Dynamics and Control of the Reaction Mass Pendulum (RMP) as a 3D Multibody System: Application to Humanoid Modeling

2011 ◽  
Author(s):  
Amit K. Sanyal ◽  
Ambarish Goswami
Keyword(s):  
Inverted Pendulum ◽  
Multibody System ◽  
Humanoid Robots ◽  
Reaction Mass ◽  
Underactuated System ◽  
Rotational Inertia ◽  
Control Scheme ◽  
Unstable Set ◽  
Dynamics And Control ◽  
And Control

Humans and humanoid robots are often modeled with different types of inverted pendulum models in order to simplify the dynamic analysis of gait, balance and fall. We have earlier introduced the Reaction Mass Pendulum (RMP), an extension of the traditional inverted pendulum models, which explicitly captures the variable rotational inertia and angular momentum of the human or humanoid. In this paper we present a thorough analysis of the RMP, which is treated as a 3D multibody system in its own right. We derive the complete kinematics and dynamics equations of the RMP system and obtain its equilibrium conditions. Next we present a nonlinear control scheme that stabilizes this underactuated system about an unstable set with a vertically upright configuration for the “leg” of the RMP. Finally we demonstrate the effectiveness of this controller in simulation.

Dynamics and Balance Control of the Reaction Mass Pendulum: A Three-Dimensional Multibody Pendulum With Variable Body Inertia

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Amit K. Sanyal ◽  
Ambarish Goswami
Keyword(s):  
Nonlinear Control ◽  
Balance Control ◽  
Three Dimensional ◽  
Reaction Mass ◽  
Unstable Equilibrium ◽  
Benchmark Problems ◽  
Underactuated System ◽  
Rotational Inertia ◽  
Equilibrium Manifold ◽  
Control Scheme

Pendulum models have been studied as benchmark problems for development of nonlinear control schemes, as well as reduced-order models for the dynamics analysis of gait, balance and fall for humanoid robots. We have earlier introduced the reaction mass pendulum (RMP), an extension of the traditional inverted pendulum models, which explicitly captures the variable rotational inertia and angular momentum of a human or humanoid. The RMP consists of an extensible “leg”, and a “body” with moving proof masses that gives rise to the variable rotational inertia. In this paper, we present a thorough analysis of the RMP, which is treated as a three-dimensional (3D) multibody system in its own right. We derive the complete kinematics and dynamics equations of the RMP system and obtain its equilibrium conditions. We show that the equilibria of this system consist of an unstable equilibrium manifold and a stable equilibrium manifold. Next, we present a nonlinear control scheme for the RMP, which is an underactuated system with three unactuated degrees of freedom (DOFs). This scheme asymptotically stabilizes this underactuated system at its unstable equilibrium manifold, with a vertically upright configuration for the “leg” of the RMP. The domain of convergence of this stabilization scheme is shown to be almost global in the state space of the RMP. Numerical simulation results verify this stability property of the control scheme and demonstrate its effectiveness in stabilizing the unstable equilibrium manifold.

scholarly journals Turning Gait Planning Method for Humanoid Robots

2018 ◽  
Vol 8 (8) ◽  
pp. 1257 ◽  
Author(s):  
Tianqi Yang ◽  
Weimin Zhang ◽  
Xuechao Chen ◽  
Zhangguo Yu ◽  
Libo Meng ◽  
...  
Keyword(s):  
Inverted Pendulum ◽  
Center Of Mass ◽  
Translational Motion ◽  
Humanoid Robots ◽  
Inverted Pendulum Model ◽  
Straight Line ◽  
Pendulum Model ◽  
The Stability ◽  
And Control ◽  
Present Simulation

The most important feature of this paper is to transform the complex motion of robot turning into a simple translational motion, thus simplifying the dynamic model. Compared with the method that generates a center of mass (COM) trajectory directly by the inverted pendulum model, this method is more precise. The non-inertial reference is introduced in the turning walk. This method can translate the turning walk into a straight-line walk when the inertial forces act on the robot. The dynamics of the robot model, called linear inverted pendulum (LIP), are changed and improved dynamics are derived to make them apply to the turning walk model. Then, we expend the new LIP model and control the zero moment point (ZMP) to guarantee the stability of the unstable parts of this model in order to generate a stable COM trajectory. We present simulation results for the improved LIP dynamics and verify the stability of the robot turning.

scholarly journals Dynamics and Control of Humanoid Robots: A Geometrical Approach

2010 ◽  
Vol 1 (4) ◽  
Author(s):  
Vladimir G. Ivancevic ◽  
Tijana T. Ivancevic
Keyword(s):  
Phase Space ◽  
Hamiltonian Dynamics ◽  
Fitness Function ◽  
Hamiltonian Formalism ◽  
Humanoid Robots ◽  
Geometrical Approach ◽  
Dynamics And Control ◽  
Definition Of ◽  
Configuration Manifold ◽  
And Control

AbstractThis paper reviews modern geometrical dynamics and control of humanoid robots. This general Lagrangian and Hamiltonian formalism starts with a proper definition of humanoid's configuration manifold, which is a set of all robot's active joint angles. Based on the ‘covariant force law’, the general humanoid's dynamics and control are developed. Autonomous Lagrangian dynamics is formulated on the associated ‘humanoid velocity phase space’, while autonomous Hamiltonian dynamics is formulated on the associated ‘humanoid momentum phase space’. Neural-like hierarchical humanoid control naturally follows this geometrical prescription. This purely rotational and autonomous dynamics and control is then generalized into the framework of modern non-autonomous biomechanics, defining the Hamiltonian fitness function. The paper concludes with several simulation examples.

Nonlinear dynamics and control of crank–slider mechanism with link flexibility and joint clearance

2015 ◽  
Vol 230 (5) ◽  
pp. 737-755 ◽  
Author(s):  
Sadeq Yaqubi ◽  
Morteza Dardel ◽  
Hamidreza Mohammadi Daniali
Keyword(s):  
Point Contact ◽  
Joint Clearance ◽  
Connecting Rod ◽  
Continuous Contact ◽  
Saturation Limit ◽  
Dynamical Behaviors ◽  
Control Scheme ◽  
Dynamics And Control ◽  
Link Flexibility ◽  
And Control

Dynamical behaviors and control of planar crank–slider mechanism considering the effects of joint clearance and link flexibility are studied. A control scheme for maintaining continuous contact is proposed. It was observed that using one actuator for control scheme might cause the actuator to reach its saturation limit, a problem that was bypassed by installing an additional actuator on connecting rod. In one actuator case, only continuous contact can be obtained, while with the aid of two actuators, point contact can be achieved. Great improvements in the performance of mechanism and reduction of vibrations are observed in the case of using an additional actuator.

scholarly journals Investigation into the Dynamics and Control of an Underwater Vehicle-Manipulator System

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Mohan Santhakumar
Keyword(s):  
Autonomous Underwater Vehicle ◽  
Underwater Vehicle ◽  
Dynamic Coupling ◽  
Parameter Uncertainties ◽  
External Disturbances ◽  
Model Reference Control ◽  
Control Scheme ◽  
Underwater Manipulator ◽  
Dynamics And Control ◽  
And Control

This study addresses the detailed modeling and simulation of the dynamic coupling between an underwater vehicle and manipulator system. The dynamic coupling effects due to damping, restoring, and inertial effects of an underwater manipulator mounted on an autonomous underwater vehicle (AUV) are analyzed by considering the actuator and sensor characteristics. A model reference control (MRC) scheme is proposed for the underwater vehicle-manipulator system (UVMS). The effectiveness of the proposed control scheme is demonstrated using numerical simulations along with comparative study between conventional proportional-integral-derivative (PID) control. The robustness of the proposed control scheme is also illustrated in the presence of external disturbances and parameter uncertainties.

scholarly journals Integrated SolidWorks and Simscape platform for the design and control of an inverted pendulum system

2020 ◽  
Vol 71 (2) ◽  
pp. 122-126
Author(s):  
Ahmed Alkamachi
Keyword(s):  
Inverted Pendulum ◽  
Controller Design ◽  
State Feedback Control ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Control Scheme ◽  
Implicit System ◽  
Physical Elements ◽  
And Control ◽  
The Mathematical Model

AbstractA single inverted pendulum on a cart (SIPC) is designed and modeled physically using SolidWorks. The model is then exported to the Simulink environment to form a Simscape model for simulation and test purposes. This type of modeling uses a physical grid tactic to model mechanical structures. It requires connection of the physical elements with physical signal converter to define the implicit system dynamics to be modeled. The integration between the SolidWorks and Simscape eliminates the need of deriving the mathematical model and provides a platform for the rapid controller design for the system. State feedback control scheme is proposed, designed, and tuned aiming to maintain the pendulum in the upright place while tracking the desired cart position. Several simulation cases are studied to prove the controller abilities. In order to examine the controller robustness, disturbance rejection and noise attenuation capabilities are also discovered.

Dynamics and control of a reaction mass actuator with centering springs

1997 ◽  
Author(s):  
Tae Lim ◽  
Kenneth Lieber ◽  
Tae Lim ◽  
Kenneth Lieber
Keyword(s):  
Reaction Mass ◽  
Dynamics And Control ◽  
And Control

Generalized Mass Metric and Recursive Momentum Formulation for Dynamics of Multibody Systems

2009 ◽  
Author(s):  
Qiang Zhao ◽  
HongTao Wu ◽  
Minghu Zhou
Keyword(s):  
Multibody System ◽  
Riemannian Metric ◽  
Specific Expression ◽  
Closed Loop Systems ◽  
Dynamics Of Multibody Systems ◽  
Mass Tensor ◽  
Generalized Momentum ◽  
Dynamics And Control ◽  
Generalized Force ◽  
And Control

Generalized mass metric in Riemannian manifold plays a central role in dynamics and control of multibody system (MBS). In this work, two profitable aspects of multibody system dynamics studies, generalized mass metric in Riemannian geometry and recursive momentum formulation, are described. Firstly, we will derive an Adjoint-based expression of Riemannian metric and operator factorization of generalized mass tensor from a general-topology rigid MBS which comprises of a special Euclidian group SE(3) set. The specific expression can help to clearly understand what reasons lead to these components (Riemannian metric) of the generalized mass tensor and how they measure the curves of generalized velocity space. Meanwhile, the power algorithm of MBS is presented based on the Adjoint map of generalized velocity and generalized force. Next, from the generalized momentum definition depending on such Riemannian mass metric, recursive momentum equations of MBS dynamics are developed for progressively more complex systems: open-chains, topological trees, and closed-loop systems. In terms of the relation principle of impulse and momentum, a new method is proposed for describing conservative MBS form a given initial orientation and location to desired final ones without needing to solve motion process.

Kinematics, Dynamics and Control of a Planar 3-DOF Tensegrity Robot Manipulator

2007 ◽  
Author(s):  
Rafael E. Vasquez ◽  
Julio C. Correa
Keyword(s):  
Nonlinear Control ◽  
Feedback Linearization ◽  
Robot Manipulator ◽  
Equation Of Motion ◽  
Tensegrity Systems ◽  
Control Scheme ◽  
Dynamics And Control ◽  
Cartesian Coordinate ◽  
Three Degree Of Freedom ◽  
And Control

In this paper the kinematic and the dynamic analysis, and a nonlinear control strategy for a planar three-degree-of-freedom tensegrity robot manipulator are addressed. A geometric method is used to obtain the set of equations that describe the position analysis. Initially, solutions to the problems concerning forward and reverse kinematic analysis are presented; then, the forward velocity coefficients matrix is obtained analytically. The Lagrangian approach is used to deduce the dynamic equation of motion and its main properties are described using the nonlinear control system theory. Finally, a feedback-linearization-based nonlinear control scheme is applied to the mechanism to follow a prescribed path in the Cartesian coordinate system. The obtained results show that lightweight mechanisms which incorporate tensegrity systems could be used in a positioning problem.

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