Unmanned aerial vehicle signal timing logic task motion planning method based on sequence decomposition

Abstract

The application provides a kind of unmanned aerial vehicle signal timing logic task motion planning method based on sequence decomposition, the application provides a kind of unmanned aerial vehicle signal timing logic task motion planning method based on sequence decomposition, first, sequence decomposition strategy is proposed, the task of unmanned aerial vehicle to destination is decomposed according to time sequence, sequence decomposition strategy makes the growth rate of predicate function of each stage be constrained by control barrier function, to ensure the feasibility of reaching task, and can process the system with relative order 2;Second, the application also proposes a dynamic constraint activation strategy according to the timing characteristics of signal time logic task, which can reduce the calculation amount of convex optimization problem and reduce the conservativeness of the application.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of unmanned aerial vehicle path planning, and particularly relates to a signal temporal logic task motion planning method for unmanned aerial vehicles based on sequence decomposition. BACKGROUND

[0002] With the continuous progress of computing chips and sensor technology, the capabilities of unmanned aerial vehicles are becoming more and more powerful, and the research on unmanned aerial vehicles is of great significance. Unmanned aerial vehicle motion planning is an important content in the research on unmanned aerial vehicles, and the traditional method usually only requires to reach a specified target point, and the task as a whole is relatively simple, and it is difficult to process complex time constraint signal temporal logic (STL). As a subfield of temporal logic, STL is very suitable for processing the access and obstacle avoidance problems of unmanned aerial vehicles with specific space-time properties.

[0003] The most basic STL motion planning method is the mixed integer linear programming (MILP) method. A binary variable is introduced for each predicate at each time step, and the STL constraint is coded into the form of MILP, and the optimal control problem is converted into a mixed integer linear programming problem, and the optimal path of the unmanned aerial vehicle is obtained iteratively. The MILP method has an exponential time complexity, and it is difficult to quickly solve when the task time is long. In order to solve this problem, people have also proposed the control barrier function (CBF) method. This method encodes each STL constraint into a one-to-one corresponding control barrier function, and converts the STL constraint into a constraint of the control amount to solve the convex optimization problem, thereby obtaining the motion path of the unmanned aerial vehicle.

[0004] However, the disadvantage of the MILP method is that when the time span of the task increases, the number of binary variables will increase exponentially, significantly increasing the burden of the calculation amount, and it is difficult to implement in real time in a complex dynamic scene. The CBF method is difficult to process systems with relative order higher than 1. SUMMARY

[0005] To solve the above problems, the application provides a signal temporal logic task motion planning method for unmanned aerial vehicles based on sequence decomposition, which realizes the motion planning of unmanned aerial vehicles with relative order higher than 1 under the STL constraint while having low computing demand.

[0006] A signal temporal logic task motion planning method for unmanned aerial vehicles based on sequence decomposition, comprising the following steps:

[0007] S1: dividing the path planning task of the unmanned aerial vehicle into an obstacle avoidance task sequence and an access task sequence wherein K O is the number of obstacles, K O is an obstacle avoidance subtask corresponding to the K d is the number of destinations, K d The visit subtasks corresponding to the destinations;

[0008] S2: Based on the relaxed quadratic programming, the control variable u(t) of the UAV when performing each obstacle avoidance subtask and each access subtask is obtained to complete the motion planning. The control variable u(t) is obtained as follows:

[0009] (u(t),δ(t))=min u(t),δ(t) u(t) 2 +pδ 2 (t)

[0010]

[0011] u min ≤u(t)≤u max

[0012] Among them, δ(t) is the slack variable, p is the set weight, u min is the lower limit of the control quantity, u max Set the upper limit of the control amount. is the indicator value when the UAV performs the k1th obstacle avoidance subtask, where if but like but a k1 is the start time of the k1th obstacle avoidance subtask, is the end time of the k1th obstacle avoidance subtask, is the predicate function used to characterize the distance between the current position of the UAV and the final target position when performing the k1th obstacle avoidance subtask, express The second-order Lie derivative along f(x), with f(x) = [Vcosθ, Vsinθ, 0] T , θ is the direction of the UAV, V is the linear velocity of the UAV, express Lie derivative along g(x), g(x) = [0, 0, 1] T , For The relevant 0th-order barrier function, for The coefficient of for The index of is an odd number, For The first-order barrier function is related to for The coefficient of for The index of is an odd number, is the indicator value when the UAV performs the k2th access subtask, where if but like but is a predicate function used to characterize that the rate of increase of the distance between the current position of the UAV and the final target position is less than the set value when executing the k2th access subtask. express Lie derivative along f(x), express Lie derivative along g(x), For The relevant 0th-order barrier function, for The coefficient of for The index of is a predicate function used to characterize that the rate of increase of the distance between the current position of the UAV and the final target position is not less than the set value when executing the k2th access subtask. express Lie derivative along f(x), express Lie derivative along g(x), For The relevant 0th-order barrier function, for The coefficient of for The index of .

[0013] Furthermore, the predicate function is calculated as follows:

[0014]

[0015] Among them, x p (t) is the position coordinate of the UAV at time t, The position coordinates of the obstacles when the UAV performs k1 obstacle avoidance tasks, The radius of the obstacle when the UAV performs k1 obstacle avoidance subtasks;

[0016] and The related 0th-order barrier function The calculation formula is as follows:

[0017]

[0018] and The first-order barrier function The calculation formula is as follows:

[0019]

[0020] wherein, is the derivative of .

[0021] Further, the calculation formula of the predicate function is:

[0022]

[0023] wherein, is a predicate function for representing the distance between the current position of the UAV and the final target position when the k2th visiting subtask is executed, and has t0is the activation time of the k2th visiting subtask, x p (t0) is the position coordinate of the UAV at the activation time t0, is the center coordinate of the k2th destination, is the radius of the k2th destination, is the derivative of , indicating the growth rate of the predicate function;

[0024] The calculation formula of the 0th order barrier function related to is:

[0025]

[0026] Further, the calculation formula of the predicate function is:

[0027]

[0028] wherein, is a predicate function for representing the distance between the current position of the UAV and the final target position when the k2th visiting subtask is executed, and has t0is the activation time of the k2th visiting subtask, x p (t0) is the position coordinate of the UAV at the activation time t0, is the center coordinate of the k2th destination, is the radius of the k2th destination, is the derivative of , indicating the growth rate of the predicate function;

[0029] The calculation formula of the 0th order barrier function related to is:

[0030]

[0031] Beneficial effects:

[0032] The present invention provides a method for motion planning of unmanned aerial vehicle (UAV) signal timing logic tasks based on sequence decomposition. The present invention provides a method for motion planning of unmanned aerial vehicle (UAV) signal timing logic tasks based on sequence decomposition. Firstly, a sequence decomposition strategy is proposed to decompose the task of the UAV reaching the destination in chronological order. The sequence decomposition strategy constrains the growth rate of the predicate function of each stage by a control barrier function to ensure the feasibility of the arrival task and can process a system with a relative order of 2. Secondly, the present invention also proposes a dynamic constraint activation strategy based on the timing characteristics of the signal timing logic task, which can reduce the computational complexity of the convex optimization problem and reduce the conservatism of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 The present invention provides a flow chart of a method for UAV signal timing logic task motion planning based on sequence decomposition. DETAILED DESCRIPTION

[0034] In order to enable those skilled in the art to better understand the solution of the present application, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application.

[0035] like Figure 1 As shown, a UAV signal timing logic task motion planning method based on sequence decomposition includes the following steps:

[0036] S1: Divide the UAV’s path planning task into an obstacle avoidance task sequence and access task sequences Among them, K O is the number of obstacles, K O The obstacle avoidance subtask corresponding to the K obstacles, d is the number of destinations, K d The visit subtasks corresponding to the destinations;

[0037] S2: Based on the relaxed quadratic programming, the control variable u(t) of the UAV when performing each obstacle avoidance subtask and each access subtask is obtained to complete the motion planning. The control variable u(t) is obtained as follows:

[0038] (u(t),δ(t))=min u(t),δ(t) u(t) 2 +pδ 2 (t)

[0039]

[0040] u min ≤u(t)≤u max

[0041] where δ(t) is a relaxation variable, p is a set weight, u min is a set lower limit of the control variable, u max is a set upper limit of the control variable, is an indicative value of the UAV when performing the k1th obstacle avoidance subtask, where if then if then is the start time of the k1th obstacle avoidance subtask, b k1 is the end time of the k1th obstacle avoidance subtask, is a predicate function used to represent the distance between the current position and the final target position of the UAV when performing the k1th obstacle avoidance subtask, denotes the second order Lie derivative along f(x), and f(x) = [Vcosθ, Vsinθ, 0] T , θ is the direction of the UAV, and V is the linear velocity of the UAV, denotes the Lie derivative along g(x), g(x) = [0, 0, 1] T , is a 0th order barrier function related to , is the coefficient of , is the exponent of , is an odd number, is a 1st order barrier function related to , is the coefficient of , is the exponent of , is an odd number, is an indicative value of the UAV when performing the k2th visiting subtask, where if then if then is a predicate function used to represent that the increasing rate of the distance between the current position and the final target position of the UAV when performing the k2th visiting subtask is less than a set value, denotes the Lie derivative along f(x), denotes the Lie derivative along g(x), is a 0th order barrier function related to , is a coefficient of is an exponent of is a predicate function for characterizing that the increasing rate of the distance between the current position of the UAV and the final target position when performing the k2th access sub-task is not less than a set value, represents the Lie derivative along f(x), represents the Lie derivative along g(x), is a 0th order barrier function related to is a coefficient of is an exponent of

[0042] That is, the present application divides the path planning task of the UAV into two categories: obstacle avoidance task and access task. The positions and sizes of the obstacles and the target region in the working space (x, y) of the UAV are determined and converted into STL constraints; for the obstacle avoidance task, a high-order control barrier function is designed to convert the STL constraints into control quantity constraints; for the access task, a sequence decomposition method is used to convert each STL constraint into two corresponding sub-constraints, and then a control barrier function method is used to constrain the control quantity; in order to reduce the computational burden and reduce the conservatism of the method, a dynamic activation mechanism is proposed; when an STL constraint is no longer needed, the control quantity constraint corresponding to the STL constraint is deactivated in the solver; finally, all activated control quantity constraints are considered, and the control quantity is obtained by solving a relaxed QP problem; the control quantity is applied to the actuator of the UAV, and the UAV motion path that satisfies the STL constraint can be obtained.

[0043] It should be noted that the signal timing logic is a predicate logic. The predicate function is evaluated as "true" or "false" at each time. In the present application, the predicate function is specified as a function for measuring the distance between the UAV and a specific point. The specific point can be the center point of the obstacle or the destination.

[0044] Further, the calculation method of the predicate function is as follows:

[0045]

[0046] Wherein, x p (t) is the position coordinates of the UAV at time t, is the position coordinates of the obstacle when the UAV performs k1 obstacle avoidance sub-tasks, is the radius of the obstacle when the UAV performs k1 obstacle avoidance sub-tasks;​​​​​

[0047] with a 0th order barrier function is calculated as follows:

[0048]

[0049] with a 1st order barrier function is calculated as follows:

[0050]

[0051] where, is the derivative of .

[0052] Further, the calculation formula of the predicate function is:

[0053]

[0054] where, is a predicate function used to represent the distance between the current position of the UAV and the final target position when performing the k2th visiting sub-task, and has t0is the activation time of the k2th visiting sub-task, x p (t0)is the position coordinate of the UAV at the activation time t0, is the center coordinate of the k2th destination, is the radius of the k2th destination, is the derivative of , indicating the growth rate of the predicate function;

[0055] with a 0th order barrier function is calculated as follows:

[0056]

[0057] Further, the calculation formula of the predicate function is:

[0058]

[0059] where, is a predicate function used to represent the distance between the current position of the UAV and the final target position when performing the k2th visiting sub-task, and has t0is the activation time of the k2th visiting sub-task, x p (t0)is the position coordinate of the UAV at the activation time t0, is the center coordinate of the k2th destination, the radius of the kth destination, the derivative of

[0060] The formula for calculating

[0061]

[0062] The process of obtaining the control variable u(t) is derived in detail below.

[0063] The dynamic model of the UAV is constructed as follows:

[0064]

[0065] where x p = [x y] T represents the position of the UAV, θ represents its direction, V > 0 represents its linear velocity, and u represents the control variable, i.e., the angular velocity of the UAV.

[0066] An STL constraint φ can be defined by the STL syntax as follows:

[0067]

[0068]

[0069] where represents that the task specification φ is satisfied at some time steps between time t+a and time t+b, and similarly, represents that the task specification φ is satisfied at every time step between time t+a and time t+b.

[0070] In step S1, assuming there are K O obstacles and K d destinations, the path planning task φ of the UAV is divided into two types: obstacle avoidance task φ obs and visiting task φ des , i.e.

[0071] φ = φ obs ∧ φ des

[0072] where is the STL constraint representing the obstacle avoidance task, is the STL constraint representing the visiting task.

[0073] Considering the kth obstacle avoidance task, the UAV must always avoid the obstacle within the specified time, which is consistent with the definition of the time operator G. Assuming x​​​p (t) represents the position of the UAV, the obstacle is not a circular obstacle in the working plane, the kth obstacle is located at x o,k with a radius of r o,k and needs to be avoided in the time period [a k , b k ], the obstacle avoidance STL constraint about this obstacle can be written as:

[0074]

[0075] The corresponding predicate function is

[0076]

[0077] This predicate function has a relative order of 2 for the system dynamics equation.

[0078] Define the high-order obstacle function as shown below, The class function is set to the power function.

[0079]

[0080] where, and n is an odd number, Then, the following control quantity constraint can be derived:

[0081]

[0082] where, represents the Lie derivative of the function along the vector field f(x). Similarly, represents the second-order Lie derivative along f(x), represents the Lie derivative along g(x), as long as the control quantity satisfies this constraint, it ensures that the UAV can avoid the obstacle region; for multiple obstacle avoidance tasks, the control quantity constraints corresponding to them need to be considered simultaneously.

[0083] Consider the k1th visit task , the UAV should reach the specified location within the specified time, which is consistent with the definition of the time operator F and U. It is worth noting that U can be represented as the combination of G and F, and the processing method of G has been discussed, therefore, the following will focus on analyzing F.

[0084] Given an STL constraint of a visit task:

[0085]

[0086] where, respectively represent the start time and end time of the constraint, represent the center and radius of the target region, and the corresponding predicate function is:

[0087]

[0088] t0is the activation time of the k2thaccess sub-task, x p (t0) is the position coordinate of the UAV at the activation time t0. The relative order of this predicate function to the system dynamics equation is 2.

[0089] At the initial time, In order to satisfy , we propose a sequence decomposition strategy to control the growth rate of the function value, so that at some time in the time interval , there is

[0090] Consider the following evaluation function to measure the growth rate of :

[0091]

[0092] Then, according to the time constraint, decompose into two sub-constraints:

[0093]

[0094] where

[0095]

[0096] The predicate function corresponding to the sub-constraint is:

[0097]

[0098] It is worth noting that the predicate function of the sub-constraint has a relative order of 1 to the system dynamics equation. Therefore, the invention can define the barrier function as:

[0099]

[0100] where, and n is an odd number, Then, the following control quantity constraint can be obtained:

[0101]

[0102] As long as the control quantity satisfies this constraint, it is ensured that the UAV can reach the target region. For multiple access tasks, the control quantity constraints corresponding to them need to be considered at the same time.

[0103] To reduce the computation and conservativeness, the present application proposes a dynamic activation mechanism to deactivate the constraints when they are no longer needed (i.e. when the target position is reached or when the obstacle avoidance is no longer needed).

[0104] Considering the obstacle avoidance task where, and k1∈{1,…,K o , the dynamic activation mechanism is added to the control constraints as follows:

[0105]

[0106] where,

[0107]

[0108] Each visiting task will be activated and processed according to the order of the time constraints, and only one task is processed at any time. Considering the visiting task where, and k2∈{1,…,K d . At t=0, only φ d,1 is decomposed, and other constraints are ignored. The control constraints corresponding to φ d,1 can be written as:

[0109]

[0110] If φ d,1 is not completed, i1 will always equal to 1. When φ d,1 is completed, the completion time t1 and the system state x(t1) are recorded and i1 is set to 0. Then, the present application decomposes φ d,2 :

[0111]

[0112] The control constraints corresponding to it are:

[0113]

[0114] If φ d,2 is not completed, i2 will always equal to 1. When φ d,2 is completed, the completion time t2 and the system state x(t2) are recorded and i2 is set to 0. By repeating the above process, the UAV can complete the visiting tasks in order.

[0115] For the total task φ=φ obs ∧φ des , the present application considers φ obs and φ desthe constraints of the sub-formula of the. A relaxed quadratic program is formulated to generate the controller u(t) to ensure the feasibility of the quadratic program and satisfy the STL constraints:

[0116] (u(t),δ(t))=min u(t),δ(t) u(t) 2 +pδ 2 (t)

[0117]

[0118] u min ≤u(t)≤u max

[0119] where δ(t)>0 is the slack variable and p>0 is its weight. The present application only adds a slack factor in the inequality corresponding to the access task. Since -δ(t)<0, this can relax the constraint on the control variable of the access problem to some extent, so that the system state may slightly violate the access task STL constraint, but it can make the optimization problem easier to find a feasible solution. The present application considers that ensuring the safety of the system itself has the highest priority, so it does not add a slack factor in the inequality corresponding to the obstacle avoidance task. The optimization problem is convex and only depends on two decision variables.

[0120] In summary, the present application provides a UAV signal timed logic task motion planning method based on sequence decomposition. First, the sequence decomposition strategy is proposed, which decomposes the UAV arrival destination task in time sequence. The sequence decomposition strategy controls the growth rate of each stage predicate function by the constraint of the control barrier function to ensure the feasibility of the arrival task and can handle systems with relative order 2. Second, the present application also proposes a dynamic constraint activation strategy according to the timing characteristics of the signal timed logic task, which can reduce the computational complexity of the convex optimization problem and reduce the conservativeness of the present application.

[0121] Of course, the present application can have other various embodiments, and those skilled in the art can certainly make various corresponding changes and modifications according to the present application without departing from the spirit and essence of the present application. However, these corresponding changes and modifications should all belong to the protection scope of the claims attached to the present application.

Claims

1. A UAV signal temporal logic task motion planning method based on sequence decomposition, characterized by: The following steps are involved: S1: Divide the UAV’s path planning task into an obstacle avoidance task sequence and access task sequences Among them, K O is the number of obstacles, K O The obstacle avoidance subtask corresponding to the K obstacles, d is the number of destinations, K d The visit subtasks corresponding to the destinations; S2: Based on the relaxed quadratic programming, the control variable u(t) of the UAV when performing each obstacle avoidance subtask and each access subtask is obtained to complete the motion planning. The control variable u(t) is obtained as follows: (u(t),δ(t))=min u(t),δ(t) u(t) 2 +pδ 2 (t) Among them, δ(t) is the slack variable, p is the set weight, u min is the lower limit of the control quantity, u max Set the upper limit of the control amount. is the indicator value when the UAV performs the k1th obstacle avoidance subtask, where if but like but is the start time of the k1th obstacle avoidance subtask, is the end time of the k1th obstacle avoidance subtask, is the predicate function used to characterize the distance between the current position of the UAV and the final target position when performing the k1th obstacle avoidance subtask, express The second-order Lie derivative along f(x), with f(x) = [Vcosθ, Vsinθ, 0] T , θ is the direction of the UAV, V is the linear velocity of the UAV, express Lie derivative along g(x), g(x) = [0, 0, 1] T , For The relevant 0th-order barrier function, for The coefficient of for The index of is an odd number, For The first-order barrier function is related to for The coefficient of for The index of is an odd number, is the indicator value when the UAV performs the k2th access subtask, where if but like but is a predicate function used to characterize that the rate of increase of the distance between the current position of the UAV and the final target position is less than the set value when executing the k2th access subtask. express Lie derivative along f(x), express Lie derivative along g(x), For The relevant 0th-order barrier function, for The coefficient of for The index of is a predicate function used to characterize that the rate of increase of the distance between the current position of the UAV and the final target position is not less than the set value when executing the k2th access subtask. express Lie derivative along f(x), express Lie derivative along g(x), For The relevant 0th-order barrier function, for The coefficient of for The index of .

2. The method for UAV signal temporal logic task motion planning based on sequence decomposition according to claim 1 is characterized in that: Predicate Function is calculated as follows: Among them, x p (t) is the position coordinate of the UAV at time t, The position coordinates of the obstacles when the UAV performs k1 obstacle avoidance tasks, The radius of the obstacle when the UAV performs k1 obstacle avoidance subtasks; and The related 0th-order barrier function The calculation formula is as follows: and The first-order barrier function The calculation formula is as follows: in, for The derivative of .

3. The method for UAV signal temporal logic task motion planning based on sequence decomposition according to claim 1 is characterized in that: Predicate Function The calculation formula is: in, is a predicate function used to characterize the distance between the current position of the UAV and the final target position when executing the k2th access subtask, and t0 is the activation time of the k2th access subtask, x p (t0) is the position coordinate of the UAV at the activation time t0, is the center coordinate of the k2th destination, is the radius of the k2th destination, for The derivative of , which indicates the growth rate of the predicate function; and The related 0th-order barrier function The calculation formula is:

4. The method for UAV signal temporal logic task motion planning based on sequence decomposition according to claim 1 is characterized in that: Predicate Function The calculation formula is: in, is a predicate function used to characterize the distance between the current position of the UAV and the final target position when executing the k2th access subtask, and t0 is the activation time of the k2th access subtask, x p (t0) is the position coordinate of the UAV at the activation time t0, is the center coordinate of the k2th destination, is the radius of the k2th destination, for The derivative of , which indicates the growth rate of the predicate function; and The related 0th-order barrier function The calculation formula is:

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