CN113485418A - Flexible rope system constraint multi-robot track generation method - Google Patents

Flexible rope system constraint multi-robot track generation method Download PDF

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CN113485418A
CN113485418A CN202110749405.5A CN202110749405A CN113485418A CN 113485418 A CN113485418 A CN 113485418A CN 202110749405 A CN202110749405 A CN 202110749405A CN 113485418 A CN113485418 A CN 113485418A
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黄攀峰
裴崇旭
张帆
沈刚辉
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Northwestern Polytechnical University
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Abstract

The invention relates to a track generation method for a flexible rope system constrained multi-robot, and belongs to the field of robot track planning research. The whole aircraft cooperative handling system is regarded as a sphere, and the length of a rope is taken as the radius; for each aircraft, setting a random expansion vector of RRT, setting a starting point and a terminating point, and performing path search to obtain a group of discrete vectors as an initial track; carrying out inverse solution on the continuous data of each dimension, and obtaining a corresponding B spline curve control point parameter as an optimized initial parameter; and selecting all B spline curve control points as optimization variables, defining the track optimization of the aircraft as a nonlinear optimization problem, and carrying out nonlinear optimization on the optimization problem to solve the optimal control point value of the B spline curve of each dimensionality in the optimization vector, thereby obtaining the polynomial expression of each dimensionality and solving the flight path of the whole aircraft formation in real time.

Description

Flexible rope system constraint multi-robot track generation method
Technical Field
The invention belongs to the field of robot trajectory planning research, and particularly relates to a trajectory generation method for multiple robots constrained by flexible ropes.
Background
In recent years, multi-robot cooperative work becomes more and more common, and common application environments include multi-unmanned aerial vehicle formation performance, multi-intelligent vehicle formation performance, unmanned aerial vehicle and intelligent vehicle air-ground cooperative work, multi-mechanical arm joint maintenance and the like. The plurality of robots are matched with each other, and the cooperative work can increase the stability of the system, improve the working strength of the system and enable the system to complete more complex tasks. Also, the complexity of the system increases due to the cooperation of multiple robots. A common problem of multi-robot cooperative operation is the problem of trajectory planning of robots, particularly after a plurality of robots are involved, the robots are prevented from colliding with each other in space-time, and the safety of the robots is guaranteed while tasks are completed. The trajectory planning for the robot becomes an inevitable requirement.
Nowadays, the task of transporting materials in coordination with multiple aircrafts is gradually revealed, and the multiple aircrafts can provide better system universality, safety and deployability in coordination with each other compared with a single aircraft, and the overall cost of the system can be reduced. In the application scenario of the aircraft transportation load, the load capacity of a single aircraft is limited or too expensive, and the energy consumption speed is high. And the use of multiple aircrafts for carrying loads in coordination can reduce the overall cost of the system and increase the transport capacity and robustness of the system. The cost is that a complex track planning algorithm is needed to generate the track of each aircraft, and the effect of avoiding obstacles between each aircraft and the load can be achieved on the premise of ensuring the whole load capacity of the system.
At present, two track planning methods for multi-aircraft formation flight tasks are generally available: one method is that an off-line flight track of one aircraft is generated firstly, then the off-line flight tracks of the other aircraft are deduced through formation array affine transformation, and then the positions of the aircraft are adjusted in real time through local track optimization in the on-line flight process so as to achieve the purpose of obstacle avoidance. For example, chinese patent application No. CN201910173841.5 proposes a cooperative control method for formation of multiple aircrafts based on model predictive control, which first initializes task requirements and related control parameters according to related constraints for control of formation of multiple aircrafts, then only performs preliminary track planning on a pilot aircraft, and then directly enters an online track implementation optimization process. The off-line track generated in the mode can cause some aircrafts in the formation not to meet obstacle avoidance constraints, however, under the condition that multiple aircraft ropes are connected to cooperatively carry loads, more constraints are considered and the constraint precision requirement is higher, more track optimization pressure is put in the online flight process, the requirement on an embedded platform with low performance is higher, and the difficulty of the cooperative transportation task is increased. The other method is that an initial flight track of an aircraft is generated by using a path searching method without considering kinematics, then paths of a plurality of aircraft are expanded, or the initial track is not specified, and then the collaborative path planning of the plurality of aircraft is carried out. For example, chinese patent application No. CN201910395051.1 proposes a multi-aircraft multi-ant colony collaborative search target method, and the method directly uses an ant colony algorithm to perform multi-aircraft collaborative trajectory optimization without generating an initial trajectory. This approach makes non-optimization algorithms prone to local minima and reduces the success rate of optimization in the presence of narrow obstacles.
Disclosure of Invention
Technical problem to be solved
In order to avoid the defects of the prior art, the invention provides a method for connecting loads by flexible ropes for multiple aircrafts and generating an aircraft track under cooperative flight. The method aims to provide the flight path of the cooperative transportation load of a plurality of aircrafts under the condition of the known grid map.
Technical scheme
A track generation method for restraining multiple robots by flexible ropes is characterized by comprising the following steps:
step 1: generating an initial path of an overall formation
1.1) obtaining map information: acquiring image information of an actual environment through computer vision, and then generating an ESDF global grid map which can provide the distance from each grid to a nearest obstacle and the gradient value far away from the obstacle;
1.2) defining RRT path search algorithm parameters: the whole matrix is regarded as a sphere which takes the load position as the center of sphere and takes the length of the rope as the radius; for each aircraft, defining a deflection angle in the vertical direction and the horizontal direction respectively; the position of each aircraft can be obtained through the load position and two deflection angles; the optimization parameters of the sphere only need to comprise the absolute position of the load and the angle value of the aircraft relative to the load, and the absolute positions of all the aircraft can be solved; setting a vector with 3+2n dimensions as a random expansion vector of RRT, wherein the 3+2n dimensions are the three-dimensional position of the load and two deflection angles of n aircrafts;
1.3) generating an initial flight track: setting a starting point and an end point, and performing path search to obtain a group of discrete vectors as an initial track;
step 2: solving track optimization initial solution parameters
2.1) carrying out interpolation on each dimension between two adjacent vectors respectively to obtain a group of approximately continuous values on each dimension;
2.2) carrying out inverse solution on the continuous data of each dimension to obtain a corresponding B spline curve control point parameter as an optimized initial parameter;
and step 3: optimizing a flight trajectory satisfying a constraint condition
3.1) selecting all B-spline curve control points as optimization variables, and inputting the parameters of the B-spline curve control points obtained in the step 2 as initial solutions;
3.2) defining the track optimization of the aircraft as a nonlinear optimization problem, wherein the optimization problem cost comprises track smoothness cost, end point constraint, dynamic feasibility constraint, inter-aircraft collision-prevention constraint, aircraft formation obstacle avoidance constraint and thrust constraint;
3.3) carrying out nonlinear optimization on the optimization problem in the step 3.2) to solve the optimal control point value of the B spline curve of each dimensionality in the optimization vector, thereby obtaining the polynomial expression of each dimensionality and solving the flight path of the whole aircraft formation in real time.
Preferably: n in step 1.2) is 2.
Preferably: the cost of the optimization problem in step 3.2) can be expressed as follows:
ftotal＝λ1fs+λ2fi+λ3fc+λ4fe+(λ5fv+λ6fa+λ7fw+λ8fwa)+λ9ff
Figure BDA0003145468600000041
Figure BDA0003145468600000042
Figure BDA0003145468600000043
Figure BDA0003145468600000044
Figure BDA0003145468600000045
Figure BDA0003145468600000046
Figure BDA0003145468600000047
Figure BDA0003145468600000048
Figure BDA0003145468600000049
wherein q is a 9-dimensional vector, amaxIs the maximum acceleration, vmaxAt maximum speed, wmaxAt maximum angular velocity, wamaxAt maximum angular acceleration, dminMinimum distance between aircraft, dmaxMaximum distance between aircraft, obsminMinimum distance allowed for obstacle avoidance, qendTo the flight end point qend，dnearTo obtain the distance from each point to the nearest obstacle from the ESDF map, λ1、λ2、λ3、λ4、λ5、λ6、λ7、λ8、λ9Is the weight of each cost.
Advantageous effects
The track generation method for the flexible rope system constrained multi-robot provided by the invention has the following advantages:
1. a two-stage track planning algorithm is used, firstly an initial track solution is found by RRT, and then the initial track solution is optimized by nonlinear optimization, so that the optimization speed can be increased, and a global optimal solution is more easily found instead of a local optimal solution;
2. the whole aircraft cooperative handling system is regarded as a sphere, the load position is taken as the center of a circle, and the rope length is taken as the radius. The rope length constraint is converted into position resolving parameters, so that the number of parameters required by optimization and the complexity of optimization are simplified;
3. the ESDF map is used for replacing a common grid map, the distance from each aircraft to the nearest barrier is easy to obtain, and the gradient value far away from the barrier at the point can be obtained, so that the calculation of the barrier avoidance cost is facilitated.
4. The thrust constraints of each aircraft are taken into account so that the optimized trajectory reduces the energy consumption of the whole system as much as possible.
5. By adjusting the optimized distance and the optimized iteration number of each time, the optimization algorithm can be used for offline global planning and online local planning.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, wherein like reference numerals are used to designate like parts throughout.
FIG. 1 is a general diagram of a multi-aircraft coordinated handling load system;
FIG. 2 is a flow chart of the overall algorithm of the system;
fig. 3 is a simulation result diagram.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The technical scheme adopted by the invention comprises the following steps:
1) generating an initial path of the whole formation;
2) solving the track optimization initial solution parameters;
3) optimizing a flight track meeting constraint conditions;
the step 1) of generating the whole formation initial path comprises the following substeps:
1.1) obtaining map information: and acquiring image information of the actual environment through computer vision, and then generating an ESDF global grid map. The ESDF map may provide the distance of each grid to the nearest obstacle and the gradient values away from the obstacle;
1.2) defining RRT path search algorithm parameters: the entire matrix is considered to be a sphere with the load position as the center of the sphere and the rope length as the radius. For each aircraft, a yaw angle is defined in the vertical direction and the horizontal direction, respectively. The position of each aircraft can be determined from the load position and the two deflection angles. The optimized parameters of the sphere only need to comprise the absolute position of the load and the angle value of the aircraft relative to the load, and the absolute positions of all the aircraft can be solved. Thus setting a 3+2 n-dimensional vector (three-dimensional position of the load and two deflection angles of n aircraft) as a random expansion vector of RRT;
1.3) generating an initial flight track: setting a starting point and an end point, and searching a path to obtain a group of discrete vectors as an initial track.
The step 2) of solving the trajectory optimization initial solution parameters comprises the following substeps:
2.1) each dimension of the vectors obtained in the step 1) is decoupled, each dimension between two adjacent vectors is interpolated respectively, and a group of approximately continuous values is obtained on each dimension;
2.2) carrying out inverse solution on the continuous data of each dimension, and obtaining the corresponding B-spline curve control point parameter as the optimized initial parameter.
The step 3) of optimizing the track meeting the constraint condition comprises the following substeps
3.1) selecting all B-spline curve control points as optimization variables, and inputting parameters of the B-spline curve control points obtained in the step 2) as initial solutions;
3.2) defining the track optimization of the aircraft as a nonlinear optimization problem, wherein the optimization problem cost comprises track smoothness cost, end point constraint, dynamic feasibility constraint, inter-aircraft collision-prevention constraint, aircraft formation obstacle avoidance constraint and thrust constraint;
3.3) converting the whole path planning problem into a nonlinear optimization problem through the steps 3.1), 3.2) and 3.3), determining a group of good initial solutions, optimization problems and optimization constraints for optimization, and performing nonlinear optimization on the optimization problem to obtain the optimal control point value of the B spline curve of each dimensionality in the optimization vector, thereby obtaining the polynomial expression of each dimensionality and solving the flight path of the whole aircraft formation in real time.
The steps are as follows:
1) generating a flight trajectory for the load comprises the sub-steps of:
1.1) obtaining map information: and acquiring image information of the actual environment through computer vision, and then generating an ESDF global grid map. The ESDF map may provide the distance of each grid to the nearest obstacle and the gradient values away from the obstacle;
1.2) defining RRT path search algorithm parameters: as shown in fig. 1, the entire aircraft coordinated handling formation is viewed as a sphere. Defining the three-dimensional coordinate of the load as [ x y z ]]Two deflection angles of each drone are respectively
Figure BDA0003145468600000071
In the invention, three unmanned aerial vehicles are taken as an example, the state of the whole array can be a 9-dimensional vector
Figure BDA0003145468600000072
And (4) showing. The length of the rope is set as r, and for any aircraft, the three-dimensional coordinate can be solved by the formula (1),
Figure BDA0003145468600000073
1.3) generating an initial flight track: taking the 9-dimensional vector as an input vector of an RRT track search algorithm, randomly generating an offset value in each dimension, then taking the position of a load as an extension direction, judging whether the matrix collides with an obstacle after each extension until the position of the load reaches an end point, and finally obtaining m discrete vectors q (m) which represent the flight path of the matrix and the matrix state at each moment;
2) solving the trajectory optimization initial solution parameters comprises the following substeps:
2.1) each dimension of the vectors obtained in the step 1) is decoupled, each dimension between two adjacent vectors is interpolated respectively, and a group of approximately continuous values is obtained on each dimension;
2.2) fitting the continuous data of each dimension into a polynomial, then carrying out inverse solution on the polynomial to obtain corresponding B-spline curve control points, and taking the control points as optimized initial parameters;
3) optimizing the trajectory to satisfy the constraint includes the substeps of:
3.1) selecting all B-spline curve control points as optimization variables, and inputting the B-spline curve control obtained in the step 2)Using the system point parameter as an initial solution, defining the optimization variables as i 9-dimensional vectors q (i), and defining the maximum acceleration as amaxMaximum velocity vmaxMaximum angular velocity of wmaxMaximum angular acceleration of wamaxMinimum distance between aircraft dminMaximum distance between aircraft dmaxAvoidance of the obstacle allows the minimum distance obsminEnd of flight qendFrom the ESDF map, the distance d from each point to the nearest obstacle can be obtainednearThe tension F of each aircraft to the rope can be reversely solved through the current formation arrangement of the aircraft;
3.2) defining a track optimization problem comprising track smoothness cost, dynamic feasibility cost, inter-aircraft collision prevention cost, aircraft formation obstacle avoidance cost, flight end arrival degree cost and thrust cost, as shown in formula (2)
ftotal＝λ1fs+λ2fi+λ3fc+λ4fe+(λ5fv+λ6fa+λ7fw+λ8fwa)+λ9ff。 (2)
λ1、λ2、λ3、λ4、λ5、λ6、λ7、λ8、λ9The weight value of each cost;
wherein, trajectory smoothness penalty: due to the particularity of the unmanned aerial vehicle system, the third derivative of the polynomial locus represents the angular speed of the Euler angle of the unmanned aerial vehicle of the locus and is related to the locus smoothness of the unmanned aerial vehicle, so that the smoothness cost function is obtained according to the derivative characteristic of the B spline curve as follows:
Figure BDA0003145468600000081
end-point arrival degree cost:
Figure BDA0003145468600000082
the cost of kinetic feasibility: q in the formulas (5) and (6) only calculates the front three-dimensional position and the corresponding load three-dimensional position, and solves the speed and acceleration cost of the load
Figure BDA0003145468600000091
Figure BDA0003145468600000092
Q in formulas (7) and (8) calculates the post-six-dimension, the corresponding angle offset of each unmanned aerial vehicle relative to the load, and the cost of the angular velocity and the angular acceleration of the relative motion of the unmanned aerial vehicles is solved
Figure BDA0003145468600000093
Figure BDA0003145468600000094
Collision cost between aircrafts:
Figure BDA0003145468600000095
the aircraft array type avoids the barrier cost: the position of each aircraft and the position of the load can be obtained by the formula (1), 8 points are taken on a rope from each aircraft to the load as collision detection points, and the cost function is as follows:
Figure BDA0003145468600000096
and thrust penalty:
Figure BDA0003145468600000097
3.3) converting the whole path planning problem into a nonlinear optimization problem through the steps 3.1) and 3.2), determining a group of optimized good initial solution and optimization problem cost functions, and carrying out nonlinear optimization on the optimization problem to obtain an optimal control point value of a B spline curve for optimizing each dimensionality, thereby obtaining a polynomial expression of each dimensionality and solving the flight path of the whole aircraft formation in real time.
The smoothness weight is defined to be 10, the end point arrival degree weight is defined to be 0.01, the dynamic feasibility weight is defined to be 0.001, the inter-aircraft anti-collision weight is defined to be 1, the aircraft array type obstacle avoidance weight is defined to be 1, and the thrust weight is defined to be 0.0001. At the moment, a planning algorithm is run on a notebook with a CPU of i5-8250u, and the cost value of each constraint is f smooth: 0.12772
f distance:0.000663906
f feasibility:9.63905e-05
f thrust:0
f obs:2.95077e-06
f_combine:0.128925
The code operation time is 0.8765s, the planned path is as shown in fig. 3, the tracks are smooth and avoid all obstacles, and do not collide with each other, all constraint conditions are met, wherein the 4 tracks of blue (broken lines) respectively refer to good initial tracks found by the unmanned aerial vehicle and the load at the front end by using the RRT algorithm, and the 4 tracks of red (smooth curves) respectively represent the final tracks of 3 unmanned aerial vehicles and the load.
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and various equivalent modifications or substitutions can be easily made by those skilled in the art within the technical scope of the present disclosure.

Claims (3)

1. A track generation method for restraining multiple robots by flexible ropes is characterized by comprising the following steps:
step 1: generating an initial path of an overall formation
1.1) obtaining map information: acquiring image information of an actual environment through computer vision, and then generating an ESDF global grid map which can provide the distance from each grid to a nearest obstacle and the gradient value far away from the obstacle;
1.2) defining RRT path search algorithm parameters: the whole matrix is regarded as a sphere which takes the load position as the center of sphere and takes the length of the rope as the radius; for each aircraft, defining a deflection angle in the vertical direction and the horizontal direction respectively; the position of each aircraft can be obtained through the load position and two deflection angles; the optimization parameters of the sphere only need to comprise the absolute position of the load and the angle value of the aircraft relative to the load, and the absolute positions of all the aircraft can be solved; setting a vector with 3+2n dimensions as a random expansion vector of RRT, wherein the 3+2n dimensions are the three-dimensional position of the load and two deflection angles of n aircrafts;
1.3) generating an initial flight track: setting a starting point and an end point, and performing path search to obtain a group of discrete vectors as an initial track;
step 2: solving track optimization initial solution parameters
2.1) carrying out interpolation on each dimension between two adjacent vectors respectively to obtain a group of approximately continuous values on each dimension;
2.2) carrying out inverse solution on the continuous data of each dimension to obtain a corresponding B spline curve control point parameter as an optimized initial parameter;
and step 3: optimizing a flight trajectory satisfying a constraint condition
3.1) selecting all B-spline curve control points as optimization variables, and inputting the parameters of the B-spline curve control points obtained in the step 2 as initial solutions;
3.2) defining the track optimization of the aircraft as a nonlinear optimization problem, wherein the optimization problem cost comprises track smoothness cost, end point constraint, dynamic feasibility constraint, inter-aircraft collision-prevention constraint, aircraft formation obstacle avoidance constraint and thrust constraint;
3.3) carrying out nonlinear optimization on the optimization problem in the step 3.2) to solve the optimal control point value of the B spline curve of each dimensionality in the optimization vector, thereby obtaining the polynomial expression of each dimensionality and solving the flight path of the whole aircraft formation in real time.
2. The method for generating a trajectory of multiple robots constrained by flexible ropes according to claim 1, wherein n in step 1.2 is 2.
3. The method for generating a flexible tether-constrained multi-robot trajectory according to claim 2, wherein the optimization problem cost in step 3.2) is expressed by the following formula:
ftotal＝λ1fs+λ2fi+λ3fc+λ4fe+(λ5fv+λ6fa+λ7fw+λ8fwa)+λ9ff
Figure FDA0003145468590000021
Figure FDA0003145468590000022
Figure FDA0003145468590000023
Figure FDA0003145468590000024
Figure FDA0003145468590000025
Figure FDA0003145468590000026
Figure FDA0003145468590000027
Figure FDA0003145468590000031
Figure FDA0003145468590000032
wherein q is a 9-dimensional vector, amaxIs the maximum acceleration, vmaxAt maximum speed, wmaxAt maximum angular velocity, wamaxAt maximum angular acceleration, dminMinimum distance between aircraft, dmaxMaximum distance between aircraft, obsminMinimum distance allowed for obstacle avoidance, qendTo the flight end point qend，dnearTo obtain the distance from each point to the nearest obstacle from the ESDF map, λ1、λ2、λ3、λ4、λ5、λ6、λ7、λ8、λ9Is the weight of each cost.
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