_high_precis_track_cubic_stewar
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	yang19_dynam_model_decoup_contr_flexib

From: yang19_dynam_model_decoup_contr_flexib:

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.

Improvement by the use of several sensors:

• HAC-LAC
• Two sensor control
• Sensor Fusion

Comparison between “two sensor control” and “sensor fusion” is given in &beijen14_two_sensor_contr_activ_vibrat.

Different strategies:

• Jacobian decoupling: in the cartesian frame or in the frame of the struts
• Modal decoupling
• SVD decoupling

Identify Jacobian for better decoupling: cheng04_multi_body_system_model_gough, gexue04_vibrat_contr_with_stewar_paral_mechan.

Link to bibliography	University	Actuators	Sensors	Control	Main Object
cleary91_protot_paral_manip	Japan	DC, gear + rack pinion	Encoder, 7um res	Decentralized (struts), PID control	Singular configuration analysis, workspace
su04_distur_rejec_high_precis_motion	Xidian (China)
huang05_smoot_stewar	Taiwan
brezina08_ni_labview_matlab_simmec_stewar_platf_desig, houska10_desig_implem_absol_linear_posit	Czech	DC			Modeling with sim-mechanics
molina08_simul_stewar	Brazil				Simulation with Matlab/Simulink
yang10_model_dof_simul_simmec	China			Decentralized PID	Simulation with Simulink/SimMechanics
kim00_robus_track_contr_desig_dof_paral_manip	Seoul	Hydraulic	LVDT	Decentralized (strut) vs Centralized (cartesian)

• merlet06_paral_robot
• taghirad13_paral
• preumont18_vibrat_contr_activ_struc_fourt_edition
• arakelian18_dynam_decoup_robot_manip

• li01_simul_fault_vibrat_isolat_point
• bishop02_devel_precis_point_contr_vibrat
• hanieh03_activ_stewar
• vivas04_contr
• afzali-far16_vibrat_dynam_isotr_hexap_analy_studies
• deng17_integ_dof_loren_actuat_gravit
• naves20_desig

• dasgupta00_stewar_platf_manip
• merlet02_still
• patel12_paral_manip_applic_survey
• buzurovic12_advan_contr_method_paral_robot_system
• furqan17_studies_stewar_platf_manip