CN107621829B - Safety zone expansion guidance method for avoiding planet landing obstacle - Google Patents
Safety zone expansion guidance method for avoiding planet landing obstacle Download PDFInfo
- Publication number
- CN107621829B CN107621829B CN201710844211.7A CN201710844211A CN107621829B CN 107621829 B CN107621829 B CN 107621829B CN 201710844211 A CN201710844211 A CN 201710844211A CN 107621829 B CN107621829 B CN 107621829B
- Authority
- CN
- China
- Prior art keywords
- detector
- obstacle
- ellipsoid
- landing
- position error
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Landscapes
- Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)
Abstract
The invention discloses a safety zone expansion guidance method for avoiding a planet landing obstacle, and belongs to the field of deep space exploration. Firstly, defining a landing point fixed connection coordinate system and an error ellipsoid principal axis coordinate system; establishing a landing dynamic equation under a landing point fixed connection coordinate system; determining an ellipsoid expansion safety zone according to the detector position error n sigma ellipsoid, and calculating a safety distance index value of the detector relative to the obstacle; a Lyapunov function is constructed based on the state of the detector and the safe distance index value of the detector relative to the obstacle, an obstacle avoidance guidance law is designed by utilizing the Lyapunov stability principle, the landing track of the detector is controlled by utilizing an acceleration instruction a, the influence of multiple disturbance and an uncertain environment on the surface of the planet on the obstacle avoidance guidance of the detector is reduced, the obstacle on the surface of the planet is effectively avoided, and autonomous safe and accurate landing is realized. The control acceleration instruction obtained by the invention is in an analytic form, does not contain complex operations such as integral and the like, meets the real-time requirement of on-line feedback control, and is beneficial to engineering application.
Description
Technical Field
The invention relates to a planet landing obstacle avoidance guidance method, in particular to a safety zone expansion guidance method for avoiding a planet landing obstacle, and belongs to the field of deep space exploration.
Background
The problem of avoiding the planet landing obstacle is an important problem of planet landing detection, and the success or failure of a planet landing detection task and the safety of a detector are related. Because the precision of in-orbit mapping and the acting distance of a sensor are limited, meteorite pits, rocks, slopes, hills and the like on the surface of a planet are difficult to completely and accurately map in the flying-around stage, and the obstacles threatening the landing safety need to be detected and avoided in real time in the landing process. In order to obtain more scientific returns, the future planet landing task seeks to land in a complex terrain area with more scientific value, so that the detector has the capacity of online obstacle detection and avoidance to guarantee the safety of the detector and realize autonomous safe landing.
In the prior art [1] (see Lopez, Ismael, McInnes, Colin R. Autonomous rendering specific functional Guidance [ J ]. Journal of Guidance, Control, and Dynamics,1995,18(2): 237-. In the prior art [2] (see Zhu SY, Cui P Y, Hu H J, Hazard detection and avidity for a planar landing base Lyapunov Control method [ C ]. Intelligent Control and automation. Beijing [ [ s.n ] ],2012), a potential function guidance method is adopted to research the problem of avoiding the landing obstacle of the small celestial body, an artificial potential field function is selected according to the threat of the current potential energy and obstacle terrain of the detector to the detector, and guidance law is deduced according to the Lyapunov stability principle, so that the obstacle in the landing process can be avoided while the detector reaches a target landing point.
The planet landing dynamics environment has more interference and strong nonlinearity and uncertainty, and brings great challenges to the landing of a detector and obstacle avoidance guidance and control. When the detector state has large uncertainty, the conventional method represented by the prior art may not effectively evaluate the threat degree of the obstacle relative to the actual detector state, thereby causing the obstacle avoidance failure.
Disclosure of Invention
The invention discloses a safety zone expansion guidance method for avoiding a planet landing obstacle, which aims to solve the technical problems of reducing the influence of multiple disturbance and uncertain environment of the planet landing on the obstacle avoidance guidance of a detector, effectively avoiding the planet surface obstacle and realizing autonomous safe and accurate landing.
The object of the present invention is achieved by the following method.
The invention discloses a safety zone expansion guidance method for avoiding a planet landing obstacle. And establishing a landing kinetic equation under the landing point fixed connection coordinate system. And determining an ellipsoid expansion safety zone of the detector according to the detector position error n sigma ellipsoid, and further calculating a safety distance index value of the detector relative to the obstacle. A Lyapunov function is constructed based on the state of the detector and the safe distance index value of the detector relative to the obstacle, an obstacle avoidance guidance law is designed by utilizing the Lyapunov stability principle, the landing track of the detector is controlled by utilizing an acceleration instruction a, the influence of multiple disturbance and an uncertain environment on the surface of the planet on the obstacle avoidance guidance of the detector is reduced, the obstacle on the surface of the planet is effectively avoided, and autonomous safe and accurate landing is realized.
The invention discloses a safety zone expansion guidance method for avoiding a planet landing obstacle, which comprises the following steps:
step one, defining a landing point fixed connection coordinate system and an error ellipsoid principal axis coordinate system.
Defining a landing site fixed coordinate system (x, y, z): the origin of coordinates O is the target landing point, and the z-axis is along the centroid O of the small celestial bodycDirection of the line to the origin O
The y-axis lies in the plane formed by the z-axis and the spin principal axis of the celestial body and is perpendicular to the z-axis, and the x-axis enables the (x, y, z) coordinate system to satisfy the right-hand rule.
Defining an error ellipsoid principal axis coordinate system (x)E，yE，zE): origin of coordinates OEAt the estimated value of the detector position, xE，yE，zEThe axes coincide with the three main axes of the detector position error n sigma ellipsoid, respectively, and satisfy the right-hand rule.
And step two, establishing a landing kinetic equation under the landing point fixed connection coordinate system.
When the target celestial body is a small celestial body, the landing kinetic equation of the detector under the landing point fixed connection coordinate system is as follows:
wherein r ═ x, y, z]TIs the position vector of the detector under the landing point fixed connection coordinate system, v ═ vx，vy，vz]TAs the velocity vector of the probe, ω ═ ωx，ωy，ωz]TIs the target celestial body spin angular velocity vector, g ═ gx，gy，gz]TIs the acceleration of the gravity of the target celestial body to which the detector is subjected, and a is the applied control acceleration command.
When the target celestial body is a planet, the spin angular velocity omega can be ignored, and the landing kinetic equation of the detector under the landing point fixed connection coordinate system is as follows:
and step three, determining an ellipsoid expansion safety area of the detector.
And calculating a detector position error n sigma ellipsoid according to the detector state estimation information, and setting the surface part and the inner part of the position error n sigma ellipsoid as an ellipsoid expansion safety zone of the detector. The position estimation error of the detector conforms to Gaussian distribution with zero mean value, and the mean value of the estimated value of the actual position r under the landing site fixed coordinate system is
The detector position error covariance matrix is C.
And (3) carrying out eigenvalue decomposition on the detector position error covariance matrix C:
UTCU＝D (3)
diagonal elements of the diagonal matrix D are all eigenvalues of the detector position error covariance matrix C, and columns of the matrix U are eigenvectors corresponding to all eigenvalues. Orthogonal transfer matrix UTFrom a landing site fixed-axis coordinate system (x, y, z) defining a detector position error covariance matrix to an error ellipsoid principal axis coordinate system (xE，yE，zE) The transformation matrix of (2). The position of the detector in the error ellipsoid principal axis coordinate system is as follows:
order to
The detector position error n σ ellipsoid equation is:
rE TErE＝1 (6)
the detector ellipsoid expansion safety zone is a part of the surface and the inner part of a detector position error n sigma ellipsoid shown by a formula, and the expression is as follows:
rE TErE≤1 (7)
and step four, calculating a safe distance index value of the detector relative to the obstacle according to the ellipsoid expansion safe area of the detector determined in the step three.
The safe distance index value of the detector relative to the obstacle comprehensively considers the influence factors of the obstacle avoidance track, wherein the influence factors of the obstacle avoidance track comprise the uncertainty factor of the detector state and the control constraint factor. Firstly, the minimum distance between the ellipsoidal expansion safety area of the detector and the obstacle is calculated, and then the set control safety distance value is subtracted to obtain a safety distance index value l.
The minimum distance between the detector ellipsoid expansion safety zone and the obstacle is firstly calculated, namely the minimum distance between the detector position error n sigma ellipsoid and the obstacle.
Considering the position and size of the obstacle, modeling the obstacle into a hemisphere, and fixedly connecting the obstacle center, namely the hemisphere center coordinate r, under a coordinate system by using a landing pointcAnd the obstacle reference radius, i.e., the hemispherical radius R, describes the position and size of the obstacle. The coordinates of the obstacle center under the error ellipsoid principal axis coordinate system are as follows:
according to the error n sigma ellipsoid between the obstacle center and the detector positionThe step 4.1 or the step 4.2 is selected to be executed to obtain the minimum distance d between the position error n sigma ellipsoid of the detector and the obstaclee。
Step 4.1, when the center of the obstacle is positioned outside the position error n sigma ellipsoid of the detector, namely:
rcE TErcE＞1 (9)
let point r on the surface of the detector position error n σ ellipsoidsIs the surface of an ellipsoid r away from the center of the obstaclecThe point of minimum distance.
Under the principal axis coordinate system of the error ellipsoid, the point rsThe coordinates of (a) are:
and satisfies the following equation:
rsE＝(I+λE)-1rcE(11)
rcE T(I+λE)-TE(I+λE)-1rcE-1＝0 (12)
where λ is the lagrange multiplier. Solving the equation-to obtain the lambda value, and thus the coordinate rsE. Due to rcEIs located outside the ellipsoid of the position error n sigma of the detector, so that the ellipsoid has a unique distance rcEThe closest point, corresponds to a solution where λ is uniquely greater than zero.
The position error n sigma ellipsoid of the detector is far away from the center r of the obstaclecThe minimum distance of (c) is:
dc＝||rsE-rcE||＝||rs-rc|| (13)
wherein
When d iscR, the obstacle is wholly positioned outside a detector position error n sigma ellipsoid, and the minimum distance between the detector position error n sigma ellipsoid and the obstacle is as follows:
de＝dc-R (14)
when d iscR is less than or equal to R, the detector position error n sigma ellipsoid is intersected with the obstacle, the obstacle part is positioned inside the detector position error n sigma ellipsoid, and the minimum distance d between the detector position error n sigma ellipsoid and the obstacleeIs 0.
Step 4.2, if the center of the obstacle is positioned in the inner part or on the surface of the detector position error n sigma ellipsoid, namely:
rcE TErcE≤1 (15)
the position error n sigma ellipsoid of the detector is far away from the center r of the obstaclecIs 0. Correspondingly, the obstacle is wholly or partially located within a detector position error n σ ellipsoid, which is the minimum distance d from the obstacleeIs 0.
Using the minimum distance d between the detector position error n sigma ellipsoid obtained in the step 4.1 or the step 4.2 and the obstacleeMinus a control safety distance dsAnd obtaining a safe distance index value l of the detector relative to the obstacle:
l＝de-ds，de≥ds(16)
wherein the safety distance d is controlledsAnd comprehensively considering control capability constraints including the configuration of the detector thruster, the thrust amplitude and the control precision of each axial thruster, and presetting values according to the configuration condition of the detector to reflect the influence of the control capability constraints of the detector on the obstacle avoidance maneuvering capability of the detector.
When the minimum distance between the detector position error n sigma ellipsoid and the obstacle is smaller than the control safety distance, the safety distance index value l is 0, namely:
l＝0，de＜ds(17)
when the safe distance index value of the detector relative to the obstacle is 0, the detector possibly collides with the obstacle under the influence of state uncertainty and control constraint, and the safety of the detector at the moment is low.
And step five, constructing a Lyapunov function according to the safe distance index value obtained in the step four.
Constructing a potential field function phi related to the state of the detector under a landing point fixed connection coordinate systemq
φq＝xTQx (18)
Wherein x ═ x, y, z, vx，vy，vz]TFor detector state variables, Q is Qi> 0, i 1, 6 is a diagonal matrix of diagonals. The potential field expressed by the above formula has only a minimum value point, and the detector target state x is 0. As long as it is ensured that the probe state x advances in the direction of the potential field decrease, the probe state will automatically approach the target landing state, i.e. the target landing position and speed are met at the same time.
Constructing a potential field function phi related to the obstacle threat according to the safe distance index value l of the detector relative to the obstacle obtained in the fourth steph
Wherein liRepresenting safe distance index values of the detector relative to the ith obstacle, k representing the number of obstacles, psi > 0 and sigma > 0 as parameters; safety distance index value l when detector is relative to obstacleiWhen reduced, the potential field function phihThe value is increased; if the designed guidance law enables the detector to advance along the direction of the potential field reduction, the detector automatically achieves obstacle avoidance;
finally, a lyapunov function phi of the form:
lyapunov function is given by phiqAnd phihThe target state of the detector is the only global minimum value point in the potential field, and the potential field value is increased when the detector approaches the obstacle, so that the autonomous obstacle avoidance and the autonomous accurate soft landing can be realized simultaneously as long as the acceleration control instruction a is designed to enable the detector to advance along the potential field reducing direction.
And step six, designing an obstacle avoidance guidance law to obtain the control acceleration a in the step five so as to realize autonomous obstacle avoidance and autonomous accurate soft landing.
And according to the value of the safety distance index D in the fourth step, selecting to execute the step 6.1 or the step 6.2 to obtain a corresponding control acceleration instruction a.
Step 6.1, when the index values of the safe distances of the detectors relative to each obstacle are all larger than 0, namely:
li＞0，i＝1，...，k (21)
order to
a＝aq+ah(24)
Wherein xs，ys，zsIs rsThree-axis coordinate of (2), xci，yci，zciIs the ith obstacle center rciAnd k is a positive real number. And when the target celestial body is a small celestial body:
the term related to the spin angular velocity ω after the equation of dynamics is developed in the form of x, y, z axis components ξ when the target celestial body is a planetx＝ξy＝ξz＝0。
Step 6.2, when the safe distance index value of the detector relative to a certain obstacle is 0, the following steps exist:
lj＝0，1≤j≤k (26)
the safety of the detector is low at this time. In order to ensure the safety of the detector, an emergency state is started to enable the detector to rise emergently, and the corresponding control acceleration instruction is as follows:
a＝[0，0，amax]T(27)
wherein a ismaxThe maximum acceleration of the thruster in the positive direction of the z axis.
And controlling the landing track of the detector by using the acceleration instruction a obtained in the sixth step, reducing the influence of multiple disturbance and unknown environment on the surface of the planet on obstacle avoidance guidance of the detector, effectively avoiding the obstacle on the surface of the planet, and realizing autonomous safe and accurate landing.
The control acceleration command a obtained in the sixth step is in an analytic form, does not contain complex operations such as integral and the like, and meets the real-time requirement of on-line feedback control.
And n values in the detector position error n sigma ellipsoid are determined according to the size requirement of an ellipsoid expansion safety zone, and the preferable n value is 3.
Has the advantages that:
1. according to the safety zone expansion guidance method for avoiding the planet landing obstacle, the influence of uncertainty of the position of the detector, control constraint and the like on the safety of the landing track is quantitatively described by introducing the ellipsoid expansion safety zone of the detector and the corresponding safety distance index, an obstacle avoidance guidance law is generated based on the dynamic safety distance index, the obstacle on the surface of the planet can be effectively avoided, the autonomous safe and accurate landing is realized, and the dynamic environment condition with high interference and strong uncertainty of the planet landing is adapted. Under the condition that the position of the detector has larger uncertainty, the obstacle avoidance effect is obviously superior to that of the traditional obstacle avoidance method.
2. The invention discloses a safety zone expansion guidance method for avoiding a planet landing obstacle. In addition, when the index value of the safe distance of the detector relative to a certain obstacle is zero, the detector is made to rise urgently to avoid possible collision, and the safety of the detector is further guaranteed.
3. According to the safety zone expansion guidance method for avoiding the planet landing obstacle, the solved control acceleration instruction is in an analytic form, complex operations such as integration and the like are not contained, the real-time requirement of on-line feedback control is met, and engineering application is facilitated.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic view of a landing site fastening coordinate system;
FIG. 3 is a schematic diagram of an error ellipsoid principal axis coordinate system;
FIG. 4 is a three-axis position simulation curve of the method of the present invention;
FIG. 5 is a three-axis velocity simulation curve of the method of the present invention;
FIG. 6 is a three-axis acceleration command simulation curve of the method of the present invention;
FIG. 7 is a three-dimensional landing simulation trajectory of the method of the present invention;
FIG. 8 is a minimum distance distribution from the center of the obstacle in a Monte Carlo simulation (obstacle 1, conventional method);
FIG. 9 is a minimum distance distribution from the center of the obstacle in a Monte Carlo simulation (obstacle 2, conventional method);
FIG. 10 is a minimum distance distribution from the center of the obstacle in a Monte Carlo simulation (obstacle 1, inventive method);
fig. 11 is a minimum distance distribution from the center of the obstacle in a monte carlo simulation (obstacle 2, inventive method).
Detailed Description
The invention is further described with reference to the following figures and examples.
Example 1
A safety zone expansion guidance method for avoiding a planet landing obstacle takes the avoidance of a small celestial body landing obstacle as an example, and the method for realizing the embodiment comprises the following steps as shown in figure 1:
step one, defining a landing point fixed connection coordinate system and an error ellipsoid principal axis coordinate system.
Defining a landing site fixed coordinate system (x, y, z): the origin of coordinates O is the target landing point, and the z-axis is along the centroid O of the small celestial bodycDirection of the line to the origin O
y axis is located on z axis and small celestial bodyThe spin principal axis is in the plane and perpendicular to the z-axis, which allows the (x, y, z) coordinate system to satisfy the right hand rule.
Defining an error ellipsoid principal axis coordinate system (x)E，yE，zE): origin of coordinates OEAt the estimated value of the detector position, xE，yE，zEThe axes coincide with the three main axes of the detector position error n sigma ellipsoid, respectively, and satisfy the right-hand rule.
And step two, establishing a landing kinetic equation under the landing point fixed connection coordinate system.
When the target celestial body is a small celestial body, the landing kinetic equation of the detector under the landing point fixed connection coordinate system is as follows:
wherein r ═ x, y, z]TIs the position vector of the detector under the landing point fixed connection coordinate system, v ═ vx，vy，vz]TWhich is the velocity vector of the detector,
is the target celestial body spin angular velocity vector, g ═ gx，gy，gz]TIs the acceleration of the gravity of the target celestial body to which the detector is subjected, and a is the applied control acceleration command.
When the target celestial body is a planet, the spin angular velocity omega can be ignored, and the landing kinetic equation of the detector under the landing point fixed connection coordinate system is as follows:
and step three, determining an ellipsoid expansion safety area of the detector.
And calculating a detector position error n sigma ellipsoid according to the detector state estimation information, and setting the surface part and the inner part of the position error n sigma ellipsoid as an ellipsoid expansion safety zone of the detector. The position estimation error of the detector is consistent with the Gaussian score with the mean value of zeroThe mean value of the estimated value of the actual position r under the landing site fixed coordinate system is
The detector position error covariance matrix is C.
And (3) carrying out eigenvalue decomposition on the detector position error covariance matrix C:
UTCU＝D
diagonal elements of the diagonal matrix D are all eigenvalues of the detector position error covariance matrix C, and columns of the matrix U are eigenvectors corresponding to all eigenvalues. Orthogonal transfer matrix UTFrom a landing site fixed-axis coordinate system (x, y, z) defining a detector position error covariance matrix to an error ellipsoid principal axis coordinate system (xE，yE，zE) The transformation matrix of (2). The position of the detector in the error ellipsoid principal axis coordinate system is as follows:
in the error ellipsoid principal axis coordinate system, an equal probability density surface of the detector position error distribution, namely an n sigma error ellipsoid equation is as follows:
rE TD-1rE＝n2(28)
order to
The detector position error n σ ellipsoid equation is:
rE TErE＝1
the detector ellipsoid expansion safety zone is a part of the surface and the inner part of a detector position error n sigma ellipsoid shown by a formula, and the expression is as follows:
rE TErE≤1
and step four, calculating a safe distance index value of the detector relative to the obstacle according to the ellipsoid expansion safe area of the detector determined in the step three.
The safe distance index value of the detector relative to the obstacle comprehensively considers the influence factors of the obstacle avoidance track, wherein the influence factors of the obstacle avoidance track comprise the uncertainty factor of the detector state and the control constraint factor. Firstly, the minimum distance between the ellipsoidal expansion safety area of the detector and the obstacle is calculated, and then the set control safety distance value is subtracted to obtain a safety distance index value l.
The minimum distance between the detector ellipsoid expansion safety zone and the obstacle is firstly calculated, namely the minimum distance between the detector position error n sigma ellipsoid and the obstacle.
Considering the position and size of the obstacle, modeling the obstacle into a hemisphere, and fixedly connecting the obstacle center, namely the hemisphere center coordinate r, under a coordinate system by using a landing pointcAnd the obstacle reference radius, i.e., the hemispherical radius R, describes the position and size of the obstacle. The coordinates of the obstacle center under the error ellipsoid principal axis coordinate system are as follows:
according to the position relation between the center of the obstacle and the position error n sigma ellipsoid of the detector, selecting and executing the step 4.1 or the step 4.2 to obtain the minimum distance d between the position error n sigma ellipsoid of the detector and the obstaclee。
Step 4.1, when the center of the obstacle is positioned outside the position error n sigma ellipsoid of the detector, namely:
rcE TErcE＞1
let point r on the surface of the detector position error n σ ellipsoidsIs the surface of an ellipsoid r away from the center of the obstaclecThe point of minimum distance. Under the principal axis coordinate system of the error ellipsoid, the point rsThe coordinates of (a) are:
and satisfies the following equation:
rsE＝(I+λE)-1rcE
rcE T(I+λE)-TE(I+λE)-1rcE-1＝0
where λ is the lagrange multiplier. Solving the equation-to obtain the lambda value, and thus the coordinate rsE. Due to rcEIs located outside the ellipsoid of the position error n sigma of the detector, so that the ellipsoid has a unique distance rcEThe closest point, corresponds to a solution where λ is uniquely greater than zero.
The position error n sigma ellipsoid of the detector is far away from the center r of the obstaclecThe minimum distance of (c) is:
dc＝||rsE-rcE||＝||rs-rc||
wherein
When d iscR, the obstacle is wholly positioned outside a detector position error n sigma ellipsoid, and the minimum distance between the detector position error n sigma ellipsoid and the obstacle is as follows:
de＝dc-R
when d iscR is less than or equal to R, the detector position error n sigma ellipsoid is intersected with the obstacle, the obstacle part is positioned inside the detector position error n sigma ellipsoid, and the minimum distance d between the detector position error n sigma ellipsoid and the obstacleeIs 0.
Step 4.2, if the center of the obstacle is positioned in the inner part or on the surface of the position error n sigma ellipsoid of the detector, namely
rcE TErcE≤1
The position error n sigma ellipsoid of the detector is far away from the center r of the obstaclecIs 0. Correspondingly, the obstacle is wholly or partially located within a detector position error n σ ellipsoid, which is the minimum distance d from the obstacleeIs 0.
Using the minimum distance d between the detector position error n sigma ellipsoid obtained in the step 4.1 or the step 4.2 and the obstacleeMinus a control safety distance dsAnd obtaining a safe distance index value l of the detector relative to the obstacle:
l＝de-ds，de≥ds
wherein the safety distance d is controlledsComprehensive consideration bagAnd the values of the control capacity constraints including the configuration of the detector thruster and the thrust amplitude and control precision of each axial thruster are preset according to the configuration condition of the detector so as to reflect the influence of the control capacity constraints of the detector on the obstacle avoidance maneuvering capacity of the detector.
When the minimum distance between the detector position error n sigma ellipsoid and the obstacle is smaller than the control safety distance, the safety distance index value l is 0, namely:
l＝0，de＜ds
when the safe distance index value of the detector relative to the obstacle is 0, the detector possibly collides with the obstacle under the influence of state uncertainty and control constraint, and the safety of the detector at the moment is low.
And step five, constructing a Lyapunov function according to the safe distance index value obtained in the step four.
Constructing a potential field function phi related to the state of the detector under a landing point fixed connection coordinate systemq
φq＝xTQx
Wherein x ═ x, y, z, vx，vy，vz]TFor detector state variables, Q is Qi> 0, i 1, 6 is a diagonal matrix of diagonals. The potential field expressed by the above formula has only a minimum value point, and the detector target state x is 0. As long as it is ensured that the probe state x advances in the direction of the potential field decrease, the probe state will automatically approach the target landing state, i.e. the target landing position and speed are met at the same time.
Constructing a potential field function phi related to the obstacle threat according to the safe distance index value l of the detector relative to the obstacle obtained in the fourth steph
Wherein liRepresenting safe distance index values of the detector relative to the ith obstacle, k representing the number of obstacles, psi > 0 and sigma > 0 as parameters; safety distance index value l when detector is relative to obstacleiWhen reducedPotential field function phihThe value is increased; if the designed guidance law enables the detector to advance along the direction of the potential field reduction, the detector automatically achieves obstacle avoidance;
finally, a lyapunov function phi of the form:
lyapunov function is given by phiqAnd phihThe target state of the detector is the only global minimum value point in the potential field, and the potential field value is increased when the detector approaches the obstacle, so that the autonomous obstacle avoidance and the autonomous accurate soft landing can be realized simultaneously as long as the acceleration control instruction a is designed to enable the detector to advance along the potential field reducing direction.
Since Q is a positive definite matrix, thus:
and phi ishIf > 0, then for any x ≠ 0, there is:
φ＞0 (30)
and is
φ → ∞, when | | | x | | → ∞ (31)
And step six, designing an obstacle avoidance guidance law to obtain the control acceleration a in the step five so as to realize autonomous obstacle avoidance and autonomous accurate soft landing.
And according to the value of the safety distance index D in the fourth step, selecting to execute the step 6.1 or the step 6.2 to obtain a corresponding control acceleration instruction a.
Step 6.1, when the index values of the safe distances of the detectors relative to each obstacle are all larger than 0, namely:
li＞0，i＝1，...，k
according to the Lyapunov stability theory, in order to stabilize the system, in addition to satisfying the condition of formula-there is also required to satisfy:
namely:
wherein the content of the first and second substances,
due to the fact that
Where Δ r is the random error. And r issOn an ellipsoid of the detector position error n sigma, i.e.
Wherein Δ rsIndependent of r. Thus:
rs＝r-Δr+Δrs(38)
then
Order to
a＝aq+ah
Where κ is a positive real number. And when the target celestial body is a small celestial body:
the term related to the spin angular velocity ω after the equation of dynamics is developed in the form of x, y, z axis components ξ when the target celestial body is a planetx＝ξy＝ξz＝0。
When the control acceleration command a is applied to the detector, the requirement is met
The conditions are also true and the system is globally stable.
Step 6.2, when the safe distance index value of the detector relative to a certain obstacle is 0, the safe distance index value exists
lj＝0，1≤j≤k
The safety of the detector is low at this time. In order to ensure the safety of the detector, an emergency state is started to enable the detector to rise emergently, and the corresponding control acceleration instruction is as follows:
a＝[0，0，amax]T
wherein a ismaxThe maximum acceleration of the thruster in the positive direction of the z axis.
And controlling the landing track of the detector by using the acceleration instruction a obtained in the sixth step, reducing the influence of multiple disturbance and unknown environment on the surface of the planet on obstacle avoidance guidance of the detector, effectively avoiding the obstacle on the surface of the planet, and realizing autonomous safe and accurate landing.
The control acceleration command a obtained in the sixth step is in an analytic form, does not contain complex operations such as integral and the like, and meets the real-time requirement of on-line feedback control.
And n values in the detector position error n sigma ellipsoid are determined according to the size requirement of an ellipsoid expansion safety zone, and the preferable n value is 3.
In example 1, a 433Eros asteroid is used as a target star for simulation verification, and the simulation conditions are as follows: under the landing site fixed connection coordinate system, the initial position of the detector is [1300, -1400, 200%]Tm, initial velocity of [ -1, 0 [)]Tm/s, the target position is the origin of a landing point fixed connection coordinate system, and the target speed is zero; the central positions of the obstacles on the surface of the small celestial body are respectively [ 500-600 ]]Tm (obstacle 1) and [340, -360 ]]Tm (obstacle 2), obstacle reference radii are all 80 m; the maximum thrust acceleration of the thruster of the detector in each axial direction is 0.05m/s2The safe distance is controlled to be 1 m.
Under a landing point fixed connection coordinate system, the standard deviation of the estimation errors of the three-axis positions of the detector is 10m, the simulation time is 3500s, the instruction curves of the position, the speed and the acceleration of the three axes of the detector in the landing process are respectively shown in fig. 4-6, and the three-dimensional landing track of the detector is shown in fig. 5. Fig. 4 and 5 show that the three-axis position and speed of the detector converge to zero, and the detector realizes accurate soft landing; in fig. 6, the region with a large change in the control acceleration command given by the guidance law corresponds to two obstacle regions that the probe passes through during the landing process; fig. 7 shows that the probe successfully avoids two obstacles in the landing process and lands at the target landing point. Simulation results show that the safety zone expansion guidance method for avoiding the planet landing obstacle can autonomously realize obstacle avoidance and accurate soft landing under the condition that the position estimation error of the detector exists.
Further Monte Carlo simulation verification is carried out, and the obstacle avoidance effect of the method is compared with that of the traditional potential function guidance method under the condition that the position estimation error of the detector is large. And (3) performing 500 times of simulation on the condition that the standard deviation of the estimation errors of the three-axis positions of the detector is 60m and other simulation conditions are unchanged.
In the Monte Carlo simulation, the standard that the detector enters the reference radius of a certain obstacle in the landing process is used as the collision standard with the obstacle, and the obstacle avoidance success is realized when the detector is always positioned beyond the reference radius of all obstacles (all 80m in the simulation) in the landing process. Monte Carlo simulation results show that under the condition that a large estimation error exists in the position of a detector, the obstacle 1 avoidance success rate of the traditional potential function guidance method is 83.1 percent (figure 8), the obstacle 2 avoidance success rate is 67.2 percent (figure 9), and the corresponding obstacle avoidance overall success rate in the landing process is 59.2 percent; the method has the avoidance success rate of 100 percent for the obstacle 1 and the obstacle 2 (fig. 10 and fig. 11), and the corresponding obstacle avoidance overall success rate in the landing process is 100 percent. Because the uncertainty of the position information of the detector is considered in the derivation process of the guidance law and is quantitatively described through the detector ellipsoid expansion safety area and the corresponding safety distance index, the method has better obstacle avoidance performance under the uncertain condition, and particularly under the conditions of larger detector position uncertainty and multi-obstacle complex terrain, the obstacle avoidance success rate is obviously higher than that of the traditional potential function guidance method.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention, and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements, etc. made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (6)
1. A safety zone expansion guidance method for avoiding a planet landing obstacle is characterized by comprising the following steps: comprises the following steps of (a) carrying out,
firstly, defining a landing point fixed connection coordinate system and an error ellipsoid principal axis coordinate system;
defining a landing site fixed coordinate system (x, y, z): the origin of coordinates O is the target landing point, and the z-axis is along the centroid O of the small celestial bodycDirection of the line to the origin O
The y axis is positioned in a plane formed by the z axis and the spin main axis of the small celestial body and is vertical to the z axis, and the x axis enables the (x, y, z) coordinate system to meet the right-hand rule;
defining an error ellipsoid principal axis coordinate system (x)E，yE，zE): origin of coordinates OEAt the estimated value of the detector position, xE，yE，zEThe axes are respectively superposed with the three main axes of the detector position error n sigma ellipsoid and meet the right-hand rule;
step two, establishing a landing kinetic equation under a landing point fixed connection coordinate system;
when the target celestial body is a small celestial body, the landing kinetic equation of the detector under the landing point fixed connection coordinate system is as follows:
wherein r ═ x, y, z]TIs the position vector of the detector under the landing point fixed connection coordinate system, v ═ vx，vy，vz]TAs the velocity vector of the probe, ω ═ ωx，ωy，ωz]TIs the target celestial body spin angular velocity vector, g ═ gx，gy，gz]TThe gravity acceleration of a target celestial body received by the detector is shown as a control acceleration instruction;
when the target celestial body is a planet, the spin angular velocity omega can be ignored, and the landing kinetic equation of the detector under the landing point fixed connection coordinate system is as follows:
step three, determining an ellipsoid expansion safety area of the detector;
calculating a detector position error n sigma ellipsoid according to the detector state estimation information, and setting the surface and the inner part of the position error n sigma ellipsoid as an ellipsoid expansion safety zone of the detector; the position estimation error of the detector conforms to Gaussian distribution with zero mean value, and the mean value of the estimated value of the actual position r under the landing site fixed coordinate system is
The position error covariance matrix of the detector isC；
And (3) carrying out eigenvalue decomposition on the detector position error covariance matrix C:
UTCU＝D (3)
diagonal elements of the diagonal matrix D are all eigenvalues of the detector position error covariance matrix C, and all columns of the matrix U are eigenvectors corresponding to all eigenvalues; orthogonal transfer matrix UTFrom a landing site fixed-axis coordinate system (x, y, z) defining a detector position error covariance matrix to an error ellipsoid principal axis coordinate system (xE，yE，zE) The transformation matrix of (2); the position of the detector in the error ellipsoid principal axis coordinate system is as follows:
order to
The detector position error n σ ellipsoid equation is:
rE TErE＝1 (6)
the detector ellipsoid expansion safety zone is a part of the surface and the inner part of a detector position error n sigma ellipsoid shown by a formula, and the expression is as follows:
rE TErE≤1 (7)
step four, calculating a safe distance index value of the detector relative to the obstacle according to the ellipsoid expansion safe area of the detector determined in the step three;
comprehensively considering the influence factors of obstacle avoidance tracks by the detector relative to the safe distance index value of the obstacle; firstly, calculating the minimum distance between an ellipsoid expansion safety area of a detector and an obstacle, and then subtracting a set control safety distance value to obtain a safety distance index value l;
firstly, calculating the minimum distance between the detector ellipsoid expansion safety area and the obstacle, namely the minimum distance between the detector position error n sigma ellipsoid and the obstacle;
considering the position and size of the obstacle, modeling the obstacle into a hemisphere, and fixedly connecting the obstacle center, namely the hemisphere center coordinate r, under a coordinate system by using a landing pointcAnd the obstacle reference radius, i.e. the hemispherical radius R, describes the position and size of the obstacle; the coordinates of the obstacle center under the error ellipsoid principal axis coordinate system are as follows:
according to the position relation between the center of the obstacle and the position error n sigma ellipsoid of the detector, selecting and executing the step 4.1 or the step 4.2 to obtain the minimum distance d between the position error n sigma ellipsoid of the detector and the obstaclee；
Step 4.1, when the center of the obstacle is positioned outside the position error n sigma ellipsoid of the detector, namely:
rcE TErcE＞1 (9)
let point r on the surface of the detector position error n σ ellipsoidsIs the surface of an ellipsoid r away from the center of the obstaclecA point of minimum distance; under the principal axis coordinate system of the error ellipsoid, the point rsThe coordinates of (a) are:
and satisfies the following equation:
rsE＝(I+λE)-1rcE(11)
rcE T(I+λE)-TE(I+λE)-1rcE-1＝0 (12)
wherein λ is Lagrange multiplier; solving the equation-to obtain the lambda value, and thus the coordinate rsE(ii) a Due to rcEIs located outside the ellipsoid of the position error n sigma of the detector, so that the ellipsoid has a unique distance rcEThe closest point, corresponding to a solution where λ is uniquely greater than zero;
the position error n sigma ellipsoid of the detector is far away from the center r of the obstaclecThe minimum distance of (c) is:
dc＝||rsE-rcE||＝||rs-rc|| (13)
wherein
When d iscR, the obstacle is wholly positioned outside a detector position error n sigma ellipsoid, and the minimum distance between the detector position error n sigma ellipsoid and the obstacle is as follows:
de＝dc-R (14)
when d iscR is less than or equal to R, the detector position error n sigma ellipsoid is intersected with the obstacle, the obstacle part is positioned inside the detector position error n sigma ellipsoid, and the minimum distance d between the detector position error n sigma ellipsoid and the obstacleeIs 0;
step 4.2, if the center of the obstacle is positioned in the inner part or on the surface of the detector position error n sigma ellipsoid, namely:
rcE TErcE≤1 (15)
the position error n sigma ellipsoid of the detector is far away from the center r of the obstaclecIs 0; correspondingly, the obstacle is wholly or partially located within a detector position error n σ ellipsoid, which is the minimum distance d from the obstacleeIs 0;
using the minimum distance d between the detector position error n sigma ellipsoid obtained in the step 4.1 or the step 4.2 and the obstacleeMinus a control safety distance dsAnd obtaining a safe distance index value l of the detector relative to the obstacle:
l＝de-ds，de≥ds(16)
wherein the safety distance d is controlledsComprehensively considering control capability constraints including the configuration of the detector thruster, thrust amplitude and control precision of each axial thruster, and presetting values according to the configuration condition of the detector to reflect the influence of the control capability constraints of the detector on the obstacle avoidance maneuvering capability of the detector;
when the minimum distance between the detector position error n sigma ellipsoid and the obstacle is smaller than the control safety distance, the safety distance index value l is 0, namely:
l＝0，de＜ds(17) when the index value of the safe distance of the detector relative to the obstacle is 0, the detector possibly collides with the obstacle under the influence of state uncertainty and control constraint, and the safety of the detector at the moment is low;
step five, constructing a Lyapunov function according to the safe distance index value obtained in the step four;
constructing a potential field function phi related to the state of the detector under a landing point fixed connection coordinate systemq
φq＝xTQx (18)
Wherein x ═ x, y, z, vx，vy，vz]TFor detector state variables, Q is Qi> 0, i 1, 6 is a diagonal matrix of diagonals; the potential field expressed by the above formula has a unique minimum value point, and is a detector target state x which is equal to 0; as long as the detector state x is ensured to advance along the direction of potential field reduction, the detector state will automatically approach to the target landing state, namely, the target landing position and speed are met simultaneously;
constructing a potential field function phi related to the obstacle threat according to the safe distance index value l of the detector relative to the obstacle obtained in the fourth steph
Wherein liRepresenting safe distance index values of the detector relative to the ith obstacle, k representing the number of obstacles, psi > 0 and sigma > 0 as parameters; safety distance index value l when detector is relative to obstacleiWhen reduced, the potential field function phihThe value is increased; if the designed guidance law enables the detector to advance along the direction of the potential field reduction, the detector automatically achieves obstacle avoidance;
finally, a lyapunov function phi of the form:
lyapunov function is given by phiqAnd phihThe target state of the detector is the only global minimum value point in the potential field, and the potential field value is increased when the detector approaches the obstacle, so that the autonomous obstacle avoidance and the autonomous accurate soft landing can be realized simultaneously as long as the acceleration control instruction a is designed to enable the detector to advance along the potential field reducing direction;
and step six, designing an obstacle avoidance guidance law to obtain the control acceleration a in the step five so as to realize autonomous obstacle avoidance and autonomous accurate soft landing.
2. The method for guiding expansion of the safety zone for avoiding the planet landing obstacle as claimed in claim 1, wherein the method comprises the following steps:
the concrete realization method of the sixth step is that,
according to the value of the safety distance index l in the fourth step, selecting to execute the step 6.1 or the step 6.2 to obtain a corresponding control acceleration instruction a;
step 6.1, when the index values of the safe distances of the detectors relative to each obstacle are all larger than 0, namely:
li＞0，i＝1，...，k (21)
order to
Wherein xs，ys，zsIs rsThree-axis coordinate of (2), xci，yci，zciIs the ith obstacle center rciThree-axis coordinates of
a＝aq+ah(24)
Wherein κ is a positive real number; and when the target celestial body is a small celestial body:
the term related to the spin angular velocity omega after the dynamic equation is expanded in the form of x, y and z axis components, and ξ when the target celestial body is a planetx＝ξy＝ξz＝0；
Step 6.2, when the safe distance index value of the detector relative to a certain obstacle is 0, the following steps exist:
lj＝0，1≤j≤k (26)
the safety of the detector is low at the moment; in order to ensure the safety of the detector, an emergency state is started to enable the detector to rise emergently, and the corresponding control acceleration instruction is as follows:
a＝[0，0，amax]T(27)
wherein a ismaxThe maximum acceleration of the thruster in the positive direction of the z axis.
3. A safety zone inflation guidance method for planet landing obstacle avoidance according to claim 1 or 2, characterized in that: and n values in the detector position error n sigma ellipsoid are determined according to the size requirement of an ellipsoid expansion safety zone, and the n value is selected to be 3.
4. The method for guiding expansion of the safety zone for avoiding the planet landing obstacle as claimed in claim 3, wherein the method comprises the following steps: and the control acceleration command a obtained in the sixth step is in an analytic form, does not contain integral complex operation, and meets the real-time requirement of on-line feedback control.
5. The method for guiding expansion of the safety zone for avoiding the planet landing obstacle as claimed in claim 4, wherein the safety zone comprises: and fourthly, the influence factors of the obstacle avoidance trajectory comprise detector state uncertainty factors and control constraint factors.
6. The method for guiding expansion of the safety zone for avoiding the planet landing obstacle as claimed in claim 5, wherein the method comprises the following steps: and n values in the detector position error n sigma ellipsoid are determined according to the size requirement of an ellipsoid expansion safety zone, and the n value is selected to be 3.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710844211.7A CN107621829B (en) | 2017-09-19 | 2017-09-19 | Safety zone expansion guidance method for avoiding planet landing obstacle |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710844211.7A CN107621829B (en) | 2017-09-19 | 2017-09-19 | Safety zone expansion guidance method for avoiding planet landing obstacle |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN107621829A CN107621829A (en) | 2018-01-23 |
| CN107621829B true CN107621829B (en) | 2020-04-21 |
Family
ID=61089749
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710844211.7A Active CN107621829B (en) | 2017-09-19 | 2017-09-19 | Safety zone expansion guidance method for avoiding planet landing obstacle |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN107621829B (en) |
Families Citing this family (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110686683B (en) * | 2019-11-01 | 2021-03-30 | 北京理工大学 | Planetary landing trajectory online optimization method based on uneven expansion ellipsoid |
| CN111924139B (en) * | 2020-08-03 | 2022-05-24 | 北京理工大学 | Small celestial body landing obstacle avoidance constant thrust control method based on expansion early warning area |
| CN112631285B (en) * | 2020-12-08 | 2021-11-23 | 北京理工大学 | Method for quickly generating small celestial body attachment autonomous obstacle avoidance track |
| CN112987783A (en) * | 2021-02-18 | 2021-06-18 | 北京理工大学 | Complex small celestial body surface landing obstacle avoidance constant thrust control method |
| CN113867143B (en) * | 2021-09-15 | 2024-05-31 | 北京理工大学 | Safety soft landing analysis obstacle avoidance guidance method for extraterrestrial celestial body |
| CN113985904B (en) * | 2021-09-28 | 2023-03-10 | 哈尔滨工业大学 | Method for generating and intelligently switching motion modes of star probe vehicle |
| CN114019792B (en) * | 2021-10-08 | 2023-08-01 | 北京控制工程研究所 | Mars atmosphere entry process lift force guidance error analysis method and system |
| CN115309057B (en) * | 2022-09-05 | 2023-08-11 | 北京理工大学 | Planet surface complex terrain area safe landing guidance method |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102040008A (en) * | 2010-12-13 | 2011-05-04 | 北京航空航天大学 | Anti-collision control method for safety of in-obit operation of formation-flying satellites |
| CN102541070A (en) * | 2012-01-20 | 2012-07-04 | 哈尔滨工业大学 | Collision avoiding method for ground testing system of satellite formation flying |
| CN102981507A (en) * | 2012-11-29 | 2013-03-20 | 北京理工大学 | Control method of soft landing autonomic obstacle avoidance fixed-thruster |
| CN105333873A (en) * | 2015-10-20 | 2016-02-17 | 北京理工大学 | Planet safe landing guidance method employing landing point on-line selection |
| CN106249756A (en) * | 2016-09-20 | 2016-12-21 | 北京理工大学 | A kind of planetary landing obstacle avoidance control method based on collision probability |
-
2017
- 2017-09-19 CN CN201710844211.7A patent/CN107621829B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102040008A (en) * | 2010-12-13 | 2011-05-04 | 北京航空航天大学 | Anti-collision control method for safety of in-obit operation of formation-flying satellites |
| CN102541070A (en) * | 2012-01-20 | 2012-07-04 | 哈尔滨工业大学 | Collision avoiding method for ground testing system of satellite formation flying |
| CN102981507A (en) * | 2012-11-29 | 2013-03-20 | 北京理工大学 | Control method of soft landing autonomic obstacle avoidance fixed-thruster |
| CN105333873A (en) * | 2015-10-20 | 2016-02-17 | 北京理工大学 | Planet safe landing guidance method employing landing point on-line selection |
| CN106249756A (en) * | 2016-09-20 | 2016-12-21 | 北京理工大学 | A kind of planetary landing obstacle avoidance control method based on collision probability |
Non-Patent Citations (3)
| Title |
|---|
| Innovative hazard detection and avoidance strategy for autonomous safe planetary landing;XiuQiang Jiang，等;《Acta Astronautica》;20161231;第126卷;第66-76页 * |
| 基于Lyapunov函数的小天体软着陆障碍规避控制方法;胡海静，等;《深空探测学报》;20150630;第2卷(第2期);第149-154页 * |
| 星际着陆自主障碍检测与规避技术;李爽，等;《航空学报》;20100831;第31卷(第8期);第1584-1592页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN107621829A (en) | 2018-01-23 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN107621829B (en) | Safety zone expansion guidance method for avoiding planet landing obstacle | |
| Zong et al. | Reactionless control of free-floating space manipulators | |
| Thanh et al. | Completion of collision avoidance control algorithm for multicopters based on geometrical constraints | |
| Chu et al. | Hybrid tension control method for tethered satellite systems during large tumbling space debris removal | |
| Goodarzi et al. | Global formulation of an extended Kalman filter on SE (3) for geometric control of a quadrotor UAV | |
| Khalaji et al. | Lyapunov-based formation control of underwater robots | |
| Ma et al. | Trajectory optimization for lunar rover performing vertical takeoff vertical landing maneuvers in the presence of terrain | |
| CN110686683A (en) | Planetary landing trajectory online optimization method based on uneven expansion ellipsoid | |
| Chen et al. | Computationally efficient trajectory planning for high speed obstacle avoidance of a quadrotor with active sensing | |
| Zhu et al. | Anti-collision zone division based hazard avoidance guidance for asteroid landing with constant thrust | |
| Gong et al. | Barrier lyapunov function-based planetary landing guidance for hazardous terrains | |
| Bojun et al. | High-precision adaptive predictive entry guidance for vertical rocket landing | |
| Vanegas et al. | Smooth 3D path planning for non-holonomic UAVs | |
| Fahimi et al. | An alternative closed-loop vision-based control approach for Unmanned Aircraft Systems with application to a quadrotor | |
| Li et al. | Robocentric model-based visual servoing for quadrotor flights | |
| Hassani et al. | Robust Finite‐Time Tracking Control Based on Disturbance Observer for an Uncertain Quadrotor under External Disturbances | |
| Guo et al. | Rapid SGCMGs singularity-escape steering law in gimbal angle space | |
| Pajak et al. | Sub-optimal trajectory planning for mobile manipulators | |
| Liu et al. | Hybrid vision/force control for underwater vehicles landing on unknown surfaces | |
| Lim et al. | Guidance laws for target localization using vector field approach | |
| Worrall et al. | Autonomous planetary rover control using inverse simulation | |
| Ramirez et al. | Stability analysis of a vision-based UAV controller: An application to autonomous road following missions | |
| Kamath et al. | Vision-based fast-terminal sliding mode super twisting controller for autonomous landing of a quadrotor on a static platform | |
| Raja et al. | Dynamic inversion-based nonlinear aiming point guidance of unmanned aerial vehicles for reactive obstacle avoidance | |
| Lv et al. | AUV Real-time Dynamic Obstacle Avoidance Strategy Based on Relative Motion. |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |