CN112631285B - Method for quickly generating small celestial body attachment autonomous obstacle avoidance track - Google Patents
Method for quickly generating small celestial body attachment autonomous obstacle avoidance track Download PDFInfo
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Abstract
本发明公开的小天体附着自主避障轨迹快速生成方法，属于深空探测技术领域。本发明通过“地形走势实时拟合”加“避障轨迹快速更新”的组合实现自适应避障制导。星载计算机根据激光测距仪测得的小天体表面高程信息序列，对地形走势进行拟合。使用当前地形拟合曲线终点的斜率以直线的形式向前延伸，对前方地形走势进行判断，评估当前飞行轨迹安全性。当前满足预设安全性要求时，按照解析能量最优制导律进行制导。当前不满足预设安全性要求时，通过调节三个方向的推力输出比例实现对轨迹几何曲率的调整，实现对参考避障轨迹的跟踪。循环进行上述地形评估和避障机动，最终达到在尽可能避免推力饱和的条件下实现地形障碍规避，完成安全附着的目标。
The invention discloses a method for quickly generating a small celestial body attachment autonomous obstacle avoidance trajectory, which belongs to the technical field of deep space detection. The present invention realizes self-adaptive obstacle avoidance guidance through the combination of "real-time fitting of terrain trends" and "fast update of obstacle avoidance trajectory". The onboard computer fits the terrain trend according to the surface elevation information sequence of the small celestial body measured by the laser rangefinder. Use the slope of the end point of the current terrain fitting curve to extend forward in the form of a straight line, judge the trend of the terrain ahead, and evaluate the safety of the current flight trajectory. When the preset safety requirements are currently met, the guidance is carried out according to the optimal guidance law of analytical energy. When the preset safety requirements are not currently met, the geometric curvature of the trajectory can be adjusted by adjusting the thrust output ratio in the three directions, and the tracking of the reference obstacle avoidance trajectory can be realized. The above terrain assessment and obstacle avoidance maneuvers are carried out cyclically, and finally the terrain obstacle avoidance is achieved under the condition of avoiding thrust saturation as much as possible, and the goal of safe attachment is achieved.
Description
Technical Field
The invention relates to a small celestial body attachment guidance method, in particular to a method for quickly generating obstacle avoidance tracks under complex morphology, and belongs to the technical field of deep space exploration.
Background
Safe and stable attachment is an important prerequisite for developing small celestial body surface inspection and sampling return tasks. In the implemented small celestial body attachment task, the lander has higher dependence degree on ground measurement and control. Because the small celestial body is far away from the earth generally, larger communication time delay exists, the attachment process adopting ground measurement and control has low efficiency, and various sudden situations cannot be dealt with in time. Therefore, the lander is required to improve the autonomous attachment capability thereof, actively adjust the attachment strategy in real time according to the result of environmental perception, and improve the attachment safety.
At present, the realization of autonomous attached guidance of small celestial bodies mainly faces the following three technical problems: firstly, the surface appearance of the small celestial body is complex, and the collision risk is high. Due to the fact that the small celestial body is large in shape irregularity, terrains such as surface boulders, steep slopes, gullies and hills are widely distributed, and therefore terrain obstacles need to be rapidly identified and avoided in the lander attachment process. Secondly, the surface environment of the small celestial body is dark and weak, and uncertainty is strong. Because the small celestial body is small in size, the environmental information near the small celestial body cannot be accurately mastered only by ground observation, and adverse factors such as projectiles and rugged topography can be discovered only by near-distance optical observation. Thirdly, the dynamics situation near the small celestial body is complex, and the disturbance influence is large. Because the small celestial body gravitational field is weak and irregularly distributed, the surface escape speed is low, the detector is acted by continuously changing gravitational force, centripetal force and tangential force when the surface moves, and is influenced by disturbance such as sunlight pressure and the like, and the adhesion control precision is difficult to improve.
The existing adhesion guidance method mainly aims at realizing 'double-zero control' by using an analytic algorithm with small calculation amount. For example, closed-loop guidance strategies such as Apollo guidance, ZEM/ZEV guidance and the like, but the simple analytic guidance law cannot consider important constraints such as paths and upper thrust limits and does not have obstacle avoidance capability. The optimal attachment trajectory is designed by using an optimal control theory, and a feedback control tracking method can solve the problem of constraint satisfaction, but the trajectory optimization takes long time and is difficult to implement on-line trajectory updating or re-planning. The curvature guidance method ensures that the lander is always attached along a convex curvature track by controlling guidance parameters, reduces the probability of collision with terrain obstacles, but the guidance strategy also belongs to a deterministic strategy, and can not quantitatively and accurately adjust the shape of the attachment track according to the perceived environmental change in the attachment process. In an environment where the surface of a small celestial body is unknown, the adoption of a deterministic attachment strategy is not beneficial to the safety of the lander. In conclusion, the autonomous guidance law for the attachment of the small celestial body needs to quickly identify obstacles according to the change condition of the terrain in the attachment process on the basis of small calculated amount and strong universality, quickly generate a reference obstacle avoidance track to accurately adjust the flight state of the lander, and simultaneously consider the thrust upper limit constraint and reduce the risk of collision between the lander and the terrain obstacle.
Disclosure of Invention
Aiming at the problems that the existing small celestial body analysis guidance strategies are deterministic strategies and cannot carry out real-time autonomous obstacle avoidance, the invention aims to provide a small celestial body attachment adaptive obstacle avoidance curvature guidance method, which has the following four advantages: (1) the control acceleration calculation step is developed on the basis of a classical analytic energy optimal guidance law, is simple in form and high in calculation speed, and can be rapidly operated in real time on a spacecraft satellite-borne computer. (2) The terrain tendency can be fit and estimated by using limited environment measurement data, and the risk of terrain obstacles can be accurately judged. (3) The reference obstacle avoidance track can be quickly generated and updated according to the terrain obstacle evaluation result, and accurate adjustment of the shape of the attachment track is realized by tracking the reference track. (4) The condition of thrust saturation can be effectively prevented from occurring by considering the requirements of adhesion safety and thrust upper limit constraint.
The purpose of the invention is realized by the following technical scheme:
the invention discloses a method for quickly generating an attached autonomous obstacle avoidance track of a small celestial body, which realizes self-adaptive obstacle avoidance guidance through a combination of 'real-time terrain trend fitting' and 'quick obstacle avoidance track updating'. In the attachment process, the laser range finder is used by the lander to measure the elevation of the surface of the lower small celestial body at intervals, and the spaceborne computer fits the terrain trend according to the elevation information sequence of the surface of the small celestial body measured by the laser range finder to obtain a terrain trend fitting curve equation. And then, extending forwards in a straight line mode by using the slope of the current terrain fitting curve end point, judging the terrain trend in front, and evaluating the safety of the current flight track. And when the current flight state meets the preset safety requirement, guidance is carried out according to the analytic energy optimal guidance law. When the current flight state does not meet the preset safety requirement, a reference obstacle avoidance track is calculated by combining a terrain tendency fitting result and the control capability of a lander engine, and the geometric curvature of the track is adjusted by adjusting the thrust output proportion in three directions, so that the reference obstacle avoidance track is tracked. And circularly carrying out the terrain assessment and obstacle avoidance maneuver, and finally achieving the goal of realizing terrain obstacle avoidance under the condition of avoiding thrust saturation as much as possible and finishing safe adhesion.
The invention discloses a method for quickly generating a small celestial body attachment autonomous obstacle avoidance track, which comprises the following steps of:
the method comprises the following steps that firstly, a satellite borne computer fits terrain trends according to a small celestial body surface elevation information sequence measured by a laser range finder to obtain a terrain trend fitting curve equation.
The lander obtains surface elevation data by using absolute height information measured by the autonomous navigation system and combining with the relative distance of the surface of the small celestial body below measured by the laser range finder, and obtains a terrain trend curve by using surface elevation sequence fitting obtained by interval measurement.
Firstly, a small celestial body surface is established by taking a preset landing point as an original point to be fixedly connected with an orthogonal coordinate system oxyz, a z axis is superposed with a normal of a local ground plane at the position of the landing point, and the positive direction points to the outside of the small celestial body. The x axis is in the local plane of the landing point and is superposed with the cross multiplication vector of the positive direction of the z axis and the rotation direction of the small celestial body, and the y axis, the x axis and the z axis jointly form a right-hand coordinate system. The lander has a current state of
Z＝[x y z u v w]T (1)
Wherein x, y and z are the positions of the lander under the surface fixed coordinate system, and u, v and w are the speeds of the lander under the surface fixed coordinate system. And defining a small celestial body surface height function as al (x, y) and representing the height of a corresponding small celestial body surface point at (x, y) under the surface fixed connection. Further defining the relative height function measured by the laser range finder as H (x, y), al (x, y) and calculating the function as
al(x,y)＝z-H(x,y) (2)
The lander is attached every tEThe time is measured once for the terrain height according to equation (2). When each measurement is finished, the terrain height values measured for the last n times till the current moment are respectively recorded as: al1、al2、al3……alnThe coordinates of the lander on the x-y plane at the corresponding n times of measurement time are respectively (x)1,y1)、(x2,y2)、(x3,y3)……(xn,yn). Wherein (x)n,yn) I.e. the horizontal position at which the lander is currently located. First, the relative height al to x relationship is fitted using an n-1 th order curve as follows
al＝a0xn-1+a1xn-2+…+an-2x+an-1 (3)
Based on the n sets of measurement data, a in formula (3)0,a1,a2,…,an-1Is a polynomial coefficient, is solved by the following linear equation set
[al1 al2 … aln]T＝C·[a0 a1 … an-1]T (4)
The fitting result is the projection of the terrain trend curve on the x-z plane, the projection on the x-y plane is fitted below, the projection curve to be solved is approximately regarded as a straight line, and the following linear function is used for fitting
y＝b0x+b1 (6)
Using data from n measurements, for coefficient b0And b1Performing linear regression
And (3) uniquely determining a terrain trend fitting curve below the flight path of the lander by using the projections (3) and (6), so as to obtain a terrain trend fitting curve equation.
Preferably, the fitting efficiency and the fitting accuracy are both considered, the terrain trend fitting curve equation shown in the formula (3) is preferably a cubic curve, that is, the value of n is preferably 4.
And step two, extending forwards in a straight line mode by using the slope of the current terrain fitting curve end point, judging the terrain trend in front, and evaluating the safety of the current flight track.
The x-axis coordinates of the starting point and the ending point of the terrain tendency extension line are x respectivelysAnd xeHas the following relations
xs＝xn (9)
xe＝xn+kp(xn-x1) (10)
In the formula (10), the extension length proportionality coefficient kpRepresenting the ratio of the length of the extension line to the length of the measurement fit curve. Line of y'n＝b0xn+b1Fitting the curve at the end point (x) of the terrainn,y'n,aln) Where the slopes of the x-z and x-y plane projections are respectively
Sxz＝(n-1)a0xn-2+(n-2)a1xn-3+…+an-3x+an-2 (11)
Sxy＝b0 (12)
Let the y-axis coordinate of the end point of the extension line be yeZ axis coordinate is aleThen there is
ale＝aln+Sxz(xe-xs) (13)
ye＝yn+Sxy(xe-xs) (14)
Parameter Sxz、Sxy、xe、ye、aleThe extension line is completely defined. And then judging whether the lander has the risk of collision with the terrain obstacle according to the height of the extension line terminal point. If the risk is high, a reference obstacle avoidance track needs to be designed, and tracking is carried out through a curvature control method. With current flying height z of the landernThe height difference of the end point of the extension line is used as a main judgment basis, and the following judgment criteria are established
High-range safety coefficient k in formulahBeing positive real, the current height z of the landernAnd the height al of the end point of the extension lineeIs proportional to the horizontal distance of the lander from the attachment point, the further the lander is from the intended attachment point, the more stringent the relative height constraint with the underlying small celestial body surface. And judging the terrain tendency in front according to a safety judgment criterion formula (15), and evaluating the collision risk, thereby realizing the evaluation of the safety of the current flight track.
And step three, conducting guidance according to the analytic energy optimal guidance law when the current flight state meets the preset safety requirement according to the current flight track safety result evaluated in the step two, returning to the step one, and continuing to conduct terrain measurement.
When the current relative elevation of the lander calculated by the spaceborne computer meets the safety judgment criterion defined by the formula (15), the landform obstacle at present is judged to be less threatened, and the lander implements the energy optimal guidance law so as to save fuel.
The lander moves in a surface fixed coordinate system and is under the combined action of the thrust of the rail-controlled engine, the gravity of the small celestial body, disturbance force generated by the rotation of the small celestial body and other unmodeled disturbance force. Since the acceleration other than the acceleration generated by the engine thrust has small influence on the movement of the lander, the dynamic equation of the lander system is simplified into the following form:
wherein r ═ x y z]T、v＝[u v w]T、
Each term in the vector u represents the component of the lander control acceleration on three axes of the surface-mount system. The design optimization index of the energy optimal guidance law is
Wherein t is0(t0＝0)、tfInitial and terminal times, respectively, and Γ is a weighting coefficient with respect to time. According to the optimal control theory, a basic variational method is used to obtain a three-axis control acceleration formula of the engine
Wherein t isgoIs an estimate of the residual time, which is the only positive real root of the following quartic equation
During the execution period of step three, every tEAnd returning to the step one, and continuing to carry out the topographic measurement.
And step four, when the current flight state does not meet the preset safety requirement according to the safety result of the current flight track evaluated in the step two, generating a reference obstacle avoidance track, tracking and avoiding the obstacle by adopting a curvature control method, returning to the step one, and continuously carrying out the terrain measurement.
When the current relative elevation of the lander calculated by the spaceborne computer does not meet the safety constraint defined by the formula (15), the landform obstacle threat at present is judged to be large, and at the moment, the lander implements a curvature guidance strategy to track the obstacle avoidance track.
Curvature C of projection curve of lander flight path on x-z plane and y-z planexzAnd CyzAs a control object for adjusting the shape of the trajectory, the following is defined
The curvature obstacle avoidance guidance law adds three thrust coefficients k on the basis of the original analytic energy optimal guidance laws (17) - (19)x、ky、kzSo that the real-time calculation method of the control acceleration is changed from (18) to the following formula
When equations (22) to (24) are substituted into trajectory curvature defining equations (20) to (21), the relationship between the curvature and the thrust coefficient is
Regarding the analytic energy optimal guidance law as a curvature obstacle avoidance guidance law at kx＝ky＝kzIn a special form of 1, the triaxial thrust coefficient is defined to be constant during the adjustment
kx+ky+kz＝3 (27)
Obtaining a determination method of the triaxial thrust coefficient under the condition of a reference track according to the expressions (25) to (27), wherein the curvature of the reference track at the current position is CrxzAnd CryzThe thrust coefficient is then the solution of the following system of linear equations:
the following provides a method for generating a reference obstacle avoidance trajectory. The projection of the reference obstacle avoidance track on an x-z plane, and the coordinate of the starting point is (x)s,zs) I.e. the x-axis and z-axis coordinates of the current position of the lander, and the velocity at the starting point is (v)xs,vzs) Slope of starting point SxzsThe formula (30) is defined, and the value of the formula is ensured to be the same as the current track slope of the lander.
Sxzs＝vzs/vxs (30)
Let the current lander acceleration be (a)xs,azs) The curvature at the starting point is
Defining the coordinate of the end point x axis of the reference obstacle avoidance track as xeThe value is the same as the end point of the terrain tendency estimation curve, and the coordinate of the z axis is zeThe terminal velocity is (v)xe,vze) The following two end point height indicators are given
Proportionality coefficient k in formula (32)r1Is a positive real number, the proportionality coefficient k in equation (33)r2Real numbers between 0 and 1. Considering both the requirement of adhesion safety and the constraint of upper limit of thrust, and referring to the end point height z of the obstacle avoidance trackeGet ze1And ze2Greater term between
ze＝max(ze1,ze2) (34)
Slope S at end point of reference obstacle avoidance trackxze＝vze/vxeIs given by
Sxze＝kr3·Sxz+(1-kr3)·(vzs/vxs) (35)
Proportional coefficient k in the formular3Positive real numbers less than 1.
Coordinates (x) of starting point of given reference obstacle avoidance tracks,zs) Endpoint coordinate (x)e,ze) Slope of origin SxzsEnd point slope SxzeAnd a curvature of origin Crxzs. Using a polynomial design curve, to satisfy the above 5 conditions, a polynomial of at least 4 th order is required
z＝c0x4+c1x3+c2x2+c3x+c4 (36)
Polynomial coefficient c0～c4Can be solved by the following linear equation set
And solving a projection curve of the reference obstacle avoidance track on a y-z plane by using the same projection curve generation method:
z＝d0y4+d1y3+d2y2+d3y+d4 (39)
solve the parameter c0～c4And d0～d4Thereafter, the reference obstacle avoidance trajectory is uniquely determined in coordinates (x)s,ys,zs) Starting from (x)e,ye,ze) Is the end point. For a certain point r on the reference obstacle avoidance trackm＝[xm ym zm]TIn other words, the curvature of the trajectory at that location is
And in the process of obstacle avoidance flight of the lander, calculating the curvature value of the reference obstacle avoidance track at the current flight position according to the formulas (40) to (41), and substituting the curvature value into the equation set (28) to obtain the value of the current triaxial thrust coefficient.
During the execution period of step four, every tEAnd time, continuing to perform the topographic measurement.
Step five: and in the whole process of the landing device attachment, quickly generating and updating a reference obstacle avoidance track according to a terrain obstacle evaluation result, and realizing accurate adjustment of the shape of the attachment track by tracking the reference track, namely repeatedly and circularly executing the first step to the fourth step according to the terrain obstacle evaluation result until the landing device reaches a preset landing point at a speed approximate to zero, and completing the attachment task.
Has the advantages that:
1. the invention discloses a method for quickly generating an attached autonomous obstacle avoidance track of a small celestial body, which aims at solving the problem that the existing guidance law is difficult to avoid surface terrain obstacles in real time in a task of attaching the small celestial body, utilizes limited environment measurement data to carry out fitting estimation on terrain trends, combines a landing segment collision risk judgment criterion, quickly evaluates the possibility of collision between the attached track and the terrain obstacles, and is favorable for quickly coping with sudden risks.
2. The invention discloses a method for quickly generating a small celestial body attachment autonomous obstacle avoidance track. The landing device can respond to the sudden risk in the attachment process in time, and the safety is improved.
3. The method for quickly generating the small celestial body attachment autonomous obstacle avoidance track disclosed by the invention can effectively balance the contradiction between the safety and the maneuvering capacity of the lander by considering both the obstacle avoidance effect and the thrust upper limit constraint in the generation and updating processes of the reference obstacle avoidance track.
4. The invention discloses a method for quickly generating small celestial body attachment autonomous obstacle avoidance tracks, which changes an elevation safety coefficient khCoefficient k in terrain fittingpAnd coefficient k in reference track designr1、kr2、kr3The value of (A) is suitable for small celestial bodies with different lander thrust conditions and different terrain relief degrees. Therefore, the method has universality on the small celestial body attachment task under different conditions.
Drawings
FIG. 1 is a flow chart of steps of a method for rapidly generating a small celestial body attachment autonomous obstacle avoidance track disclosed by the invention;
FIG. 2 is a schematic diagram of a simulated terrain of a small celestial surface near an attachment point as used in an embodiment;
FIG. 3 is a full attachment trajectory of the landing gear in an embodiment;
FIG. 4 is a reference obstacle avoidance trajectory generated for the first time in the embodiment;
fig. 5 is a reference obstacle avoidance trajectory generated from the second to sixth times in the embodiment;
FIG. 6 is a three-axis velocity profile of the landing gear in an embodiment;
FIG. 7 is a three-axis control acceleration curve of the landing gear in the embodiment;
FIG. 8 is a curvature curve of the obstacle avoidance stage of the landing gear in the embodiment;
Detailed Description
For a better understanding of the objects and advantages of the present invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings and examples.
Example 1:
in order to verify the feasibility of the method, the simulation calculation of the obstacle avoidance trajectory is performed by taking an attachment task for a certain small celestial body as an example. Firstly, a terrain simulation diagram near the landing point of the small celestial body is established under the surface fixed connection system with the predetermined landing point as the origin, the horizontal direction scale is 2000m multiplied by 2000m, and the origin is used as the center. The terrain elevation fluctuation with the fall of not more than 500m is properly added to form an obstacle to be avoided when the lander is attached, as shown in FIG. 2. The upper limit of the triaxial thrust acceleration component of the lander under the surface fixed connection is 0.02m/s2Initial position is [ 80050500 ]]m, initial velocity of [ -4-10 [)]m/s. The guidance law time weight coefficient Γ is set to 1 × 10-4The values of the other adjustable parameters are shown in table 1. The aim is that the attacher realizes 'double zero' attachment, and the relative height of the whole process is larger than zero.
TABLE 1 evaluation of the parameters used in the examples
As shown in fig. 1, the method for quickly generating the small celestial body attached autonomous obstacle avoidance track disclosed in this embodiment includes the following specific steps:
the method comprises the following steps that firstly, a satellite borne computer fits terrain trends according to a small celestial body surface elevation information sequence measured by a laser range finder to obtain a terrain trend fitting curve equation.
In this embodiment, the laser ranging of the landing device from the initial position to the ground is performed every 10 seconds. From the 40 th second, the terrain trend curve fitting using the previous 4 measurements was started. And (5) flying to 80 seconds, namely after 8 th topographic measurement and 5 th topographic curve fitting, starting an obstacle avoidance mode for the first time and calculating to generate an obstacle avoidance reference track. As can be seen from fig. 4(b), a part of the black curve close to the simulated terrain surface of the small celestial body below the flight path of the lander is the terrain trend fitting curve at the current moment. The fitting degree of the fitting curve and the terrain contour is high, which shows that the terrain fitting method provided by the invention is effective in practical application scenes.
And step two, extending forwards in a straight line mode by using the slope of the current terrain fitting curve end point, judging the terrain trend in front, and evaluating the safety of the current flight track.
In this embodiment, after a terrain trend fitting curve is generated for each terrain measurement, a trend curve is extended according to equations (9) to (14). As can be seen in fig. 4(b), at the 80 th second of the lander flight, the end part of the generated black curve is a terrain trend extension line which is continuous with the terrain trend fitting curve, and the trend of the extension line is consistent with the terrain trend of the small celestial body. In addition, the design method of fitting the terminal slope of the curve along the straight line according to the terrain trend can keep a little higher than the actual surface in the situation that the terrain is in the steep slope ascending trend, and can provide proper margin for obstacle avoidance maneuver.
And step three, conducting guidance according to the analytic energy optimal guidance law when the current flight state meets the preset safety requirement according to the current flight track safety result evaluated in the step two, returning to the step one, and continuing to conduct terrain measurement.
In this embodiment, the lander has a large bump on the lower terrain from the 80 th to the 140 th second of flight, and there is a risk of collision, so the guidance law is in the obstacle avoidance mode. And the landform obstacle risks before the 80 th second and after the 140 th second are smaller, and the lander flies according to the analytic energy optimal guidance law. As can be seen from fig. 6 and 7, when the analytic energy optimal guidance law is used, since the triaxial thrust coefficient is kept at a constant value of 1, the thrust tracking obstacle avoidance reference trajectory does not need to be frequently adjusted, and therefore the speed change curve and the thrust change curve are smooth and stable. Fig. 8 shows that the change of the track curvature tends to be stable after 140 seconds, and the characteristics of the energy optimal guidance law are analyzed.
And step four, when the current flight state does not meet the preset safety requirement according to the safety result of the current flight track evaluated in the step two, generating a reference obstacle avoidance track, tracking and avoiding the obstacle by adopting a curvature control method, returning to the step one, and continuously carrying out the terrain measurement.
In this embodiment, the reference obstacle avoidance trajectory is generated or updated 6 times in the 80 th, 90 th, 100 th, 110 th, 120 th and 130 th seconds of the flight process of the landing device, and the obstacle avoidance trajectory is tracked in the curvature adjustment manner during the 80 th to 140 th seconds. Fig. 4 and 5 show the actual flight trajectory of the lander, the terrain trend fitting curve and the extension line, and the reference obstacle avoidance trajectory when six obstacle avoidance strategies are generated. When the lander approaches a large terrain bulge, the height of the flight track is gradually raised by the obstacle avoidance strategy, so that the lander can smoothly fly over obstacles, and the collision with the surface of a small celestial body is avoided.
Step five: and in the whole process of the landing device attachment, quickly generating and updating a reference obstacle avoidance track according to a terrain obstacle evaluation result, and realizing accurate adjustment of the shape of the attachment track by tracking the reference track, namely repeatedly and circularly executing the first step to the fourth step according to the terrain obstacle evaluation result until the landing device reaches a preset landing point at a speed approximate to zero, and completing the attachment task.
And performing repeated cycle execution of the first step to the fourth step, wherein the calculated attachment track is as shown in fig. 3, and the attachment track can successfully adjust the track shape to fly over a region with a raised terrain to reach a preset landing point, so that the effectiveness of the method for quickly generating the small celestial body attachment autonomous obstacle avoidance track disclosed by the invention on the aspect of real-time and steady obstacle avoidance of the lander is verified.
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 and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (2)
1. The method for quickly generating the small celestial body attachment autonomous obstacle avoidance track is characterized by comprising the following steps of: comprises the following steps of (a) carrying out,
the method comprises the following steps that firstly, a satellite borne computer fits terrain trends according to a small celestial body surface elevation information sequence measured by a laser range finder to obtain a terrain trend fitting curve equation;
step two, extending forwards in a straight line mode by using the slope of the current terrain fitting curve end point, judging the terrain trend in front, and evaluating the safety of the current flight track;
thirdly, according to the safety result of the current flight track evaluated in the second step, when the current flight state meets the preset safety requirement, guidance is conducted according to the analytic energy optimal guidance law, and the first step is returned to continue terrain measurement;
step four, when the current flight track safety result evaluated in the step two does not meet the preset safety requirement, generating a reference obstacle avoidance track, tracking and avoiding an obstacle by adopting a curvature control method, returning to the step one, and continuously carrying out topographic survey;
step five: in the whole process of the lander attachment, a reference obstacle avoidance track is quickly generated and updated according to a terrain obstacle evaluation result, the shape of the attachment track is accurately adjusted by tracking the reference track, namely, the steps one to four are repeatedly and circularly executed according to the terrain obstacle evaluation result until the lander reaches a preset landing point at a speed which is approximately zero, and the attachment task is completely implemented;
the first implementation method comprises the following steps of,
the lander obtains surface elevation data by using absolute height information measured by an autonomous navigation system and combining with the relative distance of the surface of a small celestial body below measured by a laser range finder, and obtains a terrain trend curve by using surface elevation sequence fitting obtained by interval measurement;
firstly, establishing a small celestial body surface fixed rectangular coordinate system oxyz by taking a preset landing point as an original point, wherein a z-axis is superposed with a normal of a local ground plane of the position of the landing point, and the positive direction points to the outside of the small celestial body; the x axis is in the local plane of the landing point and is superposed with the cross multiplication vector of the positive direction of the z axis and the rotation direction of the small celestial body, and the y axis, the x axis and the z axis jointly form a right-hand coordinate system; the lander has a current state of
Z＝[x y z u v w]T (1)
Wherein x, y and z are the positions of the lander under the surface fixed coordinate system, and u, v and w are the speeds of the lander under the surface fixed coordinate system; defining a small celestial body surface height function as al (x, y) and representing the height of a corresponding small celestial body surface point at the position (x, y) under the surface fixed connection; further defining the relative height function measured by the laser range finder as H (x, y), al (x, y) and calculating the function as
al(x,y)＝z-H(x,y) (2)
The lander is attached every tEMeasuring the terrain height once according to the formula (2); when each measurement is finished, the terrain height values measured for the last n times till the current moment are respectively recorded as: al1、al2、al3……alnThe coordinates of the lander on the x-y plane at the corresponding n times of measurement time are respectively (x)1,y1)、(x2,y2)、(x3,y3)……(xn,yn) (ii) a Wherein (x)n,yn) The position is the current horizontal position of the lander; first, the relative height al to x relationship is fitted using an n-1 th order curve as follows
al＝a0xn-1+a1xn-2+…+an-2x+an-1 (3)
Based on the n sets of measurement data, a in formula (3)0,a1,a2,…,an-1Is a polynomial coefficient, is solved by the following linear equation set
[al1 al2…aln]T＝C·[a0 a1…an-1]T (4)
The fitting result is the projection of the terrain trend curve on the x-z plane, the projection on the x-y plane is fitted below, the projection curve to be solved is approximately regarded as a straight line, and the following linear function is used for fitting
y＝b0x+b1 (6)
Using data from n measurements, for coefficient b0And b1Performing linear regression
Using the projections (3) and (6), uniquely determining a terrain trend fitting curve below the flight path of the lander, and obtaining a terrain trend fitting curve equation;
the second step is realized by the method that,
the x-axis coordinates of the starting point and the ending point of the terrain tendency extension line are x respectivelysAnd xeHas the following relations
xs＝xn (9)
xe＝xn+kp(xn-x1) (10)
In the formula (10), the extension length proportionality coefficient kpRepresenting the ratio of the length of the extension line to the length of the measurement fit curve; line of y'n＝b0xn+b1Fitting the curve at the end point (x) of the terrainn,y'n,aln) Where the slopes of the x-z and x-y plane projections are respectively
Sxz＝(n-1)a0xn-2+(n-2)a1xn-3+…+an-3x+an-2 (11)
Sxy＝b0 (12)
Let the y-axis coordinate of the end point of the extension line be yeZ axis coordinate is aleThen there is
ale＝aln+Sxz(xe-xs) (13)
ye＝yn+Sxy(xe-xs) (14)
Parameter Sxz、Sxy、xe、ye、aleThe extension line is completely defined; then judging whether the lander has the risk of collision with the terrain obstacle according to the height of the extension line terminal point; if the risk is high, a reference obstacle avoidance track needs to be designed, and tracking is carried out through a curvature control method; with current flying height z of the landernThe height difference of the end point of the extension line is used as a main judgment basis, and the following judgment criteria are established
High-range safety coefficient k in formulahBeing positive real, the current height z of the landernAnd the height al of the end point of the extension lineeThe tolerable difference value is in direct proportion to the horizontal distance between the lander and the attachment point, and the farther the lander is away from the preset attachment point, the stricter the relative height constraint with the surface of the lower small celestial body is;judging the terrain tendency in front according to a safety judgment criterion formula (15), and evaluating the collision risk, thereby realizing the evaluation of the safety of the current flight track;
the third step is to realize the method as follows,
when the current relative elevation of the lander calculated by the spaceborne computer meets the safety judgment criterion defined by the formula (15), judging that the current terrain obstacle threat is small, and at the moment, the lander implements an energy optimal guidance law to save fuel;
the lander moves in a surface fixed coordinate system and is acted by the thrust of an orbit control engine, the gravity of a small celestial body, disturbance force generated by the rotation of the small celestial body and other unmodeled disturbance force; since the acceleration other than the acceleration generated by the engine thrust has small influence on the movement of the lander, the dynamic equation of the lander system is simplified into the following form:
wherein r ═ x y z]T、v＝[u v w]T、u＝[ax ay az]TEach item in the vector u represents the component of the lander control acceleration on the three axes of the surface fixed connection system; the design optimization index of the energy optimal guidance law is
Wherein t is0(t0＝0)、tfInitial and terminal times, gamma is a weight coefficient related to time; according to the optimal control theory, a basic variational method is used to obtain a three-axis control acceleration formula of the engine
Wherein t isgoFor the remaining timeEstimated value, which is the only positive real root of the following quartic equation
During the execution period of step three, every tETime, and returning to the step one, and continuing to carry out the topographic survey;
the implementation method of the fourth step is that,
when the current relative elevation of the lander calculated by the spaceborne computer does not meet the safety constraint defined by the formula (15), judging that the threat of the current terrain obstacle is large, and at the moment, implementing a curvature guidance strategy by the lander to track an obstacle avoidance track;
curvature C of projection curve of lander flight path on x-z plane and y-z planexzAnd CyzAs a control object for adjusting the shape of the trajectory, the following is defined
The curvature obstacle avoidance guidance law adds three thrust coefficients k on the basis of the original analytic energy optimal guidance laws (17) - (19)x、ky、kzSo that the real-time calculation method of the control acceleration is changed from (18) to the following formula
When equations (22) to (24) are substituted into trajectory curvature defining equations (20) to (21), the relationship between the curvature and the thrust coefficient is
Regarding the analytic energy optimal guidance law as a curvature obstacle avoidance guidance law at kx＝ky＝kzIn a special form of 1, the triaxial thrust coefficient is defined to be constant during the adjustment
kx+ky+kz＝3 (27)
Obtaining a determination method of the triaxial thrust coefficient under the condition of a reference track according to the expressions (25) to (27), wherein the curvature of the reference track at the current position is CrxzAnd CryzThe thrust coefficient is then the solution of the following system of linear equations:
a method for generating a reference obstacle avoidance trajectory is given below; the projection of the reference obstacle avoidance track on an x-z plane, and the coordinate of the starting point is (x)s,zs) I.e. the x-axis and z-axis coordinates of the current position of the lander, and the velocity at the starting point is (v)xs,vzs) Slope of starting point SxzsDefining an equation (30), and ensuring that the value of the equation is the same as the current track slope of the lander;
Sxzs＝vzs/vxs (30)
let the current lander acceleration be (a)xs,azs) The curvature at the starting point is
Defining the coordinate of the end point x axis of the reference obstacle avoidance track as xeThe value is the same as the end point of the terrain tendency estimation curve, and the coordinate of the z axis is zeThe terminal velocity is (v)xe,vze) The following two end point height indicators are given
Proportionality coefficient k in formula (32)r1Is a positive real number, the proportionality coefficient k in equation (33)r2A real number between 0 and 1; considering both the requirement of adhesion safety and the constraint of upper limit of thrust, and referring to the end point height z of the obstacle avoidance trackeGet ze1And ze2Greater term between
ze＝max(ze1,ze2) (34)
Slope S at end point of reference obstacle avoidance trackxze＝vze/vxeIs given by
Sxze＝kr3·Sxz+(1-kr3)·(vzs/vxs) (35)
Proportional coefficient k in the formular3Is a positive real number less than 1;
coordinates (x) of starting point of given reference obstacle avoidance tracks,zs) Endpoint coordinate (x)e,ze) Slope of origin SxzsEnd point slope SxzeAnd a curvature of origin Crxzs(ii) a Using a polynomial design curve, to satisfy the above 5 conditions, a polynomial of at least 4 th order is required
z＝c0x4+c1x3+c2x2+c3x+c4 (36)
Polynomial coefficient c0～c4Can be solved by the following linear equation set
And solving a projection curve of the reference obstacle avoidance track on a y-z plane by using the same projection curve generation method:
z＝d0y4+d1y3+d2y2+d3y+d4 (39)
solve the parameter c0～c4And d0～d4Thereafter, the reference obstacle avoidance trajectory is uniquely determined in coordinates (x)s,ys,zs) Starting from (x)e,ye,ze) Is the end point; for a certain point r on the reference obstacle avoidance trackm＝[xm ym zm]TIn other words, the curvature of the trajectory at that location is
In the process of obstacle avoidance flight of the lander, calculating the curvature value of the reference obstacle avoidance track at the current flight position according to the formulas (40) to (41), and substituting the curvature value into an equation set (28) to obtain the value of the current triaxial thrust coefficient;
during the execution period of step four, every tEAnd time, continuing to perform the topographic measurement.
2. The method for rapidly generating the small celestial body attachment autonomous obstacle avoidance track as claimed in claim 1, wherein the method comprises the following steps: taking the fitting efficiency and the fitting precision into consideration, the cubic curve is selected as the terrain trend fitting curve equation shown in the formula (3), namely the value of n is selected to be 4.
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