In this paper, we propose an approach which ensures the dynamicstability of a biped robot called “BIPMAN”. It is based on the correction of thetrunk center of mass acceleration and on the distribution of the forces exertedby the limbs on the trunk. This latter is performed by means of a linearprogramming method (the simplex method). The retained criterion allows tooptimize force distribution as well as trunk roll and pitch angles. Weightingfactors are introduced into this criterion in order to define criteria adaptedto specific tasks. Modifying these factors is a solution to the task transitionproblem. Many simulation results are presented to demonstrate criteria andconstraints influences on dynamic stability. They lead us to introduce a newapproach called RTCA (Real Time Criteria andConstraints Adaptation). This relies on the analysis ofposition, velocity and acceleration vectors for criterion real time adaptationand on forces analysis for constraints real time adaptation. The RTCA approach is finally validated through simulations results for a specifictask.

A calibration method for a Stewart platform has been developed as partof a project aimed at developing a calibration method for a Delta robot. TheDelta has 3 degrees of freedom (DOF) but is more complex than the Stewartplatform for calibration purposes because an extra link is inserted in eachkinematic chain between the base and the Nacelle member.

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

In this paper, we will present a new 6-DOF parallel robot using a set oftwo Delta structures. An effective method is proposed to establish explicitrelationships between the end effector co-ordinates and the active and passivejoint variables. A simulation of the 2-Delta robot on a C.A.D. Robotics systemwill also be presented. This simulation will allow us to validate the cohesionof our calculations, and to show the workspace depending on the mechanicallimits on passive joints variables. Finally, an approach is proposed to studythe influence of small clearances of the passive joint on the precision of theposition and rotation of the effector. This approach is based on a conceptsimilar to that of Yoshikawa's manipulability.

Based on the singularity-consistent parameterization framework, weanalyze motion at direct kinematics singularities for a broad class of parallelmanipulators. It will be shown that taking into account the instantaneous motiondirection of the output link, additional insight can be gained for thepossibility to move through such singularities. We argue that direct kinematicssingularities should be analyzed over the dual space which, in turn, involvesthe state of the passive joints. We perform such an analysis based on theconditioning of the equation of motion. It is shown that, depending on theinstantaneous motion direction, at certain direct kinematics singularities it ispossible to obtain a consistent solution in terms of torque. This implies thatin combination with the continuity of the singularity-consistent inversekinematic solution, motion through such direct kinematics singularities isfeasible.

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.

During the past few years, there has been an increasing demand in thefield of precision engineering for fine motion in multi-degrees of freedomsystems. These applications motivated the development of a new robotics fieldcalled microrobotics. In this paper, we review both the design guidelines formicrorobots and the advantages of using parallel robots in very high precisionapplications. Parallel micromanipulators using elastic joints as well asstructures manufactured in single solid and metallic bellows areintroduced.

This paper describes a method for finding the least fixed points of higher-order functions over finite domains using symbolic manipulation. Fixed point finding is an essential component in the calculation of abstract semantics of functional programs, providing the foundation for program analyses based on abstract interpretation. Previous methods for fixed point finding have primarily used semantic approaches, which often must traverse large portions of the semantic domain even for simple programs. This paper provides the theoretical framework for a syntax-based analysis that is potentially very fast. The proposed syntactic method is based on an augmented simply typed lambda calculus where the symbolic representation of each function produced in the fixed point iteration is transformed to a syntactic normal form. Normal forms resulting from successive iterations are then compared syntactically to determine their ordering in the semantic domain, and to decide whether a fixed point has been reached. We show the method to be sound, complete and compositional. Examples are presented to show how this method can be used to perform strictness analysis for higher-order functions over non-flat domains. Our method is compositional in the sense that the strictness property of an expression can be easily calculated from those of its sub-expressions. This is contrary to most strictness analysers, where the strictness property of an expression has to be computed anew whenever one of its subexpressions changes. We also compare our approach with recent developments in strictness analysis.

This paper presents the kinematics and dynamics of asix-degree-of-freedom platform-type parallel manipulator with six revolute legs,i.e. each leg consists of two links that are connected by a revolute joint.Moreover, each leg is connected, in turn, to the base and moving platforms bymeans of universal and spherical joints, respectively. We first introduce akinematic model for the manipulator under study. Then, this model is used toderive the kinematics relations of the manipulator at the displacement, velocityand acceleration levels. Based on the proposed model, we develop the dynamicsequations of the manipulator using the method of the natural orthogonalcomplement. The implementation of the model is illustrated by computersimulation and numerical results are presented for a sample trajectory in theCartesian space.

Execution of functional programs on distributed-memory multiprocessors gives rise to the problem of evaluating expressions that are shared between several Processing Elements (PEs). One of the main difficulties of solving this problem is that, for a given shared expression, it is not known in advance whether realizing the sharing is more cost effective than duplicating its evaluation. Realizing the sharing requires coordination between the sharing PEs to ensure that the shared expression is evaluated only once. This coordination involves relatively high communication costs, and is therefore only worthwhile when the shared expressions require much computation time to evaluate. In contrast, when the shared expression is not computation intensive, it is more cost effective to duplicate the evaluation, and thus avoid the communication overhead costs. This dilemma of deciding whether to duplicate the work or to realize the sharing stems from the unknown computation time that is required to evaluate a shared expression. This computation time is difficult to estimate due to unknown run-time evolution of loops and recursion that may be part of the expression. This paper presents an on-line (run-time) algorithm that decides which of the expressions that are shared between several PEs should be evaluated only once, and which expressions should be evaluated locally by each sharing PE. By applying competitive considerations, the algorithm manages to exploit sharing of computation-intensive expressions, while it duplicates the evaluation of expressions that require little time to compute. The algorithm accomplishes this goal even though it has no a priori knowledge of the amount of computation that is required to evaluate the shared expression. We show that this algorithm is competitive with a hypothetical optimal off-line algorithm, which does have such knowledge, and we prove that the algorithm is deadlock free. Furthermore, this algorithm does not require any programmer intervention, it has low overhead, and it is designed to run on a wide variety of distributed systems.

Sensor based robotic systems are an important emerging technology. Whenrobots are working in unknown or partially known environments, they need rangesensors that will measure the Cartesian coordinates of surfaces of objects intheir environment. Like any sensor, range sensors must be calibrated. The rangesensors can be calibrated by comparing a measured surface shape to a knownsurface shape. The most simple surface is a plane and many physical objects haveplanar surfaces. Thus, an important problem in the calibration of range sensorsis to find the best (least squares) fit of a plane to a set of 3D points.

We have formulated a constrained optimization problem to determine the leastsquares fit of a hyperplane to uncertain data. The first order necessaryconditions require the solution of an eigenvalue problem. We have shown that thesolution satisfies the second order conditions (the Hessian matrix is positivedefinite). Thus, our solution satisfies the sufficient conditions for a localminimum. We have performed numerical experiments that demonstrate that oursolution is superior to alternative methods.

A task based approach to the issue of redundant robots starts from thepremise that there are obstacles that cannot be removed from the working areaand which therefore must be avoided. This statement produces the requirement fora device with a certain degree of mobility, and stresses the need to ensure thatthe aim is twofold: reach the goal and avoid obstacles. But avoiding obstaclesis not the same objective as keeping as far away from an obstacle as possible;the primary goal is still to reach the target. In fact humans use soft contactto reach targets that are at the periphery of their reach. This soft distributedcontact has the effect of smoothing the surface of the object and hence there isan element of only being interested in obstacle detail at the appropriate scaleto achieve the task.

This paper describes a new approach to collisionavoidance based on using a global path finding algorithm, in this case usingLaplacian potential fields, in conjunction with a simple local geometricallybased algorithm for avoiding obstacles and maximising the use of manoeuvringspace in a manner which is not limited by digital computation resolution issues.This extra technique is in some ways analogous to the human soft contactapproach.

Three examples are presented to illustrate the robustness ofthe algorithm. In order to be able to compare results with other techniques, anenvironment measurement scheme is defined which gives an indication of thedifficulty of the trajectory being followed.

A common solution to the problem of handling list indexing efficiently in a functional program is to build a binary tree. The tree has the given list as frontier and is of minimum height. Each internal node of the tree stores size information (actually, the size of its left subtree) to direct the search for an element at a given position in the frontier. One application was considered in my previous pearl (Bird, 1997). There are two complementary methods for building such a tree, both of which can be implemented in linear time. One method is ‘recursive’, or top down, and works by splitting the list into two equal halves, recursively building a tree for each half, and then combining the two results. The other method is ‘iterative’, or bottom up, and works by first creating a list of singleton trees, and then repeatedly combining the trees in pairs until just one tree remains. The two methods lead to different trees, but in each case the result is a tree with smallest possible height.

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.

The lifetime of a player is defined to be the time where he gets his b-th hit, where a hit will occur with probability p. We consider the maximum statistics of N independent players. For b≠1 this is significantly more difficult than the known instance b=1. The expected value of the maximum lifetime of N players is given by logQN+(b−1)logQ logQN+ smaller order terms, where Q=1/(1−p).

It is shown that if n>n0(d) then any d-regular graph G=(V, E) on n vertices contains a set of u=[lfloor]n/2[rfloor] vertices which is joined by at most (d/2−c√d)u edges to the rest of the graph, where c>0 is some absolute constant. This is tight, up to the value of c.

We prove a generalization of a theorem of Ganter concerning the embedding of partial Steiner systems into Steiner systems. As an application we discuss a further version of the problem of Rosenfeld on embedding graphs into strongly regular graphs.

In this paper we consider the Markov process defined by

P1,1=1, Pn,[lscr]=(1−λn,[lscr])·Pn−1,[lscr]+λn,[lscr]−1·Pn−1,[lscr]−1

for transition probabilities λn,[lscr]=q[lscr] and λn,[lscr]=qn−1. We give closed forms for the distributions and the moments of the underlying random variables. Thereby we observe that the distributions can be easily described in terms of q-Stirling numbers of the second kind. Their occurrence in a purely time dependent Markov process allows a natural approximation for these numbers through the normal distribution. We also show that these Markov processes describe some parameters related to the study of random graphs as well as to the analysis of algorithms.

In generalisation of the beta law obtained under the GEM/Poisson–Dirichlet distribution in Hirth [12] we undertake here an analogous construction which results in the Dirichlet law. Our proof makes use of Hoppe's Pólya-like urn model in population genetics.

It is proved that the smallest cardinality among the maximal irredundant sets in an n–vertex graph with maximum degree Δ([ges ]2) is at least 2n/3Δ. This substantially improves a bound by Bollobás and Cockayne [1]. The class of graphs which attain this bound is characterised.