This paper studies the stable model semantics of logic programs with (abstract) constraint atoms and their properties. We introduce a succinct abstract representation of these constraint atoms in which a constraint atom is represented compactly. We show two applications. First, under this representation of constraint atoms, we generalize the Gelfond–Lifschitz transformation and apply it to define stable models (also called answer sets) for logic programs with arbitrary constraint atoms. The resulting semantics turns out to coincide with the one defined by Son et al. (2007), which is based on a fixpoint approach. One advantage of our approach is that it can be applied, in a natural way, to define stable models for disjunctive logic programs with constraint atoms, which may appear in the disjunctive head as well as in the body of a rule. As a result, our approach to the stable model semantics for logic programs with constraint atoms generalizes a number of previous approaches. Second, we show that our abstract representation of constraint atoms provides a means to characterize dependencies of atoms in a program with constraint atoms, so that some standard characterizations and properties relying on these dependencies in the past for logic programs with ordinary atoms can be extended to logic programs with constraint atoms.

The Iterator pattern gives a clean interface for element-by-element access to a collection, independent of the collection's shape. Imperative iterations using the pattern have two simultaneous aspects: mapping and accumulating. Various existing functional models of iteration capture one or other of these aspects, but not both simultaneously. We argue that C. McBride and R. Paterson's applicative functors (Applicative programming with effects, J. Funct. Program., 18 (1): 1–13, 2008), and in particular the corresponding traverse operator, do exactly this, and therefore capture the essence of the Iterator pattern. Moreover, they do so in a way that nicely supports modular programming. We present some axioms for traversal, discuss modularity concerns and illustrate with a simple example, the wordcount problem.

In this paper, we present an on-line task modification method (OTMM) to realize singularity avoidance for nonredundant and redundant manipulators at the velocity level. The method introduces a correction vector, constructed from the task velocity and the singular vector corresponding to the minimum singular value, into the task velocity. The performance is simply affected by the choice of the lower limit of the minimum singular value and a scalar adjusting function, which is monotone with respect to the minimum singular value. The method makes unnecessary avoiding the singularity point by off-line path planning for nonredundant or redundant manipulators, and the effort to check whether the singularity is escapable for redundant manipulators. The simulation results show the effectiveness of the OTMM for on-line singularity avoidance in manipulator motion control.

Arrows are an extension of the well-established notion of a monad in functional-programming languages. This paper presents several examples and constructions and develops denotational semantics of arrows as monoids in categories of bifunctors Cop × C → C. Observing similarities to monads – which are monoids in categories of endofunctors C → C – it then considers Eilenberg–Moore and Kleisli constructions for arrows. The latter yields Freyd categories, mathematically formulating the folklore claim ‘Arrows are Freyd categories.’

We have made a systematic study of the gait of a straight leg planar passive walking model through simulations and experiments. Three normalised parameters, which represent the foot radius, the position of the mass centre and the moment of inertia, are used to characterise the walking model.

In the simulation, we have obtained the fixed points and the basins of attraction of the walking models with different parameter combinations by the aid of the cell mapping method. With the results of fixed points, we investigated the effects of parameter variations on the gait descriptors, including step length, period, average speed and energy inefficiency. A model that has a large basin of attraction has been obtained, and it can start walking far from its fixed point. However, the size of the basin of attraction is not a good measurement of robustness. Thus, we proposed floors with random slope angles or stairs with random heights to test robustness. Five hundred times of simulations with 100 non-dimensional time units were implemented for each parameter combination. The times that the walker failed to arrive at the end were recorded. The simulation results showed that the model with a larger foot radius and higher position of mass centre has a lower possibility of falling on uneven floors. A large moment of inertia is helpful for walking on a random slope angle floor, while low values of moment of inertia are good for navigating random stairs.

Prototype experiments have validated the simulation results, which showed that models with larger feet have a longer step length and high speed. However, period differences were difficult to obtain in the experiments since the differences were very small. We have tested the sensitivity with the initial conditions of the models with different foot radii on a flat floor, and have also tested the robustness of the models on a floor with random slope angles. The times that the model reached the end of the floor were recorded. The experimental results showed that a large foot radius is good for improving the basin of attraction and robustness on uneven floors. Finally, the exceptions of the experiment are explained.

In this paper, we present a new method of enumeration of parallel manipulators with one end-effector. The method consists of enumerating all the manipulators possible with one end-effector that a single kinematic chain can originate. A very useful simplification for kinematic chain, mechanism and manipulator enumeration is their representation through graphs. The method is based on group theory where abstract structures are used to capture the internal symmetry of a structure in the form of automorphisms of a group. The concept used is orbits of the group of automorphisms of a colored vertex graph. The theory and some examples are presented to illustrate the method.

The FrameNet database comprises an English lexicon, organized in terms of semantic frames. Frames describe situations or entities, along with their participants and props, termed frame elements. The frames are organized in an ontology-like network. For the lexical units, corpus annotations illustrate which frame elements are typically realized, and how they behave syntactically. Texts where all content words are annotated with FrameNet information offer a detailed, structured semantic representation with a variety of uses in Natural Language Processing applications, in particular in retrieving and meaningfully organizing texts written by humans, or in making human–computer interaction more natural. Also, the FrameNet English lexicon can be replaced by lexical data from other languages, while maintaining frame information, so the model is attractive for cross-lingual resources and applications. Manual annotation produced by FrameNet and similar projects for other languages is used to train automatic frame semantic annotation systems, which add rich semantic information to any type of text, and are important components for more sophisticated semantic processing applications.

Computing a realistic velocity profile for a mobile robot is a challenging task due to the large number of kinematic and dynamic constraints involved. In order for a mobile robot to complete its task it must be able to plan and follow a trajectory. It may also be necessary to follow a given velocity profile, depending on the environment. Temporal planning, or following a given velocity profile, can be used to minimize time of motion and to avoid moving obstacles. For example, assuming the mobile robot is a smart wheelchair, it must follow a prescribed path while following a strict speed limit. This paper presents a temporal planning algorithm that is implemented on a wheeled mobile robot to be used in an indoor setting, such as a hospital ward. The path planning stage is accomplished by using cubic spline functions. A trajectory is created by assigning an arbitrary time of 1 s to each segment of the path. This trajectory is made feasible by applying a number of constraints and using a linear scaling technique. When a velocity profile is given, a non-linear time scaling technique is used to fit the mobile robot's linear velocity to the given velocity profile. A method for avoiding moving obstacles is also implemented. Simulation and experimental results showed good agreement with each other. The main contribution of this paper is in developing a temporal planning algorithm, which is capable of moving on an uneven surface (graded non-flat), and its implementation on the mobile robot at the robotics lab in the University of Saskatchewan. This algorithm is computationally very efficient as it requires low computation cost and does not involve major iterations.

The purpose of our research is to study the effects of circular arc feet on the biped walk with a geometric tracking control. The biped studied is planar and is composed of five links and four actuators located at each hip and each knee thus the biped is underactuated in single support phase. A geometric evolution of the biped configuration is controlled, instead of a temporal evolution. The input-output linearization with a PD control law and a feed forward compensation is used for geometric tracking. The controller virtually constrains 4 degrees of freedom (DoF) of the biped, and 1 DoF (the absolute orientation of the biped) remained. The temporal evolution of the remained system with impact events is analyzed using Poincaré map. The map is given by an analytic expression based on the angular momentum about the contact point. The effect of the radii of the circular arc feet on the stability is studied. As a result, the speed of convergence decreases when the radii increases, if the radius is larger than the leg length the cyclic motion is not more stable. Among the stable cyclic motion, larger radius broadens the basin of attraction. Our results agree with those obtained for passive dynamic walking on stability, even if the biped is controlled through the geometric tracking.

Motivated by the search for a body of mathematical theory to support the semantics of computational effects, we first recall the relationship between Lawvere theories and monads on Set. We generalise that relationship from Set to an arbitrary locally presentable category such as Poset and ωCpo or functor categories such as [Inj, Set] and [Inj, ωCpo]. That involves allowing the arities of Lawvere theories to be extended to being size-restricted objects of the locally presentable category. We develop a body of theory at this level of generality, in particular explaining how the relationship between generalised Lawvere theories and monads extends Gabriel–Ulmer duality.

In the simply typed λ-calculus, a hereditary substitution replaces a free variable in a normal form r by another normal form s of type a, removing freshly created redexes on the fly. It can be defined by lexicographic induction on a and r, thus giving rise to a structurally recursive normalizer for the simply typed λ-calculus. We implement hereditary substitutions in a functional programming language with sized heterogeneous inductive types , arriving at an interpreter whose termination can be tracked by the type system of its host programming language.

This paper deals with the problem of collision course checking in a dynamic environment for mobile robotics applications. Our method is based on the relative kinematic equations between moving objects. These kinematic equations are written under polar form. A transformation of coordinates is derived. Under this transformation, collision between two moving objects is reduced to collision between a stationary object and a virtual moving object. In addition to the direct collision course, we define the indirect collision course, which is more critical and difficult to detect. Under this formulation, the collision course problem is simplified, and complex scenarios are reduced to simple scenarios. In three-dimensional (3D) settings, the working space is decomposed into two planes: the horizontal plane and the vertical plane. The collision course detection in 3D is studied in the vertical and horizontal planes using 2D techniques. This formulation brings important simplifications to the collision course detection problem even in the most critical and difficult scenarios. An extensive simulation is used to illustrate the method in 2D and 3D working spaces.