We generalize Reimer's Inequality [6] (a.k.a. the BKR Inequality or the van den Berg–Kesten Conjecture [1]) to the setting of finite distributive lattices.

A novel path planner is presented for the local path planning of a single robot (represented with R) in a complicated dynamic environment. Here a series of attractive points are computed based on attractive segments for guiding R to move along a shorter path. Each attractive segment is obtained by using the full environmental knowledge and will be used for several sampling times in general. A motion controller, which is designed based on artificial moments and a robot model that has a principal motion direction line(PMDline), makes R move closely to attractive points while away from obstacles. Attractive and repulsive moments are designed, which only make R's PMDline face toward attractive points and opposite to obstacles in general, as in most cases, R will move along its PMDline with its full speed. Because of the guidance of attractive points and R's full-speed motion, the global convergence is guaranteed. Simulations indicate that the proposed path planner meets the requirements of real-time property while can optimize R's traveling path.

The design of control laws for flexible manipulators is known to be a challenging problem, when using a conventional actuator, i.e., a motor with gear. This is due to the friction of the nonlinear actuator, which causes torque dead zone and stick-slip behavior, thereby hampering the good performance of the control system. The torque needed to attenuate the vibrations, although calculated by the control law, is consumed by the friction inside the actuator, rendering it ineffective to the flexible structure control. Nonlinear friction varies with different operational conditions of the actuator and a friction compensation mechanism based on these models cannot always keep a good performance. This study proposes a new control strategy using wavelet network to friction compensation. Experimental results obtained with a flexible manipulator attest to the good performance of the proposed control law.

This paper presents a motion planning method for a simple wheeled robot in two cases: (i) where translational and rotational speeds are arbitrary, and (ii) where the robot is constrained to move forwards at unit speed. The motions are generated by formulating a constrained optimal control problem on the Special Euclidean group SE(2). An application of Pontryagin's maximum principle for arbitrary speeds yields an optimal Hamiltonian which is completely integrable in terms of Jacobi elliptic functions. In the unit speed case, the rotational velocity is described in terms of elliptic integrals, and the expression for the position is reduced to quadratures. Reachable sets are defined in the arbitrary speed case, and a numerical plot of the time-limited reachable sets is presented for the unit speed case. The resulting analytical functions for the position and orientation of the robot can be parametrically optimised to match prescribed target states within the reachable sets. The method is shown to be easily adapted to obstacle avoidance for static obstacles in a known environment.

Series elastic actuators have beneficial properties for some robot applications. Several recent implementations contain alternative placements of the compliant element to improve instrumentation design. We use a class 1 versus class 2 lever model and energy-port methods to demonstrate in this paper that these alternative placements should still be classified as series elastic actuators. We also note that the compliance of proximal series elastic actuators is reflected by an augmented gear ratio dependent on the nominal gear ratio, which is significant for small gear ratios and approaches unity for large gear ratios. This reflected compliance is shown to differ depending on the sign of the gear ratio. We demonstrate that although the reflected compliance is only marginally influenced by the magnitude of the gear ratio, there are several notable differences, particularly for small gear ratios.

In this paper the design and operation for a 2-Degree-of-Freedom, leg–wheel hybrid mobile robot are presented. A prototype of a low-cost and easy-to-use system, which is capable of straight walking and steering with two actuators only, has been designed and built. Simulation and experimental tests have been carried out to verify the engineering feasibility and operation of the proposed solution. The designed robot can be used for applications such as surveillance and inspection of disaster sites.

In this paper the tip-over stability of mobile robots during manipulation with redundant arms is investigated in real-time. A new fast-converging algorithm, called the Circles Of INitialization (COIN), is proposed to calculate globally optimal postures of redundant serial manipulators. The algorithm is capable of trajectory following, redundancy resolution, and tip-over prevention for mobile robots during eccentric manipulation tasks. The proposed algorithm employs a priori training data generated from an exhaustive resolution of the arm's redundancy along a single direction in the manipulator's workspace. This data is shown to provide educated initial guess that enables COIN to swiftly converge to the global optimum for any other task in the workspace. Simulations demonstrate the capabilities of COIN, and further highlight its convergence speed relative to existing global search algorithms.

We generalise the standard construction of realizability models (specifically, of categories of assemblies) to a wide class of computability structures, which is broad enough to embrace models of computation such as labelled transition systems and process algebras. We consider a general notion of simulation between such computability structures, and show how these simulations correspond precisely to certain functors between the realizability models. Furthermore, we show that our class of computability structures has good closure properties – in particular, it is ‘cartesian closed’ in a slightly relaxed sense. Finally, we investigate some important subclasses of computability structures and of simulations between them. We suggest that our 2-category of computability structures and simulations may offer a useful framework for investigating questions of computational power, abstraction and simulability for a wide range of models.

The semantics of logic programs was originally described in terms of two-valued logic. Soon, however, it was realised that three-valued logic had some natural advantages, as it provides distinct values not only for truth and falsehood but also for “undefined”. The three-valued semantics proposed by Fitting (Fitting, M. 1985. A Kripke–Kleene semantics for logic programs. Journal of Logic Programming 2, 4, 295–312) and Kunen (Kunen, K. 1987. Negation in logic programming. Journal of Logic Programming 4, 4, 289–308) are closely related to what is computed by a logic program, the third truth value being associated with non-termination. A different three-valued semantics, proposed by Naish, shared much with those of Fitting and Kunen but incorporated allowances for programmer intent, the third truth value being associated with underspecification. Naish used an (apparently) novel “arrow” operator to relate the intended meaning of left and right sides of predicate definitions. In this paper we suggest that the additional truth values of Fitting/Kunen and Naish are best viewed as duals. We use Belnap's four-valued logic (Belnap, N. D. 1977. A useful four-valued logic. In Modern Uses of Multiple-Valued Logic, J. M. Dunn and G. Epstein, Eds. D. Reidel, Dordrecht, Netherlands, 8–37), also used elsewhere by Fitting, to unify the two three-valued approaches. The truth values are arranged in a bilattice, which supports the classical ordering on truth values as well as the “information ordering”. We note that the “arrow” operator of Naish (and our four-valued extension) is essentially the information ordering, whereas the classical arrow denotes the truth ordering. This allows us to shed new light on many aspects of logic programming, including program analysis, type and mode systems, declarative debugging and the relationships between specifications and programs, and successive execution states of a program.

Let $k$ be a locally compact complete field with respect to a discrete valuation $v$ . Let $ \mathcal{O} $ be the valuation ring, $\mathfrak{m}$ the maximal ideal and $F(x)\in \mathcal{O} [x] $ a monic separable polynomial of degree $n$ . Let $\delta = v(\mathrm{Disc} (F))$ . The Montes algorithm computes an OM factorization of $F$ . The single-factor lifting algorithm derives from this data a factorization of $F(\mathrm{mod~} {\mathfrak{m}}^{\nu } )$ , for a prescribed precision $\nu $ . In this paper we find a new estimate for the complexity of the Montes algorithm, leading to an estimation of $O({n}^{2+ \epsilon } + {n}^{1+ \epsilon } {\delta }^{2+ \epsilon } + {n}^{2} {\nu }^{1+ \epsilon } )$ word operations for the complexity of the computation of a factorization of $F(\mathrm{mod~} {\mathfrak{m}}^{\nu } )$ , assuming that the residue field of $k$ is small.

This paper presents a study on the interpretation and bracketing of noun compounds (‘NCs’) based on lexical semantics. Our primary goal is to develop a method to automatically interpret NCs through the use of semantic relations. Our NC interpretation method is based on lexical similarity with tagged NCs, based on lexical similarity measures derived from WordNet. We apply the interpretation method to both two- and three-term NC interpretation based on semantic roles. Finally, we demonstrate that our NC interpretation method can boost the coverage and accuracy of NC bracketing.