Gravity gradiometer and navigation system using such a gravity gradiometer

Abstract

The invention relates to a gravity gradiometer comprising at least two vehicles (V1, V2), each comprising an inertial measurement unit (UMI1, UMI2) and a control unit (COM1, COM2) for controlling the vehicles along paths having separate segments for performing inertial-measurement-unit reversals and coupled segments for exchanging inertial measurements. At least one of the electronic control units is arranged so to determine, in particular from the exchanged measurements: a transformation matrix between the inertial reference frames, a correction of the linear-acceleration measurements based on an observed accelerometric model, a correction of the angular-velocity measurements based on an observed gyrometric model, and a gradient of the gravitational field. The invention also relates to a navigation system comprising such a gravity gradiometer.

Description

[0001] GRADIO-GRAVIMETER AND NAVIGATION SYSTEM USING A

[0002] TEL GRAD IO - GRAVIME TRE

[0003] The present invention relates to the fields of gravimetry and vehicle navigation.

[0004] BACKGROUND OF THE INVENTION

[0005] It is worth recalling that gravitation is one of the four fundamental forces and is commonly described by: a scalar gravitational potential <p(x,y,z) with x, y and z Cartesian coordinates in an inertial frame of reference

[0006] Gij with i, j E{x,y,z} being the components of the gravitation tensor

[0007] G: Universal gravitational constant »6.67 4 10 -11 m 3 .kg -1 .s“ 2 p(x,y,z): density at point x, y, z

[0008] In the following, the device designed to measure

[0009] ~crr uxx u xy u xz rrr the gravitational tensor u yx u yy u yz rr uzx u zy G zz For example, it is known to use gradio-gravimeters to produce gravimetric maps showing the variation in the intensity of the gravitational field in specific geographical areas.

[0010] It is understood that the accuracy of the gravity gradient measurement depends directly on the accuracy of the gradiogravimeter. This is known for gradiogravimeters based on high-precision accelerometers (on the order of pg, where g is the value of Earth's gravity). Such accelerometers are expensive.

[0011] Furthermore, it is known to use, in the field of vehicle navigation, inertial measurement units with reversal. These inertial measurement units include an inertial core which, during a measurement operation, undergoes a series of reversals around a first axis and a second axis which are substantially perpendicular to each other, in order to cancel by averaging at least part of the errors of the accelerometers and gyroscopes composing the inertial core.

[0012] SUBJECT OF THE INVENTION

[0013] The invention is intended, in particular, to perform precise measurements of gravity gradients.

[0014] SUMMARY OF THE INVENTION

[0015] For this purpose, the invention provides a gradio-gravimeter comprising at least two vehicles, each including a motorized locomotion unit, an inertial measurement unit, and an electronic telecommunication unit, all three connected to an electronic control unit. The inertial measurement units each include angular sensors and linear sensors arranged to provide angular velocity measurements and linear acceleration measurements, respectively, in an inertial frame maintained by the angular sensors of the inertial measurement unit. The vehicles are equipped with at least one device for detecting the relative position and orientation of the vehicles when they are in a predetermined state of relative proximity. The electronic control units are arranged to:

[0016] - to command the vehicles to travel separate sections of trajectory, distinct from each other from a first meeting position to a second meeting position, during which the vehicles are in a state of relative separation;

[0017] - to command a relative reversal of the inertial measurement units during the journey of at least one of the separated segments;

[0018] - command the vehicles to travel from the second meeting position a common trajectory segment during which the vehicles are in the proximity state and exchange the measurements taken by the inertial measurement units during the travel of the separate trajectory segments.

[0019] At least one of the electronic control units is configured to determine, in particular from the measurements exchanged:

[0020] - a transformation matrix between inertial frames;

[0021] - a correction of linear acceleration measurements using an observed accelerometric model;

[0022] - a correction of angular velocity measurements using an observed gyrometric model;

[0023] - a gradient of the gravitational field from od' a time integral of gravitational deviations experienced by the vehicles during their travel along the separate trajectory segments; od' a relative separation of the vehicles during their travel along the separate trajectory segments.

[0024] The invention exploits the fact that comparing linear acceleration measurements on separate trajectory segments reveals the differences in gravitational forces between those segments. Indeed, a linear acceleration sensor measures both the acceleration of the vehicle on which it is mounted and the opposite of the gravitational force acting on the vehicle. During the common trajectory segments, comparing linear acceleration measurements projected onto an inertial frame of reference allows for the deduction of linear acceleration and / or angular velocity errors in the inertial measurement units and / or calibration errors between the inertial measurement units. This improves the accuracy of linear acceleration measurements and yields relatively precise gravity gradient measurements without resorting to a conventional gradiogravimeter.

[0025] Depending on optional features, used individually or in whole or in part in combination:

[0026] - relative distance is an average of the differences between positions, during separate trajectory segments, calculated from accelerometric measurements and / or predicted from vehicle commands;

[0027] - the time integral of gravitational deviations is a simple time integral and at least one of the vehicles includes a relative speed measurement device for the vehicles characterizing the simple time integral of gravitational deviations;

[0028] - the time integral of gravitational deviations is a double time integral and at least one of the vehicles includes a measuring device for a relative distance of the vehicles characterizing the double time integral of gravitational deviations;

[0029] - said at least one of the electronic control units is arranged to calculate a simple time integral of differences between linear acceleration measurements of vehicles on separate trajectory segments, the simple time integral of differences between linear acceleration measurements characterizing the simple time integral of gravitational differences;

[0030] - said at least one of the electronic control units is arranged to calculate a double time integral of differences between the linear acceleration measurements of the vehicles on the separate trajectory segments, the double time integral of differences between the linear acceleration measurements characterizing the double time integral of the gravitational differences;

[0031] - the device for detecting a reciprocal relative orientation includes at least one element for docking vehicles in at least one predetermined relative orientation, the relative orientations being separated by approximately 180°;

[0032] - the detection device for a reciprocal relative orientation includes at least one optical camera;

[0033] - at least one of the vehicles includes a motorized reversing device for the inertial measuring unit;

[0034] - the electronic control unit of at least one of the vehicles is programmed to control the motorized locomotion unit of the vehicle to make it perform movements corresponding to rotations of the inertial measurement unit;

[0035] - at least two of the vehicles are each equipped with at least one altitude and / or immersion sensor providing an altitude measurement during the travel of the separate trajectory segments, and of which at least one of the control units is arranged to calculate at least one altitude measurement deviation and to use, when determining the gradient of the gravitational field: o an altitude measurement deviation; o a prediction of the altitude measurement deviation developed from linear acceleration commands; o an average of the position deviations of the vehicles from the separation of the vehicles until the moment of measurement of this deviation;

[0036] - at least one of the control units is arranged to: o calculate linear acceleration commands corrected for lump-sum variations of the vertical and horizontal gravitational field; o calculate a gravitational field gradient with respect to these lump-sum variations.

[0037] The invention also relates to a navigation system using such a gradio-gravimeter, comprising a navigation calculation module arranged to calculate, when vehicles are on the common trajectory segment, an estimate of the vehicle positions and speeds based also on a gravity map. According to optional features, used individually or in whole or in part in combination:

[0038] - the navigation calculation module is arranged to calculate accelerometric commands optimizing the observability of position and velocity errors using a prediction of vehicle positions and velocities and gravity mapping; the navigation calculation module is arranged to calculate: o a prediction of gravity variation along the trajectory of each vehicle from a prediction of positions and velocities and gravity mapping; o corrections to the accelerometric commands specific to each vehicle in order to compensate for the prediction of gravity variations along the trajectory of each vehicle;

[0039] - the navigation calculation module is arranged to improve gravity mapping from redundant measurements taken in the same area and provided by the gradio-gravimeter;

[0040] - at least one of the vehicles is equipped with at least one non-inertial sensor and a module for fusing measurements from the non-inertial sensor with position and velocity estimates in order to improve these position and velocity estimates;

[0041] - the navigation calculation module is arranged to calculate discrepancies between non-inertial sensor measurements and position and velocity estimates and use them to improve gravity mapping.

[0042] Other features and advantages of the invention will become apparent from the following description of a particular and non-limiting embodiment of the invention.

[0043] BRIEF DESCRIPTION OF THE DESIGNS

[0044] Reference will be made to the attached drawings, among which: [Fig. 1] is a block diagram of a gradio-gravimeter according to the invention, the vehicles being in the proximity state;

[0045] [Fig. 2] is a diagram showing the trajectory followed by each of the vehicles.

[0046] DETAILED DESCRIPTION OF THE INVENTION

[0047] With reference to the figures, the present invention is described herein as application to two vehicles VI and V2, here underwater. Vehicles VI and V2 are underwater drones. Alternatively, vehicle VI can be a piloted submarine and vehicle V2 an underwater drone; or vehicles VI and V2 can both be piloted submarines. The invention is obviously applicable to any type of land, air, or sea vehicle.

[0048] Each of the two vehicles VI, V2 comprises respectively: a motorized locomotion unit Locl, Loc2; an inertial measurement unit UMI1, UMI2; an electronic telecommunication unit Tell, Tel2; and an electronic control unit Coml, Com2 connected to the motorized locomotion unit Locl, Loc2, the inertial measurement unit UMI1, UMI2 and the electronic telecommunication unit Tell, Tel21.

[0049] Each motorized locomotion unit Locl, Loc2 comprises a propeller Pl, P2 and a steering mechanism DI, D2. The propeller Pl, P2 consists of a motor powered by a battery that drives a rotating propeller. The steering mechanism DI, D2 comprises a first electric actuator, powered by the battery, that steers directional flaps, and a second electric actuator, also powered by the battery, that steers the propeller. Since the structure and operation of the motorized locomotion units Locl, Loc2 are conventional, they will not be described in further detail here.

[0050] Each inertial measurement unit UMI1, UMI2, connected to the battery, comprises angular sensors Gl, G2 and linear sensors Al, A2 arranged to provide respectively angular velocity measurements (or gyrometric measurements) and linear acceleration measurements (or accelerometric measurements) in an inertial frame of reference for calculation, 12 maintained by the angular sensors Gl, G2 of the inertial measurement unit UMI1, UMI2. More precisely, the angular sensors Gl, G2 are here gyrometers such as axisymmetric vibrating resonator gyrometers like hemispherical resonator gyrometers (or HRG) and the linear sensors Al, A2 are here vibrating accelerometers for example of the MEMS type.The linear sensors A1, A2 are arranged along the axes of a measurement frame of the inertial measurement unit UMI1, UMI2, and the angular sensors G1, G2 measure the orientation of the measurement frame relative to the calculation inertial frame A1, 12 of the inertial measurement unit UMI1, UMI2. The calculation inertial frame A1, 12 of the inertial measurement unit UMI1, UMI2 classically corresponds to the measurement frame of the inertial measurement unit UMI1, UMI2 at the start-up of the inertial measurement unit UMI1, UMI2. The inertial measurement unit UMI1, UMI2 also includes an electronic processing unit T1, T2 connected to the angular sensors G1, G2 and the linear sensors A1, A2 to supply them with power and receive the measurement signals from said sensors.The processing unit T1, T2, for example, performs preprocessing of the measurement signals by integrating them over a predetermined period and combines the accelerometric and gyrometric measurements to determine accelerometric measurements in the inertial frame of reference for calculation (within the limits of residual gyrometric errors). Subsequently, only these accelerometric measurements in the inertial frame of reference for calculation will be considered; the gyroscopes are used only to bring the actual accelerometric measurements into the inertial frame of reference for calculation. The structure and operation of the inertial measurement units UMI1 and UMI2 are conventional and will not be detailed further here.

[0051] Each Tell, Tel2 electronic telecommunications unit, connected to the battery, includes a radio signal transmitter / receiver ER1, ER2, possibly incorporating an encryption module that allows the Com1, Com2 control units to exchange radio signals with each other. The structure and operation of the Tell, Tel2 telecommunications units are conventional and will not be described in further detail here.

[0052] Each control unit Coml, Com2, connected to the battery, includes at least one processor, a memory containing at least one computer program executable by the processor, and an electrical connection interface of the control unit Coml, Com2 to the motorized locomotion unit Locl, Loc2, to the inertial measurement unit UMI1, UMI2 and to the electronic telecommunications unit Tell, Tel2.

[0053] Vehicles VI and V2 are further equipped with at least one device for detecting the relative position and orientation of vehicles VI and V2 when they are in a predetermined state of relative proximity, in this case, a docking state. The relative position and orientation detection device includes at least one element for docking vehicles VI and V2 in a predetermined relative orientation. More specifically, vehicle VI is provided with a male centering V-bolt ve1 to cooperate with a female centering V-bolt ve2 of vehicle V2 and a male angular indexing element in1 to cooperate with a female angular indexing element in2 of vehicle V2 to maintain vehicle VI and vehicle V2 in a predetermined angular position around the central axis of the centering V-bolts ve1 and ve2. The centering Vs and angular indexing elements vél,inl and vé2,in2 determine docking references for each of the vehicles.It is understood that vehicles VI and V2 are in contact with each other when they are in the predetermined state of relative proximity and are in a predetermined relative position and orientation. Since the relative orientation can take several values ​​separated by 180°, this characteristic allows for re-engagement after a relative turnaround during separate sections of trajectory.

[0054] The Com1 and Com2 control units are arranged, and programmed here, to:

[0055] - command the motorized locomotion units Locl, Loc2 of vehicles VI, V2 to make them travel separate trajectory segments (during time Tm, see figure 2 on which the trajectory of vehicle VI is in solid line and the trajectory of vehicle V2 is in dotted line), distinct from each other from a first meeting position (at times tm0 on figure 2) to a second meeting position (at times tmf on figure 2), during which the vehicles VI, V2 are in a state of relative separation and the inertial measurement units UMI1, UMI2 perform angular velocity measurements and linear acceleration measurements;

[0056] - command the motorized locomotion units Locl, Loc2 to make vehicles VI, V2, from the second meeting position, travel a common trajectory segment (of duration Ta on figure 2) during which vehicles VI, V2 are in the predetermined state of relative proximity and exchange the measurements made by the inertial measurement units UMI1, UMI2 during the separate trajectory segments.

[0057] At least one of the Coml control units, Com2, here for example the Coml control unit, is arranged, here programmed, to determine, in particular from the exchanged measurements:

[0058] - a transition matrix between the inertial reference frames of calculation il, 12;

[0059] - a correction of linear acceleration measurements using an observed accelerometric model;

[0060] - a correction of angular velocity measurements using an observed gyrometric model;

[0061] - a time integral of gravitational deviations experienced by the vehicles during the separate trajectory segments.

[0062] More specifically, the Coml control unit is programmed to calculate, when vehicles VI, V2 are alongside and from the accelerometric measurements of vehicles VI, V2 in their respective inertial calculation frames il, 12: o a transition matrix between the inertial calculation frames il, 12; o a correction of the accelerometric measurements of the two vehicles VI, V2 using an accelerometric model observed using the norm of the accelerometric measurements of the two vehicles VI, V2; o a correction of the gyrometric measurements of the two vehicles VI, V2 using a gyrometric model observed from the successive orientations of the accelerometric measurements of the two vehicles VI, V2; o rotational speed and translational acceleration commands to be performed by each of the vehicles VI, V2 between two dockings and in their respective inertial calculation frames il, 12.The rotation speed and translation acceleration instructions are developed and transmitted to the locomotion units Loc1, Loc2 for:.

[0063] ■ program and control a separation of vehicles VI, V2 from a docking;

[0064] ■ assuming a constant gravitational field, make each of the vehicles VI, V2 travel the same distance, in the same direction and for the same duration towards a next docking location, but following a different trajectory;

[0065] ■ create the conditions of relative speeds and positions between vehicles VI, V2 necessary for the initiation of a future autonomous docking of vehicles VI, V2;

[0066] ■ optimize the observation of the terms of the accelerometric and gyrometric models during the periods when vehicles VI, V2 are docked.

[0067] On each segment of the trajectory, the directions are defined at each instant t according to:

[0068] - the accelerometer measurement acc (t) ,

[0069] - the derivative of my ac c(t') / dt of the accelerometric measurement ac c(t) •

[0070] If the common trajectory segment is sufficiently regular and at a low speed compared to the tangent speed = R Terre ^Earth cos (Latitude), the accelerometer measurement follows a cone whose base is a circle that a person skilled in the art can identify. It will be understood that Rr is the radius of the Earth, (l Terre is the Earth's rotation speed and Latitude is the latitude of vehicles VI, V2.

[0071] The evolution observed during the previous common trajectory segment is preserved during the separate trajectory segments by applying a common acceleration command CAC.

[0072] We then obtain:

[0073] Thus, x(t),ÿ(t),z(t) define a frame of reference exhibiting an evolution of orientation without discontinuity before and after the separation of the moving parts.

[0074] The acceleration commands during the separate trajectory segments are the sum of the common acceleration command CAC(t) calculated from the previous common trajectory segment and a differential acceleration command CAD^t') specific to each vehicle Vi (i being equal to 1 or 2 in the case of two vehicles or taking the values ​​1 to n in the case of n vehicles). The control of the vehicles Vi therefore aims to control the forces necessary to control the accelerometric measurements according to their acceleration command CAC(t) +

[0075] For each differential acceleration instruction common trajectory);

[0076] - the average at each instant of the differential acceleration instructions CAD^t') is not necessarily equal to 0;

[0077] - one of the vehicles may be assigned a differential acceleration setting (CAZ) l (t)=O ;

[0078] - the differential acceleration instructions CAD^t') are expressed in the inertial reference frame of calculation il, 12.

[0079] The vehicle piloting system ensures that:

[0080] Two modes of embodiment will be described for the determination of the time integral of the gravitational deviations.

[0081] According to a first embodiment, the Coml control unit is programmed to calculate:

[0082] - a simple time integral of the difference in accelerometer measurements of each of the vehicles VI, V2 between two dockings; and / or

[0083] - a double time integral of the difference in accelerometric measurements of each of the vehicles VI, V2 between two dockings.

[0084] The simple time integral of the difference in accelerometric measurements of each of the vehicles VI, V2 between two dockings characterizes the time integral of the gravitational differences experienced by the vehicles VI, V2 during their respective journeys.

[0085] The double time integral of the difference in accelerometric measurements of each of the vehicles VI, V2 between two dockings characterizes the double time integral of the gravitational differences experienced by the vehicles VI, V2 during their respective journeys.

[0086] According to a second embodiment, vehicles VI, V2 are to be equipped with a measuring device providing, taking into account the constraints on the CAD^' t) controls and the piloting of the vehicles set out above, during at least part of the journey of vehicles VI, V2: o a measurement of the relative speed between the docking references characterizing the simple time integral of the gravitational deviations suffered by vehicles VI, V2 on their respective separated trajectory segment; and / or o a measurement of a distance between the docking references characterizing the double time integral of the gravitational deviations suffered by vehicles VI, V2 on their respective separated trajectory segment.

[0087] The measuring device is, for example, a rangefinder.

[0088] It is understood that the two embodiments described above allow us to determine o the simple time integral of the gravitational deviations experienced by vehicles VI, V2 on their respective separate trajectory segments; and / or o the double time integral of the gravitational deviations experienced by vehicles VI, V2 on their respective separate trajectory segments.

[0089] The invention thus makes it possible to exploit the fact that comparing accelerometer measurements on separate trajectory segments reveals the differences in gravitational forces between those segments. It should be noted that an accelerometer measures both the acceleration of the vehicle on which it is mounted and the opposite gravitational force experienced by that vehicle.

[0090] Translational acceleration commands are generated, causing vehicles VI and V2 to move from one docking point to another via separate trajectory segments. These acceleration commands are sent to servo systems of the motorized locomotion units Loc1 and Loc2 to generate forces that enable them to follow these acceleration commands.

[0091] In order to allow a new docking of vehicles VI, V2, the acceleration instructions must respect the following conditions (here we assume that the gravity is constant on the separate trajectory segments of vehicles VI, V2): We note that these conditions are necessarily met if the CADjft commands are chosen according to the rules set out above.

[0092] If the gravitational forces are not equivalent along the separate trajectory segments, the two vehicles VI and V2 will not reach the same position or the same speed at the end of their respective separate trajectory segments. The measurement of this difference characterizes the simple and double time integrals of the gravitational differences experienced by the two vehicles VI and V2.

[0093] It is understood that along the two separate trajectory segments, the Coml control unit works differentially and will have more precision on the gravity gradient as the vehicles VI, V2 are separated from each other since this increases the difference in gravity.

[0094] Similarly, when the two vehicles VI, V2 dock after traversing separate trajectory segments (using additional acceleration commands), the above equalities will not be perfectly respected, and their dissonance will characterize the simple and double time integrals of the gravitational differences experienced by the two vehicles VI, V2. We will now detail the determination of the gravitational field gradient using the velocity / position differences between the two vehicles.

[0095] The gravitational tensor is written in the form of a ma- gravitational field, gitx.yz) the i component of the gravitational field, i, j E{x,y,z}. and {x,y,z} Cartesian and inertial frame. We also recall the following properties of gravitation:

[0096] - Gxy Gyx, Gxz Gzx, Gyz G zy r

[0097] - Gxx+Gyy+Gzz+4nGp=0 with the last term equal to s -2in the air and 0.839.10 -6 s -2 in the water.

[0098] Therefore, only five representative unknowns remain:

[0099] - of the three terms of the rotation matrix allowing the gravity gradient matrix to be made diagonal;

[0100] - of the gradient along two of the principal directions. At the beginning of the separate trajectory segments, vehicles VI, V2 are in the same position and are moving at the same speed.

[0101] At the end of the separate trajectory segments, differences in position P and speed V are measured between n vehicles Vi:

[0102] These discrepancies are due to gravity gradients assumed to be constant according to the actual or predicted position differences between the vehicles.

[0103] The speed differences between vehicles Vi at the end of the separated trajectory segments are due to the gradients of the gravitational field according to the positional differences between the vehicles:

[0104] Therefore, it can be expressed in the following form: with a xyi , has xzl > a yy i> a yzi> a zzi l e s Factors influencing the severity gradient on AV Vl (tmf') due to the choice of CAD1(t').

[0105] The positional differences between vehicles Vi at the end of the separated trajectory segments are also due to the gradients of the gravitational field according to the positional differences between the vehicles:

[0106] These equations can therefore be written in the form: with b xyi , b xzl , by yi , by Zl , b zzl factors influencing the severity gradient on AP Vl(tmf) due to the choice of CAD^t) .

[0107] G xx G X y G X z

[0108] Therefore, at each docking the Gyx gradients G yy Gyz are

[0109] G zx G zy G zz calculated from the following quantities: AV Vl (tmf) and AP Vl (tmf): measurements

[0110] — Cl X y t , Cl xzt , Clyy t Cly Zt , Cl zzt functions

[0111] — b X y lr b xzlr byy lr by Zlr b zzl functions Calculating gradients involves inverting the system of equations

[0112] The me rice

[0113] T r uxx u xy C '-'xz rr uyx u yy < rJy Z depending on the choice of CAD^t) . r uzx < rJ Z y G zz

[0114] Obtaining Rank (A) = 5 allows the inversion of the system of equations.

[0115] Several uses of gravitational deviations are possible, as will be seen later. Preferably, the rotation speed commands developed for at least one of the vehicles VI, V2 on its separate trajectory segment are such that said at least one of the vehicles VI, V2 performs rolls (of approximately 180°) around at least one axis, and advantageously two non-coincident axes, fixed in the inertial or terrestrial frame of reference. A horizontal and / or a vertical axis can be chosen. Alternatively, at least one of the inertial measurement units UMI1, UMI2 can be mounted on a rollover table controlled by the processing unit T1, T2: it is no longer the vehicle VI, V2 that undergoes the rolls, but only the inertial measurement unit UMI1, UMI2.The reversals are thus controlled in the form of angular velocity commands sent via servo systems to suitably arranged and controlled actuators in order to apply the torques necessary for these reversals.

[0116] Indeed, it is known that with reversals impacting the inertial measurement unit UMI1, UMI2:

[0117] • the effects of gyroscopic and accelerometric errors in the inertial or terrestrial frame of reference are greatly reduced (because, for the most part, they are reversed at each reversal);

[0118] • Gyroscopic and accelerometric errors are observable (and therefore compensable) by comparison between an inertial measurement unit that turns over and an inertial measurement unit that does not turn over. This comparison is, for example, feasible during docking periods (i.e., when the relative position and attitude of vehicles VI, V2 are known or measurable by non-inertial means), the simplest case being successive dockings between the two vehicles VI, V2, separated by a rotational movement globally equivalent to a turning over of at least one of the vehicles VI, V2.

[0119] Thus, the apparent stability of the accelerometric measurement becomes almost independent of long-term variations in accelerometric biases. It is noted that the best results are obtained with vibrating accelerometers, for which it is sufficient to measure the evolution of the accelerometric bias (their scaling factor error being very stable). Therefore, it is possible to achieve an accelerometric accuracy on the order of 1 pg (in three dimensions, not just along the vertical axis) with standard gyroscopes / gyrometers and accelerometers, admittedly of the inertial class, but without resorting to a high-precision accelerometer commonly called a gravimeter. Thus, the errors due to the accelerometric measurement, on the differences between their single and double integrals estimated by the two inertial measurement units UMI1 and UMI2 since the last docking, become small compared to gravitational variations of 10 pg.These variations in gravitation then become measurable and usable, for example, in a navigation system to perform recalibrations based on a cartographic reference of gravitation as we will see later.

[0120] The frequency of the reversals allows for at least one, and preferably more than ten, to be performed during the separate trajectory segment. These reversals can be carried out at predetermined times, independently on each of the vehicles VI and V2, or synchronously with respect to a common time reference. Outside of the reversal times, the angular velocity commands can be held at zero, which keeps the attitudes of vehicles VI and V2 fixed relative to the inertial frame of reference. These reversals are also advantageous during short intervals between the points of convergence.

[0121] Preferably, the control instructions for the motorized locomotion units Locl, Loc2 are developed so that the separation of the two vehicles VI, V2 at the end of the common trajectory section takes place along a docking line.

[0122] The Coml and Com2 control units:

[0123] - estimate the direction of this docking line by the difference in accelerometer measurements between vehicles VI, V2 during this separation and in their respective inertial frame il, 12;

[0124] - memorize this direction to use it as a reference to generate docking movements of each of the vehicles VI, V2 at the end of the separate trajectory segments.

[0125] The docking movements are generated:

[0126] - in a first stage, in a plane substantially perpendicular to the docking line, the two vehicles VI, V2 having cross-scanning movements arranged to facilitate the search for a coincidence between optical markers positioned on vehicles VI, V2 along this docking line; then

[0127] - in a second stage, when the coincidence of the optical reference points has been achieved, along this docking line to generate a convergence movement of vehicles VI, V2 towards each other.

[0128] The first step is carried out using Caml and Cam2 optical cameras connected to the Coml and Com2 control units respectively to provide images on which the centering Vs (Vel and V2) and the angular indexing elements (Inl and In2) will constitute visual reference points. The quality of the acceleration measurement obtained by the rollovers allows the calculation of gravity on the trajectory segments of vehicles VI and V2 and the deduction of a map of the "local" gravity gradient, that is, in the geographical area traversed by the two vehicles VI and V2.

[0129] It is possible to use this local map, measured jointly by the two vehicles VI and V2, to perform recalibrations by comparing the local map measured by the combined vehicles VI and V2 to a pre-established reference map. Comparing the map generated locally by vehicles VI and V2 to the reference map yields position and velocity errors, which manifest over a short time horizon and are affected by predictable and manageable uncertainties, based on the local variability of the gravitational field and the uncertainty of the reference map. This allows for the recalibration of the positions and velocities of vehicles VI and V2.

[0130] Alternatively, it is possible to compensate for known variations in the gravitational field in order to cancel the influence of the known gravity gradient on the effective relative positions of vehicles VI, V2. For example, if we only consider first-order variations along the vertical axis and in the horizontal plane (relative to the Earth), the compensated differential accelerometer commands CAD ipc are : This formula includes:

[0131] - the projection according to CAC(t)

[0132] - the projection perpendicular to CAC(t)

[0133] - the vertical variation (assumed to be oriented along

[0134] - the horizontal variation (Schuler effect, assumed to be oriented perpendicular to CAC)

[0135] This leads to the local simulation of a uniform gravitational field of order 1. The gravity gradient measurements developed by the gradio-gravimeter then identify the deviations from this virtual field according to the coordinate system {%, y, z}.

[0136] Alternatively, the Coml control unit has a three-dimensional gravity map that allows it to:

[0137] • predict and therefore compensate for the influence of known variations in gravity on the single and double integrals of the accelerometric measurements of each of the vehicles VI, V2;

[0138] • determine the influence of an initial error of positions and velocities on the integrals obtained on the paths affected by this initial error;

[0139] • choose routes allowing to maximize the observability of initial position and velocity errors from the measurement of differential positions and velocities between the two vehicles VI, V2.

[0140] The initial errors in positions and velocities will therefore result in differential positions and velocities between the two vehicles VI and V2 during the subsequent docking. The influence of these initial errors in positions and velocities is determined using the gravity gradient derived from the map.

[0141] Thus, the observability of position and velocity errors obtained through the comparison of trajectories between vehicles VI, V2 is predictable, controllable and manifests itself in the short term.

[0142] Alternatively, at least one of the command units (e.g., Coml) is configured to:

[0143] - calculate linear acceleration commands corrected for fixed variations in the vertical gravitational field (for example, 2.2 x 10 -6 s~ 2 has

[0144] 3.10 -6 s -2 ) and horizontal (for example, -1.5 x 10⁻¹⁰⁴) 6 s~ 2 ) ;

[0145] - calculate a gravitational field gradient with respect to these fixed variations.

[0146] More generally, the Coml control unit is programmed to deduce the positions, speeds, attitudes, and their uncertainties for the current berthing point from the positions, speeds, attitudes, and their uncertainties for the previous berthing point and:

[0147] • accelerometric measurements of vehicles VI, V2 in reference frames il, 12;

[0148] • from the measurement of their position and speed differences that have appeared since the last point of docking;

[0149] • a cartographic reference of gravitation.

[0150] The gradio-gravimeter according to the invention can be used in a navigation system comprising a navigation calculation module Navl, Nav2, here distributed over vehicles VI and V2, arranged to calculate, when vehicles VI, V2 are on the common trajectory segment, an estimate of the positions and speeds of vehicles VI, V2 also from a gravity map.

[0151] More specifically, the Navl, Nav2 navigation calculation module is integrated here into the Coml, Com2 control units of the VI, V2 vehicles and is programmed to calculate, after initialization performed when the navigation system starts and when the VI, V2 vehicles are alongside, an estimate of the positions and speeds of the VI, V2 vehicles from:

[0152] • from the previous estimation of the positions and speeds of vehicles VI, V2;

[0153] • measurements of the corrected accelerations of vehicles VI, V2 in their inertial frames 11, 12 from the previous estimation of the positions and velocities of vehicles VI, V2;

[0154] • the following information provided by the gradio-gravimeter: o the transition matrix between the inertial reference frames 11, 12 of vehicles VI, V2; o the simple integral and / or double integral of the difference in accelerometric measurements of each of the vehicles VI, V2 between two dockings (first embodiment); or the position and / or velocity differences, measured between the two vehicles VI, V2 at the end of their respective separate trajectory segments carried out since the previous docking (second embodiment);

[0155] • a gravitational mapping serving as a reference.

[0156] It should be noted that this application made possible by the invention is much more advantageous than that of a single vehicle realigning itself solely by observing gravity along a "linear" path. Indeed, in the latter case, the observability of errors is only achieved in the long term, which makes its use complex in the short term, even dangerous, and in all cases limits the accuracy of such realignment (a compromise between observability and the accuracy of inertial navigation in pure inertia).

[0157] Preferably, the Coml control unit is programmed to calculate acceleration commands for the Locl, Loc2 motorized locomotion unit, optimizing the observability of position and velocity errors by using the estimation of vehicle positions and velocities VI, V2 and gravity mapping. Even more preferably, the Navl, Nav2 navigation calculation module is programmed to:

[0158] - predict variations in gravity along the separate trajectory segment of each of the vehicles VI, V2 based on the estimation of the positions and speeds of the vehicles VI, V2 and the gravity mapping;

[0159] - calculate corrections to said acceleration instructions, specifically for each motorized locomotion unit Loc1, Loc2 in order to compensate for the variations in gravity predicted along the separate trajectory segment of each of the vehicles VI, V2.

[0160] As an indication, the following orders of magnitude are mentioned.

[0161] The vertical divergence at time t is equal to

[0162] We have t div vert ~ 674s so that the error is multiplied by 2.7 every 674 seconds. We will choose trajectory segments separated by a duration of less than 2000 seconds in the absence of an additional non-inertial sensor of the immersion type which would limit the vertical errors.

[0163] After a thousand seconds, a difference in gravitational magnitude of 10 pg between the two vehicles VI, V2 leads to a difference of 50 m in the estimates of their vertical positions. This calculation neglects the angle between the gravitations seen by the two vehicles VI, V2 due to the distance separating them (sin -1 — - — ~ 4.7 mrd for a distance ^Earth of 30 km). A gravitational deviation of 10 prad is equivalent to a position error of 64 m which, via Schuler oscillations, can lead to a velocity error of 0.08 m / s (i.e., 0.16 knots).

[0164] Alternatively, at least one of the command units (e.g., Coml) is configured to:

[0165] - calculate linear acceleration commands corrected for fixed variations in the vertical gravitational field (of 2.2 x 10 -6 s~ 2 at 3.10 -6 s -2 ) and horizontal (from — 1.5.10 -6 s~ 2 ) ;

[0166] - calculate a gravitational field gradient with respect to these fixed variations.

[0167] Alternatively, at least one of the vehicles can be equipped with at least one non-inertial sensor and run an algorithm to fuse measurements from this non-inertial sensor with position and velocity estimates obtained without this non-inertial sensor, in order to improve these position and velocity estimates. The discrepancies between the measurements from the non-inertial sensor and the position and velocity estimates obtained without this non-inertial sensor can also be used to improve gravity mapping. The non-inertial sensor could, for example, be a satellite positioning signal receiver (GNSS), an odometer, or an immersion sensor.

[0168] Alternatively, vehicles can be equipped with an immersion (or altitude) sensor. In this case, the gradiogravimeter uses relationships similar to those used for measuring gradients by velocity and position differences. However, there are some specific features. The altitude information Im is available at every instant, so Im(tmO+gAt) is the immersion measurement as a function of the sampling period At, where j represents the sample number. This information is only available depending on the verti- with c xzL '(j), Cy Zl (f)> c ZZL (J) factors influencing the severity gradient on + jAt\ due to the choice of CAD^t) .

[0169] Gxx G x y G xz

[0170] Therefore, at each docking the gradients Gyx dyy Gy Z are G zx G Z y G zz calculated from the following quantities: measurements

[0171] We obtain a new formulation, solvable under the same conditions as in the case where there is no altitude sensor:

[0172] This calculation can be done using a Kalman filter. Of course, the invention is not limited to the embodiments described but encompasses any variant falling within the scope of the invention as defined by the claims.

[0173] In particular, the gradio-gravimeter according to the invention may have a different structure from that described. The actuators involved in the reversals may be those used to follow the trajectories and / or actuators dedicated to reversing the inertial measuring unit in such a way that the actuators allow to rotate: • either the whole of the vehicle (for example using steerable propellers for a marine or aerial vehicle);

[0174] • or only the inertial measurement unit which is located within the vehicle (using a cardan joint system for example).

[0175] To improve the intrinsic stability (excluding rollovers) of angular and linear sensors, vehicles VI and V2 can be equipped with a thermal regulation device for the inertial measurement units (conduction, convection, or radiation: heat exchanger, electric heating device, radiator, etc.). At least one of the vehicles VI and V2 can have a sufficient energy reserve to recharge the other vehicle's battery during shared sections of the trajectory. Therefore, vehicles VI and V2 are equipped with matching electrical connectors that cooperate when the vehicles VI and V2 are alongside each other.

[0176] The trajectories of vehicles VI and V2 can be predetermined and expressed as a function of the accelerations that vehicles VI and V2 will undergo. Thus, rather than controlling the motorized locomotion units Loc1 and Loc2 from a complete navigation system (calculating the positions and velocities of vehicles VI and V2), accelerometric information (referred to in an inertial frame of reference, within residual gyroscopic errors) is used directly. This allows us to take advantage of the higher frequency of accelerometric information (compared to that of positions and velocities) and therefore to implement trajectory tracking control systems with a higher bandwidth. A similar approach involves using gyroscopic information (rather than attitudes) to control attitudes.To facilitate the docking of vehicles VI and V2, the vehicles VI and V2 are preferably equipped with guidance systems using, for example, optical technologies. For instance, the vehicles VI and V2 are equipped with cameras and visual markings that allow the control units Com1 and Com2 to guide the motorized locomotion units Loc1 and Loc2, progressively bringing the vehicles VI and V2 together until docking. In this case, comparing the positions, speeds, and attitudes of the two vehicles VI and V2 during the shared trajectory segment is facilitated. The control units Com1 and Com2 can be configured to implement a calibration phase during which two vehicles VI and V2, docked together, uncouple, perform a 180° turn, and then recouple while maintaining the 180° turn.During the docking periods, the estimated speeds, positions and attitudes of the two vehicles VI, V2 can be compared in order to deduce the accelerometric and / or gyroscopic and / or conventional calibration errors of the Inertial Measurement Units.

[0177] The invention can be implemented without vehicles VI and V2 being alongside each other in the predetermined state of relative proximity. In this case, the relative distances and / or orientations of the two vehicles VI and V2 are measured. The comparison of positions, speeds, and attitudes during the shared trajectory segment must then take these measurements into account.

[0178] It is possible to vary the durations of the common and separate trajectory segments in order to promote:

[0179] - either the identification of errors in inertial sensors (during the first moments of use), the duration of the separate trajectory segments is limited to the time required for the relative reversals of the vehicles;

[0180] - either the gradio-gravimetric measurement (operational operation), the durations of the common trajectory segments and the separate trajectory segments are then close (duration ratio between 0.5 and 2).

[0181] Preferably, a certain amount of time (typically a similar time in a ratio of 0.5 to 2) should be left between the docking and separation periods to ensure that the accelerometer measurement is observed during the docking period and then reproduced during the separation period as the CAC accelerometer setpoint. Performing reversals during the separated trajectory segments of one or both vehicles is optional and serves only to improve the identification of inertial sensor errors (bias, scale factor, and alignment angle).

[0182] Information transfers enabling comparison of information between vehicles VI, V2 can be carried out during docking or when the vehicles are close enough to measure their relative distances and / or orientations and exchange information.

[0183] The comparison of information can be carried out within a single vehicle VI, V2 or be decentralized across the different vehicles VI, V2.

[0184] The invention can be implemented with a three-dimensional chart: if the gravity gradient conforms to the chart's predictions, the vessel is in the correct location; otherwise, the vessel realigns itself with the chart. The invention can also be implemented with an imperfect chart: the discrepancies are then used to locally correct the chart, provided that local reorientation is possible. In the absence of a chart: the information obtained at each docking allows the chart to be updated. It is possible to determine whether the observed error is a positional error or a chart error by finding the best correlation between the chart and the position, assuming the residual discrepancy is a chart error, all while taking into account a potential measurement error.

[0185] The vehicles can be identical or different. Many useful configurations can be imagined. One example is a large, relatively inflexible ship paired with a small, highly maneuverable underwater drone. This combination allows the large ship to benefit in real time (at the frequency of dockings) from measurements of the gravitational field gradients and thus perform optimal navigation by exploiting this knowledge.

[0186] The measurement of gravitation for the purpose of creating or improving a cartographic reference of gravitation has, for example, a direct application in the search for economically exploitable geological deposits.

[0187] The gradio-gravimeter can be deployed by more than two vehicles. The measurements provided by the gradio-gravimeter can be used to improve gravity mapping through redundant measurements obtained by more than two vehicles (with only two vehicles, it is preferable to plan multiple successive journeys, which can be nested and carried out in the same area).

[0188] Angular sensors can be of any type and for example of the gyrolaser type.

[0189] Communication between the control units can be solely via electrical contact during coupling phases. The invention is applicable to any type of vehicle, piloted or unpiloted, land, nautical, underwater, aerial or space-based.

Claims

DEMANDS 1. A gravimeter comprising at least two vehicles (VI, V2), each comprising a motorized locomotion unit (Locl, Loc2), an inertial measurement unit (UMI1, UMI2), and an electronic telecommunication unit (Tell, Tel2), all three connected to an electronic control unit (Coml, Com2). The inertial measurement units each comprise angular sensors (Gl, G2) and linear sensors (A1, A2) arranged to provide angular velocity measurements and linear acceleration measurements, respectively, in an inertial frame (il, i2) maintained by the angular sensors of the inertial measurement unit. The vehicles are equipped with at least one device (vél, vé2, inl, in2) for detecting the relative position and orientation of the vehicles when they are in a predetermined state of relative proximity. The electronic control units being arranged to: - to command the vehicles to travel separate sections of trajectory, distinct from each other from a first meeting position to a second meeting position, during which the vehicles are in a state of relative separation; - to command a relative reversal of the inertial navigation systems during at least one of the separated sections; - to command the vehicles to travel, from the second meeting position, a common trajectory segment during which the vehicles are in a state of proximity and exchange measurements taken by the inertial measurement units during the separate trajectory segments; at least one of the electronic control units being arranged to determine, in particular based on the measurements exchanged: - a transformation matrix between inertial frames; - a correction of linear acceleration measurements using an observed accelerometric model; - a correction of angular velocity measurements using an observed gyrometric model; - a gradient of the gravitational field from o a time integral of gravitational deviations experienced by the vehicles during the separate trajectory segments; o a relative separation of the vehicles during the separate trajectory segments.

2. Gradio-gravimeter according to claim 1, wherein the relative distance is an average of the differences between positions, during separate trajectory segments, calculated from accelerometric measurements and / or predicted from vehicle controls.

3. Gradio-gravimeter according to claim 1 or 2, wherein the time integral of the gravitational deviations is a simple time integral and at least one of the vehicles comprises a relative speed measuring device of the vehicles characterizing the simple time integral of the gravitational deviations.

4. Gradio-gravimeter according to any one of the preceding claims, wherein the time integral of the gravitational deviations is a double time integral and at least one of the vehicles includes a measuring device for a relative distance of the vehicles characterizing the double time integral of the gravitational deviations.

5. A gravimeter according to any one of claims 3 or 4, wherein said at least one of the electronic control units (Coml) is arranged to calculate a simple time integral of differences between linear acceleration measurements of vehicles on separate trajectory segments, the simple time integral of differences between linear acceleration measurements characterizing the simple time integral of gravitational differences.

6. Gradio-gravimeter according to any one of claims 4 or 5, wherein said at least one of the electronic control units (Coml) is arranged to calculate a double time integral of differences between linear acceleration measurements of vehicles on separate trajectory segments, the double time integral of differences between linear acceleration measurements characterizing the double time integral of gravitational differences.

7. A gravimeter according to any one of the preceding claims, wherein the reciprocal relative orientation detection element (vel, ve2, inl, in2) comprises at least one vehicle docking element in at least one predetermined relative orientation, the relative orientations being separated by approximately 180 0 .

8. Gradio-gravimeter according to any one of the preceding claims, wherein the reciprocal relative orientation detection organ (vel, ve2, inl, in2) comprises at least one optical camera (caml, cam2).

9. Gradio-gravimeter according to any one of the preceding claims, in which at least one of the vehicles (VI, V2) includes a motorized reversing device for the inertial measuring unit (UMI1, UMI2).

10. A gravimeter according to any one of the preceding claims, wherein the electronic control unit (Com1, Com2) of at least one of the vehicles is programmed to control the vehicle's motorized locomotion unit (VI, V2) to make it perform movements corresponding to reversals of the inertial measurement unit (UMI1, UMI2).

11. Gradio-gravimeter according to any one of the preceding claims, wherein at least two of the vehicles are each equipped with at least one altitude and / or immersion sensor (Alt1, Alt2) providing an altitude measurement during the travel of the separate trajectory segments, and wherein at least one of the control units (Coml) is arranged to calculate at least one altitude measurement deviation and to use, in determining the gradient of the gravitational field: - a difference in altitude measurement; - a prediction of altitude measurement deviation developed from linear acceleration commands; - an average of the position differences of the vehicles from the separation of the vehicles until the moment of measurement of this difference.

12. A gravimeter according to any one of the preceding claims, wherein at least one of the control units (Coml) is arranged to: - calculate linear acceleration commands corrected for lump-sum variations in the vertical and horizontal gravitational field; - calculate a gravitational field gradient with respect to these fixed variations.

13. Navigation system comprising a gradio-gravimeter according to any one of the preceding claims, comprising a navigation calculation module (Navl, Nav2) arranged to calculate, when the vehicles (VI, V2) are on the common trajectory segment, an estimate of the positions and speeds of the vehicles also from a gravity map.

14. System according to claim 13, wherein the navigation calculation module (Navl, Nav2) is arranged to calculate accelerometric setpoints optimizing the observability of position and velocity errors in using a prediction of vehicle positions and speeds (VI, V2) and gravity mapping.

15. System according to claim 14, wherein the navigation calculation module (Navl, Nav2) is arranged to calculate: - a prediction of the variation of gravity along the trajectory of each of the vehicles (VI, V2) from a prediction of positions and speeds and the mapping of gravity; - corrections to the accelerometer instructions specific to each vehicle in order to compensate for the prediction of variations in gravity along the trajectory of each vehicle.

16. System according to any one of claims 13 to 15, wherein the navigation calculation module (Navl, Nav2) is arranged to improve gravity mapping from redundant measurements made in the same area and provided by the gradio-gravimeter.

17. System according to any one of claims 13 to 16, wherein at least one of the vehicles (VI, V2) is equipped with at least one non-inertial sensor and a module for fusing measurements from the non-inertial sensor with position and velocity estimates in order to improve these position and velocity estimates.

18. System according to claim 17, wherein the navigation calculation module (Navl, Nav2) is arranged to calculate discrepancies between the measurements of the non-inertial sensor and the estimates of positions and velocities and to use them to improve gravity mapping.

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