Trimble CenterPoint RTX service provides real-time GNSS positioning with global coverage and fast initialization. The service is transmitted via six geostationary satellites using L-band and via NTRIP. The horizontal accuracy of kinematic positioning is better than 4 cm (95%) anytime, anywhere, and it is achieved within 30 minutes.The CenterPoint RTX system is based on the generation of precise orbit and clock corrections for GNSS satellites. These corrections are generated in real time using data streams from approximately 100 globally distributed reference stations belonging to Trimble's tracking network. Since its introduction in 2011, the system has undergone two major releases (spring 2012 and spring 2013), which included general performance improvements regarding convergence time, as well as the introduction of additional services like RangePoint RTX and features like xFill. Today, Trimble CenterPoint RTX supports GPS, GLONASS and QZSS signalsIn this work, the CenterPoint RTX system was modified in order to include correction generation for Galileo and BeiDou systems, and a prototype "all-GNSS" engine was used to demonstrate the positioning performance using data from ten stations in the Asia-Pacific region, in kinematic mode, during 4 days of August 2013.The addition of Galileo and BeiDou satellites to the standard RTX processing resulted in a reduction of 37% in the convergence time (95-percentile level), and the horizontal positioning errors were reduced by 16% for the selected datasetThis represents a considerable improvement in the currently available service and great benefits are expected once the Galileo and Beidou support is enabled in the CenterPoint RTX service.Trimble has taken steps for the worldwide GNSS users to benefit from the improved CenterPoint RTX performance through Trimble's enhanced, freely available post processing service (RTX-PP). Therefore, RTX-PP was extended by an experimental service supporting Galileo and BeiDou satellites.

In June 2011, Trimble introduced the CenterPoint RTX service providing a real-time global centimeter level GNSS positioning service. The correction data stream is generated from the precise GNSS orbit and clock information derived from the Trimble world-wide CenterPoint RTX tracking network and delivered through L-band satellite links and Internet to support high precision real time applications in a number of high accuracy markets like precision agriculture, survey and construction. While the system initially was introduced supporting GPS and GLONASS satellites, developments have led to the inclusion of the QZSS satellite in early 2012. The paper describes the current status of the Trimble CenterPoint RTX system, its setup and its current performance. Special emphasis is put on the evaluation of the possibility to include BeiDou/Compass satellites. The authors have started to research the ability to integrate BeiDou/Compass into the RTX system. First results on the achievable orbit and clock quality for BeiDou/Compass satellites are presented when using the Trimble NetR9 receivers in the CenterPoint RTX tracking network.

Mid of 2011 Trimble introduced the CenterPoint RTX real-time positioning service providing cm-accurate positions for real-time applications. This service targets applications in the precision markets like Precision Agriculture, Survey and Construction, and relies on the generation of precise orbit and clock information for GPS and GLONASS satellites in real-time.The CenterPoint RTX satellite corrections are generated with data from Trimble's world-wide tracking network, consisting of approximately 100 globally distributed reference stations. A subset of currently 25 stations in the Asia-Pacific region is able to track the QZSS satellite.Unlike GPS and GLONASS, which were supported by CenterPoint RTX from the very beginning, the inclined geostationary orbit of the QZSS satellite causes some additional challenges on the orbit and clock estimation process. The most relevant aspects are the MEO satellite's higher orbit, the geometry of the orbit track, and the tracking network available in the region of interest.To achieve the biggest benefit from QZSS in a high precision positioning solution, its orbit has to be in the same coordinate frame as the GPS or GLONASS orbits. In addition to that the satellite clocks have to be commonly corrected to the corresponding time system. As QZSS has a similar signal structure as GPS, it would be intuitive to treat QZSS like an additional GPS satellite. However this is unfortunately not possible without any further ado, since all satellites of the current GPS constellation transmit L1P, L1C and L2P signals, while QZSS does not provide either L1P or L2P.This paper describes the technical aspects of the inclusion of the QZSS satellite in the orbit and clock estimation process and GNSS receiver positioning engine, as well as the respective improvement in the overall system quality caused by the use of the additional QZSS satellite. Rover performance analyses will also be shown to demonstrate the effect of the QZSS satellite on the convergence of the RTX positioning solution and the final accuracy achieved on several locations in the Asia-Pacific region.The paper describes aspects of the methodology applied in the multi-system orbit and clock estimation and validation procedure. Achieved orbit and clock accuracies over a longer time span are demonstrated and discussed. The orbit accuracy is estimated to be better than 10 cm. The clock accuracy is estimated to be better than 2 cm.

The first commercial GPS Real-time Kinematic (RTK) positioning products were released in 1993. Since then RTK technology has found its way into a wide variety of application areas and markets including Survey, Machine Control, and Precision Farming.During the last decade several researchers have advocated Precise Point Positioning (PPP) techniques as an alternative to reference station-based RTK. With the PPP technique the GNSS positioning is performed using precise satellite orbit and clock information, rather than corrections from one or more reference stations.Due to its typically long initialization time, efforts have been made by numerous organizations in attempting to improve the productivity of PPP-like solutions. As one of the numerous results of the overall GNSS community initiative, in 2011 Trimble introduced a new technology as a positioning service called CENTERPOINT RTX (TM), providing real-time cm-level accuracy without the direct use of a reference station infrastructure.In this paper we will discuss certain aspects of that service, presenting the concepts that are used in order to accomplish certain tasks in the overall system. Furthermore we will present the steps accomplished during the multi-year development of the system, as well as indicate the direction current research work is taking towards new versions of the system.

Mid of 2011 Trimble introduced the CenterPoint RTX real-time positioning service providing cm-accurate positions for real-time applications. This service targets applications in the precision markets like Precision Agriculture, Survey, Construction and relies on the generation of precise orbit and clock information for GNSS satellites in real-time. The CenterPoint RTX satellite corrections are generated with data from Trimble's world-wide tracking network, consisting of approximately 100 reference stations globally distributed. While the system initially was introduced supporting GPS and GLONASS satellites, recent developments have led to the inclusion of additional navigation satellites.The orbit estimation in the CenterPoint RTX system is based on a combination of a UD-factorized Kalman filter estimating satellite position, satellite velocity, troposphere states, integer ambiguities, solar radiation pressure parameters, harmonic coefficients, and earth orientation parameters. The prediction step in the filter is using a numerical integration of the equations of motion in connection with a dynamic force modeling. Forces considered in the approach are the earth's gravity field, lunar and solar direct tides, solar radiation pressure, solid earth tides, ocean tides, and general relativity.In the RTX orbit processing carrier phase integer ambiguities are resolved in real-time. Also, the satellite orbit states are truly estimated in real-time and continuously adapted over time to better represent the current reality. This means that the satellite positions that are evaluated by the user have prediction times of no more than a few minutes since the last orbit processing filtering update, providing negligible loss of accuracy. The RTX real-time orbit components have a typical overall accuracy of around 2.5 cm considering IGS rapid products as truth. Satellite clock estimation is an essential part of the CenterPoint RTX system. It plays a fundamental role on positioning performance due to a number of reasons.Satellite clocks map directly into line-of-sight observation modeling, yielding into a one to one error impact from clocks into GNSS observables modeling. Due to the same strong relationship, it is of fundamental importance that clocks are generated in a way to facilitate ambiguity resolution within the positioning engine. The processing speed of a clock processor is also of fundamental importance, due to the fact that any delay in computing satellite clocks is directly translated into correction latencies when computing real-time positions on the rover side. For that matter one should keep in mind that regardless how late satellite corrections get to the GNSS receiver in the field, positions have to be provided to the user as soon as the rover GNSS measurements are available. Therefore latencies typically introduce errors into the final real time position. In this paper we define real-time positioning as the computation of positions at the time when the rover observables are available, regardless the latency of the correction stream. This is a necessary concept in order to support dynamic rover GNSS positioning. Clock estimates accuracy is typically of 2 cm or better, latencies of correction signals in CenterPoint RTX are typically below 7 seconds when received at the users GNSS positioning system.The paper describes the technical aspects of the inclusion of the additional satellites in the orbit and clock estimation process and GNSS receiver positioning engine, as well as the respective improvement in the overall system quality caused by the use of the additional satellites.The paper also describes aspects of the methodology applied in the multi-system orbit and clock estimation and validation procedure. Achieved orbit and clock accuracies over a longer time span are demonstrated and discussed. It is shown that cm-accurate results are achieved with the RTX technology presented.

The first commercial GPS Real-time Kinematic (RTK) positioning products were released in 1993. Since then RTK technology has found its way into a wide variety of application areas and markets including Survey, Machine Control, and Precision Farming. Current RTK systems provide cm-accurate positioning typically with initialization times of seconds. However, one of the main limitations of RTK positioning is the need of having nearby infra-structure. This infra-structure normally includes a single base station and radio link, or in the case of network RTK, several reference stations with internet connections, a central processing center and communication links to users. In single-base, or network RTK, the distances between reference stations and the rover receiver are typically limited to 100 km.During the last decade several researchers have advocated Precise Point Positioning (PPP) techniques as an alternative to reference station-based RTK. With the PPP technique the GNSS positioning is performed using precise satellite orbit and clock information, rather than corrections from one or more reference stations. The published PPP solutions typically provide position accuracies of better than 10 cm horizontally. The major drawback of PPP techniques is the relatively slow convergence time required to achieve kinematic position accuracies of 10 cm or better. PPP convergence times are typically on the order of several tens of minutes, but occasionally the convergence may take a couple of hours depending on satellite geometry and prevailing atmospheric conditions. Long initialization time is a limiting factor in considering PPP as a practical solution for positioning systems that rely on productivity and availability. Nevertheless, PPP techniques are very appealing from a ground infrastructure and operational coverage area perspective, since precise positioning could be potentially performed in any place where satellite correction data is available.For several years, efforts have been made by numerous organizations in attempting to improve the productivity of PPP-like solutions. Simultaneously, efforts have been made to improve network RTK performance with sparsely located reference stations. Until now there has not been a workable solution for either approach. Commercial success of the published PPP solutions for high-accuracy applications has been limited by the low productivity compared to established RTK methods.In this paper we present a technology that brings together the advantages of both types of solutions, i.e., positioning techniques that do not require local reference stations while providing the productivity of RTK positioning. This means coupling the high productivity and accuracy of reference station-based RTK systems with the extended coverage area of solutions based on global satellite corrections. The outcome of this new technology is the positioning service CENTERPOINT RTXTM, which provides real-time cm-level accuracy without the direct use of a reference station infrastructure, that is suitable for many GNSS market segments. Furthermore, the RTX solution is applicable to multi-GNSS constellations. The new technology involves innovations in RTK network processing, as well as advancements in the rover RTK positioning algorithms.

Zusammenfassung Nichtlineare hybride dynamische Systemmodelle kooperativer Optimalsteuerungsprobleme ermöglichen eine enge und formale Kopplung von diskreter und kontinuierlicher Zustandsdynamik, d. h. von dynamischer Rollen-, Aktionszuweisung mit wechselnder physikalischer Bewegungsdynamik. In den resultierenden gemischt-ganzzahligen Mehrphasen-Optimalsteuerungsproblemen können Beschränkungen an diskrete und kontinuierliche Zustands- und Steuervariablen berücksichtigt werden, z. B. Formations- oder Kommunikationsanforderungen. Zwei numerische Verfahren werden untersucht: ein Dekompositionsansatz mit Branch-and-Bound und direktem Kollokationsverfahren sowie die Approximation durch große gemischt-ganzzahlige lineare Optimierungsaufgaben. Die Verfahren werden auf exemplarische Problemstellungen angewendet: Die simultane Wegpunktreihenfolge- und Trajektorienoptimierung von Luftfahrzeugen sowie die Optimierung von Rollenverteilung und Trajektorien im Roboterfußball.

Based on a nonlinear hybrid dynamical systems model a new planning method for optimal coordination and control of multiple unmanned vehicles is investigated. The time dependent hybrid state of the overall system consists of discrete (roles, actions) and continuous (e.g. position, orientation, velocity) state variables of the vehicles involved. The evolution in time of the system's hybrid state is described by a hybrid state automaton. The presented approach enables a tight and formal coupling of discrete and continuous state dynamics, i.e. of dynamic role and action assignment and sequencing as well as of the physical motion dynamics of a single vehicle modeled by nonlinear differential equations. The planning problem of determining optimal hybrid state trajectories that minimize a cost function as time or energy for optimal multi-vehicle cooperation subject to constraints including the vehicle's motion dynamics is transformed to a mixed-binary dynamic optimization problem being solved numerically. The numerical method consists of an inner iteration where multiphase optimal control problems are solved using a direct collocation method and an outer iteration based on a branch-and-bound search of the discrete solution space. The approach presented in this paper is applied to the scenarios of optimal simultaneous waypoint or target sequencing and dynamic trajectory planning for a team of unmanned aerial vehicles in a plane and to optimal role assignment and physics-based trajectories in robot soccer.

Based on a nonlinear hybrid dynamic systems approach a new paradigm for goal-oriented dynamic cooperation of multiple robots is investigated within the RoboCup scenario. The time dependent hybrid state of the whole system consists of discrete (roles, actions) and continuous (position, orientation, velocity) state variables of all mobile robots and objects involved. The evolution in time of the system’s state is described by a hybrid state automaton. The presented approach enables a tight and formal coupling of discrete and continuous state dynamics, i.e., of dynamic role and action assignment and sequencing as well as of the physical motion behavior of a single robot. The problem of optimal hybrid state trajectories that minimize a merit function for optimal multi-robot cooperation subject to further constraints is transformed to a mixed-integer dynamic optimization problem which is solved numerically. The new approach enables the integration of physics-based trajectory planning and dynamic role assignment in architectures and design methodologies for multi-robot control. The approach presented in this paper can also be applied to any other scenario of mobile multi-robot cooperation where the physical motion properties are of high significance.

A large class of optimal control problems for hybrid dynamic systems can be formulated as mixed‐integer optimal control problems (MIOCPs). A decomposition approach is suggested to solve a special subclass of MIOCPs with mixed integer inner point state constraints. It is the intrinsic combinatorial complexity of the discrete variables in addition to the high nonlinearity of the continuous optimal control problem that forms the challenges in the theoretical and numerical solution of MIOCPs. During the solution procedure the problem is decomposed at the inner time points into a multiphase problem with mixed integer boundary constraints and phase transitions at unknown switching points. Due to a discretization of the state space at the switching points the problem can be decoupled into a family of continuous optimal control problems (OCPs) and a problem similar to the asymmetric group traveling salesman problem (AGTSP). The OCPs are transcribed by direct collocation to large‐scale nonlinear programming problems, which are solved efficiently by an advanced SQP method. The results are used as weights for the edges of the graph of the corresponding TSP‐like problem, which is solved by a Branch‐and‐Cut‐and‐Price (BCP) algorithm. The proposed approach is applied to a hybrid optimal control benchmark problem for a motorized traveling salesman. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Nonlinear hybrid dynamical systems are the main focus of this paper. A modeling framework is proposed, feedback control strategies and numerical solution methods for optimal control problems in this setting are introduced, and their implementation with various illustrative applications are presented. Hybrid dynamical systems are characterized by discrete event and continuous dynamics which have an interconnected structure and can thus represent an extremely wide range of systems of practical interest. Consequently, many modeling and control methods have surfaced for these problems. This work is particularly focused on systems for which the degree of discrete/continuous interconnection is comparatively strong and the continuous portion of the dynamics may be highly nonlinear and of high dimension. The hybrid optimal control problem is defined and two solution techniques for obtaining suboptimal solutions are presented (both based on numerical direct collocation for continuous dynamic optimization): one fixes interior point constraints on a grid, another uses branch-and-bound. These are applied to a robotic multi-arm transport task, an underactuated robot arm, and a benchmark motorized traveling salesman problem.

Numerical methods for optimal control of hybrid dynamical systems are considered where the discrete dynamics and the nonlinear continuous dynamics are tightly coupled. A decomposition approach for numerically solving general mixed-integer continuous optimal control problems (MIOCPs) is discussed. In the outer optimization loop a branch-and-bound binary tree search is used for the discrete variables. The multiple-phase optimal control problems for the continuous state and control variables in the inner optimization loop are solved by a sparse direct collocation transcription method. A genetic algorithm is applied to improve the performance of the branch-and-bound approach by providing a good initial upper bound on the MIOCP performance index. Results are presented for motorized traveling salesmen problems, new benchmark problems in hybrid optimal control.

A largeclassof optimalcontrolproblemsfor hybriddynamicsystemscanbeformulatedasmixed-integeroptimalcontrol problems(MIOCPs).It is theintrinsiccombinatorialcomplexity, in additionto thenonlinearityof thecontinuous, multi-phaseoptimal control problemsthat is largely responsiblefor the challengesin the theoreticalandnumerical solutionof MIOCPs. We presenta new decompositionapproachto numericallysolvingfairly generalMICOPswith binarycontrolvariables.A BranchandBound(B&B) techniqueis appliedto efficiently searchtheentirediscretesolution spaceperforminga truncatedbinarytreesearchfor thediscretevariablesmaintainingupperandlower bounds on theperformanceindex. Thepartially relaxedbinaryvariablesat an innernodedefineanoptimalcontrolproblem with dynamicequationsdefinedin multiple phases.Its global solutionprovidesa lower boundon the performance index for all nodesof thesubtree.If thelowerboundfor agivensubtreeis greaterthanthecurrentglobalupperbound thenthatentiresubtreeneedno longerbesearched.Themany optimal controlproblemswith nonlinear , continuous statedynamicsdefinedin multiple phasessubjectto nonlinearconstraintsaresolvedmostefficiently by a sparsedirectcollocationtranscription.Hereby, themulti-phaseoptimalcontrolproblemis transcribedto a sparse,large-scale nonlinearprogrammingproblembeingsolved efficiently by a tailoredSQPmethod. Despitethe high efficiency of thesparsedirectcollocationmethod,theefficiency of thedecompositiontechniquefor MIOCPsstronglydependson thedeterminationof goodlower andupperboundson theperformanceindex beingusedto fathomingentiresubtrees throughoutthebinarytreesearch.Theproposedapproachis successfullyappliedto two new benchmarkproblemsfor hybridoptimalcontrol: a motorizedtravelingsalesmananda teamof two cooperating, motorizedsalesmen.