It has been a pleasure for me to arrange this Special Issue of Roboticaon Parallel Robots which provides 9 papers from authors from Asia, Oceania,North America and Europe; worldwide research on this topic is proof of thegrowing interest of both the scientific and the industrial areas of parallelmechanisms. I truly believe that the main reason for this enthusiasm is thatparallel mechanisms research extends from theoretical mathematics and kinematicsto applied robotics, and even beyond, creating new technologicalchallenges.

1. Robodogs

The American public has greeted the arrival of the Robodog with a great deal of enthusiasm, but not the animal rights lobby. The Robodog is, in fact, an ordinary police dog that has been equipped with the latest high tech systems, and is still under control of a human handler.

Section B of the special issue contains four papers dealing with diverse topics, viz. rehabilitation robotics applications, a software package for an automatic symbolic modelling of robots, the use of symplectic geometry, and the treatment of the Distributed Manipulation Environment method. This completes the wide review of various techniques and theoretical approaches aiming at solving the difficult problems of conventional robotics in the real world.

Section A of the special issue consisting of 13 papers covering a wide field is devoted to the topic of languages and software in robotics, with an emphasis on practical applications. Diverse themes are analysed and discussed, such as neural networks, fuzzy approaches, object-oriented programming, simulation and modelling, graphical robot languages and other pertinent topics. Authors from a number of countries have contributed papers describing recent research and different approaches to this important field, particularly in view of the potential applications in various areas.

The effects of body geometry on walking machine performance have been investigated, and a body design procedure proposed. The relationships between static workspace, body-geometry and installed joint torques have been derived. A body design procedure that uses this data is then described, and two design examples discussed. The procedure results in a body geometry which minimises the installed joint torques, and hence the machine weight, for the desired workspace area.

This paper investigates the neural network approach to solve the inverse kinematics problem of redundant robot manipulators in an environment with obstacles. The solution technique proposed requires only the knowledge of the robot forward kinematics functions and the neural network is trained in the inverse modeling manner. Training algorithms for both the obstacle free case and the obstacle avoidance case are developed. For the obstacle free case, sample points can be selected in the work space as training patterns for the neural network. For the obstacle avoidance case, the training algorithm is augmented with a distance penalty function. A ball-covering object modeling technique is employed to calculate the distances between the robot links and the objects in the work space. It is shown that this technique is very computationally efficient. Extensive simulation results are presented to illustrate the success of the proposed solution schemes. Experimental results performed on a PUMA 560 robot manipulator is also presented.

This paper reports on the existing robot force control algorithms and their composition based on the review of 75 papers on this subject. The objective is to provide a pragmatic exposition with speciality on their differences and different application conditions, and to give a guide of the existing robot force control algorithms. The previous work can be categorized into discussion, design and/or application of fundamental force control techniques, stability analysis of the various control algorithms, and the advanced methods. Advanced methods combine the fundamental force control techniques with advanced control algorithms such as adaptive, robust and learning control strategies.

A path planning method is presented based on non-autonomous dynamicmodeling of open-loops in articulated systems. It is assumed that one part ofthe mechanical system is submitted to specified motions laws, while movements ofthe complementary part are free. Thus, motion optimization is related to freejoint movements but it is achieved on the basis of the dynamic model of thewhole mechanical system. This approach introduces a non-autonomous stateequation of a special type in the sense that it can not only depend on therunning time but also on the unknown travelling time. The cost function to beminimized involves the travelling time and the actuating inputs. Optimization isachieved by applying the Pontryagin Maximum Principle which yields a newoptimality condition concerning the travelling time dependency of the statedproblem. Two simulation examples are presented. The first one shows how thedeveloped technique makes possible both the reducing and mastering the dynamiccomplexity of a four degrees of freedom-vertical manipulator. Set at fourdegrees of freedom, the second one deals with a redundant planar manipulatorcharacterized by a mobile base that is submitted to a specified drivingmotion.

In this paper, the realization of biped walking on even floor, sloping surfaces, and stairs is studied. The motion trajectories for the biped's body and its two feet are modeled by piecewise cubic polynomials. The main features of the biped robot include two variable-length legs and a moving weight which can be positioned side-to-side for balance. The contribution of this paper is gait synthesis and is experimental verification.

A method to determine the two parameter set of circular cylinders, whosesurfaces contain three given points, is presented in the context of an efficientalgorithm, based on the set of two parameter projections of the points ontoplanar sections, to compute radius and a point where the axes intersect theplane of the given points. The geometry of the surface of points, whose positionvectors represent cylinder radius, r, and axial orientation, isrevealed and described in terms of symmetry and singularity inherent in thetriangle with vertices on the given points. This strongly suggests that, givenone constraint on the axial orientation of the cylinder, there are up to sixcylinders of identical radius on the three given points. A bivariate function,in two of the three line direction Plücker coordinates, is derived to provethis. By specifying r and an axis direction, say, perpendicular to agiven direction, one obtains a sixth order univariate polynomial in one of theline coordinates which yields six axis directions. These ideas are needed in thedesign of parallel manipulators

There is a wide diversity in the functioning and programming of robots designed and programmed to assist individuals with disabilities. The planning and structure of four rehabilitation robot implementations is presented. The first is the CURL language developed for human interface and the most widely used in this field. The second, MUSIIC, explores methods for direct manipulation of objects. RoboGlyph uses symbolic constructs to assist with the direction and programming of rehabilitation robots and finally a multi-tasking operating executive is discussed that controls a bilateral head operated telerobot. These four implementations reflect a wide range of interface concepts for the intended users.

Most motion controls of mobile robots are based on the classical scheme of planning-navigation-piloting. The navigation function, the main part of which consists in obstacle avoidance, has to react with the shortest response time. The real-time constraint hardly limits the complexity of sensor data processing. The described navigator is built around fuzzy logic controllers. Besides the well-known possibility of taking into account human know-how, the approach provides several contributions: a low sensitivity to erroneous or inaccurate measures and, if the inputs of the controllers are normalised, an effective portability on various platform. To show these advantages, the same fuzzy navigator has been implemented on two mobile robots. Their mechanical structures are close, except for size and the sensing system.

This paper proposes a novel design method of a shared controller for telerobot systems. A shared controller can enlarge a reflected force by combining force reflection and compliance control. However, the maximum boundary of the force reflection gain guaranteeing the stability greatly depends upon characteristics of the elements in the system such as; a master arm which is combined with the human operator's hand, the environments where the slave arm contacts and the compliance controller. In normal practice, it is therefore, very difficult to determine such a maximum boundary of the gain. To overcome this difficulty, the paper proposes a force reflection gain-selecting algorithm based on neural network and fuzzy logic features. The method estimates characteristic of the master arm and the environments by using neural networks, and then, determines the force reflection gain from the estimated characteristics by using fuzzy logic. The algorithm can work in an on-line manner, and can be easily applied to any telerobot system because it requires no a priori knowledge on the system. The effectiveness of the proposed control scheme is verified through a series of experiments using a laboratory-made telerobot system.

In this paper we present a technique for designing planar parallelmanipulators with platforms capable of reaching any number of desired poses. Themanipulator consists of a platform connected to ground by RPR chains. The set ofpositions and orientations available to the end-effector of a general RPR chainis mapped into the space of planar quaternions to obtain a quadratic manifold.The coefficients of this constraint manifold are functions of thelocations of the base and platform R joints and the distance betweenthem. Evaluating the constraint manifold at each desired pose and defining thelimits on the extension of the P joint yields a set of equations.Solutions of these equations determine chains that contain the desired poses aspart of their workspaces. Parallel manipulators that can reach the prescribedworkspace are assembled from these chains. An example shows the determination ofthree RPR chains that form a manipulator able to reach a prescribedworkspace.

Current mobile robot ultrasonic localisation techniques use sensor systems which rely on features in a horizontal plane. The implicit assumption is that the room boundary on the horizontal plane is not obstructed by objects such as furniture. This assumption is often not realistic and restricts the versatility and portability of these systems. The solution proposed in this paper is the provision of sensing flexibility to use other 3D room boundaries (e.g. ceiling-wall intersections) as 3D natural beacons. We propose a 3D ultrasonic sensor array that uses a Maximum Likelihood Estimator to match the echo arrival times to different object classes and to determine the location of the 3D target. This method does not require fast data acquisition or powerful computing. It has been implemented on a robot localisation application with the Extended Kalman Filter. This paper is the first of two parts, and presents theoretical results on target classification and minimum transducer requirements. The second part, in the next issue of Robotica, presents experimental results on the characterisation of the sensor and its application to robot localisation, and includes the references for the both papers.

New methods have been developed to control a mechanism's realtime Cartesian motion along spatially complex curves such as Non-Uniform Rational B-splines (NURBS). The methods dynamically map the critical trajectory parameters between parameter space, Cartesian space, and joint space. Trajectory models that relate Cartesian tool speeds and accelerations to joint speeds and accelerations have been generalized so that they can be applied to most classes of robots and CNC mechanisms.

A simple and efficient predictor-corrector method uses finite difference theory to predict the parametric changes required to generate the desired curvilinear distances along the trajectory, and then correct the erorrs arising from this prediction. Polynomial approximation methods successfully approximate joint speeds and accelerations rather than require a closed-form inverse Jacobian solution.

The numerical algorithms prove to be time bounded (fixed number of computational steps), and the generated trajectories are smooth and continuous. Both simulation and physical experiments using an Open-Architecture Controller demonstrate the feasibility and usefulness of the developed trajectory generation algorithms and methods. The methods can be conducted at trajectory rates greater than 100 Hz, depending on mechanism complexity.

This paper presents the software package SYMORO+ for the automatic symbolic modelling of robots. This package permits to generate the direct geometric model, the inverse geometric model, the direct kinematic model, the inverse kinematic model, the dynamic model, and the inertial parameters identification models.

The structure of the robots can be serial, tree structure or containing closed loops. The package runs on Sun stations and PC computers, it has been developed under MATHEMATICA and C language. In this paper we give an overview of the algorithms used in the different models; the computational cost of the dynamic models of the PUMA robot are given.

In spite of its simpler structure than that of the Euler-Lagrange equations-based model, the Hamiltonian formulation of Classical Mechanics (CM) gained only limited application in the Computed Torque Control (CTC) of the rather conventional robots. A possible reason for this situation may be, that while the independent variables of the Lagrangian model are directly measurable by common industrial sensors and encoders, the Hamiltonian canonical coordinates are not measurable and can also not be computed in the lack of detailed information on the dynamics of the system under control. As a consequence, transparent and lucid mathematical methods bound to the Hamiltonian model utilizing the special properties of such concepts as Canonical Transformations, Symplectic Geometry, Symplectic Group, Symplectizing Algorithm, etc. remain out of the reach of Dynamic Control approaches based on the Lagrangian model. In this paper the preliminary results of certain recent investigations aiming at the introduction of these methods in dynamic control are summarized and illustrated by simulation results. The proposed application of the Hamiltonian model makes it possible to achieve a rigorous deductive analytical treatment up to a well defined point exactly valid for a quite wide range of many different mechanical systems. From this point on it reveals such an ample assortment of possible non-deductive, intuitive developments and approaches even within the investigations aiming at a particular paradigm that publication of these very preliminary and early results seems to have definite reason, too.

Neural networks were used to find the inverse kinematics of a two-link planar and three-link manipulator arms. The neural networks utilised were multi-layered perceptions with a back-propagation training algorithm. Because of the redundancy in the manipulators studied, this work used lookup tables for the different configurations of the manipulator arm.