A Riemannian-Geometry Approach for Modeling and Control of Dynamics of Object Manipulation under Constraints

A Riemannian-geometry approach for modeling and control of dynamics of object manipulation under holonomic or non-holonomic constraints is presented. First, position/force hybrid control of an endeffector of a multijoint redundant (or nonredundant) robot under a holonomic constraint is reinterpreted in terms of “submersion” in Riemannian geometry. A force control signal constructed in the image space of the constraint gradient is regarded as a lifting (or pressing) in the direction orthogonal to the kernel space. By means of the Riemannian distance on the constraint submanifold, stability of position control under holonomic constraints is discussed. Second, modeling and control of two-dimensional object grasping by a pair of multijoint robot fingers are challenged, when the object is of arbitrary shape. It is shown that rolling contact constraints induce the Euler equation of motion, in which constraint forces appear as wrench vectors affecting the object. The Riemannian metric is introduced on a constraint submanifold characterized with arclength parameters. An explicit form of the quotient dynamics is expressed in the kernel space with accompaniment of a pair of first-order differential equations concerning the arclength parameters. An extension of Dirichlet-Lagrange's stability theorem to redundant systems under constraints is suggested by introducing a Morse-Lyapunov function.

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Lagrangian D’Alembert Modeled Maneuverable Autonomous Non-Holonomic Mobile Robot Using a Closed Loop PD Controller

Volume 3: ASME/IEEE 2009 International Conference on Mechatronic and Embedded Systems and Applications; 20th Reliability, Stress Analysis, and Failure Prevention Conference ◽

10.1115/detc2009-86969 ◽

2009 ◽

Author(s):

E. Georgiou ◽

J. Dai

Keyword(s):

Mobile Robot ◽

Closed Loop ◽

Ad Hoc ◽

Search And Rescue ◽

Pd Controller ◽

Modeling And Control ◽

Holonomic Constraints ◽

And Control ◽

Holonomic Mobile Robot ◽

Initial Results

The motivation for this work is to develop a platform for a self-localization device. Such a platform has many applications for the autonomous maneuverable non-holonomic mobile robot classification, which can be used for search and rescue or for inspection devices where the robot has a desired path to follow but because of an unknown terrain, the device requires the ability to make ad-hoc corrections to its movement to reach its desire path. The mobile robot is modeled using Lagrangian d’Alembert’s principle considering all the possible inertias and forces generated, and are controlled by restraining movement based on the holonomic and non-holonomic constraints of the modeled vehicle. The device is controlled by a PD controller based on the vehicle’s holonomic and non-holonomic constraints. An experiment was setup to verify the modeling and control structure’s functionality and the initial results are promising.

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Modeling and Control for 2-D Grasping of an Object with Arbitrary Shape under Rolling Contact

IFAC Proceedings Volumes ◽

10.3182/20090909-4-jp-2010.00066 ◽

2009 ◽

Vol 42 (16) ◽

pp. 383-388 ◽

Cited By ~ 1

Author(s):

S. Arimoto ◽

M. Yoshida ◽

M. Sekimoto ◽

K. Tahara ◽

J.-H. Bae

Keyword(s):

Arbitrary Shape ◽

Rolling Contact ◽

Modeling And Control ◽

And Control

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Kane Method Based Dynamics Modeling and Control Study for Space Manipulator Capturing a Space Target

International Journal of Aerospace Engineering ◽

10.1155/2016/7375685 ◽

2016 ◽

Vol 2016 ◽

pp. 1-13 ◽

Cited By ~ 2

Author(s):

Yanhua Han

Keyword(s):

Attitude Control ◽

Dynamics Modeling ◽

Attitude Control System ◽

Constraint Forces ◽

Inertia Moment ◽

Modeling And Control ◽

And Control ◽

Kane Method ◽

Control Study ◽

Space Target

Dynamics modeling and control problem of a two-link manipulator mounted on a spacecraft (so-called carrier) freely flying around a space target on earth’s circular orbit is studied in the paper. The influence of the carrier’s relative movement on its manipulator is considered in dynamics modeling; nevertheless, that of the manipulator on its carrier is neglected with the assumption that the mass and inertia moment of the manipulator is far less than that of the carrier. Meanwhile, we suppose that the attitude control system of the carrier guarantees its side on which the manipulator is mounted points accurately always the space target during approaching operation. The ideal constraint forces can be out of consideration in dynamics modeling as Kane method is used. The path functions of the manipulator’s end-effector approaching the space target as well as the manipulator’s joints control torque functions are programmed to meet the soft touch requirement that the end-effector’s relative velocity to the space target is zero at touch moment. Numerical simulation validation is conducted finally.

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Modeling and Control of Multi-Body Mechanical Systems: Part I A Riemannian Geometry Approach

Advances in the Theory of Control, Signals and Systems with Physical Modeling - Lecture Notes in Control and Information Sciences ◽

10.1007/978-3-642-16135-3_1 ◽

2010 ◽

pp. 3-16 ◽

Cited By ~ 1

Author(s):

Suguru Arimoto

Keyword(s):

Riemannian Geometry ◽

Mechanical Systems ◽

Modeling And Control ◽

Multi Body ◽

And Control

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Modeling and Control of a Novel Variable-Stiffness Regenerative Actuator

Volume 2: Control and Optimization of Connected and Automated Ground Vehicles; Dynamic Systems and Control Education; Dynamics and Control of Renewable Energy Systems; Energy Harvesting; Energy Systems; Estimation and Identification; Intelligent Transportation and Vehicles; Manufacturing; Mechatronics; Modeling and Control of IC Engines and Aftertreatment Systems; Modeling and Control of IC Engines and Powertrain Systems; Modeling and Management of Power Systems ◽

10.1115/dscc2018-9054 ◽

2018 ◽

Cited By ~ 3

Author(s):

Erivelton Gualter dos Santos ◽

Hanz Richter

Keyword(s):

Position Control ◽

Lightweight Design ◽

Variable Stiffness ◽

Electrical Energy ◽

Flexible Beam ◽

Modeling And Control ◽

Electromechanical Drive ◽

Elastic Potential Energy ◽

Mechanical Dynamics ◽

And Control

This paper focuses on the design, modeling and basic control of a variable stiffness actuator to be used in combination with a regenerative electromechanical drive system. Due to the use of a flexible beam, the actuator has the ability to store and return elastic potential energy. Also, an ultracapacitor is used in the electromechanical drive, which allows electrical energy storage and return. Moreover, elastic and electrostatic energies can be exchanged, resulting in a highly efficient and lightweight design which will be beneficial for robotic prostheses, exoskeletons and other orthotic devices. The paper presents a model and calculation method for large beam deflections and the integrated electromechanical actuator model. A semiactive virtual control strategy is used to decouple the mechanical dynamics from the charge dynamics and achieve position control of the actuator. Simulation results are presented to illustrate the control system and the energy exchange features.

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Modeling and Control of a Novel High-Pressure Pneumatic Servo Valve Direct-Driven by Voice Coil Motor

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4007702 ◽

2012 ◽

Vol 135 (1) ◽

Cited By ~ 7

Author(s):

Li Baoren ◽

Gao Longlong ◽

Yang Gang

Keyword(s):

High Pressure ◽

Pid Controller ◽

Gas Flow ◽

Position Control ◽

Hybrid Control ◽

Voice Coil Motor ◽

Direct Drive ◽

Modeling And Control ◽

Servo Valve ◽

Control Scheme

High-pressure pneumatic control valves have been widely investigated during last decades. The published literature includes experimental and analytical studies on both constant value on–off valve and pressure reducing valve, but rarely on servo valve. In this paper, a novel voice coil motor (VCM) direct drive high-pressure pneumatic servo valve (HPPSV) is proposed. The mathematical model of the HPPSV including electromechanical and fluid subsystem is presented. Furthermore, the hybrid control scheme consisting of a proportional integral differential (PID) controller with velocity/acceleration feed-forward and a disturbance observer is proposed to improve the control performance of the HPPSV, taking into account the factors such as compressibility of high-pressure gas, high nonlinearity of gas flow force and friction force. The experimental results show that the spool position control system based on the proposed control scheme has strong robustness and disturbance rejection capability, and the control accuracy of the valve spool position can be enhanced greatly compared with the conventional PID controller. The study has general implications in the development of high-pressure pneumatic servo valves and high-pressure pneumatic precision control field.

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Modeling and Control of Manufacturing Processes: Getting More Involved

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2899069 ◽

1993 ◽

Vol 115 (2B) ◽

pp. 291-300 ◽

Cited By ~ 21

Author(s):

David E. Hardt

Keyword(s):

Position Control ◽

Transformation Process ◽

Actual Process ◽

Modeling And Control ◽

Control Techniques ◽

Specific Geometry ◽

Process Output ◽

Internal Properties ◽

And Control

The discipline of control has had numerous yet sporadic contacts with the manufacturing world over the past few decades, almost always as an afterthought or addendum, and typically in the role of machine and not as process control. Much of this detachment comes from an absence of control techniques that can deal directly with the actual manufacturing process, i.e., a material transformation process that produces a desired object both in terms of specific geometry and internal properties. Instead, most efforts have focused on using existing methods on process independent problems, such as position control and trajectory following, or on straightforward process parameter control, thereby only indirectly influencing the actual process output. This paper presents the reasons behind and the means to eliminate this estrangement, using the author’s own research as an example of a more direct approach to process modeling and control.

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Modeling and control of planar slippage in object manipulation using robotic soft fingers

ROBOMECH Journal ◽

10.1186/s40648-019-0143-0 ◽

2019 ◽

Vol 6 (1) ◽

Author(s):

Amin Fakhari ◽

Imin Kao ◽

Mehdi Keshmiri

Keyword(s):

Dynamic Modeling ◽

Surface Friction ◽

Object Manipulation ◽

Limit Surface ◽

Modeling And Control ◽

Grasping And Manipulation ◽

And Control ◽

Planar Contact ◽

Soft Finger ◽

Friction Limit Surface

Abstract Slippage occurrence has an important roll in stable and robust object grasping and manipulation. However, in majority of prior research on soft finger manipulation, presence of the slippage between fingers and objects has been ignored. In this paper which is a continuation of our prior work, a revised and more general method for dynamic modeling of planar slippage is presented using the concept of friction limit surface. Friction limit surface is utilized to relate contact sliding motions to contact frictional force and moment in a planar contact. In this method, different states of planar contact are replaced with a second-order differential equation. As an example of the proposed method application, dynamic modeling and slippage analysis of object manipulation on a horizontal plane using a three-link soft finger is studied. Then, a controller is designed to reduce and remove the undesired slippage which occurs between the soft finger and object and simultaneously move the object on a predefined desired path. Numerical simulations reveal the acceptable performance of the proposed method and the designed controller.

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