Gradio-gravimeter and navigation system using such a gradio-gravimeter

Abstract

A gradio-gravimeter comprising at least two vehicles (V1, V2), each with an inertial measurement unit (IMU1, IMU2) and a control unit (COM1, COM2) for guiding the vehicles along trajectories with separate segments for performing IMU flips and coupled segments for exchanging inertial measurements. At least one of the electronic control units is configured to determine, notably from the exchanged measurements: a transition 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, and a gravitational field gradient. Navigation system comprising such a gradio-gravimeter. FIGURE IN ABRIDGED DIAGRAM: Fig. 1

Description

Title of the invention: Gradio-gravimeter and navigation system using such a gradio-gravimeter The present invention relates to the fields of gravimetry and vehicle navigation. BACKGROUND OF THE INVENTION It is worth remembering that gravitation is one of the four fundamental forces and is commonly described by: - a scalar gravitational potential ¢( x. y, z ) - a gravitational field dx g(x,y,z) = d^x^z) dy — gy(x,y,z) d^xyz). dz gz(x,y,z) _ a gravitational tensor ' d^xy-z) d^xyz') d20(x,yz) ' ' dg£x,y,z} dgyxy.z) dg / xyy^ ' Gxx Gxy Gxz dx2 dydx dzdx dx dy dz r1 r1 r1 d2 < / )(xy.z) d2<^xyz) d2<gx.yz) dgjx.yz) dg / x,yz) dgjxyyz) Ufyx ^yy Uyz = dxdy dy2 dzdy — dx dy dz , G^ Gzy Gzz d^xyg) d2^xyz) d^-^yg.) dg,(xyX) dg / x.yx) dg^yz) , dxdz dydz dz2 , dx dy dz

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[0007] having the following properties: - Gif = G^ with i, j G {x, y, z} Gxx + Gyy+GU + 4nGp (x, y, z) = 0 with : - x, y and z are Cartesian coordinates in an inertial frame of reference - Gj f with i, j G {x, y, z} being the components of the gravitation tensor G: Universal gravitational constant 6.674 × 10¹¹ m³.kg⁻¹.s² p(x,y,z): density at point x, y, z In the following, the term "gravity gradiometer" or "gradio-gravimeter" is used. device designed to measure the gravitational tensor GXx Gxy Gyx Gyy Gzx Gzy GXZ' (jyz Gzz.

[0008] For example, it is known to use gradio-gravimeters to produce gravimetric maps representing the variation in the intensity of the gravitational field in specific geographical areas.

[0009] It is understood that the accuracy of the gravity gradient measurement depends directly on the accuracy of the gradiogravimeter. This is known for gradiogravimeters made from high-precision accelerometers (on the order of pg, where g is the value of Earth's gravity). Such accelerometers are expensive.

[0010] Furthermore, it is known to use, in the field of vehicle navigation, inertial measurement units with reversal. These inertial measurement units comprise 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.

[0011] SUBJECT OF THE INVENTION

[0012] The invention is notably aimed at carrying out precise measurements of gravity gradients. Summary of the invention

[0013] To this end, the invention provides a gradio-gravimeter comprising at least two vehicles, each including a motorized locomotion unit, an inertial measurement unit, and an electronic telecommunications 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: - 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; - command the vehicles to travel from the second meeting position along a section of common trajectory during which the vehicles are in a state of proximity and exchange measurements taken by inertial measurement units during separate trajectory segments.

[0014] At least one of the electronic control units is arranged to determine, in particular from 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 • a time integral of gravitational deviations experienced by the vehicles during the separated trajectory segments; • of a relative separation of vehicles during the separated sections of the trajectory.

[0015] The invention exploits the fact that comparing linear acceleration measurements on separate trajectory segments reveals the differences in gravitational forces between these segments. Indeed, it should be noted that a linear acceleration sensor measures both the acceleration of the vehicle on which it is mounted and the opposite of the gravitational force experienced by the vehicle. During the common trajectory segments, comparing the linear acceleration measurements projected onto an inertial frame of reference allows for the deduction of linear acceleration and / or angular velocity errors of the inertial measurement units and / or calibration errors of the inertial measurement units relative to each other. This improves the accuracy of linear acceleration measurements and allows for obtaining relatively precise gravity gradient measurements without resorting to a conventional gradiogravimeter.

[0016] According to optional features, used individually or in whole or in combination: - relative distance is an average of the differences between positions, during separate trajectory segments, calculated from accelerometer measurements and / or predicted from vehicle commands; - 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; - 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; 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; said at least one of the electronic control units 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; the reciprocal relative orientation detection device includes at least one vehicle docking element in at least one predetermined relative orientation, the relative orientations being separated by approximately 180°; the detection device for a reciprocal relative orientation includes at least one optical camera; at least one of the vehicles includes a motorized device for reversing the inertial measuring unit; 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 reversals of the inertial measurement unit; 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 at least one of whose control units is arranged to calculate at least one altitude measurement deviation and use it when determining the gravitational field gradient: • a difference in altitude measurement; • a prediction of altitude measurement deviation developed from linear acceleration commands; • an average of the positional differences of the vehicles from the separation of the vehicles until the moment of measurement of this difference; at least one of the control units 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.

[0017] The invention also relates to a navigation system using such a gradio-gravimeter, comprising a navigation calculation module arranged to calculate, when the vehicles are on the common trajectory segment, an estimate of the positions and speeds of the vehicles also from a gravity map.

[0018] According to optional features, used individually or in whole or in combination: - the navigation calculation module is arranged to calculate accelerometric setpoints optimizing the observability of position and velocity errors by using a prediction of vehicle positions and velocities and gravity mapping; - The navigation calculation module is designed to calculate: • a prediction of the variation of gravity along the trajectory of each of the vehicles based on 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; - the navigation calculation module is arranged to improve gravity mapping from redundant measurements taken in the same area and provided by the gradio-gravimeter; - 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; - The navigation calculation module is designed to calculate discrepancies between non-inertial sensor measurements and position and velocity estimates and use them to improve gravity mapping.

[0019] Other features and advantages of the invention will become apparent from the following description of a particular, non-limiting embodiment of the invention. Brief description of the drawings

[0020] Reference will be made to the attached drawings, among which:

[0021] [Fig-1] is a block diagram of a gradio-gravimeter according to the invention, the vehicles being in the vicinity;

[0022] [Fig.2] is a diagram showing the trajectory followed by each of the vehicles. DETAILED DESCRIPTION OF THE INVENTION

[0023] With reference to the figures, the present invention is described herein in application to two vehicles VI, V2, here underwater. The vehicles VI, V2 are underwater drones. Alternatively, vehicle VI may be a piloted submarine and vehicle V2 an underwater drone; or vehicles VI, V2 may both be piloted submarines. The invention is obviously applicable to any type of land, air, or sea vehicle...

[0024] Each of the two vehicles VI, V2 comprises respectively: a motorized locomotion unit Locl, Loc2; an inertial measurement unit UMI1, UMI2; an electronic telecommunications unit Tell, Tel2; and an electronic control unit Coml, Com2 connected to the motorized locomotion unit Locl, Loc2, to the inertial measurement unit UMI1, UMI2 and to the electronic telecommunications unit Tell, Tel21.

[0025] Each motorized locomotion unit Locl, Loc2 comprises a propeller PI, P2 and a steering mechanism Dl, D2. The propeller PI, P2 includes a motor powered by a battery that drives a rotating propeller. The steering mechanism Dl, D2 includes a first electric actuator powered by the battery that orients directional flaps and a second electric actuator powered by the battery that orients 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.

[0026] Each inertial measurement unit UMI1, UMI2, connected to the battery, comprises angular sensors Gl, G2 and linear sensors Al, A2 arranged to provide angular velocity measurements (or gyrometric measurements) and linear acceleration measurements (or accelerometric measurements), respectively, in a computational inertial frame il, i2 maintained by the angular sensors Gl, G2 of the inertial measurement unit UMI1, UMI2. More specifically, the angular sensors Gl, G2 are gyroscopes such as axisymmetric vibrating resonator gyroscopes like hemispherical resonator gyroscopes (or HRGs), and the linear sensors Al, A2 are 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, i2 of the inertial measurement unit UMI1, UMI2. The calculation inertial frame A1, i2 of the inertial measurement unit UMI1, UMI2 conventionally 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 linear sensors A1 and A2 are used to power and receive measurement signals from these sensors. The processing unit T1 and T2 performs preprocessing of the measurement signals by integrating them over a predetermined period and combines the accelerometer and gyrometer measurements to determine accelerometer measurements in the inertial frame of reference (within the limits of residual gyrometric errors). Subsequently, only these accelerometer measurements in the inertial frame of reference are considered; the gyroscopes are used only to bring the actual accelerometer measurements into the inertial frame of reference. The structure and operation of the inertial measurement units UMI1 and UMI2 are conventional and will not be described in further detail here.

[0027] Each Tell, Tel2, electronic telecommunications unit connected to the battery, comprises a radio signal transmitter / receiver ER1, ER2, optionally incorporating an encryption module enabling the Com1, Com2 control units to exchange radio signals with each other. The structure and operation of the Tell, Tel2 telecommunications units being conventional, they will not be described in further detail here.

[0028] 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.

[0029] Vehicles VI, V2 are further equipped with at least one relative position and orientation detection device for vehicles VI, V2 when vehicles VI, V2 are in a predetermined state of relative proximity, here a docking state. The relative position and orientation detection device includes at least one docking element for vehicles VI, V2 in a predetermined relative orientation. More specifically, vehicle VI is provided with a male centering V-block ve1 to cooperate with a female centering V-block 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-blocks ve1, ve2. The centering V-blocks and angular indexing elements ve1, in1 and ve2, in2 determine docking reference points 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.

[0030] The control units Com1, Com2 are arranged, and programmed here, to: - command the motorized locomotion units Locl, Loc2 of vehicles VI, V2 to make them travel separate trajectory segments (during time Tm, see [Fig.2] on which the trajectory of vehicle V1 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 [Fig.2]) to a second meeting position (at times tmf on [Fig.2]), during which 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; - command the motorized locomotion units Locl, Loc2 to make vehicles VI, V2 travel, from the second meeting position, a common trajectory segment (of duration Ta on the [Fig.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.

[0031] At least one of the control units Coml, Com2, here for example the control unit Coml, is arranged, here programmed, to determine, in particular from the exchanged measurements: - a transition matrix between the inertial reference frames of calculation il, i2; - a correction of linear acceleration measurements using a model accelerometer observed; - a correction of angular velocity measurements using an observed gyrometric model; - a time integral of gravitational deviations experienced by the vehicles during the separated trajectory segments.

[0032] 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, i2: • a transition matrix between the inertial reference frames of calculation il, i2; • a correction of the accelerometric measurements of the two vehicles VI, V2 using an accelerometric model observed using the standard of the accelerometric measurements of the two vehicles VI, V2; • a correction of the gyrometric measurements of the two vehicles VI, V2 thanks to a gyrometric model observed from the successive orientations of the accelerometric measurements of the two vehicles VI, V2; • rotation speed and translation acceleration instructions, to be carried out by each of the vehicles VI, V2 between two dockings and in their respective inertial calculation frames il, i2.

[0033] The rotational speed and translational acceleration commands are generated and transmitted to the locomotion units Loc1, Loc2 for: • program and control a separation of vehicles VI, V2 from a docking; • 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 route; • create the speed and relative position conditions between vehicles VI, V2 necessary for the initiation of a subsequent autonomous docking of vehicles VI, V2; • optimize the observation of the terms of the accelerometric and gyrometric models during the periods when vehicles VI, V2 are docked.

[0034] On each segment of the trajectory, the directions are defined at each instant t according to: - accelerometer measurement the derivative dmeS^Jd) / dt of the accelerometric measurement

[0035] If the common trajectory segment is sufficiently regular and at a low speed compared to the speed vtangent = RTen.&Terrj^, the accelerometric measurement evolves along a cone whose base is a circle that a person skilled in the art can identify. It will be understood that Rren-e is the radius of the Earth, OrOT(?) is the Earth's rotational speed, and Latitude is the latitude of vehicles VI, V2.

[0036] The evolution observed during the previous common trajectory segment is maintained during the separate trajectory segments by applying a common acceleration command

[0037] We then obtain:

[0038] . CA&(ï) - l^l pwsz(t) -

[0039] dmeë^iydt. . dCÀCiij / dt = jj«Mi =|]^3

[0040] x(t) = y(t)

[0041] Thus, x(t), y(t), defined in a frame exhibiting an evolution of orientation without discontinuity before and after the separation of the mobiles.

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[0049] The acceleration commands during the separate trajectory segments are the sum of the common acceleration command £74(70) calculated from the previous common trajectory segment and a differential acceleration command q 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 to their acceleration command £74(70 + £742)0- For each differential acceleration setpoint £742)0, we have: - (speed difference from the common trajectory); - tmfCÀD(t)dt — 0 (position deviation from the common trajectory); - the average at each instant of the differential acceleration setpoints CÂD(t) n is not necessarily equal to 0; - one of the vehicles can be assigned a differential acceleration instruction CAD,0=°; - the differential acceleration instructions £742)0 are expressed in the inertial reference frame of calculation il, i2. The vehicle piloting system ensures that: ( t ) " w ^tM^Sacci ( / ) ~ CAD^ (t) - « j^-CAD^ (t') Two implementation methods will be described for determining the time integral of gravitational deviations. According to a first embodiment, the Coml control unit is programmed to calculate: - a simple time integral of the difference in accelerometric measurements of each of the vehicles VI, V2 between two dockings; and / or - a double time integral of the difference in accelerometric measurements of each of the vehicles VI, V2 between two dockings. 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. 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.

[0050] According to a second embodiment, vehicles VI, V2 are planned to be equipped with a measuring device providing, taking into account the constraints on the CAD- ( / ) ct vehicle piloting controls described above, during at least part of the journey of vehicles VI, V2: • a measurement of the relative speed between the docking reference points characterizing the simple time integral of the gravitational differences experienced by vehicles VI, V2 on their respective separate trajectory segments; and / or • a measurement of a distance between the docking reference points characterizing the double time integral of the gravitational deviations experienced by vehicles VI, V2 on their respective separated trajectory segments.

[0051] The measuring device is, for example, a rangefinder.

[0052] It is understood that the two embodiments described above make it possible to determine • the simple time integral of the gravitational deviations experienced by vehicles VI and V2 on their respective separate trajectory segments; and / or • the double time integral of the gravitational deviations experienced by vehicles VI, V2 on their respective separate trajectory segments.

[0053] 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 the separate trajectory segments. It should be recalled that an accelerometer measures both the acceleration of the vehicle on which it is mounted and the opposite of the gravitational force acting on that vehicle.

[0054] Translational acceleration commands are generated, causing vehicles VI, 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, Loc2 to generate forces enabling them to follow these acceleration commands.

[0055] In order to allow a new docking of vehicles VI, V2, the acceleration instructions must comply with the following conditions (here it is assumed that gravity is constant on the separate trajectory segments of vehicles VI, V2):

[0056] accelerometer_setpoint d2t = tmfaccelerometer_setpoint_d2t = tmfaccelerometer_setpoint_d21 v 1 tmv V 2

[0057] M z ^»f J tMconsigne _accéU^ = ] ^consigne _accelerométriquevlat

[0058] It is noted that these conditions are necessarily met if the commands (j are chosen according to the rules set out above.

[0059] If the gravitational forces are not equivalent on the separate trajectory segments, the two vehicles VI, 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, V2.

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[0073] It is understood that along the two separate trajectory segments, the Coml control unit works in differential mode 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. Similarly, when a docking of the two vehicles VI, V2 is carried out after the passage of the separate trajectory segments (thanks to 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 suffered by the two vehicles VI, V2. We will now detail the determination of the gravitational field gradient at using the differences in speed / position between the two vehicles. The gravitation tensor is written in the form of a matrix Gxx Gxy Gyx Gyy . Gzx GZy Gxz • Gyz Gzz. With "_ _ dgfxyz), Gj— djdi “ dj $(x, y, z) being the gravitational potential, g.(x, y, z) is the i-th component of the gravitational field, i, I {x,y,z}. and {x, y, z} Cartesian and inertial coordinate systems We also recall the following properties of gravitation: OXy Gyx, Gxz GZx, GyZ GZy, Gxx+Gyy+Gzz+4irGp=0 with the last term equal to 0 s 2 in air and 0.839.106 s 2 in water. Therefore, only five representative unknowns remain: - of the three terms of the rotation matrix allowing the gravity gradient matrix to be made diagonal; - of the gradient along two of the principal directions. At the beginning of the separate trajectory sections, vehicles VI, V2 are in the same position and are moving at the same speed. At the end of the separate trajectory segments, differences in position P and speed V are measured between n vehicles Vi: AVVi (tmf) = Vvi (tmf) - iL(.VVi (tmf) (tmf)=¾ tmf) - 4 £ PVl- (tmf)

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[0089] These discrepancies are due to gravity gradients assumed to be constant according to the actual or predicted position differences between the vehicles. 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: ----s®* / | y—» _____s»— \ 2 APw(f) = t) -nLmesaœft) )dt / [G„ Gxv x \ \GZX Gzy GZZi Therefore, it can be expressed in the following form: AV Vi (tmf) = axyiGxy + aXZ}Gxz + ayyiGyy+ayziGyz+a^Gzz with axyi, axzi, avyi, ayzx azzi the factors influencing the severity gradient on AV Vi { tmf) dus au choix des CADft) The positional differences between the Vi vehicles at the end of the trajectory segments These separations are also due to the gradients of the gravitational field according to the differences in Position between the vehicles: APyi(ï) - )dt2 r * Hn\) \ t £ • / Gxx Gxy Gxz &PVi(tmf) = [xyz] GyX Gyy GyZ , Gçx GZy Ga x __ __ J Ln(mesacct{t)-^Ymesa^ (t) )dt2 dt2 x * • / zl [Gx. Gxy Gxzj 'x' [xyz] GyX Gyy GyZ y ^(CÀD.W-^.CÀDSt) )dC dt ,GZX GZy GZZi .Z. These equations can therefore be written in the form: + bx^Gxz + byyjGyy + by^Gyz + with b^. / l* 'cs factors influencing the gravity gradient on APy / (tmf) due to the choice of CAD'(t)- Therefore, at each docking, the gradients ^xy IXxz are calculated from Gyx Gy v Gy Z . Gzx GZy the following quantities: (ÀVvftmf) etAPvftmf): measures

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[0096] axyb axa, ayyi, ayzh azzi functions of CAD^t) functions of fÀn ( / t *'xw uxzv Uyyvuyw "zzi vAUj[t) Calculating gradients involves inverting the system of equations: * 1 AVVi(tmf) ®xyi ®xzi ayyi ^y~i « azzi Cj Çi « = A 'Gx / Gxz Gyy APVi(tmf) < bxyi ^xzi byyj byzi Gyz . Gzz, Gyz .Gzz, The measures Ay ( tmf ) and Apy / ( tm f ) "explore" the matrix Gxy Gyy Gzy Gxz Gyz CAD^t}- depending on the choice of Gyx Gzx Obtaining Rank(A)=5 allows the inversion of the system of equations. Several uses of gravitational differences are possible, as we will see from the following. 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 rotations (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 may be chosen. Alternatively, at least one of the inertial measurement units UMI1, UMI2 can be mounted on a rotation table controlled by the processing unit T1, T2: it is no longer the vehicle VI, V2 that undergoes the rotations, but only the inertial measurement unit UMI1, UMI2. The rotations 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 rotations. Indeed, it is known that with reversals impacting the inertial measurement unit UMI1, UMI2: • 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); • Gyroscopic and accelerometric errors are observable (and therefore compensable) by comparing an inertial measurement unit that is turning around with an inertial measurement unit that is not turning around. This comparison is possible, for example, during docking periods (i.e., that is, when the relative position and attitude of vehicles VI, V2 are known or measurable by non-inertial means), the simplest case being successive approaches between the two vehicles VI, V2, separated by a rotational movement globally equivalent to a reversal of at least one of the vehicles VI, V2.

[0097] Thus, the apparent stability of the accelerometric measurement becomes virtually independent of long-term variations in accelerometric biases. It should be 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, in 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.

[0098] The frequency of the reversals allows for at least one, and preferably more than ten, to be performed during the separated trajectory segment. These reversals can be carried out at predetermined times, independently on each of the vehicles VI, 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 leads to maintaining the attitudes of the vehicles VI, V2 fixed with respect to the inertial frame. These reversals are also advantageous during short periods between the meeting points.

[0099] 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 segment takes place along a docking line.

[0100] The Coml, Com2 control units: - estimate the direction of this docking line by the difference in accelerometric measurements between vehicles VI, V2 during this separation and in their respective inertial frame il, i2; - 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.

[0101] The berthing movements are generated: - 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 - 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.

[0102] The first step is carried out using optical cameras caml, cam 2 connected to the control units Coml, Com2 respectively in order to provide images on which the centering ves vél, vé2 and the angular indexing elements inl, in2 will constitute visual reference points.

[0103] The quality of the acceleration measurement obtained by the reversals makes it possible to calculate the gravitation on the segments of the trajectory of vehicle VI, V2 and to deduce a map of the "local" gravity gradient, that is to say in the geographical area traveled by the two vehicles VI, V2.

[0104] It is possible to use this local map measured jointly by the two vehicles VI, V2 to perform recalibrations by comparing the local map measured by the joint measurement of the two vehicles VI, V2 to a pre-established reference map. Comparing the map generated locally by vehicles VI, V2 to the reference map yields position and velocity errors, which manifest themselves over a short time horizon and are affected by predictable and controllable uncertainties, functions of 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, V2.

[0105] 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 only first-order variations are taken into account along the vertical and in the horizontal plane (relative to the terrestrial globe), the compensated differential accelerometer setpoints CADi'jK are :

[0106] c^(7)=cÂ5;(n-Æ.cÂA(o -ôH( W}

[0107] This formula contains: - the projection along (\(( f ) (CADA^-iL-CAD-At)}^2 ||CAC-]| lmn ■ i 1 / - the projection perpendicular to CÂC(t)

[0109] -ôh( j (caBa / ) [ (Cad-(n-¥L.cad-{t)\dt2\ 11 \ W> ' 1 ï 1 ! j|CACj| *w0 \ 1 £ 1 / J - the vertical variation (assumed to be oriented along — 2 2 10 6 S'2 - the horizontal variation (Schuler effect, assumed to be oriented perpendicular to (24^7)

[0110] 3 = _ . 1.5.1 (y6 ^2 71 RTerre

[0111] 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 {x, y, z}.

[0112] Alternatively, the Coml control unit has a three-dimensional gravity map which allows it to: • 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; • determine the influence of an initial error in positions and velocities on the integrals obtained over the paths affected by this initial error; • choose routes that maximize the observability of initial position and velocity errors from the measurement of differential positions and velocities between the two vehicles VI, V2.

[0113] The initial errors in positions and velocities will therefore generate differential positions and velocities between the two vehicles VI, V2 during the subsequent docking. The influence of the initial errors in positions and velocities is determined using the gravity gradient from the map.

[0114] 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.

[0115] Alternatively, at least one of the control units (e.g. Coml) is arranged to: - calculate linear acceleration commands corrected for lump-sum variations of the vertical gravitational field (for example from 2.2.10'6 r2 to 3.10 6 v2) and horizontal gravitational field (for example from - 1.5.10'6 r2); - calculate a gravitational field gradient with respect to these fixed variations.

[0116] More generally, the Coml control unit is programmed to deduce the positions, velocities and attitudes and their uncertainties for the current berthing point from the positions, velocities and attitudes and their uncertainties for the previous berthing point and: • accelerometric measurements of vehicles VI, V2 in the frames il, i2; • from the measurement of their position and speed differences that have appeared since the last point of docking; • a cartographic reference of gravitation.

[0117] 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.

[0118] More specifically, the navigation calculation module Navl, Nav2 is here integrated into the Coml, Com2 control units of vehicles VI, V2 and is programmed to calculate, after initialization performed when the navigation system is started and when vehicles VI, V2 are alongside, an estimate of the positions and speeds of vehicles VI, V2 from: • from the previous estimation of the positions and speeds of vehicles VI, V2; • measurements of the corrected accelerations of vehicles VI, V2 in their inertial frames il, i2 since the previous estimation of the positions and velocities of vehicles VI, V2; • the following information provided by the gradio-gravimeter: • the transition matrix between the inertial frames il, i2 of vehicles VI, V2; • the simple integral and / or the double integral of the difference in accelerometric measurements of each of the vehicles VI, V2 between two dockings (first embodiment); or the differences in position and / or velocity, measured between the two vehicles VI, V2 at the end of their respective separate trajectory segments carried out since the previous docking (second embodiment); • a gravity map serving as a reference.

[0119] It should be noted that this operation made possible by the invention is much more advantageous than that of a single vehicle realigning itself solely through observation of the gravity by following a "linear" path. Indeed, in the latter case, the observability of errors is only obtained in the long term, which makes its use complex in the short term, even dangerous, and in all cases hinders the precision of such recalibration (compromise between observability and precision of inertial navigation in pure inertia).

[0120] Preferably, the control unit Coml is programmed to calculate acceleration commands, intended for the motorized locomotion unit Locl, Loc2, optimizing the observability of position and velocity errors by using the estimation of vehicle positions and velocities VI, V2 and gravity mapping.

[0121] Preferably, the Navl, Nav2 navigation calculation module is programmed to: - 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; - calculate corrections to said acceleration instructions, specifically for each motorized locomotion unit Locl, Loc2 in order to compensate for the variations in gravity predicted along the section of trajectory separated from each of the vehicles VI, V2.

[0122] For guidance purposes, the following orders of magnitude are mentioned.

[0123] The vertical divergence at time t is equal to

[0124] Error Vertlca!e(i) t / -, —' >vrt ErrorVerticaf^ü)

[0125] We have t^v vert ~ 674 S 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 vertical errors.

[0126] 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 (sin1 .....~ 4.7 mrd for a distance of 30 ^Earth km).

[0127] A deviation of gravitation 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).

[0128] Alternatively, at least one of the control units (e.g. Coml) is arranged to: - calculate linear acceleration commands corrected for lump-sum variations of the vertical gravitational field (from 2.2.10'6 r2 to 3.10'6 r2) and horizontal gravitational field (from - 1.5.10-6^2); - calculate a gravitational field gradient with respect to these fixed variations.

[0129] Alternatively, at least one of the vehicles may 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 may also be used to improve gravity mapping. The non-inertial sensor may, for example, be a satellite positioning signal receiver (GNSS), an odometer, or an immersion sensor...

[0130] Alternatively, the vehicles can be equipped with an immersion (or altitude) sensor. In this case, the gradio-gravimeter uses relationships similar to those used for measuring gradients by velocity and position differences. However, there are some specific differences.

[0131] The altitude information Im is thus available at every instant so that we have Im(tm0+jAt) the immersion measurement as a function of the sampling period At, j representing the sample number.

[0132] This information is only available along the vertical considered to be _ cÆ of so that:

[0133] Mmvi(tm0+j&i) =Im.(tmO+jAt) + CAD^t) AlLjCÀDii.t) )dr = tmM-jài [G Gyz tmQ ( CAD; ( t ) - À^.CAD.( t ) ) dt 1 = c X to (J) Gxz + (J) G yz + c zzi ( j ) G^

[0134] with (j), (j), (j) influencing factors of the severity gradient on Ms. Vi (tmO+jAt). dus auchoixdes CAD i (t)-

[0135] Therefore, at each docking, the gradients Gxx Gyx G L^zx Gxy Gyy Gzy Gxz are calculated from Gyz Gz the following quantities: AVVi (Jmfy APVi (tmf} and MmVi (tmQ+jA / ): measurements «5, â^, functions of h^- h^. functions of p^n / / a uxyp uyyv>uy& "zzi LAV'IJJ ë^(j), c^(j) functions of CÀD^Z)

[0136] A new formulation is obtained, solvable under the same conditions as in the case where there is no altitude sensor

[0137] ^Vi{tmf) » ^xyi axzi ayyi ..... ^yzi azzi CÙ 6 £ __________■ •GXy' Gxz APvi(tmf) = bxzi byyi —-s» byzi Z Gyy Gyy AImVi ( tmO+jAt ) 0 cxù (J) 0 Cy zi (J) 1 P .OH ■ & OL» fi ■----------------

[0138] This calculation can be done using a Kalman filter.

[0139] 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.

[0140] In particular, the gradio-gravimeter according to the invention may have a different structure from that described.

[0141] The actuators involved in the reversals can 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 the unit to rotate: • either the entire vehicle (for example using steerable propellers for a marine or aerial vehicle); • or only the inertial measurement unit which is located within the vehicle (using a cardan joint system for example).

[0142] In order to improve the intrinsic stability (excluding rollovers) of angular sensors and linear sensors, vehicles VI, V2 can be equipped with a thermal regulation device for inertial measurement units (conduction, convection, or radiation: heat exchanger, electric heating device, radiator...).

[0143] At least one of the vehicles VI, V2 may have a sufficiently large energy reserve to allow it to recharge the battery of the other vehicle during shared sections of the trajectory. Vehicles VI, V2 are therefore provided with matching electrical connectors that cooperate when the vehicles VI, V2 are alongside each other.

[0144] The trajectories of vehicles VI, V2 can be predetermined and expressed as a function of the accelerations that vehicles VI, V2 will undergo. Thus, rather than controlling the motorized locomotion units Loc1, Loc2 from In a complete navigation system (calculating the positions and speeds of vehicles VI and V2), accelerometer data (converted to an inertial frame of reference, within the limits of residual gyroscopic errors) is used directly. This allows us to take advantage of the higher frequency of accelerometer data (compared to that of position and speed data) and therefore implement trajectory tracking control systems with a higher bandwidth. A similar approach involves using gyroscopic data (rather than attitude data) to control attitude.

[0145] To facilitate the docking of vehicles VI, V2, vehicles VI, V2 are preferably equipped with guidance systems using, for example, optical technologies. Vehicles VI, V2 are, for instance, equipped with cameras and visual markings enabling the control units Coml, Com2 to guide the motorized locomotion units Locl, Loc2 so as to progressively bring vehicles VI, V2 closer together until docking. In this case, the comparison of positions, speeds, and attitudes between the two vehicles VI, V2 during the common trajectory segment is facilitated.

[0146] The Com1, Com2 control units can be arranged to implement a calibration phase during which two vehicles VI, 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.

[0147] The invention can be implemented without vehicles VI, V2 being alongside each other in the predetermined state of relative proximity. A measurement of the relative distances and / or orientations of the two vehicles VI, V2 is then taken. The comparison of positions / speeds / attitudes during the common trajectory segment must then take these measurements into account.

[0148] It is possible to vary the durations of the common trajectory segments and the separate trajectory segments in order to promote: - either the identification of errors in the 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; - 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).

[0149] Preferably, a certain amount of time (typically a similar time in a ratio of 0.5 to 2) will be left between the periods of docking and separation in order to guarantee observing the accelerometric measurement during the docked period and then reproducing it during the separated period in the form of the accelerometric setpoint CAC.

[0150] Performing reversals during the separate trajectory segments of one or both of the vehicles is optional and only serves to improve the identification of errors in the inertial sensors (bias, scale factor and angle of incidence).

[0151] 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.

[0152] The comparison of information can be carried out within a single vehicle VI, V2 or be decentralized across the different vehicles VI, V2.

[0153] The invention can be implemented with a three-dimensional map: if the gravity gradient conforms to the expected values ​​according to the map, the location is correct; otherwise, the location is realigned with the map. The invention can also be implemented with an imperfect map: the discrepancies are then used to correct the map locally, provided that realignment is possible at specific points on the map.

[0154] In the absence of a chart: the information obtained at each berthing allows the chart to be populated. It is possible to determine whether the observed error is a position error or a chart error by finding the best correlation between the chart and the position, the residual discrepancy being assumed to be a chart error, all while taking into account a potential measurement error.

[0155] The vehicles may be identical or different. Many useful configurations can be imagined. For example, one could cite the case of a large, relatively inflexible vessel combined with a small, highly maneuverable underwater drone. This combination allows the large vessel to benefit in real time (at the frequency of dockings) from a measurement of the gravitational field gradients and thus perform optimal navigation using this knowledge.

[0156] 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.

[0157] The gradio-gravimeter can be operated 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).

[0158] Angular sensors can be of any type and for example of the gyrolaser type.

[0159] Communication between the control units can be solely by electrical contact during the coupling phases.

[0160] The invention is applicable to any type of vehicle, piloted or unpiloted, land, nautical, underwater, aerial or space-based.

Claims

1. Demands A radio-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 telecommunications 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 are 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; - command the vehicles to travel from the second meeting position along a common trajectory segment during which the vehicles are in the proximity state 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 from 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 • a time integral of gravitational differences experienced by the vehicles during the separated trajectory segments; • a relative separation of the vehicles during the separated 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 comprises a measuring device for a relative distance of the vehicles characterizing the double time integral of the gravitational deviations.

5. Gradio-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 deviations between linear acceleration measurements of vehicles on separate trajectory segments, the simple time integral of deviations between linear acceleration measurements characterizing the simple time integral of gravitation deviations.

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 deviations between linear acceleration measurements of vehicles over separate trajectory segments, the double time integral of deviations between linear acceleration measurements characterizing the double time integral of gravitation deviations.

7. Gradiogravimeter according to any one of the preceding claims, wherein the detection element (vél, vé2, inl, in2) of a reciprocal relative orientation includes at least one vehicle docking element in at least one predetermined relative orientation, the relative orientations being separated by substantially 180°.

8. Gradio-gravimeter according to any one of the preceding claims, wherein the reciprocal relative orientation detection element (vél, vé2, inl, in2) comprises at least one optical camera (caml, cam2).

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

10. Gradio-gravimeter according to any one of the preceding claims, wherein the electronic control unit (Coml, Com2) of at least one of the vehicles is programmed to control the motorized locomotion unit of the vehicle (VI, V2) to make the vehicle perform movements corresponding to reversals of the inertial measuring unit (UMI1, UMI2).

11. A 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 (Altl, Alt2) providing an altitude measurement during the travel of the separated 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, when determining the gradient of the gravitational field: - an altitude measurement deviation; - a prediction of the altitude measurement deviation developed from linear acceleration commands; - an average of the position deviations of the vehicles from the separation of the vehicles until the time of measurement of this deviation.

12. A gradio-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 lump-sum 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 position and velocity error observability using vehicle position and velocity prediction (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 gravitational variation along the trajectory of each of the vehicles (VI, V2) from a prediction of positions and velocities and the gravitational mapping; - corrections of the accelerometric commands specific to each of the vehicles in order to compensate for the prediction of gravitational variations along the trajectory of each of the vehicles.

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. 29

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 use them to improve gravity mapping.

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