SATELLITE SELECTION ALGORITHMS FOR POSITIONING, NAVIGATION AND TIMING USERS

Проведен обзор методов и алгоритмов формирования рабочего созвездия навигационных космических аппаратов при решении задач определения местоположения потребителя ГНСС. Появление новых орбитальных группировок и развитие прошлых поколений глобальных навигационных спутниковых систем (ГНСС) способствует увеличению как количества навигационных аппаратов, так и навигационных радиосигналов, излучаемых каждым спутником, в связи с чем решение проблемы выбора навигационных аппаратов является важной составляющей навигационной задачи. Рассмотрены исследования, посвященные типовым алгоритмам формирования рабочего созвездия, а также современным алгоритмам, построенным с привлечением элементов теории машинного обучения. Представлена связь ошибок определения координат потребителя, погрешностей определения псевдодальностей и пространственного расположения навигационных аппаратов и потребителя. Среди рассмотренных алгоритмов выделены три направления исследований: 1) нацеленных на поиск оптимального рабочего созвездия, обеспечивающего минимальную оценку выбранного геометрического фактора снижения точности; 2) нацеленных на поиск квазиоптимальных рабочих созвездий с целью уменьшения вычислительной сложности алгоритма ввиду большого количества видимых спутников; 3) позволяющих одновременно работать в совмещенном режиме по нескольким ГНСС. Приводятся особенности реализаций алгоритмов, их преимущества и недостатки. В заключении приведены рекомендации по изменению подхода к оценке эффективности алгоритмов, а также делается вывод о необходимости учета как геометрического расположения космических аппаратов, так и погрешности определения псевдодальности при выборе космического аппарата в рабочее созвездие The article provides an overview of methods and algorithms for forming a satellite constellation as a part of the navigation problem for the positioning, navigation and timing service. The emergence of new orbital constellations and the development of past GNSS generations increase both the number of navigation satellites and radio signals emitted by every satellite, and therefore the proper solution of satellite selection problem is an important component of the positioning, navigation and timing service. We considered the works devoted to typical algorithms of working constellation formation, as well as to modern algorithms built with the use of machine-learning theory elements. We present the relationship between user coordinates errors, pseudorange errors and the influence of spatial location of satellites and the user. Three directions of researche among reviewed algorithms are outlined: 1) finding the best satellite constellation that provides the minimum geometric dilution of precision; 2) finding quasi-optimal satellite constellation in order to reduce the computational complexity of the algorithm due to the large number of visible satellites; 3) possibility to work in a combined mode using radio signals of multiple GNSS simultaneously. The article presents the features of the algorithms' implementations, their advantages and disadvantages. The conclusion presents the recommendations to change the approach to assessing the performance of the algorithms, and concludes that it is necessary to take into account both the satellite geometric configuration, and pseudorange errors when satellite constellation is being formed

Evolving Multimodal Robot Behavior via Many Stepping Stones with the Combinatorial Multi-Objective Evolutionary Algorithm

An important challenge in reinforcement learning is to solve multimodal problems, where agents have to act in qualitatively different ways depending on the circumstances. Because multimodal problems are often too difficult to solve directly, it is often helpful to define a curriculum, which is an ordered set of sub-tasks that can serve as the stepping stones for solving the overall problem. Unfortunately, choosing an effective ordering for these subtasks is difficult, and a poor ordering can reduce the performance of the learning process. Here, we provide a thorough introduction and investigation of the Combinatorial Multi-Objective Evolutionary Algorithm (CMOEA), which allows all combinations of subtasks to be explored simultaneously. We compare CMOEA against three algorithms that can similarly optimize on multiple subtasks simultaneously: NSGA-II, NSGA-III and ϵ-Lexicase Selection. The algorithms are tested on a function-optimization problem with two subtasks, a simulated multimodal robot locomotion problem with six subtasks and a simulated robot maze navigation problem where a hundred random mazes are treated as subtasks. On these problems, CMOEA either outperforms or is competitive with the controls. As a separate contribution, we show that adding a linear combination over all objectives can improve the ability of the control algorithms to solve these multimodal problems. Lastly, we show that CMOEA can leverage auxiliary objectives more effectively than the controls on the multimodal locomotion task. In general, our experiments suggest that CMOEA is a promising algorithm for solving multimodal problems.

Extreme 3D Image Navigation in Mobile Robotics

The actual problem of determining all six coordinates of the current position of a mobile robot (unmanned aerial vehicle) from 3D-range-finding images (point clouds) generated by an onboard 3D laser sensor when moving (flying) in an unknown environment is considered. An extreme navigation algorithm based on using multidimensional optimization methods is proposed. The rules for calculating the difference between 3D images of the external environment used for optimization of the functional are described. The form of the functional of the difference of 3D images for different environments (premises, industrial-urban environment, rugged and wooded areas) has been investigated. Requirements for the characteristics of the sensor and the geometry of the external environment are formulated, the fulfillment of which ensures the correct formulation and solution of the problem of extreme navigation. The optimal methods of scanning the surrounding space are described and the conditions are substantiated, the fulfillment of which ensures the solution of the navigation problem by the proposed algorithm in real time (at the rate of movement) when processing 3D images formed by modern 3D laser sensors. In particular, the dependence between the frequency of formation of 3D images and the angular and linear velocities of motion is described, which ensures that the functional of the difference of 3D images falls into the multidimensional interval of unimodality, which guarantees a direct search of global minimum in real time. Various methods of direct search for the global minimum of the functional are tested and the fastest for the case under consideration are selected. The accuracy of solving the navigation problem is estimated and a method is proposed to reduce the accumulated error, based on using an older 3D image for correcting the calculated value of the current coordinates, which has an intersection of the view area with the current view area. The proposed method, which is a modification of the reference image method, allows reduce the total error, which grows in proportion to the number of cycles of solving the extreme navigation problem, to values that ensure the autonomous functioning of transport robots and UAVs in previously unprepared and unknown environments. The effectiveness of the proposed algorithmic and developed software and hardware for extreme navigation is confirmed by field experiments carried out in real conditions of various environments.

Relative positioning of UWB tags with deferred ranging

The aim of the work is to develop relative navigation systems based on ultrawideband signals. In a relative navigation system, measurements are transmitted not to the base station, but to mobile subscribers who solve the navigation problem. The work of the network with the SDS-TWR distance measurement protocol is shown and a method for reducing the load in the network of devices is proposed, in which delayed distance measurements are used.

Reactive navigation in partially familiar planar environments using semantic perceptual feedback

This article solves the planar navigation problem by recourse to an online reactive scheme that exploits recent advances in simultaneous localization and mapping (SLAM) and visual object recognition to recast prior geometric knowledge in terms of an offline catalog of familiar objects. The resulting vector field planner guarantees convergence to an arbitrarily specified goal, avoiding collisions along the way with fixed but arbitrarily placed instances from the catalog as well as completely unknown fixed obstacles so long as they are strongly convex and well separated. We illustrate the generic robustness properties of such deterministic reactive planners as well as the relatively modest computational cost of this algorithm by supplementing an extensive numerical study with physical implementation on both a wheeled and legged platform in different settings.

Planning of refracted starlight observation based on observability analysis

In traditional observation schemes of stellar refraction navigation, the accuracy was limited due to unreasonable observation directions. In order to ameliorate this situation, a method of refracted starlight observation based on observability analysis is proposed. The function of this method is optimally generating an observation attitude sequence according to standard trajectories of spacecraft so that the selection of a refracted starlight observation sequence can be realized. Specifically, the improvement of Fisher information matrix calculation enables this method to be qualified for the navigation problem with unsteady measurement quantities as well as the non-fully observability which is defined as the capability of estimating the system state through measurements in finite time. Here, we construct a quantitative relationship between refracted starlight measurements and system observability by means of Fisher information index ( FII). Next, the observation scheme is retrieved by searching the maximum value of the optimized variable, which includes the ( FII). Finally, we resort to the extended Kalman filter to accomplish typical trajectory navigation simulations of the observation scheme. The results indicate that our method brings more accuracy than traditional ones in estimation of position and velocity of the optimal observation scheme.

Application of lidars in the monitoring system of hydrophysical disturbances from moving objects

Object and purpose of research. The object of this research study is a physical phenomenon of lidar observation of hydrophysical disturbances from an object moving underwater confirmed by the scientific discovery registered with Russian Academy of Natural Sciences (RANS). The purpose is to briefly present the phenomenon essence and to validate the feasibility of underwater monitoring system involving lidars. Materials and methods. The work materials is the phenomenon description and publications confirming its reliability. The feasibility of underwater monitoring system employing lidars is validated by model representation of this system as a group of distributed fixed lidars, which record time instants when a moving underwater object is passing by. The navigation task of locating its coordinates and parameters of motion is solved. Main results. The results demonstrate exact solutions to the problem implemented in MATLAB programming system, which confirms that the model is adequate and its software implementation is correct. Conclusion. The purpose of the work to examine the feasibility of lidar underwater monitoring system is achieved. The new scientific results are the problem formulation and the method of solving a navigation problem to find coordinates and parameters of motion from lidar-detected instants of hydrophysical disturbances. A hypothetical lidar-based monitoring system, if verified experimentally that lidars are sufficiently long-range instruments, is a promising idea.

Inverse Reinforcement Learning Through Max-Margin Algorithm

Reinforcement Learning (RL) methods provide a solution for decision-making problems under uncertainty. An agent finds a suitable policy through a reward function by interacting with a dynamic environment. However, for complex and large problems it is very difficult to specify and tune the reward function. Inverse Reinforcement Learning (IRL) may mitigate this problem by learning the reward function through expert demonstrations. This work exploits an IRL method named Max-Margin Algorithm (MMA) to learn the reward function for a robotic navigation problem. The learned reward function reveals the demonstrated policy (expert policy) better than all other policies. Results show that this method has better convergence and learned reward functions through the adopted method represents expert behavior more efficiently.

Connecting and Closed Geodesics of a Kropina Metric

We prove some results about existence of connecting and closed geodesics in a manifold endowed with a Kropina metric. These have applications to both null geodesics of spacetimes endowed with a null Killing vector field and Zermelo’s navigation problem with critical wind.