domain: info spi

text:
Jérôme Truc
email: jerome.truc@laas.fr

Daniel Sidobre
email: daniel.sidobre@laas.fr

Rachid Alami
email: rachid.alami@laas.fr

Reactive Planning for Coordinated Handover of an Autonomous Aerial Manipulator

Keywords: Human-Robot interaction, Coordinated motion planning, Autonomous aerial manipulators

In this paper, we present a coordinated and reactive human-aware motion planner for performing a handover task by an autonomous aerial manipulator (AAM). We present a method to determine the final state of the AAM for a handover task based on the current state of the human and the surrounding obstacles. We consider the visual field of the human and the effort to turn the head and see the AAM as well as the discomfort caused to the human. We apply these social constraints together with the kinematic constraints of the AAM to determine its coordinated motion along the trajectory.

Introduction

Autonomous Aerial Manipulators (AAMs) combine the flexibility of 3D motion and object grasping using their arm. They have all the necessary components to move and interact in a human-populated environment. KHAOS presented in [START_REF] Truc | [END_REF]] provides a solution to generate human-aware trajectories for social navigation of aerial robot. These trajectories may allow an AAM to navigate in an environment populated with humans and various dynamic obstacles. It considers the kinematic constraints of the AAM and social constraints such as the visual field and the discomfort generated to humans. We know that these constraints are valid in the proximity of humans and can therefore be used for a handover task. Abrupt motions or interruptions in a robot's motion can be uncomfortable for the human and affect the human's understanding of its intention. We therefore need a system able to control smooth motion [START_REF][END_REF], [START_REF] Corsini | [END_REF]].

In this paper, we address the handover problem, which involves coordinating the navigation approach, base and arm pre-positioning, and final motions of an AAM to transfer an object to a human safely and without causing too much discomfort. After presenting the state of the art, we propose an AAM model. Then we propose a method to determine the complete final state of the AAM for a handover task. From this, we propose an extension of KHAOS to generate the complete humanaware trajectory of the AAM with the particularity of coordinating the motion of its arm and its base. Finally, we present results of trajectories generated with this extension to show the capabilities of our planner in simulation.

Related work

Handover is a generic term used in robotics to describe a joint action to exchange an object.

In our case, this action is performed between a human and a robot where each can have the role of the giver or the receiver [START_REF] Fiore | [END_REF]]. A recent review [START_REF] Ortenzi | [END_REF]] classifies the handover into two main phases, pre-handover and physical exchange of the object. This paper concerns the pre-handover phase, which itself comprises many stages. First, it is necessary to determine the grasp of the object envisaged by the human, which will induce the grasp by the robot itself [Saut et al.(2010)]. This grasp depends first of all on the geometry of the object [START_REF] Miller | [END_REF]].

Complex environments can influence the grasp choice especially when 1 objects are close to obstacles [Berenson et al.(2007)]. An interesting approach consists in generating a representative list of grasp and then choosing a good one [START_REF] Saut | Efficient models for grasp planning with a multi-fingered hand[END_REF]] possibly using neural networks [Yang et al.(2020)]. Since the gripper does not allow to relocate the object, the initial grasp is maintained throughout the task. Therefore, it is necessary to predict the evolution of the human's posture and its close environment for a good object exchange configuration [Li and Hauser(2015)]. The handover location is chosen as part of a shared effort between the human and the robot [Mainprice et al.(2012)] using a sampling-based planner and a cost map taking into account visibility, human posture, and safety [START_REF] Mainprice | [END_REF]]. The way to approach a human is studied in [START_REF] Koay | [END_REF]] where people generally prefer a frontal approach, while in [START_REF] Dautenhahn | [END_REF]] they show a preference for a left or right approach. The exchange area can be reduced by considering the constraints of the human arm [START_REF] Vianello | [END_REF]] to avoid musculoskeletal disorders. It can be applied to the robot arm in order to achieve a more sociable behaviour [START_REF] Rasch | [END_REF]].

To guide the robot's choices for a handover and to help the human understand these choices, it is important for both to communicate their intentions. Human's gaze provides a lot of information and can affect handover timing [START_REF] Moon | [END_REF]] combined with head motion [START_REF] Gharbi | [END_REF]]. Aerial robots have very limited means to communicate and can be considered as pets by humans [START_REF] Cauchard | [END_REF]]. Many signals are therefore transmitted by their motion, in particular by the shape of their trajectories [Szafir et al.(2014)] or their gestures [Jensen et al.(2018)]. Humans move and give objects by coordinating the motions of their legs and arms [START_REF] Cakmak | [END_REF]]. Numerous systems stop the motion between navigation and handover phases. To our knowledge, there is no work in Human-Robot Interaction (HRI) on the coordinated motion of an AAM interacting with a human during a handover. It is necessary to look at the fields of motion planning for mobile manipulators as presented in a review from Sandakalum et al. [START_REF] Sandakalum | [END_REF]] and co-manipulation to have find work relating to the generation of coordinated motion of a robot equipped with a mobile base and a manipulator arm.

A complete and complex model of the human is needed to take into account ergonomic requirements for a worker collaborating with a mobile manipulator [Peternel et al.(2017)]. The coordinated motion of a mobile manipulator is planned offline for precise welding tasks [START_REF] Vazquez-Santiago | Motion Planning for Kinematically Redundant Mobile Manipulators with Genetic Algorithm, Pose Interpolation, and Inverse Kinematics[END_REF]] or in real time [START_REF] Li | [END_REF]]. Only the real-time solutions are suitable in the HRI context. Several behaviors to coordinate the motion of a mobile manipulator are possible, they favor the motion of the base or the arm [Xing et al.(2021)]. The concept of manipulability defined by Yoshikawa [Yoshikawa(1985)] allows to define a good behavior [Zhang et al.(2016), [START_REF] Huang | [END_REF]], which avoids singularities from a control point of view but does not necessarily ensure a good motion in a HRI point of view.

Figure 2: AAM model used for collision checking and the platform frames consisting of the multi-rotor (larger blue cylinder), the equipped arm (small blue, cyan, red and black cylinders) and object to be exchanged (purple cylinder). Each reference frame represents a rotary joint about the z i axis.

AAM model

To demonstrate the possibilities of the proposed planning system, we realize simulations with a model build from a hexa-rotor base vehicle and a Jaco arm illustrated in Fig. 2. Jaco's arm has 6 degrees of freedom with a maximum reach of 0.9 m. The 6 propellers of the base are tilted and provide the stability and precision needed to operate in close proximity to a human. In Fig. 2 larger blue cylinder corresponds to the bounding cylinder of the hexa-rotor. The small blue, cyan, red and black bounding cylinders correspond to the parts of the kinematic chain of the arm. Finally, the purple cylinder represents an example of an object to be exchanged. We also introduce the different frames that define the location of the AAM joints as well as the end effector holding the object to be transferred (purple cylinder). Each reference frame represents a rotary joint about the z i axis.

Reactive final state estimation

We detail in this section our proposed method to define the complete final state of the AAM for a handover in a reactive way. Taking into consideration the human, the static and dynamic environment as well as the dimensions of the object to be transferred.

To approach the human in good conditions of safety and comfort during handover, many parameters must be taken into account such as: human's posture, human and robot grasp positions, the geometry of the object to be exchanged, the robot's geometry and abilities and the various obstacles in the surrounding space. To deal with these points, we propose a solution based on 3D cost grids and inverse kinematics. A first grid named human grasp grid and centered on the human with whom handover is considered, aims to determine the best possible handover position for the human's current posture and surrounding obstacles. For each posi-2 Figure 3: base goal grid (resolution = 0.2 m) when the human is looking ahead. Warm (cold) colours represent high (low) costs respectively. Pink sphere corresponds to the position of the human grasp grid used to generate the base goal grid . tion of the human grasp grid , various configurations of the object to be exchanged are tested. From the position of the object, it is possible to determine the position of the end effector and thus generate a second grid named base goal grid in order to determine the best position for the base of the AAM. By selecting the position of the end effector and the base, it is possible to define the configuration of the AAM's arm by inverse kinematics. Everything is updated in real time to allow the system to be reactive and adapt to the various changes of the situation.

human grasp grid The human grasp grid shown around the human in Fig. 1 thus represents potential human grasp positions for the envisaged handover. Each position is associated with a cost calculated using the following cost function:

C human grasp grid = C closest human hand * (C vis + C turn ) C torso dist
(1) where C closest human hand is the distance from the grid cell to the nearest human hand, C vis is the visibility cost defined in [START_REF] Truc | [END_REF]] considering human's visual field and the effort to turn the head to see the robot, C turn is an angle originating in the human torso and formed between the front of the human torso and the cell and C torso dist is the distance from the cell to the human torso.

By using this cost function, it is ensured that a target is found not far from one of the human's hands (C closest human hand ), even if it is not reachable, and that distant positions (C torso dist ) are favoured for safety. Visibility and effort to see (C vis ) are also considered to take into account the human's gaze, while a C turn cost is introduced specific to the effort required for the human to turn around regardless of the direction they are looking.

shared object Once the human grasp grid has been generated, we start to traverse it starting from the low-est cost. This gives us a position where the human can catch the shared object. In our implementation, we consider a cylindrical object that will be caught at one end by the human and other end by the AAM's end effector . The position corresponds to one end of the shared object, and we need to define the location of the other end. To do this, we sample the surrounding space by incrementing an angle around the position to define a preferred configuration of the shared object. At the end of this operation, we obtain a list of configurations for the shared object to which we apply the following cost function:

C shared object = C vis C human head dist (2)
where C vis is the visibility cost defined in [START_REF] Truc | [END_REF]] considering human's visual field and the effort to turn the head to see the robot and C human head dist is the distance between the end of the shared object caught by the AAM's end effector and the human's head base goal grid From the list of configurations of the shared object, we now know the possible positions for the end effector . Starting from the position where C shared object is minimal, we generate a new cost grid named base goal grid which this time allows us to determine the position of the AAM base. The cost function used is similar as C shared object , simply C human head dist becomes the distance between the base of the AAM and the human's head.

The result can be seen in Fig. 3 where the position of the human grasp grid that is being considered is represented by a pink sphere close to the human's right hand. We can notice the absence of a position at the back of the human as this would force the base to be too close to the human, which is not acceptable with our parameters. Lowest costs corresponding to cold colours correspond well to the positions furthest from the human and in his visual field.

AAM's arm

The last step is to determine the configuration of the AAM's arm. This is done by the use of inverse kinematics starting from the position of the end effector and linking the position of the base. The orientation of the end effector is fixed by the grasp on the shared object, so the solution of the inverse kinematics is unique. The calculation is performed for each cell of the base goal grid to select the most interesting configuration. To do this, we sum the visibility cost ( N i=1 C vis with N the number of links in the arm) of each part of the arm to keep the lowest cost configuration. Thus, we favour the visibility of the arm by the human.

AAM Coordinated motion

To deal with the case of coordinated motion for an AAM performing a handover task, we propose an extension of KHAOS presented in [START_REF] Truc | [END_REF]]. Complete state representation of the AAM is given as follows:

AAM state                    x B , y B , z B v x,B , v y,B , v z,B q w,B , q x,B , q y,B , q z,B    for the Base µ i=1..6 for the arm x O , y O , z O v x,O , v y,O , v z,O q w,O , q x,O , q y,O , q z,O    for the Object
(3) which includes the positions x B , y B , z B (and

x O , y O , z O ), the speeds v x,B , v y,B , v z,B (and v x,O , v y,O , v z,O ),
and then the quaternions q w,B , q x,B , q y,B , q z,B (and q w,O , q x,O , q y,O , q z,O ) for the base (and the object) respectively. Manipulator arm joint states are also represented by µ i .

Noisy trajectories KHAOS is based on a stochastic optimizer that generates a large number of noisy trajectories around its input trajectory to be optimized. It then sorts the randomly drawn positions according to human-aware costs, and the robot's kinematic constraints to update the optimised trajectory. Initially used to generate a trajectory for the base of an AAM, we first propose to use a KHAOS trajectory applied to the object to be transferred to the human. Instead of the positions of the base, it is therefore the positions of the object that are noisy. In addition to the object positions, we also noise the joint states µ i of the arm. From the positions of the object and the arm joint states µ i , we can determine the position of the base by direct kinematics.

Human-aware costs and kinematic constraints Costs and constraints used in the initial KHAOS version [START_REF] Truc | [END_REF]] are reused in this extension for coordinated motion. Namely, C dis is representative of the discomfort caused to humans considering relative speed and distance between humans and AAM, C vis considering the visual field of the human and the effort to turn the head and see the robot, C obstacle related to collisions with the environment and finally the kinematic constraints of the AAM are applied to the object and the AAM's base. In addition we propose two additional costs: C torque = | μi | to limit torque variations of the arm along the trajectory and C gap = z O -z B -d to manage the difference in altitude between the base and the object where z O is the altitude of the object, z B is the altitude of the base and d is a configurable distance allowing the gap between the object and the base to be set.

All these costs are used to sort the noisy states of the AAM and generate a human-aware trajectory that respects the kinematic constraints of the AAM. The trajectory thus provides a smooth and coordinated motion of the AAM.

Simulation results

Using the previously proposed AAM model, Fig. 1 shows a first coordinated handover. The approach is frontal and the human's field of view has little impact. We observe a smooth motion allowing the robot to perform a handover task without having to stop between navigation and arm deployment phases. The influence of the human's field of view is shown in Fig. 4 where the AAM starts several metres to the left of the human. The trajectory is deviated so that the AAM appears and signals its presence to the human before completing its approach. We observe that the speed of the AAM accelerates strongly at the start and is quickly limited by the discomfort constraints limited to 0.15 in this example. The AAM becomes visible about 10s before the end of its motion where the visibility cost is maximized. Thereafter, the visibility cost is progressively reduced, indicating the planner's ability to make the AAM visible during the handover.

Finally, Fig. 5 shows the AAM starting several metres behind the walls where the human is located. The human is located in a confined space simulating a situation where he is working on an electrical panel while waiting for the AAM to bring him a tool (purple cylinder). The current state of the human and the surrounding obstacles do not allow direct access for a handover. The planner therefore proposes a final state for the AAM located at the back of the human by approaching the tool close to his left hand, which is the most available hand in this configuration.

Conclusion

We present an extension of KHAOS [START_REF] Truc | [END_REF]] to address the handover problem. Initially designed to generate the human-aware trajectory of a multi-rotor respecting its kinematic constraints, we extend the system to an autonomous aerial manipulator (AAM). We introduce a method to compute the AAM final state reactively for a safe handover while limiting the discomfort caused to the human. We use the constraints initially applied in KHAOS, especially the consideration of the kinematic constraints of the AAM, the discomfort caused to humans and their visual field. Two additional constraints specific to the AAM arm and the object to be transferred to the human are introduced. We thus generate a human-aware trajectory for the coordinated motion of the AAM that is smooth and safe while benefiting from the reactivity of KHAOS.

Figure 4 :

 4 Figure 4: Human's visual field effect when the AAM approaches from the side: a) AAM coordinated motion deviated to move into the human's field of view before approaching. b) Magnitude speed, Discomfort cost and normalized visibility cost over time for AAM base and object. The maximum discomfort value is set to 0.15, limiting the AAM speed.

Figure 5 :

 5 Figure 5: Human working on an electrical panel in a confined space. AAM starts several meters behind the walls and proposes handover behind the human's back.

This work was partially supported by the French National Research Agency :project Flying Co-Worker, https://www.laas.fr/projects/flying_coworker, grant ANR-18-CE33-0001), the European Commission (AnDy, GA. n. 731540; CHIST-ERA -HEAP) and the Artificial and Natural Intelligence Toulouse Institute -Institut 3iA (ANITI) under grant agreement No: ANR-19-PI3A-0004.


S J Edwards

P A Cross

J B Barnes

D Bétaille

A Methodology

  L'archive ouverte pluridisciplinaire

INTRODUCTION

Early in 1994 the first truly automatic, centimetre level real-time kinematic (RTK) GPS system was introduced. By observing signals on both L1 and L2 frequencies it was able to resolve automatically ambiguities (initialise), even whilst moving (On-The-Fly). GPS equipment manufacturers and surveyors alike were quick to develop applications for the new technology. Indeed, during the past two or three years the RTK technique has become the preferred surveying method for a wide variety of applications (especially in engineering). This trend does, however, raise a number of performance related issues worthy of serious consideration. One obvious question is how accurate is a particular RTK system? It is relatively simple to assess the precision of such systems but to examine accuracy in a truly kinematic environment is non trivial, especially in environments that exhibit variable (in time and space) multipath conditions. Other questions include: how fast can the system recover initial ambiguities, how is this speed affected by dynamic environments such as multipath and foliage, how do differing satellite geometries and DOP (Dilution Of Precision) values affect system performance, and how does one know that the resolved ambiguities are correct? In short, how would one go about benchmarking a RTK GPS system? This paper presents a number of tests, which together might form the basis of a methodology for the assessment of the performance of such systems, together with some typical results that might be obtained. Detailed analysis of such test results may go a long way to answering some of the questions raised. It should be noted that the tests have been carried out using a variety of commercial RTK systems, including the Ashtech Z12, Leica SR9500 and the Trimble 4000SSI. No significant differences have been noted in receiver performance and specific receivers are not identified in the various tests undertaken, as the point of this paper is to discuss the design of benchmarking tests and to give typical results.

KINEMATIC TESTS

One of the fundamental problems in the development of benchmark tests for RTK GPS is how to assess accuracy as well as precision. In order to achieve this in a truly kinematic environment the 'true position' of the roving GPS antenna must be recorded at the same instance that a GPS position is recorded. One place at which a facility capable of doing this has been constructed is at the Central Laboratory of Roads and Bridges, Nantes, France. The facility known as SESSYL, is essentially a mobile petrol-powered train that can carry a GPS receiver and antenna and which travels on an oval track (about 180m in length) with a known trajectory (Plate 1). GPS positions can be compared with 'true positions' in order to measure their accuracy (rather than just the precision). Although the track is located in a basically clean multipath environment, multipath can be induced by attaching a metal plate to the train and by parking large vehicles near to the track (Plate 2). Complete losses of lock can also be caused by temporarily erecting a wire mesh tunnel over part of the track. In February 1997 a number of tests were carried out using SESSYL and are reported here. The objective was to:

• assess the accuracy of an RTK system using different antenna combinations in both clean and multipath environments, and

• measure the speed of recovery of ambiguities (On-The-Fly) after complete loss of lock on all satellites.

Plate 1. SESSYL GPS RTK testing facility Plate 2. SESSYL Multipath Plate and Multipath inducing lorry

Method

A total of six tests were designed, three in a clean multipath environment and three in a medium to high multipath environment. Each test used different antenna combinations at the base and rover receivers (choke ring/choke ring, geodetic/geodetic and geodetic/standard RTK). In addition a number of parameters were set prior to the start of each test: kinematic real time solution based on an elevation mask of 15 degrees, constant train speed of 3km/h (0.83m/s) which equates approximately to one complete lap every 4 minutes, position computation/recording rate 1 Hz and an initialisation period of 10 minutes prior to test commencement, in order to ensure ambiguities were fixed. Average baseline lengths were in the order of 100m.

Each test comprised a total of five complete circuits of the track. This figure was (at that time) a function of the SESSYL facility itself and represents the maximum amount of positional data (from the on-board encoders) that could be recorded for any given test. It is worth noting that this aspect of the test facility has been improved since February 1997. For each test performed in a benign multipath environment the tunnel was erected over the track on the final two laps and on the final lap for tests in multipath conditions. This enabled ambiguity recovery times (On-The-Fly) to be computed for the different antenna combinations.

This procedure provides the opportunity to assess the performance of an RTK GPS system in terms of both, accuracy and precision. Moreover, it is easy to envisage individual tests being repeated at different times, and with different satellite constellations and DOP values, thus providing more data on system performance.

Results

Table 1 presents measurement accuracy and precision results for the six SESSYL tests developed, for each of the different antenna combinations in benign (tests 1-3) and multipath (tests 4-6) environments. Statistics for minimum vector (i.e. 3D vector), cross track and height errors for each test are given. These results are based on trajectory comparisons between the RTK and the SESSYL reference trajectory and serve as typical examples of the type of analysis that might be carried out on the data recorded for each experiment.

Commentary

Considering the minimum vector, cross track and height difference values in Table 1, a number of trends emerge. For example in a benign multipath environment using a choke ring antenna at both the base and rover receivers the standard deviations for the minimum vector error are 0.0030m and 0.0028m respectively. Using a pair of geodetic antennas, these errors appear to be only slightly worse, with respective values of 0.0037m and 0.0031m. The more normal combination of geodetic antenna at the base and a standard or lightweight antenna at the rover receiver, leads to a further degradation of system performance, with resulting standard deviations of 0.0042m and 0.0073m for benign and multipath environments respectively. Note that all tests 1-6 were carried out with different satellite geometries so definite conclusions regarding antenna combinations are difficult to draw -the point here is simply to show that there are many factors impacting on the accuracy of RTK GPS.

On the basis of standard deviation values alone it would appear that the use of a choke ring antenna combination does not significantly improve system performance. However in the presence of multipath the use of such an antenna combination gives rise to a maximum vector error of 0.0154m compared to 0.0357m for a geodetic antenna combination. Not surprisingly a geodetic/lightweight antenna combination yields an even larger maximum error of 0.0526m. Such results indicate that when there is significant multipath the use of a choke ring antenna can successfully reduce its effect, but when there is no multipath it makes very little difference.

Similar trends to those outlined for minimum vector error are reflected in both cross track and height differences. For example cross track standard deviation values for both choke ring and geodetic antenna combinations are in the order of 0.004m, in both benign and multipath environments. However these values rise to 0.0044m and 0.0069 for the standard RTK antenna combination in clean and multipath environments respectively. The maximum cross track value recorded using a standard antenna combination was -0.0310m. Results for height difference errors reflect this trend to an even greater degree. For example using a standard antenna combination in a multipath environment gives rise to standard deviation in height errors of 0.0128m and a maximum error of -0.0470m.

In addition to the assessment of the accuracies of RTK GPS, the SESSYL facility provided a means whereby the speed of ambiguity recovery could also be examined in a truly kinematic environment. For instance, the ambiguity recovery times presented in Table 2 although not conclusive give some insight as to the effect of multipath on the speed of the initialisation process. In test number six, the presence of multipath resulted in the RTK system failing to resolve ambiguities, after passing through the wire mesh tunnel.

Although the results presented in Tables 1 and2 are typical and generally consistent with those reported in the literature, it is important to note that not all the error patterns reflect only GPS errors. For example graphical plots of the results for tests 1 and 3 (choke ring) revealed cross track offsets. These were probably due to the rover antenna not being mounted exactly coincident with the SESSYL reference point. Also some cyclic patterns were evident which repeated with track length due to centrifugal forces when the train was travelling around the circular parts of the track.

AMBIGUITY RESOLUTION TESTS

A crucial factor in the operational use of RTK GPS is the speed with which it can initialise (i.e. solve for integer ambiguities), prior to the commencement of a survey or at some point during it following 'loss of lock' due to the masking of some or all of the satellites (for instance after passing under a bridge). In an optimum environment, free from multipath and obstructions one might reasonably expect any RTK system to resolve for integer ambiguities in around 2 minutes (120 sec) or less. Of greater interest, however, is the effect that varied dynamic environments with medium/high multipath, or partial tree cover might have on initialisation times.

Following the somewhat inconclusive results obtained from the SESSYL ambiguity resolution tests, the following experiments were designed to examine further RTK ambiguity resolution performance. Of particular interest was ambiguity resolution under harsh conditions, namely in the presence of high multipath and under partial tree cover. The overall objective was to:

• assess the speed and accuracy of an RTK system for the computation of initial integer ambiguities with different satellite geometries.

Method

The method adopted for these experiments was to undertake a series of controlled reinitialisations of the RTK system over a period of time. This was achieved by using successive antenna pulls (removal of antenna leads) at the rover receiver forcing total loss of lock to all satellites, as though driving under a bridge. Two environments were chosen, a concrete rooftop (known to induce high levels of multipath) and an area of medium to dense tree cover (Plates 3 and 4 respectively). Average baseline lengths were 10m and 50m respectively for the rooftop and tree cover environments.

Only the standard RTK system antenna combination was tested (geodetic/standard), the receiver parameters for these tests were kept the same as for the SESSYL experiments. Each test consisted of a 1 minute (60 sec) antenna pull, followed by a 5 minute (300 sec) reinitialisation period.

Commentary

On examination of the results presented in Table 3 it would appear overall, that DOP values do not play a significant role in the speed of ambiguity recovery. For example in test 13, the speed of ambiguity resolution was determined to be 71 seconds and the mean PDOP value for the test period was 3.50. This compares to test 2, where the resolution time and PDOP value are 124 seconds and 2.03 respectively. Moreover in test 19 the RTK system failed to resolve ambiguities despite very low PDOP value of 2.26. Closer inspection of the results would appear to suggest that the number of satellites being used by the RTK system in its computations has a more significant effect on ambiguity resolution times. For example during test periods 2, 3 and 4, seven satellites were being used for ambiguity resolution purposes yielding initialisation times of 124, 119 and 120 seconds respectively, yet the associated PDOP values of 2.03, 1.91 and 1.92 were all very low. In contrast tests 9, 10 and 12 gave rise to faster initialisation times utilising fewer satellites and higher PDOP values. This trend can be seen more clearly in Figures 1 and2. The results presented in Table 4 together with Figures 3 and4 (tree canopy environment) further demonstrate this pattern. For example the RTK system failed to resolve ambiguities in tests 17, 19 and 20 when seven or more satellites were being utilised in solution computations, despite the associated PDOP values of 2.59, 1.78 and 1.90 being very low. Overall though, the results obtained in a tree canopy environment would appear to suggest (perhaps not surprisingly) that ambiguity resolution times are greater when the GPS signals are partially obscured by foliage.

SIGNAL TRACKING SENSITIVITY TEST

The experiments outlined in the preceding section provide a method of testing the ability of an RTK system to recover ambiguities in two differing dynamic environments. However during a typical survey the rover antenna is often moving within such environments, e.g. an urban area or along a hedgerow containing mature trees. Of particular interest is the ability of an RTK system to deliver fixed ambiguity solutions whilst moving through such an environment which will cause temporary degradation/obscuring of the GPS signals. A method of quantifying system performance in just such an environment now outlined below.

Method

The methods used for this test could range from the very complex to the very simple. One simple test would be to mount the roving RTK antenna on to the roof of a vehicle, and then drive the vehicle along an avenue of trees. The tree canopies would interfere with the incoming GPS signals to varying degrees as the vehicle moved along. The result would be degradation in signal quality and an increase in the noise within the system, which might well affect the ability of the system to deliver fixed ambiguity solutions. Figure 3 shows the location of the test circuit used for this purpose. The average baseline length for this test was in the order of 200m. The section from A to B provides intermittent tree cover (Plate 5) with the remainder of the circuit being on open terrain thus allowing the RTK system to reinitialise. System parameters were again set to those used in the SESSYL tests, i.e. update rate of 1 Hz and an elevation mask of 15 degrees.

Results

Table 5 summarises a typical set of test results in terms of numbers of fixed ambiguity solutions for each pass between points A and B, and as a percentage of the total potential number of fixed ambiguity solutions for each individual complete circuit based on an update rate of 1 Hz.

Commentary

The results presented in Table 3 suggest that it is difficult for an RTK system to deliver continuous fixed ambiguity positions in an environment where the GPS signals are degraded or partially masked. Throughout the whole of the test period there were always more than six satellites above an elevation of 15 degrees (although some may have been masked). Results for the first test period represent the total number of fixed ambiguity solutions for the complete test period i.e. for all 21 complete circuits. This figure represents just 37.3% of the total number of possible positions that could have been recorded at a 1 second update rate. The remaining individual test runs produced results ranging form zero to 46.9%. Overall these results would suggest that a systems tolerance to signal degradation is an area where further development might be considered.

CONCLUSIONS

We live in a world in which it is expected that the quality and performance of almost everything we buy and/or use can be described by a set of standard parameters (albeit often empirical). Indeed such parameters (when fully understood and properly interpreted) can be extremely helpful when selecting between choices. For instance when buying a car it would be natural to compare an enormous number of them: fuel consumption, top speed, boot (trunk) capacity, length and width, safety and comfort features, etc.

In the geodetic sciences we have been used to dealing with fewer parameters, perhaps just accuracy, range and weight, but with RTK GPS the situation is far more complicated, as this paper has shown. It is important to consider, inter alia, accuracy, time to resolve ambiguities and ability to maintain lock, as well as others (not addressed here) such as operating distance.

Unfortunately, and unlike traditional systems, all (or at least most) of these things depend very heavily of the prevailing conditions (multipath, level of masking, nature of dynamics, etc) and on a number of system features (type of antennas, satellite geometry, number of satellites, etc), so assigning suitable parameters is not a simple task.

This paper has indicated a number of tests that could perhaps be used to develop standard parameters to describe the performance of RTK GPS. What is now needed is for professional and scientific bodies to take the initiative in designing standard tests in standard conditions. It will then be possible for all potential users to make informed judgements between competing equipment. At the moment it is extremely difficult for anyone, even someone with a deep knowledge of GPS, to select hardware in an objective manner.

Figure 3 .

 3 Figure 3. Time to fix v PDOP Figure 4. Time to fix v No. SV's (Tree canopy environment) (Tree canopy environment)

Figure 3 .

 3 Figure 3. Signal tracking Test Location

Table 2

 2

	Test Antenna Minimum Vector (m)		Cross Track Diff (m)		Height Diff (m)
	No. comb	sd	mean max	min	sd	mean max	min	sd	mean max	min	environment
	1 cr/cr	0.0030 0.0062 0.0181 0.0001 0.0039 -0.0042 0.0125 -0.0176 0.0038 0.0006 0.0096 -0.0146	clean
	2 geo/geo 0.0037 0.0074 0.0186 0.0007 0.0038 -0.0042 0.0088 -0.0144 0.0058 0.0017 0.0177 -0.0186	clean
	3 geo/std 0.0042 0.0088 0.0284 0.0005 0.0044 -0.0037 0.0107 -0.0280 0.0049 0.0061 0.0212 -0.0159	clean
	4 cr/cr	0.0028 0.0056 0.0154 0.0001 0.0035 -0.0031 0.0142 -0.0129 0.0040 -0.0009 0.0095 -0.0125 multipath
	5 geo/geo 0.0031 0.0064 0.0357 0.0001 0.0039 -0.0041 0.0097 -0.0271 0.0038 0.0021 0.0232 -0.0110 multipath
	6 geo/std 0.0073 0.0136 0.0526 0.0003 0.0069 -0.0046 0.0159 -0.0310 0.0128 -0.0022 0.0318 -0.0470 multipath
	Test Antenna		Ambs	Ambs	Recovery	Ambs	Ambs		Recovery
	No. combination	Amb Recovery -Tunnel Pass (1) Amb Recovery -Tunnel Pass (2)
			Lost	Recovered Time (s)	Lost	Recovered Time (s)
	1 cr/cr		461407	461514		107	461636	461740	104
	2 geo/geo		463728	463871		143	463937	464044	107
	3 geo/std		466456	466564		107	466665	466753	88
	4 cr/cr		474673	474791		118
	5 geo/geo		476623	476672		49
	6 geo/std		478841	F		F

cr/cr = choke ring antenna (base and rover receiver), geo/geo = geodetic antenna (base/rover) geo/std = geodetic antenna (base receiver), standard RTK antenna (rover receiver)

Table 1. SESSYL RTK Positioning Test Results

Table

2

presents results of speed of recovery of integer ambiguities (On-The-Fly) for the six tests. These have been calculated by comparing the times at which the RTK system lost and recovered ambiguities. . SESSYL On-The-Fly ambiguity resolution results

  During this re-initialisation period both float and fixed RTK solutions of the rover antenna were recorded, enabling accurate determination of the exact epoch when ambiguities were resolved by comparing the RTK fixed ambiguity solution with that previously surveyed by rapid static method. A series of these tests were performed over a continuous two hour period, the overall timing of which was considered significant, as it should offer a range of satellite availability and DOP values.ResultsTables3 and 4present some typical results, which might be expected utilising the procedure, outlined in the foregoing for high multipath and tree canopy environments respectively. The last two columns in each table show the number of satellites used for ambiguity resolution and subsequent positioning and the mean PDOP value for each test. Plots of these values against the time taken to fix ambiguities for each test period are shown inFigures 1,[START_REF] Ashkenazi | Standards for Benchmarking Differential GPS[END_REF][START_REF] Peyret | SESSYL: the study of the positioning systems for road construction robotics[END_REF][START_REF] Roberts | DGPS Diseases: Are the Seismic Contractors Immune?[END_REF]

	Test Test Period Time	Time Ambs Time to	No. of	Mean
	No.	On	Off	Resolved Fix (s)	SV's	PDOP
							Value
	1	209880	210180	NA	NA	7	2.12
	2	210240	210540	210364	124	7	2.03
	3	210600	210900	210719	119	7	1.91
	4	210960	211260	211080	120	7	1.92
	5	211320	211620	211583	263	5	3.41
	6	211680	211980	211753	73	5,6	2.78
	7	212040	212340	212113	73	6,5	2.74
	8	212400	212700	212529	129	5	3.00
	9	212760	213060	212836	76	5	3.08
	10 213120	213420	213196	76	5	3.17
	11 213480	213780	213600	120	5	3.29
	12 213840	214140	213913	73	5	3.38
	13 214200	214500	214271	71	5	3.50
	14 214560	214860	214647	87	5	3.50
	15 214920	215220	214991	71	5	3.50
	16 215280	215580	215374	94	5	3.49
	17 215640	215940	215750	110	5,6	3.21
	18 216000	216300	216133	133	6,7	3.29
	Plate 3. High Multipath environment 19 216360 216660 F F	7,6	2.26
	20 216720	217020	216868	148	6	2.35
	F = Failed to resolve ambiguities
	Plate 4. Medium dense tree foliage area

Table 3

 3

	. Ambiguity Resolution Times and PDOP values
	(Multipath environment)

Table 4 .

 4 Ambiguity Resolution Times and PDOP values (Tree canopy environment)

Table 5 .

 5 Number/Percentage of Fixed Ambiguity Solutions