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Yangmin Li 0001

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25 papers
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IROS Conference 2025 Conference Paper

Learning-Based Motion Controller for Reconfigurable Microswarms

  • Yamei Li
  • Yunxi Tang
  • Yun Wang
  • Yangmin Li 0001
  • Lidong Yang

Motion control of magnetic microswarms has attracted extensive attention due to its significance in microrobots-based biomedical applications such as targeted drug delivery. However, such reconfigurable microswarms are subject to complex interactions between individuals and environments which make accurate modeling challenging. These complexities of microswarms poses challenges for precise motion control, as traditional controllers often rely on precise mathematical models and manual parameter tuning that limits their scalability and efficiency. Learning-based methods, such as Deep Reinforcement Learning (DRL), offer an alternative but require large datasets (usually on the order of millions) and extensive exploration which may cause the microswarms instability in physical environments due to unreasonable actions during early training therefore results in the sim-to-real gap. Moreover, traditional DRL focuses on instantaneous state-action mappings, neglecting the sequential dependencies critical for accurate motion control, leading to low tracking accuracy in complex scenarios. To address these challenges, we propose a Learning from Demonstration (LfD)-based motion control framework, which inherently encode compensatory behaviors and task-specific adaptability into neural networks, enabling adaptive performance even under unmodeled disturbances. Furthermore, the neural networks consider a time series of microswarm states to determine the future control actions, enabling the system to learn sequential dependencies and transitions between states so as to ensure smooth and accurate motion control. Simulations and comparative experiments validate our framework’s effectiveness and demonstrate superior control accuracy and adaptability to microswarm’s shape changes.

IROS Conference 2023 Conference Paper

A Rotor Flywheel Robot: Land-air Amphibious Design and Control

  • Chunzheng Wang
  • Yunyi Zhang
  • Chuanzhao Li
  • Wei Wang 0034
  • Yangmin Li 0001

Most land-air amphibious UAVs feature a four-wheel design that limits their adaptability in narrow and uneven spaces. This study proposes the rotor flywheel as a new land-air design that integrates a one-wheel structure and eight-rotor wings for more flexible motion. The dynamics model is then conducted with the Kane method, finding two power-saving self-balance state while rolling. Its controller design highlights the multi-input decoupling approach utilizing feedback, along with the dynamic model-based component to enable efficient control of its intricate operations. Results of simulations and experimental tests have validated the stability and adaptability of the mode-switching and rolling of the robot in ground motion.

IROS Conference 2019 Conference Paper

Improved Mechanical Design and Simplified Motion Planning of Hybrid Active and Passive Cable-Driven Segmented Manipulator with Coupled Motion

  • Tianliang Liu
  • Zonggao Mu
  • Wenfu Xu
  • Taiwei Yang
  • Kailing You
  • Haiming Fu
  • Yangmin Li 0001

Cable-driven segmented manipulators (CDSMs) featured by superior dexterity, light and slender body are excellent candidates for operations in confined environments. However, the stiffness and load capacity of such manipulators have been a challenge due to their structural elasticity. In this paper, we propose an improved mechanism design based on the preliminary work to enhance the linkage accuracy and arm continuity without sacrificing the dexterity, high stiffness and load capacity of CDSM. The manipulator is composed of 4 improved hybrid active-passive linkage segments. Its short and long linkage cables with pretension mechanism are designed to keep equal angles of adjacent joints. An improved separable small driving control box is also designed with both quick release and load mechanism and stroke amplification mechanism. Then the size of control box can still remain small, even the number of segments and the joint limit angles increase. Considering the improved in-segment linkage characteristic, traditional kinematic equations and Jacobian matrix are greatly simplified with Denavit-Hartenberg (D-H) method. Further trajectory tracking planning based on the simplified kinematics solved the Cartesian space planning for task design. Finally, a prototype system is developed to perform the linkage accuracy and comprehensive obstacle avoidance experiments. Experimental results show that the developed hybrid active and passive CDSM has relatively high accuracy and super dexterity.

IROS Conference 2018 Conference Paper

A Cable-Driven Redundant Spatial Manipulator with Improved Stiffness and Load Capacity

  • Tianliang Liu
  • Zonggao Mu
  • Haomiao Wang
  • Wenfu Xu
  • Yangmin Li 0001

With a light and slender body, a cable-driven redundant spatial manipulator (CRSM) has flexible manipulability and high maneuverability in confined environment. However, compared with revolute rigid manipulators, such type of manipulators generally has low stiffness and weak load capacity. In this paper, we propose a new mechanism design to improve the stiffness and load capacity without sacrificing the manipulator dexterity and the end-effector accuracy. The manipulator is composed of 3 active-passive-linkage segments and 1 active tool end-effector. Each active-passive segment has 2 degrees of freedom (DOFs) driven by three evenly distributed cables. Pretension mechanism and linkage cables are designed to keep strict equal angles of adjacent joints. A separable control box, which contains all the motors and cable transmission mechanisms is also designed with a quick release-and-lock mechanism. Therefore, the robotic arm can be easily removed and installed. Based on the equal angle characteristic, kinematic equations of manipulator are established with Denavit-Hartenberg (D-H) method and the Jacobian matrix is also simplified. Further analysis of the workspace supplies the guidance for the task design and motion planning. Finally, a prototype system is developed to perform the stiffness and load capacity experiments. Experimental results show that the developed CRSM has relatively high stiffness and load capacity.

IROS Conference 2017 Conference Paper

A regularized on-line sequential extreme learning machine with forgetting property for fast dynamic hysteresis modeling

  • Zelong Wu
  • Hui Tang 0003
  • Sifeng He
  • Jian Gao 0002
  • Xin Chen 0005
  • Chengqiang Cui
  • Yunbo He
  • Kai Zhang

Piezoelectric ceramics(PZT)actuator has been widely used in flexure-guided nanopositioning stage because of their high resolution. However, it is quite hard to achieve high-rate precision positioning control because of the complex hysteresis nonlinearity effect of PZT actuator. Thus, an online RELM algorithm with forgetting property(FReOS-ELM) is proposed to handle this issue. Firstly, we adopt regularized extreme learning machine(RELM)to build an intelligent hysteresis model. The training of the algorithm is completed only in one step, which avoids the shortcomings of the traditional hysteresis model based on artificial neural network(ANN) that slow training speed and easy to fall into the local minimum. Then, based on the regularized on-line sequential extreme learning machine(ReOS-ELM), an on-line RELM algorithm with forgetting property(FReOS-ELM) is designed, which can avoid the computational load of ReOS-ELM in the process of adding new data for learning on-line. In the experiment, a real-time voltage signal with varying frequencies and amplitudes is adopted, and the output displacement data of the nanopositioning stage is also acquired and analyzed. The results powerfully verify that the performance of the established hysteresis model based on the proposed FReOS-ELM is satisfactory, which can be used to improve the practical positioning performance for flexure nanopositioning stage.

ICRA Conference 2014 Conference Paper

Model based sliding mode control for a 3-DOF translational micro parallel positioning stage

  • Shunli Xiao
  • Yangmin Li 0001

This paper presents mechanical system dynamics modeling analysis and control of a novel compliant flexure-based micro-parallel positioning stage. The designed microparallel positioning stage consists of a mobile plate, a fixed base, and three limbs with identical kinematic structure. Certain geometric conditions are adopted to make the mobile plate with purely 3 translational degrees of freedoms. Each limb connects the mobile base to the fixed plate through a P (prismatic) joint and two U(universal) joints in sequence, where P joint is the active joint driven by a pair of novel electromagnetic actuators assembled on the fixed base. The prototype of the designed system is fabricated, dynamics model of the manipulator is constructed through Lagrange method and sliding mode controller is designed based on the dynamics model.

IROS Conference 2013 Conference Paper

A novel flexure-based dual-arm robotic system for high-throughput biomanipulations on micro-fluidic chip

  • Hui Tang 0003
  • Yangmin Li 0001
  • Xiao Xiao 0006

In recent years, robotic bio-manipulation emerges as a hot research topic in the micro/nano technology. In these applications, biological cell microinjection is a focus since it is a critical process for the further biological research such as genetic engineering and pharmacology research. This study aims to develop a novel robotic biomanipulation system combining with the micro-fluidic chip technology to improve the cell manipulation stability and throughput. Two novel flexure-based large-workspace micromanipulators with modified differential lever displacement amplifier (MDLDA) are presented in this paper. After a series of optimal designs and mechanism modeling, the mechanism performances are evaluated by the FEA method. Finally, the proposed micromanipulators are fabricated and visual-servo controlled to perform the practical zebrafish embryos injection task. In this work, two piezoelectric (PZT) actuators P-216. 80 (open-loop travel is 120 μm) and one PZT actuator P-840. 20 (open-loop travel is 30 μm) are utilized in the compliant mechanisms, the experiment results indicate that the displacement amplification ratios can reach up to 30. 6 and 17. 6, thus the maximum output displacements can achieve around 3. 1273 mm and 0. 528 mm, the rotation angle of the left micromanipulator can reach to around 26. 5°. Both theoretical derivation and experimental implementation results well verify the advanced performance of the developed system.

ICRA Conference 2013 Conference Paper

Development and assessment of a novel hydraulic displacement amplifier for piezo-actuated large stroke precision positioning

  • Hui Tang 0003
  • Yangmin Li 0001
  • Xiao Xiao 0006

In recent years, piezo-actuated micro/nano positioning stages emerge as a significant tool in the nanotechnology. However, the shortcomings of small positioning stroke and hysteresis of piezoelectric actuators have constrained their further development and applications. In this paper, a novel piezo-actuated hydraulic displacement amplifier (PHDA) based on Pascal's law and area differential principle is first proposed aiming to solve the contradictions among positioning stroke, positioning resolution and mechanism dimension in piezo-actuated micro/nano positioning stages. After a series of optimal designs, the proposed PHDA mechanism is fabricated and experimentally tested. In this study, a piezoelectric (PZT) actuator P-840. 20 with open-loop travel of 30 μm is employed, the experimental results indicate that the displacement amplification ratio can reach up to 34. 6, thus the maximum output displacement can achieve up to around 1. 02 mm. Both theoretical derivation and prototype test results testify the well performance of the proposed mechanism. This new amplifier can be widely extended to practical precision manipulation applications in case of large motion range required.

ICRA Conference 2013 Conference Paper

Development of a large working range flexure-based 3-DOF micro-parallel manipulator driven by electromagnetic actuators

  • Shunli Xiao
  • Yangmin Li 0001

This paper presents the design and analysis of a novel compliant flexure-based micro-parallel positioning stage for micro active vibration isolation application. The stage is constructed with a symmetric structure by employing three parallel PUU legs, a moving platform and a fixed platform. It is driven by 6 electromagnetic actuators and with 3 translational DOFs. The mobility characters of the stage is analyzed and proved via FEA method. The compliance modeling of the stage is conducted by resorting to compliance matrix method, and analytical models for electromagnetic forces are also established, both mechanical structure and electromagnetic model are validated by finite element analysis (FEA) performed with ANSYS. The mechanical structure is analyzed in a multi-physics environmental simulation and electromagnetic actuators are applied in ANSYS too. Both FEA and the analytical models well demonstrate that the movement of the stage is purely translational. The prototype of the designed system is fabricated, preliminary test shows the design is successful. With the parameters designed in the paper, the stage can have large working space, very high resolution and heavy work-load ability as well.

ICRA Conference 2012 Conference Paper

Mobility and kinematic analysis of a novel dexterous micro gripper

  • Shunli Xiao
  • Yangmin Li 0001

The paper presents the design and analysis of a dexterous micro-gripper with two fingers and each finger has 2-DOF translational movement function. The two fingers can move independently in hundreds of microns' range, and can cooperate with each other to realize complex operation for micro objects. The mobility characteristics and the inverse parallel kinematic model of a single finger are analyzed by resorting to screw theory and compliance and stiffness matrix method, which are validated by finite-element analysis (FEA). Both FEA and the theoretical model have well validated the movement of the fingers moving in translational way, the designed micro gripper can realize a lot of complex functions. Properly selecting the amplification ratio and the stroke of the PZT, we can mount the gripper onto a positioning stage to realize a larger motion range, which will make it be widely used in micro parts assembly and bio-operation systems.

IROS Conference 2012 Conference Paper

Optimal design, modeling and analysis of a 2-DOF nanopositioning stage with dual-mode: Towards High-Rate AFM scanning

  • Hui Tang 0003
  • Yangmin Li 0001

A compliant 2-DOF nanopositioning stage with a novel concept of dual-mode driven is proposed in this paper aiming to improve the scanning performance of the Atomic Force Microscope (AFM). The stage is featured with nanoscale positioning precision, high bandwidth, long scanning range and fully decoupled structure, which can be selected to work in dual working modes. Based upon the matrix method, the discussions in terms of output compliance, input stiffness and dynamics modeling via Lagrange equation have been performed in detail. Moreover, a series of optimal designs have been implemented using Particle Swarm Optimization (PSO) algorithm. The results of the finite-element analysis (FEA) indicate that the first natural frequency is approximated 583 Hz, the amplification ratio in two axes is about 4, thus the maximum scanning range can reach up to around 341 μm × 341 μm without material failure, while the cross-coupling between the two axes is kept within 2%. All the results indicate that the presented mechanism possesses a good performance for high-rate AFM scanning.

ICRA Conference 2011 Conference Paper

Modeling and control of rate-dependent hysteresis for a piezo-driven micropositioning stage

  • Qingsong Xu 0002
  • Yangmin Li 0001

Piezoelectric hysteresis usually relies on the frequency of the input signal. Most of the existing rate-dependent models use a lot of parameters to capture the rate-dependent hysteresis. In this paper, a simple rate-dependent hysteresis model is proposed to describe the frequency dependency effect of a micropositioning stage driven by piezoelectric actuators. This model is extended from an enhanced Coleman-Hodgdon (C-H) model. It has only 9 parameters and exhibits an accuracy better than 97%. The dependencies of the model parameters on the input rate are derived based on open-loop experimental tests. As inverse rate-dependent C-H model is established to construct a feedforward compensation. Experimental results demonstrate the effectiveness of the rate-dependent model over the traditional rate-independent one. The feedforward in conjunction with a PID feedback control is constructed to further attenuate the modeling errors and creep effects. Results show that the combined control scheme suppresses the tracking error by more than 8 times compared to the stand-alone PID control. It provides a sound base of practical control of the micropositioning system for micro/nano scale manipulation.

IROS Conference 2010 Conference Paper

Optimal design and fabrication of a piezoactuated flexure XYZ parallel micropositioning stage

  • Qingsong Xu 0002
  • Yangmin Li 0001

This paper presents the design and fabrication process of a new piezoelectrically actuated flexure-based XYZ compliant parallel-kinematics micropositioning stage with totally decoupled properties. The proposed XYZ stage consists of three limbs which are assembled in an orthogonal manner, and it has both input and output decoupling properties. Analytical models for kinematics, statics, and dynamics of the XYZ stage are established, which are validated by finite element analysis performed with ANSYS. Based on the derived models, architectural parameters of the stage are optimized and a prototype is developed for experimental studies. The results not only verify the effectiveness of the conducted optimum design but also confirm the well-decoupled performance of the XYZ stage, which will be used to execute micro-/nanomanipulation tasks.

IROS Conference 2009 Conference Paper

Active vibration control based on a 3-DOF dual compliant parallel robot using LQR algorithm

  • Yuan Yun
  • Yangmin Li 0001

In recent years, many applications in precision engineering require a careful isolation of the instrument from the vibration sources by adopting active vibration isolation system to achieve a very low remaining vibration level especially for the very low frequency under 10Hz vibration signals. In this paper, based on the previous research experiences in the systematical modeling and study of parallel robots, a hybrid robot is described and the vibration model is given by using Lagrange's equations. Then the present study addresses the issues related to the active vibration control schemes for the MIMO system using LQR algorithm. Finally, numerical simulations on the effect of active vibration control are presented.

IROS Conference 2009 Conference Paper

Global sliding mode-based tracking control of a piezo-driven XY micropositioning stage with unmodeled hysteresis

  • Qingsong Xu 0002
  • Yangmin Li 0001

In this paper, a global sliding mode control (GSMC) scheme is implemented on a piezo-driven XY parallel micropositioning stage to compensate for the unmodeled hysteresis aiming at a sub-micron accuracy motion tracking control. The GSMC controller is designed with the consideration of all uncertainty bounds. In the controller implementation, a high-gain velocity observer is adopted to estimate the feedback velocity from the measured position. The effectiveness of the GSMC over ordinary SMC and traditional PID control is demonstrated through simulations, while the variations of design parameters on control performances are examined as well. Results show that the GSMC can reduce the hysteresis to a negligible level and lead to a sub-micron accuracy tracking with tolerance to some degrees of external disturbances, which provides a sound base of practical control of the micropositioning system for micro/nano scale manipulation.

IROS Conference 2008 Conference Paper

Design of a new decoupled XY flexure parallel kinematic manipulator with actuator isolation

  • Yangmin Li 0001
  • Qingsong Xu 0002

The design procedure for a totally decoupled XY flexure parallel kinematic manipulator is presented in this paper. The designed XY stage is featured with flexure hinges and a relatively simple structure. The output decoupling is allowed by the employment of compound parallelogram flexure, and the input decoupling is implemented by actuation isolation which is enabled by the double compound parallelogram flexure with large transverse stiffness. An improved displacement amplifier is adopted to amplify the stroke of linear actuator and to simplify the stage architecture. Kinematic models of both the amplifier and the XY stage are conducted by resorting to compliance analysis based on matrix method, which are validated by finite element analysis performed with ANSYS. The presented results are helpful for the design of a new XY flexure parallel manipulator for micro/nano scale manipulation.

ICRA Conference 2008 Conference Paper

Optimum design and development of an XY flexure micromanipulator for micro scale positioning

  • Yangmin Li 0001
  • Qingsong Xu 0002

This paper presents the design and development procedures of a new decoupled XY micromanipulator for micro scale positioning applications. The manipulator is featured with parallel-kinematic architecture, flexure hinge-based joints, and piezoelectric actuation. Based on the lumped model, the efficient models for kinematics, statics and dynamics of the XY stage have been obtained, which are verified by resorting to the finite element analysis via ANSYS software package. Moreover, the stage dimensions are optimized through the particle swarm optimization (PSO) approach, and a manipulator with performances satisfying the requirements is generated. Furthermore, a prototype of the manipulator has been fabricated via the wire-EDM process. The developed micromanipulator is expected to be adopted in practical applications.

IROS Conference 2006 Conference Paper

A New Method of Executing Multiple Auxiliary Tasks by Redundant Nonholonomic Mobile Manipulators

  • Yugang Liu
  • Yangmin Li 0001

This paper addresses the multiple tasks performing issues for redundant nonholonomic mobile manipulators. An extended gradient projection redundancy resolution scheme is proposed which can determine the directions of self-motion to perform multiple secondary tasks. This scheme is easy to use and can avoid algorithm singularities. A general dynamic modeling method is presented in consideration of nonholonomic constraints, interactive motions and self-motions. A real-time fuzzy logic self-motion planner is devised to create desired self-motion magnitudes and a robust adaptive neural-network controller is designed to accomplish multiple secondary tasks without affecting the primary one in the workspace. The effectiveness of the proposed algorithm is verified through simulations for a 3DOF manipulator atop a 3-wheeled mobile platform system

ICRA Conference 2006 Conference Paper

Novel Design and Modeling of a Mobile Parallel Manipulator

  • Yangmin Li 0001
  • Qingsong Xu 0002
  • Yugang Liu

A novel design of a mobile parallel manipulator (MPM), which is composed by a multi-degree of freedom (DOF) parallel robot and an autonomous wheeled mobile platform, is proposed in this paper to overcome the shortcomings of the parallel robot and perform high accuracy tasks. Both the position and differential kinematics problems for the hybrid system are solved in details, and the dynamic model for the MPM is derived via Lagrangian formulation approach with simplifying hypotheses. Furthermore, taking the MPM self motion into consideration due to its redundancy, the dynamic control in task space is implemented by employing a model-based controller. Simulation results illustrate that not only the control algorithms are effective well, but also the established dynamic models are accurate enough as well

IROS Conference 2006 Conference Paper

Stiffness Modeling of a Spatial 3-DOF Compliant Parallel Micromanipulator

  • Qingsong Xu 0002
  • Yangmin Li 0001

The stiffness modeling for a compliant parallel manipulator (CPM) is very important since it provides a basis for the characterization of static, modal, and dynamic behavior of the CPM. This paper presents the stiffness modeling of a three-prismatic-revolute-cylindrical (3-PRC) CPM with orthogonally mounted actuators, that is designed to provide three spatial translational DOF for nano scale manipulation. A straightforward method is developed to establish the analytical stiffness model for a spatial CPM by considering the compliance of each compliant element, which is then applied to stiffness modeling of the 3-PRC CPM. Furthermore, the finite element analysis is carried out to validate the developed model. And to demonstrate the utility of the stiffness model, the influence of architectural parameters on stiffness factors is analyzed, which is valuable for a cost-effective design of the CPM

IROS Conference 2005 Conference Paper

A new task-consistent overturn prevention algorithm for redundant mobile modular manipulators

  • Yangmin Li 0001
  • Yugang Liu

This paper presents a new algorithm for automatic overturn prevention and path following control of redundant nonholonomic mobile modular manipulators. According to modular robot concept, a new dynamic modeling method is proposed in consideration of interactive motions, nonholonomic constraints and self-motions. Then, an online self-motion planner (SMP) and a robust adaptive neural-fuzzy controller (RANFC) are devised; the former is used to generate desired self-motions in a real-time manner, while the latter is used to prevent the robot from overturning and to control the end-effector to follow a desired spacial trajectory at the same time. The proposed algorithm does not need exact apriori knowledge of dynamic parameters and can suppress bounded external disturbance effectively. Simulation results for a real robot demonstrate that the proposed algorithm is effective.

IROS Conference 2005 Conference Paper

Dynamic analysis of a modified DELTA parallel robot for cardiopulmonary resuscitation

  • Yangmin Li 0001
  • Qingsong Xu 0002

The concept of a medical robot constructed by parallel mechanisms for chest compressions in rescuing a patient is proposed in this paper. In light of the requirements of cardiopulmonary resuscitation (CPR) from medical aspects, a new translational parallel manipulator (TPM) employing the architecture of a modified version of DELTA parallel robot is designed, which utilizes an architectural optimization methodology for such applications. The mobility and velocity analysis of the manipulator is carried out in details. By introducing a simplifying hypothesis, the inverse dynamic modeling is performed based upon the principle of virtual work. Moreover, the dynamic control using computed torque method is implemented, and simulation results illustrate the well performance of the control algorithm. The research works lay a sound foundation on developing a medical robot prototype to assist in CPR operation.

ICRA Conference 2005 Conference Paper

Kinematics and Dexterity Analysis for a Novel 3-DOF Translational Parallel Manipulator

  • Yangmin Li 0001
  • Qingsong Xu 0002

A new three degrees of freedom translational parallel manipulator (TPM) with fixed actuators, called a general 3-PRC TPM, is proposed in this paper. The mobility of the manipulator is analyzed via screw theory. The inverse kinematics, forward kinematics, and velocity analysis are performed and the singularity problems are investigated afterwards, which can be applied to a general 3-PRC TPM regardless of actuators arrangement. With the variation on actuators layout angle, the reachable workspace of the manipulator is generated and compared. Especially, it is illustrated that the manipulator in principle possesses a uniform workspace with a constant hexagon shape cross section. Furthermore, the dexterity characteristics is investigated in the global sense. Simulation results show that different specific tasks should be considered when the actuators layout angles of a general 3-PRC TPM are designed.

IROS Conference 2005 Conference Paper

Stability on multi-robot formation with dynamic interaction topologies

  • Yangmin Li 0001
  • Xin Chen 0012

The formation task achieved by multiple robots is a tough issue because of the limitations of the sensing abilities and communicating functions among them. Due to an individual robot can only handle local information, an adjacency graph is applied to describe the relationship among multiple robots. Since the relative positions among robots change from time to time, the topology graph describing information exchange is variant. A local control strategy is proposed for an individual robot based on NN control with robust terms. It has been proved that under an assumption of adjacency matrices associated with interaction graph being always connected, the system will converge based on the individual control strategy and multiple robots can construct an unique formation even if interaction topology is variant.

ICRA Conference 2003 Conference Paper

Parameters identification and vibration control for modular manipulators

  • Yangmin Li 0001
  • Yugang Liu
  • Xiaoping Liu
  • Zhaoyang Peng

The joint parameters of redundant manipulators are prerequisite data for effective dynamics control. An identification method via fuzzy theory and Genetic Algorithm has been presented to study modular redundant robots. The Genetic Algorithm is used in the fuzzy optimization expecting to obtain global optimal solutions. Experimental modal analysis and Finite Element Method have been exploited in dynamics modeling. The joint parameters of a 9-DOF modular redundant robot have been identified. Active vibration control has been approached to a simplified 4-DOF modular manipulator by DOF reduction to the 9-DOF modular manipulator.

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