scholarly journals Mechanics and Control of a Terrestrial Vehicle Exploiting a Nonholonomic Constraint for Fishlike Locomotion

2013 ◽  
Author(s):  
Tony Dear ◽  
Scott David Kelly ◽  
Matthew Travers ◽  
Howie Choset
Keyword(s):  
Mechanical System ◽  
Nonholonomic Constraint ◽  
Equations Of Motion ◽  
Geometric Mechanics ◽  
Velocity Control ◽  
Joint Velocity ◽  
And Control

We present a novel mechanical system, the “landfish,” which takes advantage of a combination of articulation and a nonholonomic constraint to exhibit fishlike locomotion. We apply geometric mechanics techniques to establish the equations of motion in terms of the system’s nonholonomic momentum and analyze the system’s equilibrium properties. Finally, we demonstrate its locomotion capabilities under several controllers, including heading and joint velocity control.

scholarly journals Analysis of the brachistochronic motion of a variable mass nonholonomic mechanical system

2016 ◽  
Vol 43 (1) ◽  
pp. 19-32 ◽  
Author(s):  
Bojan Jeremic ◽  
Radoslav Radulovic ◽  
Aleksandar Obradovic
Keyword(s):  
Differential Equations ◽  
Mechanical System ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Variable Mass ◽  
Nonholonomic Constraints ◽  
Initial Position ◽  
Mass Particle ◽  
Control Forces ◽  
And Control

The paper considers the brachistochronic motion of a variable mass nonholonomic mechanical system [3] in a horizontal plane, between two specified positions. Variable mass particles are interconnected by a lightweight mechanism of the ?pitchfork? type. The law of the time-rate of mass variation of the particles, as well as relative velocities of the expelled particles, as a function of time, are known. Differential equations of motion, where the reactions of nonholonomic constraints and control forces figure, are created based on the general theorems of dynamics of a variable mass mechanical system [5]. The formulated brachistochrone problem, with adequately chosen quantities of state, is solved, in this case, as the simplest task of optimal control by applying Pontryagin?s maximum principle [1]. A corresponding two-point boundary value problem (TPBVP) of the system of ordinary nonlinear differential equations is obtained, which, in a general case, has to be numerically solved [2]. On the basis of thus obtained brachistochronic motion, the active control forces, along with the reactions of nonholonomic constraints, are determined. The analysis of the brachistochronic motion for different values of the initial position of a variable mass particle B is presented. Also, the interval of values of the initial position of a variable mass particle B, for which there are the TPBVP solutions, is determined.

On the Dynamics Behavior and a Control Design to a Nonlinear 2-DOF Vibrating Gyroscopic-MEMS Model

2011 ◽  
Author(s):  
Nelson Jose´ Peruzzi ◽  
Fa´bio Roberto Chavarette ◽  
Jose´ Manoel Balthazar
Keyword(s):  
Mechanical System ◽  
Mechanical Energy ◽  
Equations Of Motion ◽  
Time History ◽  
Electrical Energy ◽  
Micro Electro Mechanical System ◽  
Mems Gyroscope ◽  
Time Histories ◽  
System Equations ◽  
And Control

In this paper, we deal with the nonlinear dynamics, the transfer of energy and control of the vibrations of a Micro Electro-mechanical System (MEMS) gyroscope. The MEMS are micro-transducers whose operation is based on elastic and electrostatic forces that convert electrical energy into mechanical energy and vice-versa. These systems can be modeled by 2-DOF spring-mass-damper system and the coupling of the system equations is performed by Coriolis force. This coupling is responsible for the energy transfers of the two vibration modes (drive-mode and sense-mode) and for the resonance in MEMS gyroscope. The governing equations of motion have periodic coefficients and as the dimensions of the quantities involved in the system may be inconsistent it is not advisable the use of perturbation methods for the solution of the MEMS gyroscope. For this reason, in the dynamic analysis and control of the vibrations of the MEMS gyroscope, we used a technique based on Chebyshev polynomial expansion, the iterative Picard and transformation of Lyapunov-Floquet (L–F). For the analysis of the dynamic of the micro electro-mechanical system gyroscope, we did the diagram of stability, phase planes and time history of transfer of energy. Finally, we did the control of the unstable orbit to a desired periodic one and compared the phase planes of orbits desired and controlled and time histories of energy transfer of the controlled and non-controlled system.

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

scholarly journals Assessment of Linearization Approaches for Multibody Dynamics Formulations

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Francisco González ◽  
Pierangelo Masarati ◽  
Javier Cuadrado ◽  
Miguel A. Naya
Keyword(s):  
Mechanical System ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Practical Applications ◽  
Linearization Methods ◽  
Highly Nonlinear ◽  
Wide Range ◽  
The Way

Formulating the dynamics equations of a mechanical system following a multibody dynamics approach often leads to a set of highly nonlinear differential-algebraic equations (DAEs). While this form of the equations of motion is suitable for a wide range of practical applications, in some cases it is necessary to have access to the linearized system dynamics. This is the case when stability and modal analyses are to be carried out; the definition of plant and system models for certain control algorithms and state estimators also requires a linear expression of the dynamics. A number of methods for the linearization of multibody dynamics can be found in the literature. They differ in both the approach that they follow to handle the equations of motion and the way in which they deliver their results, which in turn are determined by the selection of the generalized coordinates used to describe the mechanical system. This selection is closely related to the way in which the kinematic constraints of the system are treated. Three major approaches can be distinguished and used to categorize most of the linearization methods published so far. In this work, we demonstrate the properties of each approach in the linearization of systems in static equilibrium, illustrating them with the study of two representative examples.

Vibration analysis of multiple degrees of freedom mechanical system with dry friction

2012 ◽  
Vol 227 (7) ◽  
pp. 1505-1514 ◽  
Author(s):  
SD Yu ◽  
BC Wen
Keyword(s):  
Mechanical System ◽  
Dry Friction ◽  
Degrees Of Freedom ◽  
Simple Procedure ◽  
Mathematical Problem ◽  
Equations Of Motion ◽  
Inequality Constraints ◽  
Integration Scheme ◽  
Time Step ◽  
Multiple Degrees Of Freedom

This article presents a simple procedure for predicting time-domain vibrational behaviors of a multiple degrees of freedom mechanical system with dry friction. The system equations of motion are discretized by means of the implicit Bozzak–Newmark integration scheme. At each time step, the discontinuous frictional force problem involving both the equality and inequality constraints is successfully reduced to a quadratic mathematical problem or the linear complementary problem with the introduction of non-negative and complementary variable pairs (supremum velocities and slack forces). The so-obtained complementary equations in the complementary pairs can be solved efficiently using the Lemke algorithm. Results for several single degree of freedom and multiple degrees of freedom problems with one-dimensional frictional constraints and the classical Coulomb frictional model are obtained using the proposed procedure and compared with those obtained using other approaches. The proposed procedure is found to be accurate, efficient, and robust in solving non-smooth vibration problems of multiple degrees of freedom systems with dry friction. The proposed procedure can also be applied to systems with two-dimensional frictional constraints and more sophisticated frictional models.

scholarly journals Modeling a Knuckle-Boom Crane Control to Reduce Pendulum Motion Using the Moving Frame Method

2019 ◽  
Author(s):  
Maren Eriksen Eia ◽  
Elise Mari Vigre ◽  
Thorstein Ravneberg Rykkje
Keyword(s):  
Equations Of Motion ◽  
Moving Frame ◽  
Web Pages ◽  
Moving Frames ◽  
Pendulum Motion ◽  
Moving Frame Method ◽  
Frame Method ◽  
The Masses ◽  
And Control ◽  
Boom Crane

Abstract A Knuckle Boom Crane is a pedestal-mounted, slew-bearing crane with a joint in the middle of the distal arm; i.e. boom. This distal boom articulates at the ‘knuckle (i.e.: joint)’ and that allows it to fold back like a finger. This is an ideal configuration for a crane on a ship where storage space is a premium. This project researches the motion and control of a ship mounted knuckle boom crane to minimize the pendulum motion of a hanging load. To do this, the project leverages the Moving Frame Method (MFM). The MFM draws upon Lie group theory — SO(3) and SE(3) — and Cartan’s Moving Frames. This, together with a compact notation from geometrical physics, makes it possible to extract the equations of motion, expeditiously. The work reported here accounts for the masses and geometry of all components, interactive motor couples and prepares for buoyancy forces and added mass on the ship. The equations of motion are solved numerically using a 4th order Runge Kutta (RK4), while solving for the rotation matrix for the ship using the Cayley-Hamilton theorem and Rodriguez’s formula for each timestep. This work displays the motion on 3D web pages, viewable on mobile devices.

scholarly journals A Simulation Model for Computing the Loads Generated at Landing Site During Helicopter Take-Off or Landing Operation

2019 ◽  
Vol 2019 (2) ◽  
pp. 59-75
Author(s):  
Jarosław Stanisławski
Keyword(s):  
Equations Of Motion ◽  
Landing Site ◽  
Simulation Method ◽  
Rigid Bodies ◽  
Landing Gear ◽  
Rotor Blades ◽  
Wind Gust ◽  
The Galerkin Method ◽  
Lumped Masses ◽  
And Control

Summary The paper presents simulation method and results of calculations determining behavior of helicopter and landing site loads which are generated during phase of the helicopter take-off and landing. For helicopter with whirling rotor standing on ground or touching it, the loads of landing gear depend on the parameters of helicopter movement, occurrence of wind gusts and control of pitch angle of the rotor blades. The considered model of helicopter consists of the fuselage and main transmission treated as rigid bodies connected with elastic elements. The fuselage is supported by landing gear modeled by units of spring and damping elements. The rotor blades are modeled as elastic axes with sets of lumped masses of blade segments distributed along them. The Runge-Kutta method was used to solve the equations of motion of the helicopter model. According to the Galerkin method, it was assumed that the parameters of the elastic blade motion can be treated as a combination of its bending and torsion eigen modes. For calculations, data of a hypothetical light helicopter were applied. Simulation results were presented for the cases of landing helicopter touching ground with different vertical speed and for phase of take-off including influence of rotor speed changes, wind gust and control of blade pitch. The simulation method may help to define the limits of helicopter safe operation on the landing surfaces.

The Integrated Mission Simulator

SIMULATION ◽  
1964 ◽  
Vol 2 (2) ◽  
pp. R-9-R-23
Author(s):  
Edward E. Markson ◽  
John L. Stricker
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Landing Site ◽  
Euler Angle ◽  
Space Mission ◽  
Six Degrees Of Freedom ◽  
Guidance And Control ◽  
Manned Space ◽  
And Control ◽  
Guidance Technique

Space mission simulator programs may be divided into two broad categories: (1) training tools (quali tative devices often simulating a continuous mission), and (2) laboratory tools (quantitative devices treating the mission in phases, each phase being programmed separately to obtain optimum scaling). This paper describes the development of an analog program capable of continuously simulating an entire lunar mission in six degrees of freedom with high resolu tion throughout. The reported work logically traces the program development through the equations of motion, the guidance and control equations, and the analog mechanization. The translation equations are de veloped using a modified form of Encke's method; two reference origins are utilized at the two points of primary interest—the landing site and the target vehicle—such that the displacements are approach ing a minimum in the regions where the highest reso lution is required. The variables are rescaled as this region is approached to obtain maximum accuracy. Relays, stepping switches and diode gates are used for rescaling and to re-reference origins. A particular Euler angle sequence is selected based on matrix validity criteria applied to the mission. A previously reported guidance technique is shown to be appli cable to all phases of the mission. It is concluded that the method demonstrated in this paper leads to minimum computer loading for simulating a manned space mission without program discontinuities. Supporting data include an analog- computed trajectory representative of a long-dura tion mission, which is compared in detail with a digital solution.

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