scholarly journals The Analysis of Constrained Impulsive Motion

2003 ◽  
Vol 70 (4) ◽  
pp. 583-594 ◽  
Author(s):  
L.-S. Wang ◽  
W.-T. Chou
Keyword(s):  
Conservation Law ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Fundamental Principle ◽  
Velocity Variation ◽  
Impulsive Motion ◽  
Kinematic Constraints ◽  
Systematic Scheme ◽  
Impulsive Constraints ◽  
Impulsive Problems

Impulsive problems for mechanical systems subject to kinematic constraints are discussed in this paper. In addition to the applied impulses, there may exist suddenly changed constraints, or termed impulsive constraints. To describe the states of the system during the impulsive motion, three different phases, i.e., prior motion, virtual motion, and posterior motion, are defined which are subject to different sets of constraints, and thus have different degrees-of-freedom. A fundamental principle, i.e., the principle of velocity variation, for the constrained impulsive motion is enunciated as a foundation to derive the privileged impulse-momentum equations. It is shown that for a system with no applied impulse, a conservation law can be stated as the conservation of the virtual-privileged momenta. The proposed methodology provides a systematic scheme to deal with various types of impulsive constraints, which is illustrated in the paper by solving the constrained impulsive problems for the motion of a sleigh.

scholarly journals Observer-based robust integral of the sign of the error control of class I of underactuated mechanical systems: Theory and real-time experiments

2021 ◽  
pp. 014233122110313
Author(s):  
Afef Hfaiedh ◽  
Ahmed Chemori ◽  
Afef Abdelkrim
Keyword(s):  
Real Time ◽  
Error Control ◽  
Degrees Of Freedom ◽  
Sliding Mode ◽  
Mechanical Systems ◽  
Class I ◽  
Control Input ◽  
Underactuated Mechanical Systems ◽  
Control Scheme ◽  
And Performance

In this paper, the control problem of a class I of underactuated mechanical systems (UMSs) is addressed. The considered class includes nonlinear UMSs with two degrees of freedom and one control input. Firstly, we propose the design of a robust integral of the sign of the error (RISE) control law, adequate for this special class. Based on a change of coordinates, the dynamics is transformed into a strict-feedback (SF) form. A Lyapunov-based technique is then employed to prove the asymptotic stability of the resulting closed-loop system. Numerical simulation results show the robustness and performance of the original RISE toward parametric uncertainties and disturbance rejection. A comparative study with a conventional sliding mode control reveals a significant robustness improvement with the proposed original RISE controller. However, in real-time experiments, the amplification of the measurement noise is a major problem. It has an impact on the behaviour of the motor and reduces the performance of the system. To deal with this issue, we propose to estimate the velocity using the robust Levant differentiator instead of the numerical derivative. Real-time experiments were performed on the testbed of the inertia wheel inverted pendulum to demonstrate the relevance of the proposed observer-based RISE control scheme. The obtained real-time experimental results and the obtained evaluation indices show clearly a better performance of the proposed observer-based RISE approach compared to the sliding mode and the original RISE controllers.

Coordination of Movements of Two-Handed 12-DOF Robot Manipulators at Their Joint Manipulation

2021 ◽  
pp. 11-18
Author(s):  
L.A. Karginov ◽  
E.I. Vorobyov ◽  
A.K. Kovalchuk
Keyword(s):  
Inverse Problem ◽  
Initial Data ◽  
Degrees Of Freedom ◽  
Control Flow ◽  
Flow Chart ◽  
Hierarchical Approach ◽  
Kinematic Scheme ◽  
Kinematic Constraints ◽  
Generalized Coordinates ◽  
Research Show

The study focuses on a two-handed robot with twelve degrees of freedom, six for each arm, and gives an example of calculating generalized coordinates for the two-armed robot limbs at their joint manipulation. The initial data for obtaining generalized coordinates are represented by the location of the work object, which is a cube. When solving the problem, the last arm links reach the faces of the work object with a given orientation. To obtain generalized coordinates, we used a hierarchical approach, which is based on an algorithm for solving the inverse problem of kinematics, and developed a control flow chart. The values ??of generalized robot coordinates were obtained for each location of the object of work, taking into account the kinematic constraints in the joints of the robot actuator. Findings of research show that it is possible to obtain generalized coordinates for the coordinated movement of the robot actuators with tree-like kinematic scheme.

Simulation of Planar Dynamic Mechanical Systems With Changing Topologies: Part I — Characterization and Prediction of the Kinematic Constraint Changes

1987 ◽  
Author(s):  
B. J. Gilmore ◽  
R. J. Cipra
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Rigid Bodies ◽  
State Variables ◽  
Kinematic Constraint ◽  
Kinematic Constraints ◽  
Force Closure ◽  
Simulation Strategy ◽  
Reaction Forces ◽  
Discontinuous Equations

Abstract Due to changes in the kinematic constraints, many mechanical systems are described by discontinuous equations of motion. This paper addresses those changes in the kinematic constraints which are caused by planar bodies contacting and separating. A strategy to automatically predict and detect the kinematic constraint changes, which are functions of the system dynamics, is presented in Part I. The strategy employs the concepts of point to line contact kinematic constraints, force closure, and ray firing together with the information provided by the rigid bodies’ boundary descriptions, state variables, and reaction forces to characterize the kinematic constraint changes. Since the strategy automatically predicts and detects constraint changes, it is capable of simulating mechanical systems with unpredictable or unforeseen changes in topology. Part II presents the implementation of the characterizations into a simulation strategy and presents examples.

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