Optimal maintenance policies under different operational schedules

In the reliability literature, maintenance time is usually ignored during the optimization of maintenance policies. In some scenarios, costs due to system failures may vary with time, and the ignorance of maintenance time will lead to unrealistic results. This paper develops maintenance policies for such situations where the system under study operates iteratively at two successive states: up or down. The costs due to system failure at the up state consist of both business losses & maintenance costs, whereas those at the down state only include maintenance costs. We consider three models: Model A, B, and C: Model A makes only corrective maintenance (CM). Model B performs imperfect preventive maintenance (PM) sequentially, and CM. Model C executes PM periodically, and CM; this PM can restore the system as good as the state just after the latest CM. The CM in this paper is imperfect repair. Finally, the impact of these maintenance policies is illustrated through numerical examples.

The geometry of optimal control solutions on some six dimensional lie groups

This paper examines optimal solutions of control systems with drift defined on the orthonormal frame bundle of particular Riemannian manifolds of constant curvature. The manifolds considered here are the space forms Euclidean space E-3, the spheres S-3 and the hyperboloids H-3 with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1,3). The optimal controls of these systems are solved explicitly in terms of elliptic functions. In this paper, a geometric interpretation of the extremal solutions is given with particular emphasis to a singularity in the explicit solutions. Using a reduced form of the Casimir functions the geometry of these solutions are illustrated.

Optimal 3D surface reconstruction from multiview photographic images

This paper describes a new method for reconstructing 3D surface using a small number, e.g. 10, of 2D photographic images. The images are taken at different viewing directions by a perspective camera with full prior knowledge of the camera configurations. The reconstructed object's surface is represented a set of triangular facets. We empirically demonstrate that if the viewing directions are uniformly distributed around the object's viewing sphere, then the reconstructed 3D points optimally cluster closely on a highly curved part of the surface and are widely, spread on smooth or fat parts. The advantage of this property is that the reconstructed points along a surface or a contour generator are not undersampled or underrepresented because surfaces or contours should be sampled or represented with more densely points where their curvatures are high. The more complex the contour's shape, the greater is the number of points required, but the greater the number of points is automatically generated by the proposed method Given that the viewing directions are uniformly distributed, the number and distribution of the reconstructed points depend on the shape or the curvature of the surface regardless of the size of the surface or the size of the object.

Exact error estimates and optimal randomized algorithms for integration

Exact error estimates for evaluating multi-dimensional integrals are considered. An estimate is called exact if the rates of convergence for the low- and upper-bound estimate coincide. The algorithm with such an exact rate is called optimal. Such an algorithm has an unimprovable rate of convergence. The problem of existing exact estimates and optimal algorithms is discussed for some functional spaces that define the regularity of the integrand. Important for practical computations data classes are considered: classes of functions with bounded derivatives and Holder type conditions. The aim of the paper is to analyze the performance of two optimal classes of algorithms: deterministic and randomized for computing multidimensional integrals. It is also shown how the smoothness of the integrand can be exploited to construct better randomized algorithms.

Impedance mismatch: some differences between the way humans and robots control interaction forces

In over forty years of research robots have made very little progress still largely confined to industrial manufacture and cute toys, yet in the same period computing has followed Moores Law where the capacity double roughly every two years. So why is there no Moores Law for robots? Two areas stand out as worthy of research to speedup progress. The first is to get a greater understanding of how human and animal brains control movement, the second to build a new generation of robots that have greater haptic sense, that is a better ability to adapt to the environment as it is encountered. A remarkable property of the cognitive-motor system in humans and animals is that it is slow. Recognising an object may take 250 mS, a reaction time of 150 mS is considered fast. Yet despite this slow system we are well designed to allow contact with the world in a variety of ways. We can anticipate an encounter, use the change of force as a means of communication and ignore sensory cues when they are not relevant. A better understanding of these process has allowed us to build haptic interfaces to mimic the interaction. Emerging from this understanding are new ways to control the contact between robots, the user and the environment. Rehabilitation robotics has all the elements in the subject to not only enable and change the lives of people with disabilities, but also to facilitate revolution change in classic robotics.

Museum robots: multi-robot systems for public exhibition

Mobile robots provide a versatile platform for research, however they can also provide an interesting educational platform for public exhibition at museums. In general museums require exhibits that are both eye catching and exciting to the public whilst requiring a minimum of maintenance time from museum technicians. In many cases it is simply not possible to continuously change batteries and some method of supplying continous power is required. A powered flooring system is described that is capable of providing power continuously to a group of robots. Three different museum exhibit applications are described. All three robot exhibits are of a similar basic design although the exhibits are very different in appearance and behaviour. The durability and versatility of the robots also makes them extremely good candidates for long duration experiments such as those required by evolutionary robotics.

Solving optimal control problems with state constraints using nonlinear programming and simulation tools

This paper illustrates how nonlinear programming and simulation tools, which are available in packages such as MATLAB and SIMULINK, can easily be used to solve optimal control problems with state- and/or input-dependent inequality constraints. The method presented is illustrated with a model of a single-link manipulator. The method is suitable to be taught to advanced undergraduate and Master's level students in control engineering.