scholarly journals Effect of circular arc feet on a control law for a biped

Robotica ◽  
2009 ◽  
Vol 27 (4) ◽  
pp. 621-632 ◽  
Author(s):  
T. Kinugasa ◽  
C. Chevallereau ◽  
Y. Aoustin
Keyword(s):  
Degrees Of Freedom ◽  
Temporal Evolution ◽  
Contact Point ◽  
Basin Of Attraction ◽  
Control Law ◽  
Leg Length ◽  
Circular Arc ◽  
Geometric Evolution ◽  
Cyclic Motion ◽  
The Stability

SUMMARYThe purpose of our research is to study the effects of circular arc feet on the biped walk with a geometric tracking control. The biped studied is planar and is composed of five links and four actuators located at each hip and each knee thus the biped is underactuated in single support phase. A geometric evolution of the biped configuration is controlled, instead of a temporal evolution. The input-output linearization with a PD control law and a feed forward compensation is used for geometric tracking. The controller virtually constrains 4 degrees of freedom (DoF) of the biped, and 1 DoF (the absolute orientation of the biped) remained. The temporal evolution of the remained system with impact events is analyzed using Poincaré map. The map is given by an analytic expression based on the angular momentum about the contact point. The effect of the radii of the circular arc feet on the stability is studied. As a result, the speed of convergence decreases when the radii increases, if the radius is larger than the leg length the cyclic motion is not more stable. Among the stable cyclic motion, larger radius broadens the basin of attraction. Our results agree with those obtained for passive dynamic walking on stability, even if the biped is controlled through the geometric tracking.

Tracking a joint path for the walk of an underactuated biped

Robotica ◽  
2004 ◽  
Vol 22 (1) ◽  
pp. 15-28 ◽  
Author(s):  
Christine Chevallereau ◽  
Alexander Formal'sky ◽  
Dalila Djoudi
Keyword(s):  
Inverted Pendulum ◽  
Temporal Evolution ◽  
Biped Robot ◽  
Degree Of Freedom ◽  
Control Law ◽  
Reference Trajectory ◽  
Geometric Evolution ◽  
Cyclic Motion ◽  
Single Support Phase ◽  
Support Phase

This paper presents a control law for the tracking of a cyclic reference path by an under-actuated biped robot. The robot studied is a five-link planar biped. The degree of under-actuation is one during the single support phase. The control law is defined in such a way that only the geometric evolution of the biped configuration is controlled, but not the temporal evolution. To achieve this objective, we consider a parametrized control. When a joint path is given, a five degree of freedom biped in single support becomes similar to a one degree of freedom inverted pendulum. The temporal evolution during the geometric tracking is completely defined and can be analyzed through the study of a model with one degree of freedom. Simple analytical conditions, which guarantee the existence of a cyclic motion and the convergence towards this motion, are deduced. These conditions are defined on the reference trajectory path. The analytical considerations are illustrated with some simulation results.

A multi-configuration kinematic model for active drive/steer four-wheel robot structures

Robotica ◽  
2015 ◽  
Vol 34 (10) ◽  
pp. 2309-2329 ◽  
Author(s):  
Edgar A. Martínez-García ◽  
Erik Lerín-García ◽  
Rafael Torres-Córdoba
Keyword(s):  
Degrees Of Freedom ◽  
Rotation Axis ◽  
Contact Point ◽  
Linear Equations ◽  
Kinematic Model ◽  
Robotic Systems ◽  
Control Law ◽  
Special Design ◽  
Wheel Drive ◽  
Four Wheel Drive

SUMMARYIn this study, a general kinematic control law for automatic multi-configuration of four-wheel active drive/steer robots is proposed. This work presents models of four-wheel drive and steer (4WD4S) robotic systems with all-wheel active drive and steer simultaneously. This kinematic model comprises 12 degrees of freedom (DOFs) in a special design of a mechanical structure for each wheel. The control variables are wheel yaw, wheel roll, and suspension pitch by active/passive damper systems. The pitch angle implies that a wheel's contact point translates its position over time collinear with the robot's lateral sides. The formulation proposed involves the inference of the virtual z-turn axis (robot's body rotation axis) to be used in the control of the robot's posture by at least two acceleration measurements local to the robot's body. The z-turn axis is deduced through a set of linear equations in which the number of equations is equal to the number of acceleration measurements. This research provides two main models for stability conditions. Finally, the results are sustained by different numerical simulations that validate the system with different locomotion configurations.

Pointwise Optimal Control of Dynamical Systems Described by Constrained Coordinates

1999 ◽  
Vol 121 (4) ◽  
pp. 594-598 ◽  
Author(s):  
V. Radisavljevic ◽  
H. Baruh
Keyword(s):  
Optimal Control ◽  
Dynamical Systems ◽  
Feedback Control ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Control Law ◽  
Algebraic Equations ◽  
The Stability ◽  
The Mathematical Model

A feedback control law is developed for dynamical systems described by constrained generalized coordinates. For certain complex dynamical systems, it is more desirable to develop the mathematical model using more general coordinates then degrees of freedom which leads to differential-algebraic equations of motion. Research in the last few decades has led to several advances in the treatment and in obtaining the solution of differential-algebraic equations. We take advantage of these advances and introduce the differential-algebraic equations and dependent generalized coordinate formulation to control. A tracking feedback control law is designed based on a pointwise-optimal formulation. The stability of pointwise optimal control law is examined.

Nonlinear Feedback Law for Tracking Control of DC-Actuated Robots

1999 ◽  
Author(s):  
L. Beji ◽  
M. Pascal
Keyword(s):  
Singular Perturbations ◽  
Tracking Control ◽  
Degrees Of Freedom ◽  
Control Law ◽  
Nonlinear Feedback ◽  
Serial Robot ◽  
The Stability ◽  
Stability Results ◽  
Three Degrees Of Freedom

Abstract In this paper, a nonlinear feedback law for tracking control of robots is proposed. The dynamic of actuators and only position measurements are taking into account to design the control law. The stability results are obtained from the passivity property of the system, and using singular perturbations techniques. Simulation tests are performed on a three degrees-of-freedom serial robot to illustrate our control law.

Shimmy model for electric vehicle with independent suspensions

2017 ◽  
Vol 232 (3) ◽  
pp. 330-340 ◽  
Author(s):  
Tian Mi ◽  
Gabor Stepan ◽  
Denes Takacs ◽  
Nan Chen
Keyword(s):  
Electric Vehicle ◽  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Structural Parameters ◽  
Contact Point ◽  
Dynamic Responses ◽  
Simulation Results ◽  
The Stability ◽  
Linearized Model ◽  
Wheel Shimmy

A 5-degrees-of-freedom shimmy model is established to analyse the dynamic responses of an electric vehicle with independent suspensions. Tyre elasticity is considered by means of Pacejka’s magic formula. Under the nonslip assumption for the leading contact point, tyre–road constraint equations are derived. Numerical simulation is conducted with different structural parameters and initial conditions to observe the shimmy phenomenon. Simulation results indicate that Hopf bifurcation occurs at a certain vehicle forward speed. Moreover, suspension structural parameters, such as caster angle, affect wheel shimmy. The linearized model of the system presents the stability boundaries, which agree with the simulation results. The results of this study not only provide a theoretical reference for shimmy attenuation, but also validate the effectiveness of the provided model, which can be used in further dynamic analysis of vehicle shimmy.

scholarly journals Velocity and acceleration level inverse kinematic calculation alternatives for redundant manipulators

Meccanica ◽  
2021 ◽  
Author(s):  
Dóra Patkó ◽  
Ambrus Zelei
Keyword(s):  
Degrees Of Freedom ◽  
Direct Method ◽  
Tracking Error ◽  
Inverse Kinematic ◽  
Linear Feedback ◽  
Joint Position ◽  
Stability Properties ◽  
Acceleration Level ◽  
Error Elimination ◽  
The Stability

AbstractFor both non-redundant and redundant systems, the inverse kinematics (IK) calculation is a fundamental step in the control algorithm of fully actuated serial manipulators. The tool-center-point (TCP) position is given and the joint coordinates are determined by the IK. Depending on the task, robotic manipulators can be kinematically redundant. That is when the desired task possesses lower dimensions than the degrees-of-freedom of a redundant manipulator. The IK calculation can be implemented numerically in several alternative ways not only in case of the redundant but also in the non-redundant case. We study the stability properties and the feasibility of a tracking error feedback and a direct tracking error elimination approach of the numerical implementation of IK calculation both on velocity and acceleration levels. The feedback approach expresses the joint position increment stepwise based on the local velocity or acceleration of the desired TCP trajectory and linear feedback terms. In the direct error elimination concept, the increment of the joint position is directly given by the approximate error between the desired and the realized TCP position, by assuming constant TCP velocity or acceleration. We investigate the possibility of the implementation of the direct method on acceleration level. The investigated IK methods are unified in a framework that utilizes the idea of the auxiliary input. Our closed form results and numerical case study examples show the stability properties, benefits and disadvantages of the assessed IK implementations.

Stability of Ring-Type MEMS Gyroscopes Subjected to Stochastic Angular Speed Fluctuation

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Samuel F. Asokanthan ◽  
Soroush Arghavan ◽  
Mohamed Bognash
Keyword(s):  
Angular Velocity ◽  
Degrees Of Freedom ◽  
Microelectromechanical Systems ◽  
Damping Ratio ◽  
Operating Conditions ◽  
System Stability ◽  
System Response ◽  
Ring Type ◽  
Mems Gyroscopes ◽  
The Stability

Effect of stochastic fluctuations in angular velocity on the stability of two degrees-of-freedom ring-type microelectromechanical systems (MEMS) gyroscopes is investigated. The governing stochastic differential equations (SDEs) are discretized using the higher-order Milstein scheme in order to numerically predict the system response assuming the fluctuations to be white noise. Simulations via Euler scheme as well as a measure of largest Lyapunov exponents (LLEs) are employed for validation purposes due to lack of similar analytical or experimental data. The response of the gyroscope under different noise fluctuation magnitudes has been computed to ascertain the stability behavior of the system. External noise that affect the gyroscope dynamic behavior typically results from environment factors and the nature of the system operation can be exerted on the system at any frequency range depending on the source. Hence, a parametric study is performed to assess the noise intensity stability threshold for a number of damping ratio values. The stability investigation predicts the form of threshold fluctuation intensity dependence on damping ratio. Under typical gyroscope operating conditions, nominal input angular velocity magnitude and mass mismatch appear to have minimal influence on system stability.

scholarly journals Galloping Stability and Wind Tunnel Test of Iced Quad Bundled Conductors considering Wake Effect

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Xiaohui Liu ◽  
Ming Zou ◽  
Chuan Wu ◽  
Mengqi Cai ◽  
Guangyun Min ◽  
...  
Keyword(s):  
Wind Tunnel ◽  
Transmission Lines ◽  
Degrees Of Freedom ◽  
Wind Tunnel Test ◽  
Aerodynamic Coefficients ◽  
Wake Effect ◽  
Aerodynamic Coefficient ◽  
Set Up ◽  
The Stability ◽  
Three Degrees Of Freedom

A new quad bundle conductor galloping model considering wake effect is proposed to solve the problem of different aerodynamic coefficients of each subconductor of iced quad bundle conductor. Based on the quasistatic theory, a new 3-DOF (three degrees of freedom) galloping model of iced quad bundle conductors is established, which can accurately reflect the energy transfer and galloping of quad bundle conductor in three directions. After a series of formula derivations, the conductor stability judgment formula is obtained. In the wind tunnel test, according to the actual engineering situation, different variables are set up to accurately simulate the galloping of iced quad bundle conductor under the wind, and the aerodynamic coefficient is obtained. Finally, according to the stability judgment formula of this paper, calculate the critical wind speed of conductor galloping through programming. The dates of wind tunnel test and calculation in this paper can be used in the antigalloping design of transmission lines.

Numerical and Experimental Approaches to Investigate the Stability of a Motorcycle Vehicle

2006 ◽  
Author(s):  
Federico Cheli ◽  
Marco Bocciolone ◽  
Marco Pezzola ◽  
Elisabetta Leo
Keyword(s):  
Degrees Of Freedom ◽  
Structural Parameters ◽  
Experimental Tests ◽  
Roll Angle ◽  
Longitudinal Motion ◽  
Reference Trajectory ◽  
Steering Angle ◽  
Steady State Condition ◽  
The Stability ◽  
Linearized Model

The study of motorcycle’s stability is an important task for the passenger’s safety. The range of frequencies involved for the handling stability is lower than 10 Hz. A numerical model was developed to access the stability of a motorcycle vehicle in this frequency range. The stability is analysed using a linearized model around the straight steady state condition. In this condition, the vehicle’s vertical and longitudinal motion are decoupled, hence the model has only four degrees of freedom (steering angle, yaw angle, roll angle and lateral translation), while longitudinal motion is imposed. The stability was studied increasing the longitudinal speed. The input of the model can be either a driver input manoeuvre (roll angle) or a transversal component of road input able to excite the vibration modes. The driver is introduced in the model as a steering torque that allows the vehicle to follow a reference trajectory. To validate the model, experimental tests were done. To excite the vehicle modes, the driver input was not taken into account considering both the danger for the driver and the repeatability of the manoeuvre. Two different vehicle configurations were tested: vehicle 1 is a motorcycle [7] and vehicle 2 is a scooter. Through the use of the validated model, a sensitivity analysis was done changing structural (for example normal trail, steering angle, mass) and non structural parameters (for example longitudinal speed).

scholarly journals Design of a 2DoF Ankle Exoskeleton with a Polycentric Structure and a Bi-Directional Tendon-Driven Actuator Controlled Using a PID Neural Network

Actuators ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 9
Author(s):  
Taehoon Lee ◽  
Inwoo Kim ◽  
Yoon Su Baek
Keyword(s):  
Neural Network ◽  
Degrees Of Freedom ◽  
Plantar Flexion ◽  
Length Change ◽  
Talocrural Joint ◽  
Lower Limb Exoskeleton ◽  
Exoskeleton Robot ◽  
The Difference ◽  
Ankle Exoskeleton ◽  
The Stability

Lower limb exoskeleton robots help with walking movements through mechanical force, by identifying the wearer’s walking intention. When the exoskeleton robot is lightweight and comfortable to wear, the stability of walking increases, and energy can be used efficiently. However, because it is difficult to implement the complex anatomical movements of the human body, most are designed simply. Due to this, misalignment between the human and robot movement causes the wearer to feel uncomfortable, and the stability of walking is reduced. In this paper, we developed a two degrees of freedom (2DoF) ankle exoskeleton robot with a subtalar joint and a talocrural joint, applying a four-bar linkage to realize the anatomical movement of a simple 1DoF structure mainly used for ankles. However, bidirectional tendon-driven actuators (BTDAs) do not consider the difference in a length change of both cables due to dorsiflexion (DF) and plantar flexion (PF) during walking, causing misalignment. To solve this problem, a BTDA was developed by considering the length change of both cables. Cable-driven actuators and exoskeleton robot systems create uncertainty. Accordingly, adaptive control was performed with a proportional-integral-differential neural network (PIDNN) controller to minimize system uncertainty.

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