A path planning method for robot patrol inspection in chemical industrial parks

Safety patrol inspection in chemical industrial parks is a complex multi-objective task with multiple degrees of freedom.Traditional pointer instruments with advantages like high reliability and strong adaptability to harsh environment,are widely applied in such parks.However,they rely on manual readings which have problems like heavy patrol workload,high labor cost,high false positives/negatives and poor timeliness.To address the above problems,this study proposes a path planning method for robot patrol in chemical industrial parks,where a path optimization model based on improved iterated local search and random variable neighborhood descent(ILS-RVND)algorithm is established by integrating the actual requirements of patrol tasks in chemical industrial parks.Further,the effectiveness of the model and algorithm is verified by taking real park data as an example.The results show that compared with GA and ILS-RVND,the improved algorithm reduces quantification cost by about 24%and saves patrol time by about 36%.Apart from shortening the patrol time of robots,optimizing their patrol path and reducing their maintenance loss,the proposed algorithm also avoids the untimely patrol of robots and enhances the safety factor of equipment.

ERGODIC THEOREM FOR INFINITE ITERATED FUNCTION SYSTEMS

A set of contraction maps of a metric space is called an iterated function systems. Iterated function systems with condensation, can be considered infinite iterated function systems. Infinite iterated function systems on compact metric spaces were studied. Using the properties of Banach limit and uniform contractiveness, it was proved that the random iterating algorithms for infinite iterated function systems on compact metric spaces-satisfy ergodicity. So the random iterating algorithms for iterated function systems with condensation satisfy ergodicity, too.

AFFINE TRANSFORMATION IN RANDOM ITERATED FUNCTION SYSTEMS

Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, that the figure reconstructed by the new random IFS is the image of the origin figure reconstructed by old IFS under a given affine transformation. Two particular examples are used to show this approach.

ON THE GENERALIZATIONS OF DENJOY-WOLFF THEOREM

We consider generalizations of Denjoy-Wolff theorem on strongly pseudoconvex domains. Beardon [3] gave a general Denjoy-Wolff theorem in hyperbolic domain in the complex plane. Our main results are generalizations of Beardon＇s result in a higher dimensional setting.

Almost sure T-stability and convergence for random iterative algorithms

The purpose of this paper is to study the almost sure T-stability and convergence of Ishikawa-type and Mann-type random iterative algorithms for some kind of C-weakly contractive type random operators in a separable Banach space. Under suitable conditions, the Bochner integrability of random fixed points for this kind of random operators and the almost sure T-stability and convergence for these two kinds of random iterative algorithms are proved.

A RANDOM FIXED POINT ITERATION FOR THREE RANDOM OPERATORS ON UNIFORMLY CONVEX BANACH SPACES

In the present paper we introduce a random iteration scheme for three random operators defined on a closed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixed point of three random operators. The result is also an extension of a known theorem in the corresponding non-random case.

ON INTERIOR POINTS OF THE JULIA SET J(R) FOR RANDOM DYNAMICAL SYSTEM R

The authors consider the random iteration of serval functions.Denote byJ(R)the Julia set for the random iteration dynamical system formed by a set of complex functionsR={R 1,R 2,…,R M}.Some sufficient conditions are given forJ(R)to have no interior points.Also some conditions are given forJ(R)to have interior points but fail to be the extended plane.In addition,J(az n,bz n)(n≥2,ab≠0)andJ(z 2+c 1,z 2+c 2)are investigated and some interesting results are obtained.

RANDOM ITERAtION OF HOLOMORPHIC SELF-MAPS OVER BOUNDED DOMAINS IN C^N

This paper studies the asymptotic properties of the random iterations of both the form G. = f1 o f2 o''' o fn and the form Fn= fn o fn-1 o''' o f1, where {fn} H(Ω,Ω) and Ω C ￣N is a bounded domain. It is found that, under some conditions, Gn or Fn tends to a point in Ω as Ω→ ∞. Some examples are also given to show that the conditions that we have given can not be dropped in general. Moreover, a complete description is given for Fn or Gn to tend to a point in Ω under the condition fn→ f.