Landing Posture Control of a Generalized Twin-Body System Via Methods of Input-Output Linearization and Computed Torque

2007 ◽  
Author(s):  
Yi-Ling Yang ◽  
Paul C.-P. Chao ◽  
Cheng-Kuo Sung
Keyword(s):  
Structural Damage ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Posture Control ◽  
Body System ◽  
Input Output ◽  
Bipedal Robot ◽  
Nonlinear Equations Of Motion ◽  
Computed Torque ◽  
Input Output Linearization

This study is dedicated to achieve landing posture control of a generalized twin-body system using the methods of input-output linearization and computed torque. The twin-body system is a simplified model of bipedal robot, and the success in landing posture control would prevent structural damage. To the end, the dynamic equations are built based on Newton-Euler formulation. The technique of input-output linearization is next applied to the original nonlinear equations of motion, which is followed by adopting the method of computed torque to achieve desired landing postures. While designing the controller, system singularities are circumvented by choosing controllable set of initial conditions and stable landing postures. There are two uncontrollable postures that are immovable under input torques or/and the coupling centripetal and Coriolis forces. Finally, simulation results show that the designed controller is capable of performing desired landing posture control.

Nonlinear Bending-Torsion Flutter of a Cantilever Wing Subjected to Parametric Excitation

2005 ◽  
Author(s):  
R. A. Ibrahim ◽  
S. C. Castravete
Keyword(s):  
Parametric Excitation ◽  
Multiple Scales ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Air Flow ◽  
Parametric Instability ◽  
Flow Speed ◽  
Nonlinear Bending ◽  
Nonlinear Flutter ◽  
Nonlinear Equations Of Motion

This study deals with the nonlinear flutter of a cantilever wing in the absence and presence of parametric excitation that acts in the plane of highest rigidity. The nonlinear equations of motion in the presence of an incompressible fluid flow are derived using Hamilton’s principle. The regions of parametric instability are obtained for different values of flow speed. In the neighborhood of combination parametric resonance, the nonlinear response is determined using the multiple scales method for different values of flow speed. In the absence of parametric excitations, numerical simulation is performed for flow speeds at the critical flutter speed. It is found that the nonlinear flutter of the two modes depends on initial conditions, and exhibits symmetric periodic oscillations. Under parametric excitation and in the absence of air flow, each mode oscillates at its own natural frequency. In the presence of air flow, the two modes possess the same frequency response. Depending on the flow speed the response could be periodic, quasi-periodic, or chaotic.

Determination of the initial conditions by solving boundary value problem method for period-one walking of a passive biped walking robots

Robotica ◽  
2015 ◽  
Vol 35 (1) ◽  
pp. 166-188 ◽  
Author(s):  
Masoumeh Safartoobi ◽  
Morteza Dardel ◽  
Mohammad Hassan Ghasemi ◽  
Hamidreza Mohammadi Daniali
Keyword(s):  
Boundary Value Problem ◽  
Limit Cycles ◽  
Initial Conditions ◽  
Boundary Value ◽  
Equations Of Motion ◽  
Continuation Method ◽  
Basin Of Attraction ◽  
Initial Guess ◽  
Walking Robots ◽  
Nonlinear Equations Of Motion

SUMMARYWith regard to the small basin of attraction of the passive limit cycles, it is important to start from a proper initial condition for stable walking. The present study investigates the passive dynamic behaviors of two-dimensional bipedal walkers of a compass gait model with different foot shapes. In order to find proper initial conditions for stable and unstable period-one gait limit cycles, a method based on solving the nonlinear equations of motion is presented as a boundary value problem (BVP). An initial guess is required to solve the related BVP that is obtained by solving an initial value problem (IVP). For parametric analysis purposes, a continuation method is applied. Simulation results reveal two, period-one gait cycles and the effects of parameters variation for all models.

Differential Formulation for the Coefficient of Restitution of a Rigid Link

2015 ◽  
Vol 762 ◽  
pp. 175-182 ◽  
Author(s):  
Dorian Cojocaru ◽  
Dan B. Marghitu
Keyword(s):  
Mobile Robots ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Coefficient Of Restitution ◽  
Numerical Techniques ◽  
Differential Impact ◽  
Differential Formulation ◽  
Nonlinear Contact ◽  
Nonlinear Equations Of Motion ◽  
The Impact

The differential impact equations of motion are developed using an nonlinear contact force. The nonlinear equations of motion are written using symbolical MATLAB and are solved using numerical techniques. The impact equations are based on the Kogut-Etsion model. The numerical results are obtained for different geometries of the link, different coefficients of friction, and different initial conditions. The coefficient of restitution (COR) is discussed for specific cases. The results can be used for the impact of mobile robots with different type of surfaces.

Two-degree-of-freedom Controller Design for Uncertain Processes Using Input/output Linearization Control Technique

2011 ◽  
Vol 11 (1) ◽  
pp. 16 ◽  
Author(s):  
Pisit Sukkarnkha ◽  
Chanin Panjapornpon
Keyword(s):  
Disturbance Rejection ◽  
Control Structure ◽  
Control Method ◽  
Random Noise ◽  
Degree Of Freedom ◽  
Control Technique ◽  
Input Output ◽  
Tracking Controller ◽  
Two Degree Of Freedom ◽  
Input Output Linearization

In this work, a new control method for uncertain processes is developed based on two-degree-of-freedom control structure. The setpoint tracking controller designed by input/output linearization technique is used to regulate the disturbance-free output and the disturbance rejection controller designed is designed by high-gain technique. The advantage of two-degree-of-freedom control structure is that setpoint tracking and load disturbance rejection controllers can be designed separately. Open-loop observer is applied to provide disturbance-free response for setpoint tracking controller. The process/disturbance-free model mismatches are fed to the disturbance rejection controller for reducing effect of disturbance. To evaluate the control performance, the proposed control method is applied through the example of a continuous stirred tank reactor with unmeasured input disturbances and random noise kinetic parametric uncertainties. The simulation results show that both types of disturbances can be effectively compensated by the proposed control method.

On the Parametric Excitation of Pendulum-Type Vibration Absorber

1961 ◽  
Vol 28 (3) ◽  
pp. 330-334 ◽  
Author(s):  
Eugene Sevin
Keyword(s):  
Energy Transfer ◽  
Numerical Solution ◽  
Parametric Excitation ◽  
Equations Of Motion ◽  
Vibration Absorber ◽  
Single Cycle ◽  
Linearized System ◽  
Nonlinear Equations Of Motion ◽  
Beam Oscillation ◽  
Energy Interchange

The free motion of an undamped pendulum-type vibration absorber is studied on the basis of approximate nonlinear equations of motion. It is shown that this type of mechanical system exhibits the phenomenon of auto parametric excitation; a type of “instability” which cannot be accounted for on the basis of the linearized system. Complete energy transfer between modes is shown to occur when the beam frequency is twice the simple pendulum frequency. On the basis of a numerical solution, approximately 150 cycles of the beam oscillation take place during a single cycle of energy interchange.

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