CN115525063A - Trajectory planning method for unmanned helicopter - Google Patents
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Abstract
The invention provides a trajectory planning method for an unmanned helicopter, which comprises global planning and local planning; in the global planning, a smooth and collision-free initial minimized Snap track is obtained by adopting a sampling-based path planning algorithm RRT algorithm, and the track is used as a default path of subsequent local planning; in the local planning, the result of the global planning is used as the default path of the actual flight, a section of the initial path of the flight is taken out from the result of the global planning, a polynomial curve is adopted to fit the initial path, the track planning problem is converted into a quadratic planning problem, finally, the polynomial coefficient and the piecewise time are decoupled, and the real-time track is obtained by solving the piecewise time. The invention can realize real-time trajectory planning of unknown environment, ensures that obstacles are avoided in the flight process, and generates a real-time trajectory with feasible dynamics.
Description
Technical Field
The invention relates to the field of real-time trajectory planning and control law design of unmanned helicopters, in particular to a trajectory planning method for an unmanned helicopter.
Background
The trajectory planning has great significance for the application of the unmanned helicopter, such as scenes of fruit condition monitoring, pesticide spraying, post-disaster searching and rescuing, logistics transportation and the like. In the field of unmanned helicopter motion planning at present, two planning algorithms are commonly adopted:
one method is to combine the flight path planning with the trajectory control, plan a collision-free flight path from a starting point to a terminal point by using a flight path planning algorithm, and then track the generated flight path in real time by using an airborne flight control system, so as to ensure that the unmanned helicopter flies in a flight envelope. The current common track planning method comprises the following steps: algorithm a, RRT algorithm, heuristic search algorithm, etc. However, the planning method is insufficient in consideration of flight dynamics constraint of the unmanned helicopter in a track planning stage, and only a relatively conservative flight path can be generated in order to ensure that the unmanned helicopter is always in a flight envelope.
And the other method is to convert the trajectory planning problem into an optimal control problem, discretize the flight process, directly optimize the control quantity of each discrete point and generate the final flight trajectory by solving the optimal control problem. Common numerical solution methods include: the direct conversion method, the direct target shooting method and the like are often applied to the optimization of landing trajectories of helicopters, the trajectory planning of helicopters after single-shot failure and the like. The method has the problems that a flight dynamics model needs to be called repeatedly, the calculation time is long, and the trade-off between the calculation time and the calculation precision is needed, so that the method cannot be applied to the real-time trajectory planning of the unmanned helicopter, and the obstacle avoidance function cannot be realized.
At present, no report is found on the real-time track planning research of obstacle avoidance of the unmanned helicopter.
Disclosure of Invention
The invention provides a trajectory planning method for an unmanned helicopter to solve the problems in the prior art, which realizes real-time trajectory planning of an unknown environment, ensures that obstacles are avoided autonomously in the flight process, and generates a dynamically feasible real-time trajectory.
The invention provides a trajectory planning method for an unmanned helicopter, which comprises global planning and local planning; in global planning, a sampling-based path planning algorithm RRT algorithm is adopted, intermediate track points are supplemented according to prior environment information and task points issued by a user, so that a path without obstacles is formed, the path is subjected to smoothing treatment by utilizing a differential flat theory to obtain a smooth and collision-free initial minimized Snap track, and the track is used as a default path of subsequent local planning; in the local planning, taking the result of the global planning as a default path of actual flight, taking a section of the result of the global planning as an initial path of flight, and fitting the initial path by adopting a polynomial curve; the obstacle avoidance function of the obstacle is achieved by calculating an obstacle penalty function, a curvature penalty function and a deviation penalty function, a feasible path is obtained, a plurality of track points are selected from the feasible path, the track points are used as constraint of track planning, a piecewise polynomial is adopted to represent the track, the track planning problem is converted into a quadratic planning problem by applying a differential flat theory, the polynomial coefficient and the piecewise time are decoupled, and the real-time track is obtained by solving the piecewise time.
The global planning comprises the following specific steps:
firstly, searching to obtain a feasible collision-free path by using an RRT algorithm;
then based on 3 assumptions:
1) During the flying process, the acceleration of the airframe in the horizontal plane is smaller.
2) The current attitude angles theta and phi of the helicopter and the attitude angle during balancing
The difference in (c) is small.
3) During flight, the vertical acceleration under the earth axis is much smaller than the gravitational acceleration, i.e.
Establishing a simplified helicopter flight dynamics equation and proving the differential flatness of the flight dynamics equation, namely:
in the formula, theta represents the pitch angle of the machine body, phi represents the roll angle of the machine body,
and
the pitch angle and attitude angle at the time of leveling are shown.
And
representing the pitch angle rate and the angular acceleration rate,
and
the roll-angle acceleration rate is shown,
and
indicating yaw rate and angular acceleration rate.
Is an intermediate calculation parameter, which is defined as follows
In the formula: x, Y and Z respectively represent the body coordinates under the earth axis system; superscripts (3), (4) represent the 3, 4 derivatives of the coordinates over time.
Let the locus be p i The square of the fourth derivative of the trajectory as a function of time is used as the objective function for the global planning:
solving the track p by adopting a nonlinear programming solver i And finally, taking out the path information from the planned track as a global planning result.
The specific process of the local planning is as follows:
firstly, taking a global planning result as a default path of actual flight, taking a section of the global planning result as an initial path of flight, and fitting the initial path by adopting a polynomial curve;
secondly, an obstacle avoidance function of the obstacle is realized by calculating an obstacle penalty function, a curvature penalty function and a deviation penalty function, a feasible path is obtained, and a plurality of track points are selected from the feasible path;
the following formula is adopted as an optimized objective function:
f total ＝λ 1 f c +λ 2 f o +λ 3 f s (5)
in the formula, f c A term representing a curvature penalty function, which is expressed in terms of the integral of curvature over time, with the expectation that an excessively small turning radius will not occur during path planning; f. of o Representing a distance potential function of the track to the obstacle, and used for avoiding the obstacle; f. of s For limiting the distance between the generated local path and the global path; lambda [ alpha ] 1 ,λ 2 ,λ 3 Represent their weights;
the integral of curvature over time is used to represent the curvature penalty function of the objective function, with an exponential function as the basis function for the objective function, i.e.:
f c ＝∫c(k)dt
k represents the curvature of a point on the path, when k > k 0 When c (k) rises rapidly, k 0 The value of (a) is determined by the current speed; α and r affect the magnitude and slope of the function;
selecting an exponential function as a basic function of the barrier potential function, and describing the distance between the planned path and the global path by using the exponential function:
wherein d represents the distance between a point on the path and an obstacle, and d 0 Indicating a warning range if d < d 0 The barrier potential function increases rapidly and α and r are parameters for adjusting the magnitude and slope of the function.
Then, the track points are used as constraint of track planning, a piecewise polynomial is adopted to represent the track, and a differential flat theory is applied to convert the track planning problem into a quadratic planning problem:
and finally, decoupling the polynomial coefficient and the piecewise time, and solving the piecewise time to obtain the real-time track.
The invention has the beneficial effects that:
1. the real-time trajectory planning of the unmanned helicopter is realized for the first time.
2. Compared with the flight path planning, the flight dynamic model of the unmanned helicopter is considered in the path planning stage, so that the path planning result is more reliable.
3. Compared with an optimal control method, the method has the advantages that the solving speed is increased, the unmanned helicopter can autonomously avoid the obstacle in the flight process, and the real-time obstacle avoiding function in the flight process is realized.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a general flowchart of a trajectory planning method for an unmanned helicopter according to the present invention.
FIG. 2 is a simplified helicopter flight dynamics model used in trajectory planning.
Fig. 3 shows the set of feasible paths obtained by the RRT algorithm.
Fig. 4 shows the shortest path after pruning.
Fig. 5 shows the smoothed global trajectory.
Fig. 6 is a schematic view of local environment information processing, which shows the local environment information range input for each local planning.
Fig. 7 is a flow chart of the real-time planning of the local trajectory.
Fig. 8 is a prior map for global planning before starting a flight.
Fig. 9 is a real environment in actual flight.
FIG. 10 is a comparison of a locally planned trajectory and a globally planned trajectory.
FIG. 11 is a time image of the velocity resulting from stitching.
FIG. 12 is a stitched attitude angle over time image.
Fig. 13 is a stitched angular rate versus time image.
Fig. 14 is a time image of angular acceleration resulting from stitching.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
As shown in fig. 1, the overall process of the trajectory planning method for an unmanned helicopter provided by the present invention is as follows:
before a flight task starts, firstly, a smooth and collision-free initial minimized Snap track is generated for a given task target and given prior environment information by adopting a sampling-based path planning algorithm RRT algorithm, and the track is used as a default path of subsequent local planning. And then, in the actual flying process of the unmanned helicopter, errors may occur between the prior environment information and the actual environment, and a real-time feasible track which meets the dynamic constraint and is free of collision is generated by adopting a local planning algorithm based on environment information updated at a certain frequency.
Global planning
Firstly, global planning is carried out, and the first step of the global planning is to adopt an RRT algorithm, supplement intermediate track points according to prior environment information and task points issued by users, so as to form a path without obstacles. The RRT algorithm is an incremental construction method, in the construction process, the algorithm continuously generates state points randomly in a search space, if the point is located at a collision-free position, a node closest to the node in a search tree is searched for as a reference node, the reference node starts to extend towards the random node with a certain step length, and the position of an end point of an extension line is taken as an effective node and added into the search tree. The growing process of the search tree is continued until the target node is within a certain distance from the search tree. The search algorithm then finds a shortest path connecting the starting point to the end point in the search tree. The RRT algorithm adds two steps of reselecting a parent node and rewire on the basis of the RRT algorithm, so that the RRT algorithm has progressive optimality.
After the intermediate track points are supplemented by the RRT algorithm, the second step of the global planning, namely the track smoothing process, is started. It is necessary here to introduce the differential flat theory. Differential flattening theory is a concept proposed by Filess et al for nonlinear systems. Mellinger et al demonstrate that the dynamic model of the quadrotor is differentially flat under the assumption of neglecting aerodynamic drag, that is: there is a set of inputs that can be used to represent both the state quantities and the manipulated variables of a four-rotor system, and their finite derivatives, which we refer to as flat outputs. Therefore, the optimal control problem in the original state space is converted into a nonlinear programming problem in a flat output space, the dimension of the programming space is reduced, and the difficulty of the optimal control problem is reduced. ZHAO DI et al derives the differential flatness properties of the helicopter on this basis and uses them for trajectory optimization when the helicopter is landing on a ship.
Suppose that the force applied by a helicopter at a certain moment in trajectory planning is as shown in fig. 2. Intermediate coordinate system X V Y V Z V The angle phi is obtained by rotating the ground axis system around the Z axis, and the angle theta and phi are further rotated around the Y axis and the Z axis to obtain the body axis system X B Y B Z B . In the trimmed state, the resultant force acting on the body in addition to the gravity is recorded as
(hereinafter referred to as "resultant force"), the resultant force in an arbitrary motion state is denoted as F, which follows
Let us denote the angular difference of σ, α.
We introduce three assumptions:
1) And during the flight process, the acceleration in the horizontal plane is small.
2) The current attitude angles theta and phi of the helicopter and the attitude angle during balancing
The difference in (c) is small.
3) During flight, the vertical acceleration under the earth axis is much smaller than the gravitational acceleration, i.e.
By assuming 1), one can get:
expanding the third column of the above equation, one can obtain:
considering again hypothesis 2), we can approximate:
that is, the direction of the resultant force F within the body axis is unchanged, since during flight the rotor pull T is always the main component of the resultant force F (neglecting rotor flap dynamics), so:
considering again hypothesis 3), then one can get:
selecting X, Y and Z as flat output, representing the course direction of the unmanned helicopter by the speed direction, and representing the other two attitude angles, the angular speed and the angular acceleration rate of the unmanned helicopter as follows:
in the formula:
it is thus demonstrated that the helicopter flight dynamics model satisfies differential flatness under appropriate assumptions. Therefore, we can perform non-linear programming on X, Y, Z and then map back into the state space.
And we note that the trajectory p i Has positive correlation with the body attitude angular acceleration rate of the fourth derivative (Snap), so that a stable trajectory can be obtained by minimizing the fourth derivative of the trajectory.
The track is taken as the result of global planning, but in subsequent real-time planning, the time item of the global track is not considered and is only stored as a path in the onboard computer.
Let us assume that the existing four-unmanned helicopter starts from point A, approaches points B, C and D, and finally reaches point E. FIG. 3 shows the set of feasible paths obtained by RRT algorithm, FIG. 4 shows the shortest paths after pruning, P 1 、P 2 、P 3 Representing the intermediate track points supplemented by RRTs. Fig. 5 shows the smoothed global trajectory.
Local planning
Through the previous section, a global path is obtained based on task requirements and prior environment information, but safety in an autonomous flight process cannot be guaranteed. Because the prior environmental information is often not accurate enough, unknown obstacles may appear at any time during the flight. Therefore, the trajectory needs to be dynamically adjusted on the basis of global planning according to the current local environment information of the unmanned helicopter. When the unmanned helicopter is ready to start actual flight, firstly, a priori map input before is abandoned, only a global track result planned in advance is reserved as an initial path, and instead, real-time environment information is obtained by a sensor. The dashed circle in fig. 6 represents the local map range obtained by the sensor when actually flying to point P. In this way, the real-time updating of the local environment information in the algorithm is realized.
Next, a method for representing a trajectory needs to be found, and a polynomial curve is used to represent a local trajectory due to the advantages of simple form of the polynomial curve and easy derivation of end point constraints of coefficients of the polynomial curve. The flow chart of the local planning is shown in fig. 7.
In the process of trajectory planning, the obstacle avoidance requirement and the dynamic constraint are considered most preferentially, however, the two requirements have two different characteristics: the barrier penalty function for avoiding the barrier occupies a large amount of computing resources, but whether the track meets the barrier avoiding requirement is very intuitive, the optimization is easy, and the optimization efficiency is high; the penalty function for satisfying the dynamic constraint is small in calculation amount, but needs repeated iterative calculation. If the two are optimized together, the defects of the two can be simultaneously possessed. At present, in the field of robot trajectory planning, the main idea for solving the problems is to solve the obstacle avoidance requirement and the requirement for satisfying the dynamic constraint separately: firstly, path planning is carried out to obtain a path meeting the obstacle avoidance requirement, and then a plurality of track points are selected from the path. These track points will become the constraint points that the unmanned helicopter must pass through during the subsequent track optimization, and generally, as long as these track points are relatively close, we can consider that the aircraft does not touch the obstacle during the track planning.
First, path planning is performed. We use the following formula as the objective function for optimization:
f total ＝λ 1 f c +λ 2 f o +λ 3 f s (18)
in the formula (f) c A curvature penalty function term is expressed, which is expressed by the integral of curvature over time, and which is expected not to generate too small a turning radius in the course of path planning; fo represents a distance potential function of the trajectory to the obstacle for avoiding the obstacle; f. of s For limiting the distance between the generated local path and the global path; lambda [ alpha ] 1 ,λ 2 ,λ 3 Representing their weights.
We use the integral of curvature over time to represent the curvature penalty function of the objective function, with an exponential function as the basis function of the objective function, i.e.:
f c ＝∫c(k)dt
k represents the curvature of a point on the path, when k > k 0 When c (k) rises rapidly, k 0 The value of (c) is determined by the current speed. Alpha and r affect the magnitude and slope of the function.
The patent also selects an exponential function as the basis function for the barrier potential function:
wherein d represents the distance between a point on the path and an obstacle, and d 0 Indicating a warning range if d < d 0 The obstacle potential function increases rapidly and α and r are parameters for adjusting the magnitude and slope of the function.
Similarly, an exponential function is used to describe the distance between the planned path and the global path.
After the local path is obtained, we take several track points from the local path. These track points divide the path into M segments and we describe the trajectory we are planning with M polynomial curves of degree N. If the trajectory is optimized directly at this point, we need to optimize 3 × (N + 1) × M polynomial coefficients, and also the time allocated by M piecewise polynomial trajectories. The computational effort for such optimization can be exponential.
Since we found in the previous section on the derivation of the differential flatness, the integration of the square of the fourth derivative of the trajectory over time can make the unmanned helicopter smoother during flight. And if only the integral of the square of the fourth derivative of the trajectory over time is taken as the objective function of the optimization, the polynomial coefficients can be directly solved at this time if the optimization problem can be converted into a quadratic optimization problem given the time allocated to each section of the polynomial.
Therefore, we only need to optimize the time of each polynomial curve.
Thus, the content of the real-time planning of the local track is completed. As shown in fig. 8, is a prior map for global planning before the start of a flight. Fig. 9 shows a real environment in actual flight. It can be seen that fig. 9 has some variations over fig. 8: the height of the mountain body becomes high, and in addition, a plurality of buildings (rectangular L) are added 1 ) And a beacon (rectangle L) 2 ). The existing unmanned helicopter takes off from the point A in a hovering state, approaches the points B, C and D and finally reaches the point EAnd hovers. The attitude change during flight is required to be small and without excessive steering input. Fig. 10 is a trajectory of the final actual flight, and it can be found that the unmanned helicopter avoids the newly added obstacle. The five-pointed star in the figure is the mission point defined initially by the user, the dotted line is the global trajectory, and the solid line is the trajectory of the actual flight. Since the mission points are just above the newly added obstacle, in order to avoid collisions, the actual flight does not completely pass each mission point. FIG. 11 is a velocity image over time resulting from stitching. Fig. 12 is a stitched attitude angle versus time image. Fig. 13 is a time image of the angular rate resulting from stitching. Fig. 14 is a time image of angular acceleration resulting from stitching. The invention can realize the track planning of the unknown environment and generate the real-time track meeting the dynamic constraint.
The embodiments in the present specification are described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, for the apparatus embodiment, the above is only a preferred embodiment of the present invention, and since it is basically similar to the method embodiment, it is described simply, and the relevant points can be referred to the partial description of the method embodiment. The above description is only for the specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and the protection scope of the present invention should be covered by the principle of the present invention without departing from the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.
Claims (4)
1. A trajectory planning method for an unmanned helicopter is characterized by comprising the following steps: the method comprises the steps of global planning and local planning; in global planning, a sampling-based path planning algorithm RRT algorithm is adopted, intermediate track points are supplemented according to prior environment information and task points issued by a user, so that a path without obstacles is formed, the path is subjected to smoothing treatment by utilizing a differential flat theory to obtain a smooth and collision-free initial minimized Snap track, and the track is used as a default path of subsequent local planning; in the local planning, taking the result of the global planning as a default path of actual flight, taking a section of the result of the global planning as an initial path of flight, and fitting the initial path by adopting a polynomial curve; the obstacle avoidance function of the obstacle is achieved by calculating an obstacle penalty function, a curvature penalty function and a deviation penalty function, a feasible path is obtained, a plurality of track points are selected from the feasible path, the track points are used as constraint of track planning, a piecewise polynomial is adopted to represent the track, the track planning problem is converted into a quadratic planning problem by applying a differential flat theory, the polynomial coefficient and the piecewise time are decoupled, and the real-time track is obtained by solving the piecewise time.
2. The trajectory planning method for the unmanned helicopter of claim 1, wherein the global planning specifically comprises the following steps:
firstly, searching to obtain a feasible collision-free path by using an RRT algorithm;
then based on 3 assumptions:
1) In the flying process, the acceleration of the aircraft body in the horizontal plane is relatively small;
2) The current attitude angles theta and phi of the helicopter and the attitude angle during balancing
The difference of (a) is small;
3) During flight, the vertical acceleration under the earth axis is much smaller than the gravitational acceleration, i.e.
Establishing a simplified helicopter flight dynamics equation and proving the differential flatness of the flight dynamics equation, namely:
in the formula: theta represents the pitch angle of the body, phi represents the roll angle of the body,
and
representing the pitch angle and attitude angle at the moment of leveling,
and
representing the pitch angle rate and the angular acceleration rate,
and
the roll-angle acceleration rate is shown,
and
representing yaw rate and angular acceleration rate, a ⊥ 、
j ⊥ 、
s ⊥ 、
Is an intermediate calculation parameter, which is defined as follows:
in the formula: x, Y and Z respectively represent the body coordinates under the earth axis system; superscripts (3), (4) represent the 3, 4 derivatives of the coordinates over time.
Let the locus be p i Taking the square of the fourth derivative of the trajectory as a function of time as the objective function of the global plan:
solving the track p by adopting a nonlinear programming solver i And finally, taking out the path information from the planned track as a global planning result.
3. The trajectory planning method for the unmanned helicopter of claim 1, wherein the specific process of the local planning is as follows:
firstly, taking a global planning result as a default path of actual flight, taking a section of the global planning result as an initial path of flight, and fitting the initial path by adopting a polynomial curve;
secondly, an obstacle avoidance function of the obstacle is realized by calculating an obstacle penalty function, a curvature penalty function and a deviation penalty function, a feasible path is obtained, and a plurality of track points are selected from the feasible path;
then, the track points are used as constraint of track planning, a piecewise polynomial is adopted to represent the track, and a differential flat theory is used to convert the track planning problem into a quadratic planning problem;
and finally, decoupling the polynomial coefficient and the piecewise time, and solving the piecewise time to obtain the real-time track.
4. The trajectory planning method for an unmanned helicopter of claim 3, characterized in that: the selection of the plurality of track points comprises the following specific processes:
the following formula is adopted as an optimized objective function:
f total ＝λ 1 f c +λ 2 f o +λ 3 f s (5)
in the formula (f) c A term representing a curvature penalty function, which is expressed in terms of the integral of curvature over time, with the expectation that an excessively small turning radius will not occur during path planning; f. of o Representing a distance potential function of the track to the obstacle, and used for avoiding the obstacle; f. of s For limiting the distance between the generated local path and the global path; lambda [ alpha ] 1 ，λ 2 ，λ 3 Represent their weights;
the integral of curvature over time is used to represent the curvature penalty function of the objective function, with an exponential function as the basis function for the objective function, i.e.:
f c ＝∫c(k)dt
k represents the curvature of a point on the path, when k > k 0 When c (k) is too fastFast rise, k 0 The value of (a) is determined by the current speed; α and r affect the magnitude and slope of the function;
selecting an exponential function as a basic function of the barrier potential function, and describing the distance between the planned path and the global path by using the exponential function:
wherein d represents the distance between a point on the path and an obstacle, and d 0 Indicating a warning range if d < d 0 The barrier potential function increases rapidly and α and r are parameters for adjusting the magnitude and slope of the function.
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Cited By (2)
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| CN116263605A (en) * | 2023-04-21 | 2023-06-16 | 杭州国辰机器人科技有限公司 | Mobile robot smooth and real-time collision avoidance method based on nonlinear optimization |
| CN116449852A (en) * | 2023-06-13 | 2023-07-18 | 麦岩智能科技(北京)有限公司 | Track planning method, track planning device, electronic equipment and medium |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN116263605A (en) * | 2023-04-21 | 2023-06-16 | 杭州国辰机器人科技有限公司 | Mobile robot smooth and real-time collision avoidance method based on nonlinear optimization |
| CN116449852A (en) * | 2023-06-13 | 2023-07-18 | 麦岩智能科技(北京)有限公司 | Track planning method, track planning device, electronic equipment and medium |
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