Control and Virtual Reality Simulation of Tendon Driven Mechanisms

In this paper the authors present a control strategy for tendon driven mechanisms. The aim of the control system is to find the correct torques which the motors have to exert to make the end effector describe a specific trajectory. In robotic assemblies this problem is often solved with closed loop algorithm, but here a simpler method, based on a open loop strategy, is developed. The difficulties in the actuation are in keeping the belt tight during all working conditions. So an innovative solution of this problem is presented here. This methodology can be easily applied in real time monitoring or very fast operations. For this reason several virtual reality simulations, developed using codes written in Virtual Reality Markup Language, are also presented. This approach is very efficient because it requires a very low cpu computation time, small size files, and the manipulator can be easily put into different simulated scenarios.     

Peer to peer trade in HTM5 meta model for agent oriented cloud robotic systems

Cloud computing is a methodology and not a technology. Adaptation of cloud computing services for robotic applications is relatively straightforward while adaptation of underlying ideas will require a new design attitude. Cloud computing is a cost-effective and dynamic business model. Currently cloud robotics is understood as a client server methodology which enables robots utilize resources and services placed at centralized servers. These cloud servers treat robots as any other client computer offering them platform, infrastructure, process or algorithm as a service. HTM5 is an OMG MDA based multi-view meta-model for agent oriented development of cloud robotic systems. HTM5 encourages design of peer-to-peer service ecosystems based on an open registry and matchmaking mechanism. In peer-to-peer cloud robotics, a robot can trade its hardware, software and functional resources as a service to other robots in the ecosystem. The peer-to-peer trade in such systems may be driven by contracts and relationships between its member agents. This article discusses trade-view model of HTM5 methodology and its use in developing a cloud robotic ecosystem that implements peer-to-peer, contract based economy. The article also presents a case study with experiments that implement distributed artificial intelligence and peer-to-peer service oriented trade on simulated and real robot colonies.     

A decomposition approach for the kinematic synthesis of tendon‐driven manipulators

This article describes a decomposition methodology for the kinematic synthesis of tendon‐driven manipulators (TDMs). Based on the QR factorization, the complex transformation between vectors in the tendon‐space and the joint‐space of an n‐DOF TDM with n+1 tendons is decomposed as a two‐step transformation. An orientation matrix is used to characterize the vector transformation between the (n+1)‐dimensional tendon‐space and the n‐dimensional intermediate equivalent tendon‐space. An equivalent structure matrix is also introduced for the vector transformation between the n‐dimensional equivalent tendon‐space and n‐dimensional joint‐space. Design equations for synthesizing a TDM to possess kinematic isotropic transmission characteristics with proper tendon routing and pulley sizes are derived. ©1999 John Wiley & Sons, Inc.     

A cohesive modeling technique for theoretical and experimental estimation of damping in serial robots with rigid and flexible links

Dynamic model incorporating damping characteristics, namely joint damping and structural damping in flexible links, of the serial robots with rigid and flexible links is presented. A novel procedure, based on the unified approach of theoretical formulation and analysis of experimental data, is proposed for the estimation of damping coefficients. First, the dynamic model of a robotic system with rigid and flexible links is presented. Next, the modifications in the dynamic model due to the considerations of damping characteristics of joints and structural damping characteristics of the flexible links are presented. A systematic methodology based on analysis of data obtained from experiments is presented for estimation and determination of damping coefficients of rigid-flexible links. The determination of joint damping coefficients, is based on the logarithmic decay of the amplitude of the oscillations of robotic links, while the structural damping coefficients are estimated mainly using the modal analysis and the method of evolving spectra. The method of evolving spectra, based on the Fast Fourier Transform of the decay of the amplitude in structural vibrations of the robot links in progressive windows is used to estimate the structural damping ratios while the critical structural coefficients are determined using the modal analysis. The methodology is illustrated through a series of simple experiments on simple robotic systems. The experimental results are then compared with the simulation results incorporating the damping coefficients determined using the proposed procedure. The comparisons leads to the validation of the proposed dynamic modeling technique, modeling of the damping characteristics, and the method proposed for estimation of damping coefficients for rigid-flexible link robotic systems.     

Simulation‐based actuator selection for redundantly actuated robot mechanisms

This article presents a simulation‐based strategy for sizing the actuators of a redundantly actuated robotic mechanism. The class of robotic mechanisms we consider may contain one or more closed loops and possess an arbitrary number of active and passive joints, and the number of actuators may exceed the mechanism's kinematic degrees of freedom. Our approach relies on a series of dynamic simulations of the mechanism, by applying Taguchi's method to systematically perform the simulations. To efficiently perform each of the dynamic simulations, we develop, using tools from modern screw theory, new recursive algorithms for the forward and inverse dynamics of the class of redundantly actuated mechanisms described. © 2002 Wiley Periodicals, Inc.     

A systematic method for the hybrid dynamic modeling of open kinematic chains confined in a closed environment

This work presents a systematic method for the dynamic modeling of multi-rigid links confined within a closed environment. The behavior of the system can be completely characterized by two different mathematical models: a set of highly coupled differential equations for modeling the confined multi-link system when it has no impact with surrounding walls; and a set of algebraic equations for expressing the collision of this open kinematic chain system with the confining surfaces. In order to avoid the Lagrangian formulation (which uses an excessive number of total and partial derivatives in deriving the governing equations of multi-rigid links), the motion equations of such a complex system are obtained according to the recursive Gibbs–Appell formulation. The main feature of this paper is the recursive approach, which is used to automatically derive the governing equations of motion. Moreover, in deriving the motion equations, the manipulators are not limited to planar motions only. In fact, for systematic modeling of the motion of a multi-rigid-link system in 3D space, two imaginary links are added to the \(n\)-real links of a manipulator in order to model the spatial rotations of the system. Finally, a 2D and a 3D case studies are simulated to demonstrate the effectiveness of the proposed approach.     

Kinematics of grasping and manipulation of a B‐spline surface object by a multifingered robot hand

Kinematics of grasping and manipulation by a multifingered robotic hand where multifinger surfaces are in contact with an object is solved. The surface of the object was represented by B‐spline surfaces to model objects of various shapes. The fingers were modeled by cylindrical links and a half ellipsoid fingertip. Geometric contact equations have been solved for all possible contact combinations between the finger surface and the object. The simulation system calculated joint displacements and contact locations for a given trajectory of the object. Since there are no closed form solutions for contact or intersection between these surfaces, kinematics of grasping was solved by recursive numerical calculation. The initial estimate of the contact point was obtained by approximating the B‐spline surface by a polyhedron. As for the simulation of manipulation, exact contact locations were updated by solving the contact equations according to the given contact conditions such as pure rolling, twist‐rolling, or slide‐twist‐rolling. Several examples of simulation of grasping and manipulation are presented. ©1999 John Wiley & Sons, Inc.     

Symbolic modeling and dynamic simulation of robotic manipulators with compliant links and joints

The explicit, non-recursive symbolic form of the dynamic model of robotic manipulators with compliant links and joints are developed based on a Lagrangian-assumed mode of formulation. This form of dynamic model is suitable for controller synthesis, as well as accurate simulations of robotic applications. The final form of the equations is organized in a form similar to rigid manipulator equations. This allows one to identify the differences between rigid and flexible manipulator dynamics explixitly. Therefore, current knowledge on control of rigid manipulators is likely to be utilized in a maximum way in developing new control algorithms for flexible manipulators.

Computer automated symbolic expansion of the dynamic model equations for any desired manipulator is accomplished with programs written based on commercial symbolic manipulation programs (SMP, MACSYMA, REDUCE). A two-link manipulator is used as an example. Computational complexity involved in real-time control, using the explicit, non-recursive form of equations, is studied on single CPU and multi-CPU parallel computation processors.     

A recursive, numerically stable, and efficient simulation algorithm for serial robots with flexible links

A methodology for the formulation of dynamic equations of motion of a serial flexible-link manipulator using the decoupled natural orthogonal complement (DeNOC) matrices, introduced elsewhere for rigid bodies, is presented in this paper. First, the Euler Lagrange (EL) equations of motion of the system are written. Then using the equivalence of EL and Newton–Euler (NE) equations, and the DeNOC matrices associated with the velocity constraints of the connecting bodies, the analytical and recursive expressions for the matrices and vectors appearing in the independent dynamic equations of motion are obtained. The analytical expressions allow one to obtain a recursive forward dynamics algorithm not only for rigid body manipulators, as reported earlier, but also for the flexible body manipulators. The proposed simulation algorithm for the flexible link robots is shown to be computationally more efficient and numerically more stable than other algorithms present in the literature. Simulations, using the proposed algorithm, for a two link arm with each link flexible and a Space Shuttle Remote Manipulator System (SSRMS) are presented. Numerical stability aspects of the algorithms are investigated using various criteria, namely, the zero eigenvalue phenomenon, energy drift method, etc. Numerical example of a SSRMS is taken up to show the efficiency and stability of the proposed algorithm. Physical interpretations of many terms associated with dynamic equations of flexible links, namely, the mass matrix of a composite flexible body, inertia wrench of a flexible link, etc. are also presented. The work has been carried out in the Dept. of Mechanical Engineering, Indian Institute of Technology Delhi, New Delhi 110016, India.     

An improved dynamic modeling of a multibody system with spherical joints

A dynamic modeling of multibody systems having spherical joints is reported in this work. In general, three intersecting orthogonal revolute joints are substituted for a spherical joint with vanishing lengths of intermediate links between the revolute joints. This procedure increases sizes of associated matrices in the equations of motion, thus increasing computational burden of an algorithm used for dynamic simulation and control. In the proposed methodology, Euler parameters, which are typically used for representation of a rigid-body orientation in three-dimensional Cartesian space, are employed to represent the orientation of a spherical joint that connects a link to its previous one providing three-degree-of-freedom motion capability. For the dynamic modeling, the concept of the Decoupled Natural Orthogonal Complement (DeNOC) matrices is utilized. It is shown in this work that the representation of spherical joints motion using Euler parameters avoids the unnecessary introduction of the intermediate links, thereby no increase in the sizes of the associated matrices with the dynamic equations of motion. To confirm the efficiency of the proposed representation, it is illustrated with the dynamic modeling of a spatial four-bar Revolute-Spherical–Spherical-Revolute (RSSR) mechanism, where the CPU time of the dynamic modeling based on proposed methodology is compared with that based on the revolute joints substitution. Finally, it is explained how a complex suspension and steering linkage can be modeled using the proposed concept of Euler parameters to represent a spherical joint.     

Scalar sensor-based adaptive manipulation for source seeking

This paper considers a class of robotic manipulation that can automatically trace an unknown source of a scalar field by sensors attached to links of a robotic manipulator. To achieve this, one approach is to model the field map by a radial basis function (RBF) network and to update its weights in a recursive way so that the gradient estimate can be available in realtime to command the end-effector toward the target source. In this paper, we investigate the practical implementation of this autonomous manipulation scheme and demonstrate its performance through experimental tests. Firstly, we provide a selection guideline for the Gaussian-type RBF network. Secondly, the field estimation algorithm is simplified to a suboptimal estimator instead of the original recursive least square (RLS) filter previously used. Thirdly, a cross-coupled parameter estimator is newly introduced for global convergence of the combined control law. The overall control scheme is experimentally demonstrated using a two link planar robot. A smooth gray scale map is devised to represent the unknown physical potential field with its scalar values measured by color sensors on robot links. The effect of under fitting of the field model is also investigated through the experimental results.     

Formulation of dynamics,actuation, and inversion of a three‐dimensional two‐link rigid body system

In this paper, three issues related to three‐dimensional multilink rigid body systems are considered: dynamics, actuation, and inversion. Based on the Newton‐Euler equations, a state space formulation of the dynamics is discussed that renders itself to inclusion of actuators, and allows systematic ways of stabilization and construction of inverse systems. The development here is relevant to robotic systems, biological modeling, humanoid studies, and collaborating man‐machine systems. The recursive dynamic formulation involves a method for sequential measurement and estimation of joint forces and couples for an open chain system. The sequence can start from top downwards or from the ground upwards. Three‐dimensional actuators that produce couples at the joints are included in the dynamics. Inverse methods that allow estimation of these couples from the kinematic trajectories and physical parameters of the system are developed. The formulation and derivations are carried out for a two‐link system. Digital computer simulations of a two‐rigid body system are presented to demonstrate the feasibility and effectiveness of the methods. © 2005 Wiley Periodicals, Inc.     

Dynamic Analysis and Distributed Control of the Tetrobot Modular Reconfigurable Robotic System

Reconfigurable robotic systems can be adapted to different tasks or environments by reorganizing their mechanical configurations. Such systems have many redundant degrees of freedom in order to meet the combined demands of strength, rigidity, workspace kinematics, reconfigurability, and fault tolerance. In order to implement these new generations of robotic system, new approaches must be considered for design, analysis, and control. This paper presents an efficient distributed computational scheme which computes the kinematics, dynamics, redundancy resolution, and control inputs for real-time application to the control of the Tetrobot modular reconfigurable robots. The entire system is decomposed into subsystems based on a modular approach and Newton's equations of motion are derived and implemented using a recursive propagation algorithm. Two different dynamic resolution of redundancy schemes, the centralized Jacobian method and the distributed virtual force method, are proposed to optimize the actuating forces. Finally, distributed dynamic control algorithms provide an efficient modular implementation of the control architecture for a large family of configurations.     

The actuation efficiency,a measure of acceleration capability for nonredundant robotic manipulators

This article presents a performance measure, the actuation efficiency, which describes the imbalance between the end‐effector accelerations achievable in different directions of nonredundant robotic manipulators. A key feature of the proposed measure is that in its development the differences in units between translational and rotational accelerations are treated in a physically meaningful manner. The measure also indicates oversized actuators, since this contributes to the imbalance in achievable accelerations. The development of this measure is based on the formulation of the dynamic capability equations. The shape of the dynamic capability hypersurface, which is defined by the dynamic capability equations, is a weak indicator of the level of imbalance in achievable end‐effector accelerations. © 2005 Wiley Periodicals, Inc.     

Efficient recursive algorithm for the operational space inertia matrix of branching mechanisms

This article describes an efficient recursive algorithm for the computation of the operational space inertia matrix of an n-link branching robotic mechanism with multiple (m) operational points. The proposed algorithm achieves the complexity of O(nm + m ³). Since m can be considered as a small constant in practice, as the number of links increases, this algorithm performs significantly better than the existing O(n ³ + m ³) symbolic method. The experimental results of this algorithm are presented using real-time dynamic simulation.     

A geometric method for determining joint rotations in the inverse kinematics of robotic manipulators

An inverse‐kinematics algorithm has been developed to evaluate the joint rotations of a robotic manipulator given the orientation of its hand link. The method mimics the way a person would determine the joint rotations by assembling the links comprising the robot mechanism and making adjustments in the joint displacements until the hand link is in the desired situation. An example is given where it is shown that the method is reasonably robust, can be applied to any design of robot, and is competitive with alternative highly‐mathematical, specific‐robot specialized, computational‐intensive schemes. ©2000 John Wiley & Sons, Inc.     

A distributed parameter model for the dynamics of flexible-link robots

In this paper a model is developed for kinematic and dynamic analysis of flexible robots undergoing general three-dimensional motion. For modeling robotic links, distributed mass and flexibility are considered without discretization. Some modeling issues are discussed, and parameters characterizing the real design of a robot are introduced into the analysis. The concept of a fictitious rigid link is presented to consider the rigid body motion of a link separately, and to account for possibly complex link shapes. Based on Jourdain's principle, an alternative formulation is proposed to derive the dynamic equations of flexible robots. The equations of motion are developed and analyzed in detail. The vibrations of links are described by linear, inhomogeneous partial differential equations, with homogeneous, nonlinear, time-dependent boundary conditions. © 1998 John Wiley & Sons, Inc.     

Analysis of an iterative scheme for approximate regulation for nonlinear systems

This paper concerns the analysis of an iterative scheme delivering approximate control laws for the tracking regulation problems for nonlinear systems. The procedure can be applied to finite‐ and infinite‐dimensional systems, and the underlying methodology derives from the geometric methods, which have been developed for both linear and nonlinear systems. In the nonlinear case, the main tool is the center manifold theorem. Indeed, in the geometric methodology, under the assumption that the signals to be tracked are generated by a finite‐dimensional exo‐system, the desired control is obtained by solving a pair of operator equations called the regulator equations. In this paper, we extend the concept of regulator equations to what we refer to as the dynamic regulator equations. Just as it is generally quite difficult to solve the regulator equations, it can be equally difficult to solve the dynamic regulator equations. As the authors have already shown in the linear case, a straightforward attempt to solve the dynamic regulator equations leads to a singular system, which can be regularized to obtain an iterative scheme that provides approximate control laws that provide accurate tracking with very a small tracking error after only a couple of iterations. In this paper, we generalize the iterative scheme to nonlinear systems and provide error estimates for the first 3 iterations. Both finite‐ and infinite‐dimensional examples are given to validate the estimates. We comment that the method has also been applied to a wide range of nonlinear distributed parameter examples described in the references.     

Mockup‐driven fast‐prototyping methodology for Web application development

Web application development can be very complicated without an appropriate framework, architecture and application model. A good implementation model can help application developers communicate with clients, consolidate the design before starting the development, speed up the development, and make the code highly reusable. This paper proposes a mockup‐driven fast prototyping methodology (MODFM) for the development of Web applications. It is built on the most recent Web technologies: EJB, JSP, Servlet, XML, Struts, and Web application server. A two‐tier Model‐View‐Controller (MVC) architecture is proposed as the underlying backbone and a supporting environment is tailored specifically in order to enable development. Two basic supporting tools are provided: the dynamic menu generator and the generic code generator, which produce code for front‐end, back‐end and database schemas. MODFM helps to generate fully functional mockup systems for the client to review at an early analysis stage, and continues to provide guidance throughout follow‐on development phases. Real‐life experiences on the use of this methodology in industry are presented as examples. Copyright © 2003 John Wiley & Sons, Ltd.