Pham Thuc Anh Nguyen

Dynamics and control of a set of dual fingers with soft tips

This paper attempts firstly to derive a mathematical model of the dynamics of a set of dual fingers with soft and deformable tips which grasps and manipulates a rigid object with some dexterity. To gain a physical insight into the problem, consideration is restricted to the case that the motion of the whole system is confined to a horizontal plane. Secondly on the basis of the derived model it is shown that the rotation of the object can be indirectly controlled by the change of positions of the center points of both contact areas on the object. Then, each of the center points of contact areas can be positioned by inclining the last link of each corresponding finger against the object. It is further shown that, when both forces of pressing the object becomes almost equal, the equation of motion of the object in terms of rotational angles assumes the form of a harmonic oscillator with a forcing term, which can be regulated coordinately by the relative angle between the two last links contacting with the object. It is also shown that dynamics of this system satisfy passivity. Finally, design problems of control for dynamic stable grasping and enhancing dexterity in manipulating things are discussed on the basis of passivity analysis.

Principles of superposition for controlling pinch motions by means of robot fingers with soft tips

This paper analyzes the dynamics and control of pinch motions generated by a pair of two multi-degrees-of-freedom robot fingers with soft and deformable tips pinching a rigid object. It is shown firstly that passivity analysis leads to an effective design of a feedback control signal that realizes dynamic stable pinching (grasping), even if extra terms of Lagranges multipliers arise from holonomic constraints of tight area-contacts between soft finger-tips and surfaces of the rigid object and exert torques and forces on the dynamics. It is shown secondly that a principle of superposition is applicable to the design of additional feedback signals for controlling both the posture (rotational angle) and position (some of task coordinates of the mass center) of the object provided that the number of degrees of freedom of each finger is specified for satisfying a condition of stationary resolution of controlled position state variables. The details of feedback signals are presented in the case of a special setup consisting of two robot fingers with two degrees of freedom.

Stable pinching by a pair of robot fingers with soft tips under the effect of gravity

This paper analyses lumped-parameter dynamics of a pair of robot fingers with soft and deformable tips pinching a rigid object under the effect of a gravity force. The dynamics of the system in which area contacts between the finger-tips and the surfaces of the object arise are compared with those of a pair of rigid robot fingers with rigid contacts with an object, with or without effect of the gravity. It is then shown that there exists a sensory feedback from measurement of finger joint angles and the rotational angle of the object to command inputs to joint actuators, and this feedback connection from sensing to action realizes secure grasping of the object in a dynamic sense and regulation of the object posture. It is further shown that there are various types of other feedback connections from sensing to action, which can be used in combination of feedback signals for stable grasping and posture control of the object for realizing sophisticated object manipulation.

Robotic pinching by means of a pair of soft fingers with sensory feedback

This paper proposes a pair of single or multi-DOF robot fingers with soft and deformable tips that can pinch an object stably in a dynamic sense with the aid of real-time sensory feedback. To realize dynamic stable pinching, a practical method of using optical devices is proposed for measuring both the maximum displacement of finger-tip deformation and the relative angle between the object surface and each of finger links. It is shown that the overall closed-loop system of a pair of two single-DOF fingers with soft tips with real-time sensory feedback of the difference between the centers of two area-contacts at both sides of the object becomes asymptotically stable. This means that the pair achieves dynamic stable grasping (pinching). In the case of a pair of 1-DOF and 2-DOF fingers with soft tips, it is shown that the proposed method of closed-loop feedback of the difference between the centers of two area-contacts and the rotational angle of the object can establish not only dynamic stable grasping but also regulation of the posture of the object.

Performance of pinching motions of two multi-DOF robotic fingers with soft-tips

This paper shows the performance of dynamic motion of dual multi-degree of freedom fingers with soft tips in fine manipulation of an object via computer simulation. A mathematical model of its dynamics is described as a system of ordinary differential equations expressing motions of the fingers-object setup together with algebraic constraints due to tight area contacts between the finger tips and surfaces of the object. A constraint stabilization method is used for solving numerically the differential algebraic system, and a design principle of superposition of feedback control signals is applied for controlling the pinching motion of the dual multi-degree of freedom fingers with soft tips. Furthermore, problems of dynamic stable grasping, controlling object rotational angle and regulating position of the mass center of the object, are considered simultaneously and their performances in a coordinated fine motion are illustrated by simulation results.

Dexterous manipulation of an object by means of multi-DOF robotic fingers with soft tips

This article analyzes the dynamics of motion of various setups of two multiple degree-of-freedom (DOF) fingers that have soft tips, in fine manipulation of an object, and shows performances of their motions via computer simulation. A mathematical model of these dynamics is described as a system of nonlinear differential equations expressing motion of the overall fingers-object system together with algebraic constraints due to tight area contacts between the finger-tips and surfaces of the object. First, problems of (1) dynamic, stable grasping and (2) regulation of the object rotational angle by means of a setup of dual two-DOF fingers, are treated. Second, the problem of regulating the position of the object mass center by means of a pair of two-DOF and three-DOF fingers is considered. Third, a set of dual three-DOF fingers is treated, in order to let it perform a sophisticated task, which is specified by a periodic pattern of the object posture and a constant internal force. In any case, there exist sensory-motor coordinations, which are described by analytic feedback connections from sensing to actions at finger joints. In the cases of setpoint control problems, convergences of motion to secure grasping together with the specified object rotational angle and/or the specified object mass center position, are proved theoretically. A constraint stabilization method (CSM) is used for solving numerically the differential algebraic equations to show performances of the proposed sensory-feedback schemes.

Manipulation of a circular object without object information

This paper proposes a manipulation of a circular object in a horizontal plane by a pair of finger robots. This method guarantees the dynamic stability of the system and does not require any object models and object sensing to manipulate the object. It is assumed that there is no friction between the object and the horizontal plane and it is possible to be adequately large friction between the fingertips and the object. We examine the condition of stable grasping of a circular object and propose controllers for stable grasping and for controlling its approximate relative orientation angle without object sensing. The experimental results show the validity of the controller.

Computer simulation of controlled motion of dual fingers with soft tips grasping and manipulating an object

In the previous paper, the dynamics of a set of dual multi-joint fingers with soft, deformable tips grasping and manipulating a rigid object were formulated by a system of nonlinear differential equations of Euler-Lagranges formalism. Although geometric constraints of tight area contacts have been pointed out, they were neglected purposely in motion equations of the system in order to avoid increasing complication arising in design of control laws and in the analysis of the stability of the dynamics. On the basis of passivity, sensory feedback control schemes for stably grasping an object by a set of dual soft-tip fingers and regulating the objects posture have been explored and a proof for asymptotic convergences of controlled variables has been presented by theoretical analysis without showing any simulation result. In this paper, first, we carry out a numerical simulation based on the thorough dynamics of the overall system and, secondly, find the important role of constraint forces arising from tight area contacts between soft finger-tips and the object. The paper shows that ignorance of these constraints does not yield any faithful motion of the system even in an approximate sense, although the terms do not induce any work and are irrelevant to the passivity. In fact, in simulation, it causes increased instabilities of state variables and it should be concluded that they cannot be neglected in the dynamics. Thirdly, motions of the object–fingers system under geometric constraints of tight area contacts have been expressed by a set of mixed nonlinear differential and algebraic equations. Then, the overall system dynamics for simulation in which the constraint conditions are taken into account are developed by using the idea of a constraints stabilization method. Computer simulation results have confirmed the effectiveness of the proposed control laws. In particular, it is verified that the constraint forces appearing in the directions tangential to the object surfaces converge to zero quickly as stable grasping is realized. Finally, a stick graph of simulated motion is presented to illustrate a process of grasping and manipulating a rigid object by soft fingers.

Iterative learning of impedance control

This paper proposes an iterative learning control scheme for impedance control of robotic tasks when the tool endpoint covered by soft and deformable material presses a rigid object or environment at a prescribed periodic force pattern. To this end, an iterative learning control scheme for a class of linear dynamical systems with a negative feedback structure is analyzed and convergence of the proposed learning update law after a sufficient number of repetitions is proved. It is shown that this convergence realizes impedance matching in a sense of electric circuit theory of the feedback system can be expressed as a lumped-parameter electric circuit. The iterative learning control scheme is then applied for a case of impedance control of robotic tasks when the characteristics of reproducing force of the deformable material is nonlinear in its displacement and unknown and the tool mass is uncertain. Simulation results are also presented, which show effectiveness of the proposed learning control scheme.

Learning of robot tasks on the basis of passivity and impedance concepts

Abstract This paper aims at explaining why a simple iterative learning scheme for complicated robot dynamics with strong nonlinearities works well in acquiring any prescribed desired motion over a finite time interval or any desired periodic motion. It is firstly shown that passivity or dissipativity as an input–output property of a given system plays a key role in the capability of learning iteratively a desired motion through repeated practices. It is then shown in the simplest case when the tool endpoint is free to move that a simple iterative scheme of learning enables robots to make a progressive advance in a sense of zero-impedance matching at every trial of operation. In case of impedance control when a soft and deformable finger-tip presses a rigid object or environment, it is shown that, for a given desired periodic force of physical interaction between the soft finger tip and the rigid object, the robot learns steadily the desired periodic tasks.