Dynamics and simulation of compliant motion of a manipulator

Sba: Controle & Automação Sociedade Brasileira de Automatica, 2011

Este artigo considera o problema de controle de postura para sistemas robóticos com restrições cinemáticas. A ideia principal é considerar as restrições cinemáticas dos mecanismos a partir de suas equações estruturais, ao invés de usar explicitamente a equação de restrição. Um estudo de caso para robôs paralelos e robôs cooperativos é discutido baseado nos conceitos de cinemática direta, cinemática diferencial, singularidades e controle cinemático. Resultados de simulação, obtidos a partir de um mecanismo F our-Bar linkage, uma plataforma de Gough-Stewart planar e dois robôs cooperativos, ilustram a aplicabilidade e versatilidade da metodologia proposta.

A systematic approach for designing analytical dynamics and servo control of constrained mechanical systems is proposed. Fundamental equation of constrained mechanical systems is first obtained according to Udwadia-Kalaba approach which is applicable to holonomic and nonholonomic constrained systems no matter whether they satisfy the D'Alember's principle. The performance specifications are modeled as servo constraints. Constraint-following servo control is used to realize the servo constraints. For this inverse dynamics control problem, the determination of control inputs is based on the Moore-Penrose generalized inverse to complete the specified motion. Second-order constraints are used in the dynamics and servo control. Constraint violation suppression methods can be adopted to eliminate constraint drift in the numerical simulation. Furthermore, this proposed approach is applicable to not only fully actuated but also underactuated and redundantly actuated mechanical systems. Two-mass spring system and coordinated robot system are presented as examples for illustration. Citation: Xiaoli Liu, Shengchao Zhen, Kang Huang, Han Zhao, Ye-Hwa Chen, Ke Shao. A systematic approach for designing analytical dynamics and servo control of constrained mechanical systems. IEEE/CAA Journal of Automatica Sinica, 2015, 2(4): 382-393

A framework for the analysis and control of manipulator systems with respect to the dynamic behavior of their end-effectors is developed. First, issues related to the description of end-effector tasks that involve constrained motion and active force control are discussed. The fundamentals of the operational space formulation are then presented, and the unified approach for motion and force control is developed. The extension of this formulation to redundant manipulator systems is also presented, constructing the end-effector equations of motion and describing their behavior with respect to joint forces. These results are used in the development of a new and systematic approach for dealing with the problems arising at kinematic singularities. At a singular configuration, the manipulator is treated as a mechanism that is redundant with respect to the motion of the end-effector in the subspace of operational space orthogonal to the singular direction.

Journal of The Franklin Institute-engineering and Applied Mathematics, 1986

A geometrical setting for the Newtonian mechanics of mechanical manipulators is presented. The configuration space of the mechanical system is modelled by a differentiable manifold. The kinematics of the system is formulated on the tangent and double tangent bundles of the corifiguration space, and forces are defined as elements of the cotangent bundle. The dynamical properties of the system are introduced by specifying a Riemannian metric on the configuration space. The metric is used in order to generate the generalized momenta and the kinetic energy from the generalized velocities, and the connection it induces makes it possible to formulate a generalization of Newton's second law relating generalized forces and generalized accelerations.

Mechanics Research Communications, 2006

In this paper modified first-order decoupled equations of motion for rigid serial manipulators are presented. Motivated the results obtained by On first-order decoupling of equations of motion for constrained dynamical systems. Transactions of the ASME Journal of Applied Mechanics 62, 216.] slightly different inertial quasi-velocities are proposed. Instead of generalized velocity components (GVC) one useful form of GVCÕs is introduced here. It is shown that the modified quantities (called here modified inertial generalized velocity components-MIGVC) lead to some interesting properties which give different look at manipulator dynamics. Some properties arising from MIGVC are also discussed. An example of 3 d.o.f. 3-D robot DDArm illustrates the results.

Multibody System Dynamics, 2009

In the present work, a new energy-momentum conserving time-stepping scheme for multibody systems comprising screw joints is developed. In particular, it is shown that the underlying rotationless formulation of multibody dynamics along with a specific coordinate augmentation technique makes possible the energy-momentum discretization of the screw pair. In addition to that, control (or servo) constraints are treated within the rotationless framework of multibody dynamics. The control constraints are used to partially prescribe the motion of a multibody system. In particular, control constraints, in conjunction with the coordinate augmentation technique, make possible to solve inverse dynamics problems by applying the present simulation approach.

2022

The paper presents a development of an automated computational procedure for constrained dynamics (CoPCoD) dedicated to derivation of dynamical models of mechanical systems, e.g. manipulators both ground and space or mobile robotic systems, which can be composed of rigid and flexible links. They may be subjected to constraints, which are referred to as programmed, may come from performance requirements, e.g. work or services a system is dedicated to. The CoPCoD structure offers systematic modeling of either open or closed loop constrained structures and results in computationally efficient numerical dynamical equations derivation. The CoPCoD development has its background in the generalized programmed motion equations (GPME) algorithm developed successfully for rigid models of mechanical systems subjected to high order nonholonomic constraints, however, the GPME was not fully automated for computer equation derivations. The two main motivations that underlie the CoPCoD development a...

Mechanism and Machine Theory, 1996

Al~tract-This paper deals with the symbolic modeling of manipulators with flexible links. First, we recall the generalization of the Newton Euler equations for an open chain of flexible links. These equations are obtained by applying the D'Alembert's principle to each isolated free body of the chain with Eulerian rigid velocities and Lagrangian elastic ones. This formalism allows us to find the intrinsic dynamic model of links. Second, we force the individual virtual fields to verify the joint equations. For that, we proceed to a recursive symbolic computation of partial velocities and accelerations. Next, a matricial assembling of the dynamics of free bodies allows us to establish the minimal set of symbolic dynamic equations of an open chain.