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The work describes a hybrid algorithm for the dynamic formation of a robot's movement route in nondeterministic environments with bypassing stationary and nonstationary obstacles for two-dimensional space, based on the integration of wave and ant algorithms, which makes it possible to build trajectories of minimum length in real time with simultaneous optimization of a number of criteria for the quality of the constructed path. Restrictions preventing the construction of a trajectory from the current position are identified during the construction process. The trajectory is constructed step by step. The entire trajectory connecting the robot's initial position with the target position is a collection of individual sections. The time complexity of the algorithm depends on the lifespan of the colony, l (number of iterations); the number of graph vertices, n; the number of ants, m; and is estimated as O(ln2m). [ABSTRACT FROM AUTHOR]

Objectives: Distances are functions of spatial positions. Precisely revealing the functional relationship which quantitatively embodies the transmission of uncertainty from spatial positions to their distance, a key scientific problem in need of being solved urgently in geomatics, has important theoretical and practical significance. Methods: Aiming at the limitation of presently available solution of the above mentioned problem, under the premise of that the real position corresponding with the observed one of an uncertain point follows the complete spatial random distribution within the error circle, we have derived the probability distribution function of the distance uncertainty and the corresponding density function containing an uncertain point and those between two uncertain points respectively in two-dimensional space. The latter has been employed to explore the transmission law of point uncertainties to distance uncertainties, opening up a new way for studying and solving the problem of distance uncertainties. Results: The results show that for all cases: (1) When the radius of the error circle (corresponding to the point position accuracy) and the observed distance between points change simultaneously, their ratio has a significant positive correlation with the level of distance uncertainties. (2) When the former remains constant, the distance uncertainty has a significant negative correlation with the latter. (3) When the latter remains constant, the distance uncertainty has a significant positive correlation with the former. Conclusions: As far as the distance uncertainty of cases containing an uncertain point and the one of those between two uncertain points are concerned, the latter is obviously greater than the former when the radius of the error circle and the observed distance between points are consistent for both of them. Otherwise they are not comparable. [ABSTRACT FROM AUTHOR]

• We derived the probability distribution functions and probability density functions on distance uncertainty measurement. • We explore the law of uncertainty transmitting from endpoint positions to distances by means of the established models. • We verified the effectiveness and advantages of our method by comparing it with Monte Carlo method in the case study. Distances are functions of spatial positions, therefore distance uncertainties should be resulted from transmission of spatial position uncertainties via the functional relationships accordingly. How to model the transmission precisely, a challenging problem in GIScience, has increasingly drawn attentions during the past several decades. Aiming at the limitations of presently available solutions to the problem, this article derived probability distribution functions and corresponding density functions of distance uncertainties in two-dimensional space related to one or two uncertain endpoints respectively, under the premise that real positions, corresponding with the observed position of an uncertain point, follow the kernel function within its error circle. The density functions were employed to explore the diffusing law of uncertainty information from point positions to distances, which opened up a new way for thoroughly solving problems of measuring distance uncertainties. It turns out that the proposed methods in this article are more efficient, robust than the corresponding Monte Carlo ones, which verifies their effectiveness and advantages. [ABSTRACT FROM AUTHOR]