CN113759983A - Anti-disturbance unmanned aerial vehicle collision avoidance method based on differential flatness - Google Patents
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Abstract
The invention relates to the technical field of robots, in particular to an anti-disturbance unmanned aerial vehicle collision avoidance method based on differential flatness. The disturbance of the unmanned aerial vehicle is accurately and rapidly learned and estimated by utilizing an incremental Gaussian process, and corresponding compensation is carried out according to the prediction result of the disturbance in the processes of trajectory planning and unmanned aerial vehicle control, so that the unmanned aerial vehicle based on differential flatness control can still realize real-time collision avoidance in the disturbance.
Description
Technical Field
The invention relates to the technical field of robots, in particular to an anti-disturbance unmanned aerial vehicle collision avoidance method based on differential flatness.
Background
The differential flatness of the unmanned aerial vehicle can enable the unmanned aerial vehicle to obtain the control quantity of the unmanned aerial vehicle system through specific output values and various derivatives and correlation operation. Collision avoidance algorithms for drones have been implemented in the prior art using this property. These algorithms utilize this technique to greatly reduce the amount of computation required to control collision avoidance for drones. When the unmanned aerial vehicle has limited computing power, the algorithms can still plan a new collision-free track and quickly calculate corresponding control quantity so as to realize real-time collision avoidance. But these algorithms are difficult to deal with the interference that environmental and modeling errors create on drones. These algorithms assume that the disturbances in the environment are small and that the modeling of the drone is accurate. In reality, the two factors cannot be ignored, so that the disturbance of the two to the drone can greatly reduce the performance of the algorithm.
Disclosure of Invention
The invention provides an anti-disturbance unmanned aerial vehicle collision avoidance method based on differential flatness to overcome the defects in the prior art, so that the unmanned aerial vehicle based on differential flatness control can still realize real-time collision avoidance in disturbance.
In order to solve the technical problems, the invention adopts the technical scheme that: an anti-disturbance unmanned aerial vehicle collision avoidance method based on differential flatness comprises the following steps:
s1, an incremental Gaussian process receives an actual state q of the unmanned aerial vehicle and an unmanned aerial vehicle state predicted by an unmanned aerial vehicle model and compares the actual state q and the unmanned aerial vehicle state predicted by the unmanned aerial vehicle model to calculate the disturbance effect on the unmanned aerial vehicle at the moment, the position and the speed of the unmanned aerial vehicle are used as input, and the disturbance on the unmanned aerial vehicle is used as output, so that a data set is constructed; when the incremental Gaussian process receives the actual state of the unmanned aerial vehicle at the current moment, the disturbance of the unmanned aerial vehicle at the current moment is presumed by comparing the actual state with data in a data set, and a predicted average value m and a variance e are provided;
s2, receiving the given three-time guidable track by a track re-planning module, and planning a new collision-free track r which is as close to the original track as possible for the unmanned aerial vehicle by using a safety barrier;
s3, controlling quantity u of the unmanned aerial vehicle to be [ f omega ], wherein f is propulsive force generated by a rotor wing of the unmanned aerial vehicle, and omega is rotating speed of three Euler angles; according to the generated new track r, the PID controller firstly corrects the corresponding part of the track by using the predicted average value m of the incremental Gaussian process to counteract the influence of disturbance on the unmanned aerial vehicle; then the PID controller generates a corresponding feedforward control quantity by using the corrected track and the differential flatness property, and generates a feedback control quantity by using a difference value between the actual state q and the track r of the unmanned aerial vehicle, wherein the final control quantity u is the sum of the two control quantities;
s4, the control quantity is respectively input into the unmanned aerial vehicle model and the unmanned aerial vehicle, and the unmanned aerial vehicle model predicts the state of the unmanned aerial vehicle at the next moment according to the control quantity; the unmanned aerial vehicle outputs the actual state q of the unmanned aerial vehicle at the moment through the sensor at the next moment after receiving the control quantity;
and S5, when the unmanned aerial vehicle is out of the safe state, namely when an index control barrier function hij <0 exists, the track replanning module replans a new track by using the state of the unmanned aerial vehicle at the current moment, and helps the unmanned aerial vehicle to return to the safe region.
Further, the step S2 includes:
s21, calculating a control quantity capable of tracking an original track according to the current state of the current unmanned aerial vehicle and the original track by using a pole configuration controller, wherein the control quantity is the acceleration of the unmanned aerial vehicle;
s22, constructing an unmanned aerial vehicle model, and considering that descending airflow below the unmanned aerial vehicle influences the stability of the unmanned aerial vehicle below, setting the vertical distance of the unmanned aerial vehicle to be large enough until the unmanned aerial vehicle below cannot be influenced by the descending airflow; setting the unmanned aerial vehicle model to be in a shape of a capsule close to a cuboid;
s23, constructing a corresponding index control barrier function hij according to the model of the unmanned aerial vehicle; every two unmanned aerial vehicles can calculate an index control barrier function according to the position and the safety distance;
s24, in order to enable all the index control barrier functions hij to be constantly established, corresponding safety limits are established for the state of the unmanned aerial vehicle; each index control barrier function hij corresponds to a safety limit; considering that a certain difference exists between the disturbance average value predicted by the incremental Gaussian process and the real disturbance, predicting the worst case with high confidence by using the prediction variance e, and then adding the worst case into the calculation of the safety limit; finally, all the safety limits are concentrated to construct a safety barrier certificate;
s25, combining a safety barrier to prove that the unmanned aerial vehicle performance limit and the control quantity limit are limited, and constructing a new control quantity v which can enable the unmanned aerial vehicle to avoid collision and is as close to the original control quantity v' as possible through secondary planning;
and S26, combining the control quantity v and a dynamic model of the unmanned aerial vehicle to generate a new collision-free track r.
Further, the model of the unmanned aerial vehicle constructed in step S22 is: x is the number of4+y4+(z/k)4<Ds, where k>1 is the coefficient and Ds is the safe radius; xyz is the position of the midpoint in space when the center of mass of the unmanned aerial vehicle is taken as the origin of the coordinate system.
Go toStep (S23) of indicating numerical control barrier function hijThe expression of (a) is: h isij＝(xi-xj)4+(yi-yj)4+[(zi-zj)/k]4-(Dsi+Dsj)4(ii) a Wherein [ x ]i,yi,zi]And [ x ]j,yj,zj]Respectively, the positions of two unmanned aerial vehicles, DsiAnd DsjIs the safe radius of two unmanned planes.
Further, the expression of the safety limit is as follows: : h isij (3)+K·[hij hij (1)hij (2)]TAnd the K is obtained by a pole allocation method.
Further, in step S24, if the serial number of the drone group is 1,2, ·, m, the security constraint between any two drones i and j is converted into aij·v≤BijWherein v ═ v1,v2,···,vm]For all unmanned aerial vehicle's controlled variables, controlled variables viRepresenting jerk of drone i, AijAnd BijFrom hij (3)+K·[hij hij (1)hij (2)]TCalculated to be more than or equal to 0; finally, all safety limits are intensively constructed to form a safety barrier which proves that A.v is less than or equal to B, and the control quantity of all unmanned aerial vehicles can be limited, wherein A and B respectively limit all AijAnd BijAnd longitudinally splicing to form the finished product.
Further, in step S25, the objective function of quadratic programming is | | v-v' | | computationally2And satisfies the condition that A.v is less than or equal to B, and for any unmanned aerial vehicle i, | | ai-di||∞<gi，||vi||∞<ViWherein a isi,di,gi,ViAnd estimating the disturbance of the unmanned aerial vehicle, the upper limit of the acceleration of the unmanned aerial vehicle and the upper limit of the control quantity of the unmanned aerial vehicle for the actual acceleration of the unmanned aerial vehicle and the incremental Gaussian process respectively.
Further, in step S4, the output actual state q of the drone includes a drone position, a drone speed, and a drone acceleration.
The present invention also provides an electronic device comprising:
a memory for storing a computer program;
a processor for implementing the steps of the above method when executing the computer program.
The invention also provides a computer-readable storage medium having stored thereon a computer program which, when executed by a processor, performs the steps of the method described above.
Compared with the prior art, the beneficial effects are: according to the disturbance-resistant unmanned aerial vehicle collision avoidance method based on the differential flatness, the disturbance on the unmanned aerial vehicle is accurately and rapidly learned and estimated by utilizing the incremental Gaussian process, and corresponding compensation is carried out according to the prediction result of the disturbance in the processes of trajectory planning and unmanned aerial vehicle control, so that the unmanned aerial vehicle based on the differential flatness control can still realize real-time collision avoidance in the disturbance.
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FIG. 1 is a schematic diagram of the control relationship of the present invention.
Detailed Description
The drawings are for illustration purposes only and are not to be construed as limiting the invention; for the purpose of better illustrating the embodiments, certain features of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted. The positional relationships depicted in the drawings are for illustrative purposes only and are not to be construed as limiting the invention.
As shown in fig. 1, an anti-disturbance unmanned aerial vehicle collision avoidance method based on differential flatness includes the following steps:
step 1, an incremental Gaussian process receives an actual state q of the unmanned aerial vehicle and a state of the unmanned aerial vehicle predicted by an unmanned aerial vehicle model and compares the actual state q and the state of the unmanned aerial vehicle predicted by the unmanned aerial vehicle model to calculate the disturbance effect on the unmanned aerial vehicle at the moment, and the position and the speed of the unmanned aerial vehicle are used as input, and the disturbance on the unmanned aerial vehicle is used as output, so that a data set is constructed; when the incremental Gaussian process receives the actual state of the unmanned aerial vehicle at the current moment, the disturbance of the unmanned aerial vehicle at the current moment is presumed by comparing the actual state with data in a data set, and a predicted average value m and a variance e are provided; a larger variance represents a greater uncertainty in the prediction.
Step 2, a track re-planning module receives the given three-time guidable track and uses a safety barrier to prove that a new collision-free track r which is as close to the original track as possible is planned for the unmanned aerial vehicle; the method specifically comprises the following steps:
s21, calculating a control quantity capable of tracking an original track according to the current state of the current unmanned aerial vehicle and the original track by using a pole configuration controller, wherein the control quantity is the acceleration of the unmanned aerial vehicle;
s22, constructing an unmanned aerial vehicle model: x is the number of4+y4+(z/k)4<Ds, where k>1 is the coefficient and Ds is the safe radius; xyz is the position of the middle point in space when the center of mass of the unmanned aerial vehicle is taken as the origin of a coordinate system; considering that the stability of the unmanned aerial vehicle below the unmanned aerial vehicle is influenced by the downdraft below the unmanned aerial vehicle, the vertical distance of the unmanned aerial vehicle is set to be large enough until the unmanned aerial vehicle below is not influenced by the downdraft; setting the unmanned aerial vehicle model to be in a shape of a capsule close to a cuboid;
s23, constructing a corresponding index control barrier function hij, h according to the model of the unmanned aerial vehicleijThe expression of (a) is: h isij＝(xi-xj)4+(yi-yj)4+[(zi-zj)/k]4-(Dsi+Dsj)4(ii) a Wherein [ x ]i,yi,zi]And [ x ]j,yj,zj]Respectively, the positions of two unmanned aerial vehicles, DsiAnd DsjThe safe radius of two unmanned planes; every two unmanned aerial vehicles can calculate an index control barrier function according to the position and the safety distance;
s24. in order to make all the indexes control the barrier function hij>When 0 is always true, corresponding safety limits, namely h, are established for the state of the unmanned aerial vehicleij (3)+K·[hij hij (1)hij (2)]TMore than or equal to 0, wherein K is obtained by a pole allocation method; each index control barrier function hij corresponds to a safety limit; considering that a certain difference exists between the disturbance average value predicted by the incremental Gaussian process and the real disturbance, predicting the worst case with high confidence by using the prediction variance e, and then adding the worst case into the calculation of the safety limit; the serial number of the unmanned aerial vehicle group is 1,2, the safety limit between any two unmanned aerial vehicles i and j is converted into Aij·v≤BijWherein v ═ v1,v2,···,vm]For all unmanned aerial vehicle's controlled variables, controlled variables viRepresenting jerk of drone i, AijAnd BijFrom hij (3)+K·[hij hij (1)hij (2)]TCalculated to be more than or equal to 0; finally, all safety limits are intensively constructed to form a safety barrier which proves that A.v is less than or equal to B, and the control quantity of all unmanned aerial vehicles can be limited, wherein A and B respectively limit all AijAnd BijLongitudinally splicing to form the structure;
s25, combining a safety barrier to prove that the unmanned aerial vehicle performance limit and the control quantity limit are limited, and constructing a new control quantity v which can enable the unmanned aerial vehicle to avoid collision and is as close to the original control quantity v' as possible through secondary planning; the quadratic programming has the objective function of | | | v-v' | | purple2And satisfies the condition that A.v is less than or equal to B, and for any unmanned aerial vehicle i, | | ai-di||∞<gi，||vi||∞<ViWherein a isi,di,gi,ViEstimating disturbance of the unmanned aerial vehicle, an upper limit of the acceleration of the unmanned aerial vehicle and an upper limit of the control quantity of the unmanned aerial vehicle for the actual acceleration of the unmanned aerial vehicle and an incremental Gaussian process respectively;
and S26, combining the control quantity v and a dynamic model of the unmanned aerial vehicle to generate a new collision-free track r.
Step 3, controlling the unmanned aerial vehicle by using the control quantity u as [ f omega ], wherein f is the propulsive force generated by the rotor wing of the unmanned aerial vehicle, and omega is the rotating speed of three Euler angles; according to the generated new track r, the PID controller firstly corrects the corresponding part of the track by using the predicted average value m of the incremental Gaussian process to counteract the influence of disturbance on the unmanned aerial vehicle; and then the PID controller generates a corresponding feedforward control quantity by using the corrected track and the differential flatness property, and generates a feedback control quantity by using a difference value between the actual state q of the unmanned aerial vehicle and the track r, wherein the final control quantity u is the sum of the two.
Step 4, the control quantity is respectively input into the unmanned aerial vehicle model and the unmanned aerial vehicle, and the unmanned aerial vehicle model predicts the state of the unmanned aerial vehicle at the next moment according to the control quantity; and the unmanned aerial vehicle outputs the actual state q of the unmanned aerial vehicle at the moment through the sensor at the next moment after receiving the control quantity, wherein the actual state q comprises the position, the speed and the acceleration of the unmanned aerial vehicle.
And 5, when the unmanned aerial vehicle is out of the safe state, namely when an index control barrier function hij <0 exists, the track replanning module replans a new track by using the state of the unmanned aerial vehicle at the current moment to help the unmanned aerial vehicle return to the safe region.
In the invention, the disturbance caused by environment and modeling error is learned and estimated by an incremental Gaussian process, and a prediction average value m and a variance e are provided; and carrying out correlation operation on the safety limit of the unmanned aerial vehicle by using an exponential control barrier function and each derivative thereof according to a dynamic model of the unmanned aerial vehicle, wherein the dynamic model of the unmanned aerial vehicle contains a prediction variance e when the safety limit is calculated, and is used for calculating the safety limit. The newly planned track is obtained by secondary planning, and the secondary planning comprises safety limit, unmanned aerial vehicle performance limit and control quantity limit; and the PID controller correspondingly compensates the control quantity by using the prediction average value of the incremental Gaussian process and controls the unmanned aerial vehicle by using the differential flatness. In conclusion, the disturbance resisting unmanned aerial vehicle collision avoidance method based on the differential flatness provided by the invention utilizes the incremental Gaussian process to accurately and rapidly learn and estimate the disturbance suffered by the unmanned aerial vehicle, and carries out corresponding compensation according to the prediction result of the disturbance in the processes of trajectory planning and unmanned aerial vehicle control, so that the unmanned aerial vehicle based on the differential flatness control can still realize real-time collision avoidance in the disturbance.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.
It should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.
Claims (10)
1. An anti-disturbance unmanned aerial vehicle collision avoidance method based on differential flatness is characterized by comprising the following steps:
s1, an incremental Gaussian process receives an actual state q of the unmanned aerial vehicle and an unmanned aerial vehicle state predicted by an unmanned aerial vehicle model and compares the actual state q and the unmanned aerial vehicle state predicted by the unmanned aerial vehicle model to calculate the disturbance effect on the unmanned aerial vehicle at the moment, the position and the speed of the unmanned aerial vehicle are used as input, and the disturbance on the unmanned aerial vehicle is used as output, so that a data set is constructed; when the incremental Gaussian process receives the actual state of the unmanned aerial vehicle at the current moment, the disturbance of the unmanned aerial vehicle at the current moment is presumed by comparing the actual state with data in a data set, and a predicted average value m and a variance e are provided;
s2, receiving the given three-time guidable track by a track re-planning module, and planning a new collision-free track r which is as close to the original track as possible for the unmanned aerial vehicle by using a safety barrier;
s3, controlling quantity u of the unmanned aerial vehicle to be [ f omega ], wherein f is propulsive force generated by a rotor wing of the unmanned aerial vehicle, and omega is rotating speed of three Euler angles; according to the generated new track r, the PID controller firstly corrects the corresponding part of the track by using the predicted average value m of the incremental Gaussian process to counteract the influence of disturbance on the unmanned aerial vehicle; then the PID controller generates a corresponding feedforward control quantity by using the corrected track and the differential flatness property, and generates a feedback control quantity by using a difference value between the actual state q and the track r of the unmanned aerial vehicle, wherein the final control quantity u is the sum of the two control quantities;
s4, the control quantity is respectively input into the unmanned aerial vehicle model and the unmanned aerial vehicle, and the unmanned aerial vehicle model predicts the state of the unmanned aerial vehicle at the next moment according to the control quantity; the unmanned aerial vehicle outputs the actual state q of the unmanned aerial vehicle at the moment through the sensor at the next moment after receiving the control quantity;
s5, when the unmanned aerial vehicle is out of the safe state, a certain exponential control barrier function h existsij<And when the unmanned aerial vehicle is in the safe area, the trajectory replanning module replans a new trajectory by using the state of the unmanned aerial vehicle at the current moment, so that the unmanned aerial vehicle can return to the safe area.
2. The method for avoiding collision of disturbance-resistant unmanned aerial vehicle based on differential flatness as claimed in claim 1, wherein the step S2 includes:
s21, calculating a control quantity capable of tracking an original track according to the current state of the current unmanned aerial vehicle and the original track by using a pole configuration controller, wherein the control quantity is the acceleration of the unmanned aerial vehicle;
s22, constructing an unmanned aerial vehicle model, and considering that descending airflow below the unmanned aerial vehicle influences the stability of the unmanned aerial vehicle below, setting the vertical distance of the unmanned aerial vehicle to be large enough until the unmanned aerial vehicle below cannot be influenced by the descending airflow; setting the unmanned aerial vehicle model to be in a shape of a capsule close to a cuboid;
s23, constructing a corresponding index control barrier function h according to the model of the unmanned aerial vehicleij(ii) a Every two unmanned aerial vehicles can calculate an index control barrier function according to the position and the safety distance;
s24, in order to control all indexes to the barrier function hij>If 0 is always true, corresponding safety limit is established for the state of the unmanned aerial vehicle; each exponential control barrier function hijEach corresponds to a safety limit; considering that the average value of the disturbance predicted by the incremental Gaussian process has a certain difference with the real disturbance, the worst case is predicted with high confidence by using the prediction variance eThen adding the safety limit calculation into the safety limit calculation; finally, all the safety limits are concentrated to construct a safety barrier certificate;
s25, combining a safety barrier to prove that the unmanned aerial vehicle performance limit and the control quantity limit are limited, and constructing a new control quantity v which can enable the unmanned aerial vehicle to avoid collision and is as close to the original control quantity v' as possible through secondary planning;
and S26, combining the control quantity v and a dynamic model of the unmanned aerial vehicle to generate a new collision-free track r.
3. The method for avoiding collision of disturbance-resistant unmanned aerial vehicle based on differential flatness as claimed in claim 2, wherein the model of unmanned aerial vehicle constructed in step S22 is: x is the number of4+y4+(z/k)4<Ds, where k>1 is the coefficient and Ds is the safe radius; xyz is the position of the midpoint in space when the center of mass of the unmanned aerial vehicle is taken as the origin of the coordinate system.
4. The method as claimed in claim 3, wherein the step S23 is performed by controlling the barrier function hijThe expression of (a) is: h isij＝(xi-xj)4+(yi-yj)4+[(zi-zj)/k]4-(Dsi+Dsj)4(ii) a Wherein [ x ]i,yi,zi]And [ x ]j,yj,zj]Respectively, the positions of two unmanned aerial vehicles, DsiAnd DsjIs the safe radius of two unmanned planes.
5. The differential flatness-based disturbance rejection unmanned aerial vehicle collision avoidance method according to claim 4, wherein the safety limit is expressed by: h isij (3)+K·[hij hij (1)hij (2)]TAnd the K is obtained by a pole allocation method.
6. According to claim 5The disturbance-resistant unmanned aerial vehicle collision avoidance method based on differential flatness is characterized in that in step S24, the serial number of the unmanned aerial vehicle group is 1,2, and then the safety limit between any two unmanned aerial vehicles i and j is converted into aij·v≤BijWherein v ═ v1,v2,···,vm]For all unmanned aerial vehicle's controlled variables, controlled variables viRepresenting jerk of drone i, AijAnd BijFrom hij (3)+K·[hijhij (1)hij (2)]TCalculated to be more than or equal to 0; finally, all safety limits are intensively constructed to form a safety barrier which proves that A.v is less than or equal to B, and the control quantity of all unmanned aerial vehicles can be limited, wherein A and B respectively limit all AijAnd BijAnd longitudinally splicing to form the finished product.
7. The method according to claim 6, wherein in step S25, the quadratic programming objective function is | | | v-v' | (| magnetic circuit)2And satisfies the condition that A.v is less than or equal to B, and for any unmanned aerial vehicle i, | | ai-di||∞<gi，||vi||∞<ViWherein a isi,di,gi,ViAnd estimating the disturbance of the unmanned aerial vehicle, the upper limit of the acceleration of the unmanned aerial vehicle and the upper limit of the control quantity of the unmanned aerial vehicle for the actual acceleration of the unmanned aerial vehicle and the incremental Gaussian process respectively.
8. The method for avoiding collision of disturbance-resistant unmanned aerial vehicle based on differential flatness according to any one of claims 1 to 7, wherein in the step S4, the output actual state q of unmanned aerial vehicle comprises unmanned aerial vehicle position, speed and acceleration.
9. An electronic device, comprising:
a memory for storing a computer program;
a processor for implementing the steps of the method according to any one of claims 1 to 8 when executing the computer program.
10. A computer-readable storage medium, characterized in that a computer program is stored on the computer-readable storage medium, which computer program, when being executed by a processor, carries out the steps of the method according to any one of claims 1 to 8.
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