• Title/Summary/Keyword: euler-lagrange equation

Search Result 87, Processing Time 0.026 seconds

A Study on the efficient control of an elastic manipulator moving in a vertical plane (수직면에서 작동하는 탄성 매니퓰레이터의 효율적인 제어에 관한 연구)

  • 강준원;이중섭;권혁조;오재윤;정재욱
    • Proceedings of the Korean Society of Precision Engineering Conference
    • /
    • 1996.11a
    • /
    • pp.318-322
    • /
    • 1996
  • This paper presents a technique to control a robot which has a flexible manipulator moving in a vertical plane. The flexible manipulator is modeled as an Euler-Bernoulli beam. Elastic deformation is represented using the assumed modes method. A comparison function which satisfies all geometric and natural boundary conditions of a cantilever beam with an end mass is used as an assumed mode shape. Lagrange's equation is utilized for the development of a discretized model. A control algorithm is developed using a simple PID control technique. The proportional, integral and derivative control gains are determined based on the dominant pole placement method and tuned to show no overshoot and having a short settling time. The effectiveness of the developed control scheme is showed experimentally. In the position control experiment, three different end masses are used. The experimental results shows little overshoot, no steady state error, and less than 2.5 second settling time in case of having an end mass which is equivalent to 45% of the total system weight. Also the residual vibration of the end point is effectively controlled.

  • PDF

A Study on the Modeling and Control of a Flexible One-Link Manipulator Moving in a Vertical Plane (수직면에서 회전운동 하는 단일 탄성링크를 가지는 매니퓰레이터의 모델링과 제어에 관한 연구)

  • Kim, Jongdae;Oh, Seokhyung;Kim, Kiho;Oh, Chaeyoun
    • Journal of the Korean Society for Precision Engineering
    • /
    • v.13 no.11
    • /
    • pp.132-142
    • /
    • 1996
  • This paper presents a technique to model and control a manipulator which has a flexible link and moves in a vertical plane. The flexible link is modeled as an Euler-Bernoulli Beam. Elastic deformation of the flexible link is represented using the assumed modes method. A comparison function which satisfies all geometric and natural boundary conditions of a cantilever beam with an end mass is used as an assumed mode shape. Lagrange's equation is utilized for the development of a discretized model. This paper presents a simple technique to improve the correctness of the developed model. The final model including the shortening effect due to elastic deformation correlates very well with experimental results. The free body motion simulation shows that two assumed modes for the representation of the elastic deformation is proper in terms of the model size and correctness. A control algorithm is developed using PID control technique. The proportional, integral and derivative control gains are determined based on dominant pole placement method with a rigid one-link manipulator. A position control simulation shows that the control algorithm can be used to control the position and residual oscillation of the flexible one-link manipulator effectively.

  • PDF

PID Control of a flexible robot rotating in vertical plane (수직면에서 회전운동을 하는 탄성로봇의 PID 제어)

  • Kang, Junwon;Oh, Chaeyoun;Kim, Kiho
    • Journal of the Korean Society for Precision Engineering
    • /
    • v.14 no.11
    • /
    • pp.34-41
    • /
    • 1997
  • This paper presents a technique to control a very flexible robot moving in a vertical plane. The flexible robot is modeled as an Euler-Bernoulli beam. Elastic deformation is approximated using the assmed modes method. A comparison function which satisfies all geometric and natural boundary conditions of a cantilever beam with an end mass is used as an assumed mode shape. Lagrange's equation is utilized for the development of a discretized model. A control algorithm is developed using a simple PID cnotrol tech- nique. The proportional, integral and deivative control gains are determined based on the dominant pole placement method and tuned to show no overshoot and no steady state error, and short settling time. The effectiveness of the developed control scheme is showed in the hub angular diaplacement control experiment. Three different end masses are uned in the experiment. The experimental results show that developed control algorithm is very effective showing little overshoot, no steady state error, and less than 2.5 second settl- ing time in case of having an end mass which is equivalent to 45% of the manipulator mass. Also the experimental results show that the residual vibration fo the end point is effectively controlled.

  • PDF

Design of a Transformable Spherical Robot Based on Multi-Linkage Structure (복합 링크 구조 기반의 가변형 구형로봇 설계)

  • Kang, Hyeongseok;Joe, Seonggun;Lee, Dongkyu;Kim, Byungkyu
    • Journal of Aerospace System Engineering
    • /
    • v.11 no.6
    • /
    • pp.26-33
    • /
    • 2017
  • We propose a variable frame structure connected with telescopic mast-shaped shaft for a robot displaying outstanding ability to cross obstacles, and for effective traction control. The wireless control system was built to extend and contract a deployable mechanism, which is shaped into a hoberman sphere assembled with frame structures. In order to develop important parameters for efficient locomotion, we derived an Euler-Lagrange equation for the spherical robot. According to the equation, the DC motor was selected. A prototype mechanism was tested and a Finite-Element Analysis (FEA) was conducted in parallel. Using these data, we constructed a deployable spherical robot with structural stability. The deployable robot moved at a speed of 0.85 m/s from 520 mm to 650 mm.

Photon Mapping-Based Rendering Technique for Smoke Particles (연기 파티클에 대한 포톤 매핑 기반의 렌더링 기법)

  • Song, Ki-Dong;Ihm, In-Sung
    • Journal of the Korea Computer Graphics Society
    • /
    • v.14 no.4
    • /
    • pp.7-18
    • /
    • 2008
  • To realistically produce fluids such as smoke for the visual effects in the films or animations, we need two main processes: a physics-based modeling of smoke and a rendering of smoke simulation data, based on light transport theory. In the computer graphics community, the physics-based fluids simulation is generally adopted for smoke modeling. Recently, the interest of the particle-based Lagrangian simulation methods is increasing due to the advantages at simulation time, instead of the grid-based Eulerian simulation methods which was widely used. As a result, because the smoke rendering technique depends heavily on the modeling method, the research for rendering of the particle-based smoke data still remains challenging while the research for rendering of the grid-based smoke data is actively in progress. This paper focuses on realistic rendering technique for the smoke particles produced by Lagrangian simulation method. This paper introduces a technique which is called particle map, that is the expansion and modification of photon mapping technique for the particle data. And then, this paper suggests the novel particle map technique and shows the differences and improvements, compared to previous work. In addition, this paper presents irradiance map technique which is the pre-calculation of the multiple scattering term in the volume rendering equation to enhance efficiency at rendering time.

  • PDF

Nonlinear numerical modelling for the effects of surface explosions on buried reinforced concrete structures

  • Nagy, N.;Mohamed, M.;Boot, J.C.
    • Geomechanics and Engineering
    • /
    • v.2 no.1
    • /
    • pp.1-18
    • /
    • 2010
  • The analysis of structure response and design of buried structures subjected to dynamic destructive loads have been receiving increasing interest due to recent severe damage caused by strong earthquakes and terrorist attacks. For a comprehensive design of buried structures subjected to blast loads to be conducted, the whole system behaviour including simulation of the explosion, propagation of shock waves through the soil medium, the interaction of the soil with the buried structure and the structure response needs to be simulated in a single model. Such a model will enable more realistic simulation of the fundamental physical behaviour. This paper presents a complete model simulating the whole system using the finite element package ABAQUS/Explicit. The Arbitrary Lagrange Euler Coupling formulation is used to model the explosive charge and the soil region near the explosion to eliminate the distortion of the mesh under high deformation, while the conventional finite element method is used to model the rest of the system. The elasto-plastic Drucker-Prager Cap model is used to model the soil behaviour. The explosion process is simulated using the Jones-Wilkens-Lee equation of state. The Concrete Damage Plasticity model is used to simulate the behaviour of concrete with the reinforcement considered as an elasto-plastic material. The contact interface between soil and structure is simulated using the general Mohr-Coulomb friction concept, which allows for sliding, separation and rebound between the buried structure surface and the surrounding soil. The behaviour of the whole system is evaluated using a numerical example which shows that the proposed model is capable of producing a realistic simulation of the physical system behaviour in a smooth numerical process.

Kinematic and Dynamic Analyses of Human Arm Motion

  • Kim, Junghee;Cho, Sungho;Lee, Choongho;Han, Jaewoong;Hwang, Heon
    • Journal of Biosystems Engineering
    • /
    • v.38 no.2
    • /
    • pp.138-148
    • /
    • 2013
  • Purpose: Determining an appropriate path is a top priority in order for a robot to maneuver in a dynamically efficient way especially in a pick-and-place task. In a non-standardized work environment, current robot arm executes its motion based on the kinematic displacements of joint variables, though resulting motion is not dynamically optimal. In this research we suggest analyzing and applying motion patterns of the human arm as an alternative to perform near optimum motion trajectory for arbitrary pick-and-place tasks. Methods: Since the motion of a human arm is very complicated and diverse, it was simplified into two links: one from the shoulder to the elbow, and the other from the elbow to the hand. Motion patterns were then divided into horizontal and vertical components and further analyzed using kinematic and dynamic methods. The kinematic analysis was performed based on the D-H parameters and the dynamic analysis was carried out to calculate various parameters such as velocity, acceleration, torque, and energy using the Newton-Euler equation of motion and Lagrange's equation. In an attempt to assess the efficacy of the analyzed human motion pattern it was compared to the virtual motion pattern created by the joint interpolation method. Results: To demonstrate the efficacy of the human arm motion mechanical and dynamical analyses were performed, followed by the comparison with the virtual robot motion path that was created by the joint interpolation method. Consequently, the human arm was observed to be in motion while the elbow was bent. In return this contributed to the increase of the manipulability and decrease of gravity and torque being exerted on the elbow. In addition, the energy required for the motion decreased. Such phenomenon was more apparent under vertical motion than horizontal motion patterns, and in shorter paths than in longer ones. Thus, one can minimize the abrasion of joints by lowering the stress applied to the bones, muscles, and joints. From the perspectives of energy and durability, the robot arm will be able to utilize its motor most effectively by adopting the motion pattern of human arm. Conclusions: By applying the motion pattern of human arm to the robot arm motion, increase in efficiency and durability is expected, which will eventually produce robots capable of moving in an energy-efficient manner.