The tip of a flexible needle with a bevel tip approximately follows a planar arc when it is inserted into soft tissue only with the force applied to the needle along the needle axis. The direction of the arc can be controlled by the rotation input around the needle axis. This flexible and steerable needle has been shown to have a considerable potential in clinical applications due to its maneuverability and steerability. Beyond the needle insertion to a single destination, this paper concerns obtaining needle trajectories that reach multiple targets. Specifically, we propose an algorithm for the insertion of a flexible needle to travel from a single insertion point (i.e. port) to multiple targets. The insertion is motivated by the observation that multiple targets can be reached by the flexible needle through a combination of insertion, partial retraction, turning, and reinsertion of the flexible needle. In this paper we develop an insertion algorithm that minimizes tissue damage during the needle insertion to multiple targets. To this end, a cost function which computes the length of needle trajectory that can be thought of as the tissue damage is defined, and is minimized. Through the minimization, we find the optimal insertion parameters such as the port location, the insertion direction at the port, the targeting order, the turning angles, and the lengths of forward insertions and retractions. To reduce the computation time, we perform workspace analysis for this approach to filter out the no-solution cases. We present numerical examples of the simulated needle insertion for multiple targets with and without obstacles and show the benefit of the proposed method in terms of the tissue damage and the number of skin punctures. Extensions of the proposed approach to more complex cases such as more than three target points and maneuvering around spherical obstacles are also discussed.

This paper focuses on the mechanism design of a slide-block structure and its application on a biomimetic modular robotic fish for three-dimensional swimming. First, as a barycenter-adjustor, the slide-block structure is integrated into a mechanical design of a robotic fish, which is constructed by a control module, a driving module, and a fan-shaped caudal fin. The three-dimensional locomotion of robotic fish is decomposed into two-dimensional locomotion in horizontal plane and ascent–descent locomotion in vertical plane. Both the kinematics of the horizontal swim and the dynamics of the ascent–descent swim are analyzed by the curve fitting method. Finally, experimental results validate the three-dimensional swimming capability of the robotic fish. Furthermore, the impact of two design parameters on the swimming capability of the robotic fish is discussed by the experimental method. The experimental results confirm that the robotic fish with one driving module and a fan-shaped low-aspect-ratio caudal foil can produce higher propulsive speed than other parameter combinations.

Three-DOF manipulators were employed for juggling of polygonal objects in order to have full control over object's configuration. Dynamic grasp condition is obtained for the instances that the manipulators carry the object on their palms. Manipulation problem is modeled as a nonlinear optimal control problem. In this optimal control problem, time of free flight is used as a free parameter to determine throw and catch times. Cost function is selected to get maximum covered horizontal distance using minimum energy. By selecting third-order polynomials for joint motions, the problem is changed to a constrained parameter selection problem. Adaptive particle swarm optimization method is consequently employed to solve the optimization problem. Effectiveness of the optimization algorithm is verified by a set of simulations in MSC. ADAMS.

This paper describes some experiences of using fractal image compression as the subject of an assignment for a functional programming course using Haskell. The students were fascinated by the reproduction of images from their encodings and engaged well with the exercise which involved only elementary functional programming techniques.

In this study, some geometric, kinematic, and dynamic aspects of the design of a Stewart-Gough platform are examined. The focus of the analyses is on a particular Stewart-Gough platform that we have constructed. The analysis begins with workspace simulations for different moving platform orientations. The computations extend to a parametric study of some geometric and kinematic constraints: Joint angle, rotation angle, and limb length. Actuator force is another parameter considered; and the triple relationship between workspace, joint angle, and actuator force is discussed. Parametric analyses are culminated with a brief discussion of the real design parameters.

Correct handling of names and binders is an important issue in meta-programming. This paper presents an embedding of constraint logic programming into the αML functional programming language, which provides a provably correct means of implementing proof search computations over inductive definitions involving names and binders modulo α-equivalence. We show that the execution of proof search in the αML operational semantics is sound and complete with regard to the model-theoretic semantics of formulae, and develop a theory of contextual equivalence for the subclass of αML expressions which correspond to inductive definitions and formulae. In particular, we prove that αML expressions, which denote inductive definitions, are contextually equivalent precisely when those inductive definitions have the same model-theoretic semantics. This paper is a revised and extended version of the conference paper (Lakin, M. R. & Pitts, A. M. (2009) Resolving inductive definitions with binders in higher-order typed functional programming. In Proceedings of the 18th European Symposium on Programming (ESOP 2009), Castagna, G. (ed), Lecture Notes in Computer Science, vol. 5502. Berlin, Germany: Springer-Verlag, pp. 47–61) and draws on material from the first author's PhD thesis (Lakin, M. R. (2010) An Executable Meta-Language for Inductive Definitions with Binders. University of Cambridge, UK).

We study the mixing properties of permutations obtained as a product of two uniformly random permutations of fixed cycle types. For instance, we give an exact formula for the probability that elements 1,2,. . .,k are in distinct cycles of the random permutation of {1,2,. . .,n} obtained as a product of two uniformly random n-cycles.

This paper tackles the problem of motion planning and control of a car-like robot in an obstacle-ridden workspace. A kinematic model of the vehicle, governed by a homogeneous system of first-order differential equations, is used. A solution to the multi-tasking problem of target convergence, obstacle avoidance, and posture control is then proposed. The approach of solving the problem is two-fold. Firstly, a novel velocity algorithm is proposed to drive the car-like robot from its initial position to the target position. Secondly, a single layer artificial neural network is trained to avoid disc-shaped obstacles and provide corresponding weights, which are then used to develop a function for the steering angles. Thus, our method does not need a priori knowledge of the environment except for the goal position. With the help of the Direct Method of Lyapunov, it is shown that the proposed forms of the velocity and steering angle ensure point stability. For posture stability, we model the two parallel boundaries of a row-structured parking bay as continua of disk-shaped obstacles. Thus, our method is extendable to ensuring posture stability, which gives the desired final orientation. Computer simulations of the generated path are presented to illustrate the effectiveness of the method.

Bootstrap percolation (BP) has been used effectively to model phenomena as diverse as emergence of magnetism in materials, spread of infection, diffusion of software viruses in computer networks, adoption of new technologies, and emergence of collective action and cultural fads in human societies. It is defined on an (arbitrary) network of interacting agents whose state is determined by the state of their neighbors according to a threshold rule. In a typical setting, BP starts by random and independent “activation” of nodes with a fixed probability p, followed by a deterministic process for additional activations based on the density of active nodes in each neighborhood (θ activated nodes). Here, we study BP on random geometric graphs (RGGs) in the regime when the latter are (almost surely) connected. Random geometric graphs provide an appropriate model in settings where the neighborhood structure of each node is determined by geographical distance, as in wireless ad hoc and sensor networks as well as in contagion. We derive bounds pc′, pc″ on the critical thresholds such that for all p > p″c full percolation takes place, whereas for p < p′c it does not. We conclude with simulations that compare numerical thresholds with those obtained analytically.

Let X1, …, Xn be non-negative, independent and identically distributed random variables with a common distribution function F, and denote by X1:n ≤ ··· ≤ Xn:n the corresponding order statistics. In this paper, we investigate the second-order regular variation (2RV) of the tail probabilities of Xk:n and Xj:n − Xi:n under the assumption that $\bar {F}$ is of the 2RV, where 1 ≤ k ≤ n and 1 ≤ i < j ≤ n.

For a fixed permutation τ, let $\mathcal{S}_N(\tau)$ be the set of permutations on N elements that avoid the pattern τ. Madras and Liu (2010) conjectured that $\lim_{N\rightarrow\infty}\frac{|\mathcal{S}_{N+1}(\tau)|}{ |\mathcal{S}_N(\tau)|}$ exists; if it does, it must equal the Stanley–Wilf limit. We prove the conjecture for every permutation τ of length 5 or less, as well as for some longer cases (including 704 of the 720 permutations of length 6). We also consider permutations drawn at random from $\mathcal{S}_N(\tau)$, and we investigate properties of their graphs (viewing permutations as functions on {1,. . .,N}) scaled down to the unit square [0,1]2. We prove exact large deviation results for these graphs when τ has length 3; it follows, for example, that it is exponentially unlikely for a random 312-avoiding permutation to have points above the diagonal strip |y−x| < ε, but not unlikely to have points below the strip. For general τ, we show that some neighbourhood of the upper left corner of [0,1]2 is exponentially unlikely to contain a point of the graph if and only if τ starts with its largest element. For patterns such as τ=4231 we establish that this neighbourhood can be extended along the sides of [0,1]2 to come arbitrarily close to the corner points (0,0) and (1,1), as simulations had suggested.

This paper considers generalized birthday problems, in which there are d classes of possible outcomes. A fraction fi of the N possible outcomes has probability αi/N, where $\sum_{i=1}^{d} f_{i} =\sum_{i=1}^{d} f_{i}\alpha_{i}=1$. Sampling k times (with replacements), the objective is to determine (or approximate) the probability that all outcomes are different, the so-called uniqueness probability (or: no-coincidence probability). Although it is trivial to explicitly characterize this probability for the case d=1, the situation with multiple classes is substantially harder to analyze.

Parameterizing k≡ aN, it turns out that the uniqueness probability decays essentially exponentially in N, where the associated decay rate ζ follows from a variational problem. Only for small d this can be solved in closed form. Assuming αi is of the form 1+φiɛ, the decay rate ζ can be written as a power series in ɛ; we demonstrate how to compute the corresponding coefficients explicitly. Also, a logarithmically efficient simulation procedure is proposed. The paper concludes with a series of numerical experiments, showing that (i) the proposed simulation approach is fast and accurate, (ii) assuming all outcomes equally likely would lead to estimates for the uniqueness probability that can be orders of magnitude off, and (iii) the power-series based approximations work remarkably well.

A key challenge at the core of many Natural Language Processing (NLP) tasks is the ability to determine which conclusions can be inferred from a given natural language text. This problem, called the Recognition of Textual Entailment (RTE), has initiated the development of a range of algorithms, methods, and technologies. Unfortunately, research on Textual Entailment (TE), like semantics research more generally, is fragmented into studies focussing on various aspects of semantics such as world knowledge, lexical and syntactic relations, or more specialized kinds of inference. This fragmentation has problematic practical consequences. Notably, interoperability among the existing RTE systems is poor, and reuse of resources and algorithms is mostly infeasible. This also makes systematic evaluations very difficult to carry out. Finally, textual entailment presents a wide array of approaches to potential end users with little guidance on which to pick. Our contribution to this situation is the novel EXCITEMENT architecture, which was developed to enable and encourage the consolidation of methods and resources in the textual entailment area. It decomposes RTE into components with strongly typed interfaces. We specify (a) a modular linguistic analysis pipeline and (b) a decomposition of the ‘core’ RTE methods into top-level algorithms and subcomponents. We identify four major subcomponent types, including knowledge bases and alignment methods. The architecture was developed with a focus on generality, supporting all major approaches to RTE and encouraging language independence. We illustrate the feasibility of the architecture by constructing mappings of major existing systems onto the architecture. The practical implementation of this architecture forms the EXCITEMENT open platform. It is a suite of textual entailment algorithms and components which contains the three systems named above, including linguistic-analysis pipelines for three languages (English, German, and Italian), and comprises a number of linguistic resources. By addressing the problems outlined above, the platform provides a comprehensive and flexible basis for research and experimentation in textual entailment and is available as open source software under the GNU General Public License.

We consider the social welfare model of Naor [20] and revenue-maximization model of Chen and Frank [7], where a single class of delay-sensitive customers seek service from a server with an observable queue, under state dependent pricing. It is known that in this setting both revenue and social welfare can be maximized by a threshold policy, whereby customers are barred from entry once the queue length reaches a certain threshold. However, no explicit expression for this threshold has been found. This paper presents the first derivation of the optimal threshold in closed form, and a surprisingly simple formula for the (maximum) revenue under this optimal threshold. Utilizing properties of the Lambert W function, we also provide explicit scaling results of the optimal threshold as the customer valuation grows. Finally, we present a generalization of our results, allowing for settings with multiple servers.

A non-overconstrained three-DOF parallel orientation mechanism that is kinematically equivalent to the Agile Eye is presented in this paper. The output link (end-effector) of the mechanism is connected to the base by one spherical joint and by another three identical legs. Each leg comprises of, in turns from base, a revolute joint, a universal joint, and three prismatic joints. The three lower revolute joints are active joints, while all other joints are passive ones. Based on a special configuration, some three projective angles of the end-effector coordinates are fully decoupled with respect to the input actuated joints, that is, by actuating any revolute joint the end-effector rotates in such a way that the corresponding projective angle changes with the same angular displacement. The fully decoupled motion is analyzed geometrically and proved theoretically. Besides, the inverse and direct kinematics solutions of the mechanism are provided based on the geometric reasoning and theoretical proof.

In this study, we attempt to develop a biped dinosaur-like walking robot by focusing on its nervous system as well as its mechanism. We developed a robot ‘Dinobot’ on the basis of palaeontological knowledge on dinosaurs and extant animals. In addition, we employed typical biologically inspired walking gait generation and control methods derived from an extant vertebrate's nervous system. In particular, we utilized a central pattern generator (CPG), which is a locomotion rhythm generator in a vertebrate's spinal cord, to generate the robot's walking rhythm. Moreover, a reflex centre was placed below CPG and it produced joint torque of the legs in the swing and stance phases. Thus, we successfully achieved adaptive 3D dynamic walking generated by the interaction between the original mechanism of dinosaurs and the nervous system of extant animals. Our future goal is to find out a dinosaur's robust locomotive nervous system suitable for its mechanism.

Biped robots have gained much attention for decades. A variety of researches have been conducted to make them able to assist or even substitute for humans in performing special tasks. In addition, studying biped robots is important in order to understand human locomotion and to develop and improve control strategies for prosthetic and orthotic limbs. This paper discusses the main challenges encountered in the design of biped robots, such as modeling, stability and their walking patterns. The subject is difficult to deal with because the biped mechanism intervenes with mechanics, control, electronics and artificial intelligence. In this paper, we collect and introduce a systematic discussion of modeling, walking pattern generators and stability for a biped robot.

This paper proposes an efficient implementation of a force-closure test for frictional three-finger grasps. The implementation is based on a condition that transforms force-closure testing into the problem of convex hull intersection in projective space. The proposed implementation further reduces the problem into the problem of computing whether a line segment intersects a convex hull of at most four points. Implementation results are presented along with a thorough performance analysis and comparison with several existing methods. The results are also verified with arbitrary precision floating point computation. This provides comparison of qualitative error resulting from floating point roundoff. The result shows that the proposed implementation outperforms other methods in terms of speed and precision.