Group-theoretical methods in manipulator kinematics and symbolic computations

This paper may be considered as a logical continuation of previous investigations where all manipulator problems are treated on the basis of the vector-parametrization of the SO(3) group. The simple composition law of the vector-parameter Lie group, as of its nice properties, reduces the computational burden in solving the direct kinematical problem (DKP) and the inverse kinematical problem (IKP), as in dynamic modelling, by about 25–30% in comparison with other methods used until now. This fact has been proved in our earlier works and it becomes stronger when the manipulator problems are considered at the pure group configurational manifold level. The last statement is the subject of the present paper. Through the vector parametrization of the space motions, DKP and IKP take more efficient forms and this efficiency is increased by using symbolic computations.Research partially supported by Bulgarian NSF grant No. MM 63/91.     

Hybrid force and motion control of flexible joint parallel manipulators using inverse dynamics approach

An inverse dynamics control algorithm is developed for hybrid motion and contact force trajectory tracking control of flexible joint parallel manipulators. First, an open-tree structure is considered by the disconnection of adequate number of unactuated joints. The loop closure constraint equations are then included. Elimination of the joint reaction forces and the other intermediate variables yield a fourth-order relation between the actuator torques and the end-effector position and contact force variables, showing that the control torques do not have an instantaneous effect on the end-effector contact forces and accelerations because of the flexibility. The proposed control law provides simultaneous and asymptotically stable control of the end-effector contact forces and the motion along the constraint surfaces by utilizing the feedback of positions and velocities of the actuated joints and rotors. A two degree of freedom planar parallel manipulator is considered as an example to illustrate the effectiveness of the method.     

Optimal design for robust control of uncertain flexible joint manipulators: a fuzzy dynamical system approach

A novel fuzzy dynamical system approach to the control design of flexible joint manipulators with mismatched uncertainty is proposed. Uncertainties of the system are assumed to lie within prescribed fuzzy sets. The desired system performance includes a deterministic phase and a fuzzy phase. First, by creatively implanting a fictitious control, a robust control scheme is constructed to render the system uniformly bounded and uniformly ultimately bounded. Both the manipulator modelling and control scheme are deterministic and not IF-THEN heuristic rules-based. Next, a fuzzy-based performance index is proposed. An optimal design problem for a control design parameter is formulated as a constrained optimisation problem. The global solution to this problem can be obtained from solving two quartic equations. The fuzzy dynamical system approach is systematic and is able to assure the deterministic performance as well as to minimise the fuzzy performance index.     

An improved approach to the inverse dynamic analysis of parallel manipulators by a given virtual screw

This paper provides an improved approach to the inverse dynamic analysis of parallel manipulators (PMs) based on the screw theory and Jourdain’s principle of virtual power. First, velocity and acceleration mappings from the Cartesian coordinate system to the screw system are established. Next, by introducing a novel concept of virtual screw that is formulated by a combination of virtual angular velocity and virtual linear velocity, four theorems are defined and proven to build the dynamic equations of PMs. Owing to the existing expression of acceleration screws and the introduced virtual screw, the proposed approach not only has the advantages of intuitive physical concepts and universal form but also avoids the difficult derivatives of time and the determination of generalized velocities, which is employed by conventional methods and is determined difficultly for some hybrid PMs. Finally, taking a 1PU?+?3UPS PM as an instance, the inverse dynamic analysis and numerical examples are presented to demonstrate the feasibility of the proposed approach.     

Comparison of joint angle,velocity and acceleration estimators for hydraulically actuated manipulators to a novel dynamical approach

Excavators are used for a wide range of applications like earthworks and material handling. Assistance systems are becoming more common to support the operator. For monitoring and control based assistance functions the angular position, velocity and acceleration of the joints from the working implement are required. Commercial systems often use inertial measurement units, consisting of triaxial accelerometers and gyroscopes, to accomplish an estimation of those states. A novel joint angle, velocity and acceleration estimation for hydraulic manipulators is proposed and compared to state of the art methods. A decentralized kinematic filter using no information about the underlying system and a centralized kinematic filter taking the system kinematics into account are implemented as state of the art approaches. Both filters only use inertial measurement units to obtain information about the current state of the system. The novel centralized dynamic filter uses the same information as the centralized kinematic filter and extends it by a dynamic model containing additional information about the angular acceleration due to pressure readings of the hydraulic cylinders. Kalman filtering is used to combine the derived system and measurement models with the sensor information. The methods are evaluated on a material handling excavator for single and coupled movements of the working implement. The novel centralized dynamic filter enables improvements for the angular acceleration estimation compared to the decentralized and centralized kinematic filter. Less noise of the acceleration estimation and a better tracking of the actual acceleration are shown.     

An approach to adaptive control of robotic manipulators

The control synthesis for the robotic systems in which parameters are partially unknown is considered. We propose synthesis of robust, non-adaptive, decentralized control which has to stabilize robots for all allowable variations of the parameters. If the robust non-adaptive control cannot withstand all expected variations of parameters, we propose synthesis of indirect adaptive control, i.e. the estimation of the robot parameters is performed first and then used for adjusting the decentralized control gains. The non-adaptive and adaptive control syntheses are illustrated by simulation of an industrial robot with unknown payload mass.     

A novel formulation for determining joint constraint loads during optimal dynamic motion of redundant manipulators in DH representation

The kinematic representations of general open-loop chains in many robotic applications are based on the Denavit–Hartenberg (DH) notation. However, when the DH representation is used for kinematic modeling, the relative joint constraints cannot be described explicitly using the common formulation methods. In this paper, we propose a new formulation of solving a system of differential-algebraic equations (DAEs) where the method of Lagrange multipliers is incorporated into the optimization problem for optimal motion planning of redundant manipulators. In particular, a set of fictitious joints is modeled to solve for the joint constraint forces and moments, as well as the optimal dynamic motion and the required actuator torques of redundant manipulators described in DH representation. The proposed method is formulated within the framework of our earlier study on the generation of load-effective optimal dynamic motions of redundant manipulators that guarantee successful execution of given tasks in which the Lagrangian dynamics for general external loads are incorporated. Some example tasks of a simple planar manipulator and a high-degree-of-freedom digital human model are illustrated, and the results show accurate calculation of joint constraint loads without altering the original planned motion. The proposed optimization formulation satisfies the equivalent DAEs.     

An application of computer algebra to algebraic topology

In this work we study a certain formal power series that is of considerable interest to algebraic topologists, the [p ^k ]-series. We define the series in a purely combinatorial way and indicate its usefulness. Then, by using computer algebra techniques, we compute it up to a high coefficient. Our computation has led to some interesting information on the coefficients of the [p ^k ]-series.     

Workspace and dynamic performance evaluation of the parallel manipulators in a spray-painting equipment

The paper deals with the workspace and dynamic performance evaluation of the PRR–PRR parallel manipulator in spray-painting equipment. Functional workspace of planar fully parallel robots is often limited because of interference among their mechanical components. The proposed 3-DOF planar parallel manipulator with two kinematic chains connecting the moving platform to the base can reduce interference while still maintaining 3 DOFs. Based on the kinematics, four working modes are analyzed and singularity is studied. The workspace is investigated and the inverse dynamics is formulated using the virtual work principle. The dynamic performance evaluation indices are designed on the basis of maximum and minimum magnitude of acceleration vector of the moving platform produced by a unit actuated force. The index not only can evaluate the accelerating performance of a manipulator, but also can reflect the isotropy of accelerating performance. Workspace and dynamic performances of the four working modes are compared and the optimal working mode for the painting of a large object with conical surface is determined.     

A stiffness adjustment mechanism maximally utilizing elastic energy of a linear spring for a robot joint

This paper proposes a mechanism that adjusts mechanical stiffness around a robot joint and utilizes whole elastic energy of an elastic element. The proposed mechanism consists of a lead screw mechanism, a linear spring, and wires. The lead screw mechanism moves a nut of the lead screw mechanism to change a bending point of the wire, which connects the linear spring and the lead screw mechanism. Then, moment arm and ratio of joint rotation to extension of the spring are varied. As a result, joint stiffness is adjusted. Because this mechanism does not apply tension to the spring for the stiffness adjustment, whole elastic energy of the spring can be utilized for joint rotation. This utilization can minimize weight and size of the elastic element. Additional advantages of the proposed mechanism are mechanical simplicity, wide range of adjustable stiffness, and no energy consumption for keeping constant stiffness. We analyze characteristics of the proposed mechanism and compare with other mechanisms in detail. Device development and experimental results are provided for demonstrating the effectiveness of the proposed mechanism.     

The generalized momentum approach to the dynamic modeling of a 6-dof parallel manipulator

Dynamic modeling is of great importance regarding computer simulation and advanced control of parallel manipulators. Due to their closed-loop structure and kinematic constraints, dynamic modeling of parallel manipulators presents an inherent complexity. Despite the intensive investigation in this topic of robotics, mostly conducted in the last 2 decades, additional research still has to be done in this area. The dynamic model of a parallel manipulator is usually developed using the Newton–Euler or the Lagrange methods. Nevertheless, additional approaches were also investigated, such as the virtual work, and screw theory based approaches. In this paper, an approach based on the manipulator generalized momentum is studied. This approach is used to obtain the dynamic model of a six degrees-of-freedom parallel manipulator. The involved computational effort is evaluated and compared with the one involved within the classic Lagrange’s formulation. It is showed the proposed approach presents a much lower computational burden.     

An approach to automatic adaptation of assembly models

Adaptation plays a fundamental role in case-based design. However, after decades of efforts, automatic adaptation is still an open issue. In works of case-based design, a designer usually chooses a start-up product model (a candidate model) of moderate complexity based on a query model possessing primary new design requirements (kinematic semantics and geometry), then achieves the target design by adapting the candidate model according to the new design requirements and human interventions are often indispensable. To smartly adapt the candidate model to fit the new design requirements, a novel approach to automatic adaptation of assembly models is proposed in this paper. First, in order to effectively identify the corresponding links and interfaces between two non-preregistered assembly models as relevant elements, an attributed kinematic graph is put forward and adopted. Second, based on the attributed kinematic graph, the kinematic semantics of the candidate model is automatically adapted to that of the query model. Third, through performing interface layout transferring, the geometry of the candidate model is automatically adapted to that of the query model based on the corresponding links and interfaces. A prototype system is also implemented to verify the effectiveness of the proposed approach.     

An approach for automatic generation of adaptive hypermedia in education with multilingual knowledge discovery techniques

This work describes a framework that combines techniques from Adaptive Hypermedia and Natural Language processing in order to create, in a fully automated way, on-line information systems from linear texts in electronic format, such as textbooks. The process is divided into two steps: an off-line processing step, which analyses the source text, and an on-line step, which executes when a user connects to the system with a web browser, moment at which the contents and hyperlinks are generated. The framework has been implemented as the Welkin system, which has been used to build three adaptive on-line information sites in a quick and easy way. Some controlled experiments have been performed with real users aimed to provide positive feedback on the implementation of the system.     

An innovative approach for automatic generation,verification and optimization of part programs in turning

Continuous innovation of products and optimization of manufacturing processes are of fundamental importance for preserving competitiveness. In the last decades, several approaches based on analytic models for optimization of basic machining operations such as cylindrical turning and face milling have been developed. However, the analytic approaches may not be adequate for real industrial applications, since they are based on average cutting parameters and thus they are not capable of taking into account the effect of complex geometries and instantaneous cutting conditions. In this paper, an innovative integrated system for automatic generation of optimized part programs in turning based on realistic machining simulation is proposed. The system components are described in detail and the machining simulator is validated by comparison with the results of real cutting tests. Then, the optimization approach is applied to a simple case study. The results show that the behavior of the cost function is rather complex, even for simple workpieces. Moreover, the simulator can detect unfeasible combinations of cutting parameters and thus reduce inline part program refinement and optimization. The optimal combination of cutting parameters determined by the new system was competitive with the solutions derived from tool specifications or proposed by a machining expert.     

An approach to automatic deductive synthesis of functional programs

The work deals with automatic deductive synthesis of functional programs. Formal specification of a program is taken as a mathematical existence theorem and while proving it, we derive a program and simultaneously prove that this program corresponds to given specification. Several problems have to be resolved for automatic synthesis: the choice of synthesis rules that allows us to derive the basic constructions of a functional program, order of rule application and choice of a particular induction rule. The method proposed here is based on the deductive tableau method. The basic method gives rules for functional program construction. To determine the proof strategy we use some external heuristics, including rippling. And for the induction hypothesis formation the combination of rippling and the deductive tableau method became very useful. The proposed techniques are implemented in the system ALISA (Automatic Lisp Synthesizer) and used for automatic synthesis of several functions in the Lisp language. The work has been partially supported by RFBR grant 05-01-00948a.     

Mobolic: An automated approach to exercising mobile application GUIs using symbiosis of online testing technique and customated input generation

The increasingly prevalent use of mobile devices has raised the popularity of mobile applications. Therefore, automated testing of mobile applications has become an extremely important task. However, it is still a challenge to automatically generate tests with high coverage for mobile applications due to their specific nontrivial structure and the highly interactive nature of graphical user interfaces (GUIs). In this paper, we propose a novel automated GUI testing technique for mobile applications, namely, Mobolic. In this approach, tests with high coverage are automatically generated and executed by combining the online testing technique and customated input generation. Employing the online testing technique, Mobolic systematically explores the app GUI without falling in a loop. It generates relevant events “on the fly” that are followed by an immediate execution. In addition, involving the customated input generation, Mobolic automatically generates relevant user inputs such as user‐predefined, concrete, or random ones. We implemented Mobolic and evaluated its performance on 10 real‐world open‐source Android applications. Our experimental results show the effectiveness and efficiency of Mobolic in terms of achieved code coverage and overall exercising time.     

A direct approach with computerized symbolic computation for finding a series of traveling waves to nonlinear equations

A direct approach with computerized symbolic computation is applied to construct a series of traveling wave solutions for nonlinear equations. Compared with most existing symbolic computation methods such as tanh method and Jacobi function method, the proposed method not only gives new and more general solutions, but also provides a guideline to classify the various types of the solution according to some parameters.     

An approach to the problem of regional accent in automatic speech recognition

An approach to the problem of inter-speaker variability in automatic speech recognition is described which exploits systematic vowel differences in a two-stage process of adaptation to individual speaker characteristics. In stage one, an accent identification procedure selects one of four gross regional English accents on the basis of vowel quality differences within four calibration sentences. In stage two, an adjustment procedure shifts the regional reference vowel space onto the speaker's vowel space as calculated from the accent identification data. Results for 58 speakers from the four regional accent areas are presented.     

An automatic approach to reaching consensus in multiple attribute group decision making

In this work, we consider the problem of consensus of multiple attribute group decision making, and develop an automatic approach to reaching consensus among group opinions. In the process of group decision making, each expert provides his/her preferences over the alternatives with respect to each attribute, and constructs an individual decision matrix. The developed approach first aggregates these individual decision matrices into a group decision matrix by using the additive weighted aggregation (AWA) operator, and then establishes a convergent iterative algorithm to gain a consentaneous group decision matrix. Then based on the consentaneous group decision matrix, the approach utilizes the AWA operator to derive the overall attribute values of alternatives, by which the most desirable alternative can be found out. Finally, we detailedly expound the implementation process of the approach with a practical example.