An unmanned aerial vehicle pose coupling path planning method based on dual quaternions
By using dual quaternions to uniformly represent the pose of the UAV and map it to the motion vector space, the problem of position and attitude coupling optimization of the UAV in complex environments is solved, and efficient and stable path planning is achieved.
Patent Information
- Application Number
- CN202610481289.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-04-13
- Publication Date
- 2026-07-10
AI Technical Summary
Existing UAV path planning methods suffer from high computational cost and poor path smoothness in complex 3D environments, and are difficult to effectively couple position and attitude information, resulting in insufficient flight feasibility and stability.
Dual quaternions are used to represent the spatial position and attitude of the UAV in a unified manner, a pose model is constructed, and the optimization problem is mapped to the motion vector space through motion operators. An objective function is established and iteratively solved to generate a path that satisfies the flight constraints.
It achieves unified modeling and collaborative optimization of UAV position and attitude, reduces computational complexity and time, improves the stability and efficiency of path planning, and significantly enhances path planning performance.
Smart Images
Figure CN122360474A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of UAV path planning, and in particular to a UAV pose-coupled path planning method based on dual quaternions. Background Technology
[0002] With the rapid development of drone technology, it has been widely used in logistics, environmental monitoring, disaster relief, and other fields. In these applications, drones need to fly safely and efficiently from their starting position to their target position in complex three-dimensional environments, which places high demands on autonomous path planning technology.
[0003] Currently, various methods have been proposed for the path planning problem of unmanned aerial vehicles (UAVs). Traditional methods, such as graph search algorithms like A* and Dijkstra, can search for feasible paths in discrete space, but suffer from problems such as high computational cost and poor path smoothness in complex 3D environments. Intelligent optimization algorithms, such as particle swarm optimization and genetic algorithms, while possessing global search capabilities, suffer from slow convergence and susceptibility to local optima in high-dimensional complex environments.
[0004] More importantly, the flight of a UAV is a six-degree-of-freedom motion process involving position and attitude, but many existing methods mainly focus on spatial position trajectory while ignoring or simplifying the impact of attitude changes. Some methods separate position planning and attitude planning, which makes it difficult to effectively describe the coupling relationship between the two, resulting in the planned path potentially not matching the actual flight dynamics, affecting the feasibility and stability of the flight.
[0005] In terms of pose representation, traditional methods such as Euler angles suffer from gimbal-locked singularities; rotation matrices have many parameters and are computationally complex; while quaternions can avoid singularities, they can only describe rotations and cannot uniformly represent translation information. Although dual quaternions, as a mathematical tool that can simultaneously and compactly represent rotations and translations, have been studied in robotics, directly applying dual quaternions for pose coupling optimization in the field of UAV path planning still faces challenges. Because dual quaternions themselves must satisfy unit constraints and orthogonality constraints, the optimization model built upon them becomes a high-dimensional, nonlinear optimization problem with complex constraints, which is difficult to solve and has low computational efficiency, limiting its practical application.
[0006] Therefore, there is an urgent need for a new path planning method that can effectively couple the position and attitude information of UAVs within a unified framework and solve the resulting high-dimensional constraint optimization problem, thereby generating safe, smooth flight paths that conform to the dynamic characteristics of UAVs in complex environments. Summary of the Invention
[0007] The purpose of this invention is to provide a UAV pose-coupled path planning method based on dual quaternions. By uniformly modeling the spatial motion state of the UAV, the position and attitude of the UAV can be expressed under the same mathematical framework. The position and attitude are optimized simultaneously during the path planning process, thereby obtaining a UAV flight path that meets the flight constraints.
[0008] The technical solution adopted in this invention is:
[0009] A method for UAV pose-coupled path planning based on dual quaternions includes the following steps:
[0010] Dual quaternions are used to uniformly represent the spatial position and attitude of the UAV, and a pose model of the UAV in three-dimensional space is constructed.
[0011] The flight path of the UAV is discretized into a sequence of path nodes consisting of multiple path nodes, and the pose of each path node is parameterized as a motion vector.
[0012] A dual quaternion optimization model is established based on the pose model and the path node sequence. The objective function of the optimization model includes path smoothing term, obstacle avoidance term and flight dynamics constraint term.
[0013] By using the predefined motion operator M and the identity dual quaternion operator The dual quaternion optimization model in the dual quaternion space is equivalently mapped to the motion optimization model in the motion vector space; wherein, the motion operator M is used to map the dual quaternions one by one to the motion vectors, and the unit dual quaternion operator... This is used to map motion vectors to dual quaternions, and satisfies that for any motion vector x, we have , Represent the set of unit dual quaternions;
[0014] The motion optimization model is iteratively solved in the motion vector space, and the motion vectors of the path node sequence are updated to obtain the optimal path node sequence that satisfies all flight constraints.
[0015] The optimal path node sequence is smoothed to generate a continuous executable flight trajectory for the UAV from the initial pose to the target pose.
[0016] Furthermore, the expression for the dual quaternion is:
[0017] (1);
[0018] in, It is a dual quaternion; A quaternion representing the real part of rotation information; The dual part representing translation information; ε is the dual unit, satisfying .
[0019] Furthermore, the path node sequence of a single drone The expression:
[0020] (2);
[0021] in, The i-th path node represents the UAV pose; N represents the number of path nodes.
[0022] For scenarios involving collaborative tasks involving multiple drones, the pose sequence of the multiple drones is represented as follows:
[0023] (13);
[0024] in, This represents the pose of the UAV corresponding to the i-th path node of the k-th UAV; k represents the UAV number.
[0025] Furthermore, the number of path nodes is adjusted based on the path curvature or environmental complexity, using the following formula:
[0026] (12);
[0027] in, Number of basic path nodes; As an indicator of environmental complexity; This is the adjustment coefficient.
[0028] Furthermore, the objective function Represented as:
[0029] ,
[0030] in, For path smoothing, For obstacle avoidance, For flight dynamics constraints, , , These are the weighting coefficients for each sub-item.
[0031] Furthermore, the weighting coefficients are dynamically adjusted based on obstacle density during the path planning process:
[0032] (11);
[0033] in, represents the dynamic weight parameter of the i-th sub-item of the objective function. The number of sub-items in the objective function.
[0034] Specifically, in one implementation, K is set to 3. When there are many obstacles in the environment, the obstacle avoidance weight ω2 is increased; when the environment is relatively open, the smoothness weight ω1 is increased to obtain a smoother path.
[0035] Furthermore, the flight constraints include altitude constraints, attitude change constraints, and obstacle avoidance constraints;
[0036] The altitude constraint is to ensure that the drone's flight altitude satisfies the following expression:
[0037] (8);
[0038] in, This represents the flight altitude of the i-th path node; and These represent the minimum and maximum permitted flight altitudes, respectively.
[0039] To ensure the flight stability of the UAV, the attitude change constraint term should satisfy the following: The attitude change between adjacent path nodes should meet the following requirements.
[0040] (9);
[0041] in, Indicates the maximum permissible range of attitude changes;
[0042] Obstacle avoidance constraints are designed to ensure that the UAV's path nodes maintain a safe distance from obstacles in the environment during path planning.
[0043] (10);
[0044] in, Indicates the distance from the path node to the obstacle; This is the safe distance threshold.
[0045] Furthermore, for multi-drone collaborative mission scenarios, the objective function of the dual quaternion optimization model is... Furthermore, collision avoidance constraints between drones are included. To prevent collisions between drones, a safe distance constraint is added to the path optimization model as follows:
[0046] (14);
[0047] in, This indicates the position of the k-th drone at the i-th path node; This indicates the position of the j-th drone at the i-th path node; This refers to the minimum safe distance between drones.
[0048] Furthermore, the expression for the motion vector is:
[0049] (3);
[0050] in, Represents the rotation vector. Represents the translation vector;
[0051] Motion Operator The expression is:
[0052] (4);
[0053] (5);
[0054] in, For the unit dual quaternion space; Let it be the motion vector space; This represents the rotation vector extracted from the unit quaternion. This represents the translation vector extracted from the dual quaternion.
[0055] Unit dual quaternion operator The expression is:
[0056] (6);
[0057] (7);
[0058] in, Represented by motion vectors The unit dual quaternion generated by the mapping, For mappings that generate unit quaternions from rotation vectors, This is the pure quaternion form corresponding to the translation vector. Denotes the dual unit, used to distinguish between the real and dual parts in a dual quaternion, satisfying and .
[0059] Furthermore, the optimal path node sequence is smoothed using cubic spline interpolation, fifth-order polynomial curve fitting, or Bezier curve fitting methods.
[0060] Furthermore, the method of the present invention also includes: sensing environmental changes in real time during the flight of the UAV along the planned trajectory; when the detected environmental changes exceed a predetermined threshold, using the current pose of the UAV as a new starting point, and replanning the remaining unflighted path locally.
[0061] The present invention adopts the above technical solutions and has the following beneficial effects compared with the prior art: (1) By introducing dual quaternions, the UAV path planning problem is transformed from position trajectory optimization to pose coupling optimization problem, realizing unified modeling and collaborative optimization of position and attitude, and changing the problem structure from the optimization variable level. (2) In view of the problem that dual quaternions have unit constraints and algebraic constraints that lead to high optimization complexity, the present invention introduces motion operators to map the optimization problem in the dual quaternion space to the motion vector space, thereby reducing the difficulty of solving and improving the optimization efficiency. This processing method is not a conventional technical means in the existing path planning method. (3) In terms of path representation, the present invention represents the UAV path as a pose sequence and performs overall optimization on the pose sequence, so that the relationship between position and attitude changes can be simultaneously constrained during the path generation process, avoiding the incoordination problem caused by the separation of path and attitude processing in the prior art. (4) The present invention introduces motion operator M and unit dual quaternion operator. This method transforms the original dual quaternion optimization problem into an unconstrained optimization problem in the motion vector space. Simultaneously, it reduces the 8-dimensional variables represented by dual quaternions to 6-dimensional motion vector variables, effectively reducing the scale of optimization variables and improving computational efficiency. It avoids the handling of unit and orthogonal constraints in dual quaternions, reducing the computational complexity caused by constraint optimization. Compared to the traditional two-stage dual quaternion optimization method, this mapping allows rotation and translation to be optimized simultaneously in a unified model, thus avoiding error propagation problems. After this mapping, the stability of the optimization model is improved by over 90%, and the computation time is reduced by more than 20%, significantly improving path planning performance. Attached Figure Description
[0062] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments;
[0063] Figure 1 This is a schematic diagram of the structure of a UAV pose-coupled path planning method based on dual quaternions according to the present invention.
[0064] Figure 2 This is a schematic diagram of the path nodes and pose of the UAV of the present invention;
[0065] Figure 3 This is a schematic diagram of the UAV path planning task of the present invention;
[0066] Figure 4 This is a schematic diagram of the UAV path planning results of the present invention. Detailed Implementation
[0067] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings.
[0068] like Figures 1 to 4 As shown in any of the accompanying figures, this invention discloses a UAV pose-coupled path planning method based on dual quaternions. By uniformly modeling the UAV's spatial motion state, the UAV's position and attitude are expressed within the same mathematical framework. Furthermore, position and attitude are simultaneously optimized during path planning, thereby obtaining a UAV flight path that satisfies flight constraints. The method includes the following steps:
[0069] (1) Dual quaternions are used to uniformly represent the spatial position and attitude of the UAV, and a pose model of the UAV in three-dimensional space is constructed. In this embodiment, in order to simultaneously describe the spatial position and attitude information of the UAV, dual quaternions are used to uniformly represent the pose of the UAV. Dual quaternions can describe rotation and translation in rigid body motion within the same mathematical framework. The expression of dual quaternions is:
[0070] (1);
[0071] in, It is a dual quaternion; A quaternion representing the real part of rotation information; The dual part representing translation information; ε is the dual unit, satisfying Using the above expression method, the attitude information and spatial position of the UAV can be uniformly represented as dual quaternions, thereby realizing coupled modeling of UAV pose.
[0072] In this embodiment, the UAV flight environment is represented as a three-dimensional spatial environment model, and an initial pose and a target pose are set within this environment. The UAV's initial pose is represented as... The pose of the UAV target is represented as .like Figure 3 As shown, the path planning task is to determine the path from the initial pose while satisfying environmental constraints. Planning to target pose A feasible pose path.
[0073] (2) Discretize the flight path of the UAV into a sequence of path nodes consisting of multiple path nodes, and parameterize the pose of each path node as a motion vector; that is, in the process of path planning, the flight trajectory of the UAV can be represented as a set of continuous pose sequences.
[0074] Specifically, the path node sequence of a single drone The expression:
[0075] (2);
[0076] in, The i-th path node represents the UAV pose; N represents the number of path nodes.
[0077] like Figure 2 As shown, each path node contains not only the UAV's spatial position but also its attitude information, thus providing a complete description of the UAV's motion state during flight. Using this pose sequence representation, the UAV path planning problem can be transformed into an optimization problem of the pose sequence.
[0078] Furthermore, in another embodiment, the present invention can be extended to multi-drone collaborative mission scenarios. In this embodiment, for multi-drone collaborative mission scenarios, the pose sequence of the multiple drones is represented as follows:
[0079] (13);
[0080] in, This represents the pose of the UAV corresponding to the i-th path node of the k-th UAV; k represents the UAV number.
[0081] As a feasible implementation, in the basic implementation, the UAV path is discretely represented by a fixed number of path nodes N. In another implementation, the number of path nodes can be dynamically adjusted according to the complexity of the environment. For example, when there are many obstacles in the UAV's flight area, the number of path nodes can be increased to improve path planning accuracy; in areas with simpler environments, the number of path nodes can be reduced to decrease computational complexity. The aforementioned number of path nodes is adjusted according to the path curvature or environmental complexity, and the specific adjustment formula is as follows:
[0082] (12);
[0083] in, Number of basic path nodes; As an indicator of environmental complexity; This is the adjustment coefficient.
[0084] (3) A dual quaternion optimization model is established based on the pose model and the path node sequence. The objective function of the optimization model includes a path smoothing term, an obstacle avoidance term, and a flight dynamics constraint term. Represented as:
[0085] ,
[0086] in, For path smoothing, For obstacle avoidance, For flight dynamics constraints, , , These are the weighting coefficients for each sub-item.
[0087] In the basic implementation, the path optimization model uses fixed weight coefficients ω1, ω2, and ω3 to balance path smoothness, obstacle avoidance performance, and dynamic constraints. In another implementation, the weight coefficients are dynamically adjusted based on obstacle density during path planning.
[0088] (11);
[0089] in, represents the dynamic weight parameter of the i-th sub-item of the objective function. The number of sub-items in the objective function.
[0090] Specifically, in one implementation, K is set to 3. When there are many obstacles in the environment, the obstacle avoidance weight ω2 is increased; when the environment is relatively open, the smoothness weight ω1 is increased to obtain a smoother path.
[0091] (4) Through the predefined motion operator M and the identity dual quaternion operator The dual quaternion optimization model in the dual quaternion space is equivalently mapped to the motion optimization model in the motion vector space; wherein, the motion operator M is used to map the dual quaternions one by one to the motion vectors, and the unit dual quaternion operator... This is used to map motion vectors to dual quaternions, and satisfies that for any motion vector x, we have , Represent the set of unit dual quaternions;
[0092] Furthermore, in this embodiment, in order to reduce the constraint complexity in the dual quaternion optimization model and achieve an effective solution to the UAV pose optimization problem, a motion operator and a unit dual quaternion operator are introduced to establish the mapping relationship between the dual quaternion space and the motion vector space.
[0093] The expression for the motion vector is:
[0094] (3);
[0095] in, Represents the rotation vector. Represents the translation vector;
[0096] Motion Operator The expression is:
[0097] (4);
[0098] (5);
[0099] in, For the unit dual quaternion space, Let it be the motion vector space; This represents the rotation vector extracted from the unit quaternion. This represents the translation vector extracted from the dual quaternion.
[0100] Unit dual quaternion operator The expression is:
[0101] (6);
[0102] (7);
[0103] in, Represented by motion vectors The unit dual quaternion generated by the mapping, For mappings that generate unit quaternions from rotation vectors, This is the pure quaternion form corresponding to the translation vector. Denotes the dual unit, used to distinguish between the real and dual parts in a dual quaternion, satisfying and .
[0104] The above motion operators Unit dual quaternion operator Under certain conditions, a bijective relation is formed, thereby establishing an equivalent mapping relationship between the motion vector space and the identity dual quaternion space. During model transformation, the motion operator... The unit dual quaternion operator is used to establish a one-to-one correspondence between the dual quaternion space and the motion vector space, so as to realize the transformation of the optimization variable space.
[0105] (5) Iteratively solve the motion optimization model in the motion vector space and update the motion vector of the path node sequence to obtain the optimal path node sequence that satisfies all flight constraints.
[0106] Furthermore, the flight constraints mentioned above include altitude constraints, attitude change constraints, and obstacle avoidance constraints;
[0107] The altitude constraint is to ensure that the drone's flight altitude satisfies the following expression:
[0108] (8);
[0109] in, This represents the flight altitude of the i-th path node; and These represent the minimum and maximum permitted flight altitudes, respectively.
[0110] To ensure the flight stability of the UAV, the attitude change constraint term should satisfy the following: The attitude change between adjacent path nodes should meet the following requirements.
[0111] (9);
[0112] in, Indicates the maximum permissible range of attitude changes;
[0113] Obstacle avoidance constraints are designed to ensure that the UAV's path nodes maintain a safe distance from obstacles in the environment during path planning.
[0114] (10);
[0115] in, Indicates the distance from the path node to the obstacle; This is the safe distance threshold.
[0116] Based on the above constraints, the path node sequence of the UAV is... Iterative updates are performed. In each iteration, the current path is evaluated, and the poses of the path nodes are adjusted to gradually converge the path towards a feasible solution. For example... Figure 4 As shown, the final generated path can simultaneously satisfy: flight safety constraints, pose continuity requirements, and environmental obstacle avoidance requirements.
[0117] Furthermore, for multi-drone collaborative mission scenarios, the objective function of the dual quaternion optimization model is... Furthermore, collision avoidance constraints between drones are included. To prevent collisions between drones, a safe distance constraint is added to the path optimization model as follows:
[0118] (14);
[0119] in, This indicates the position of the k-th drone at the i-th path node; This indicates the position of the j-th drone at the i-th path node; This refers to the minimum safe distance between drones.
[0120] Furthermore, the method of the present invention also includes: sensing environmental changes in real time during the flight of the UAV along the planned trajectory; when the detected environmental changes exceed a predetermined threshold, using the current pose of the UAV as a new starting point, and replanning the remaining unflighted path locally.
[0121] In another embodiment, this technical solution can also be applied to dynamic environment path planning problems. When new obstacles appear in the environment or the position of obstacles changes, the current UAV pose can be used to determine the path planning method. Perform local replanning on the remaining path. Let the current path node be... Then for the remaining path sequence:
[0122] (15);
[0123] The path optimization process is re-executed to generate new feasible paths.
[0124] (6) Perform trajectory smoothing on the optimal path node sequence to generate a continuous executable flight trajectory for the UAV from the initial pose to the target pose. Further, as a feasible implementation, cubic spline interpolation, fifth-order polynomial curve fitting, or Bézier curve fitting methods are used to smooth the trajectory of the optimal path node sequence. For example, the Bézier curve form is:
[0125] (16);
[0126] in, For control points; By fitting path nodes with Bezier curves, the path curvature variation can be further reduced, making the drone's flight trajectory smoother.
[0127] The present invention adopts the above technical solutions and has the following beneficial effects compared with the prior art: (1) By introducing dual quaternions, the UAV path planning problem is transformed from position trajectory optimization to pose coupling optimization problem, realizing unified modeling and collaborative optimization of position and attitude, and changing the problem structure from the optimization variable level. (2) In view of the problem that dual quaternions have unit constraints and algebraic constraints that lead to high optimization complexity, the present invention introduces motion operators to map the optimization problem in the dual quaternion space to the motion vector space, thereby reducing the difficulty of solving and improving the optimization efficiency. This processing method is not a conventional technical means in the existing path planning method. (3) In terms of path representation, the present invention represents the UAV path as a pose sequence and performs overall optimization on the pose sequence, so that the relationship between position and attitude changes can be simultaneously constrained during the path generation process, avoiding the incoordination problem caused by the separation of path and attitude processing in the prior art. (4) The present invention introduces motion operator M and unit dual quaternion operator. This method transforms the original dual quaternion optimization problem into an unconstrained optimization problem in the motion vector space. Simultaneously, it reduces the 8-dimensional variables represented by dual quaternions to 6-dimensional motion vector variables, effectively reducing the scale of optimization variables and improving computational efficiency. It avoids the handling of unit and orthogonal constraints in dual quaternions, reducing the computational complexity caused by constraint optimization. Compared to the traditional two-stage dual quaternion optimization method, this mapping allows rotation and translation to be optimized simultaneously in a unified model, thus avoiding error propagation problems. After this mapping, the stability of the optimization model is improved by over 90%, and the computation time is reduced by more than 20%, significantly improving path planning performance.
[0128] Obviously, the described embodiments are only a part of the embodiments of this application, not all of them. Without conflict, the embodiments and features in the embodiments of this application can be combined with each other. The components of the embodiments of this application described and illustrated herein can generally be arranged and designed in various different configurations. Therefore, the detailed description of the embodiments of this application is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.
Claims
1. A method for UAV pose-coupled path planning based on dual quaternions, characterized in that, Includes the following steps: Dual quaternions are used to uniformly represent the spatial position and attitude of the UAV, and a pose model of the UAV in three-dimensional space is constructed. The flight path of the UAV is discretized into a sequence of path nodes consisting of multiple path nodes, and the pose of each path node is parameterized as a motion vector. A dual quaternion optimization model is established based on the pose model and the path node sequence. The objective function of the optimization model includes path smoothing term, obstacle avoidance term and flight dynamics constraint term. By using the predefined motion operator M and the identity dual quaternion operator The dual quaternion optimization model in the dual quaternion space is equivalently mapped to the motion optimization model in the motion vector space; wherein, the motion operator M is used to map the dual quaternions one by one to the motion vectors, and the unit dual quaternion operator... Used to map motion vectors to dual quaternions; The motion optimization model is iteratively solved in the motion vector space, and the motion vectors of the path node sequence are updated to obtain the optimal path node sequence that satisfies all flight constraints. The optimal path node sequence is smoothed to generate a continuous executable flight trajectory for the UAV from the initial pose to the target pose.
2. The method for UAV pose coupling path planning based on dual quaternions according to claim 1, characterized in that, The expression for dual quaternions is: (1)； in, It is a dual quaternion; A quaternion representing the real part of rotation information; The dual part representing translation information; ε is the dual unit, satisfying .
3. The method for UAV pose coupling path planning based on dual quaternions according to claim 1, characterized in that, Path node sequence of a single drone The expression: (2)； in, This represents the UAV pose corresponding to the i-th path node; N represents the number of path nodes. For scenarios involving collaborative tasks involving multiple drones, the pose sequence of the multiple drones is represented as follows: (13)； in, This represents the pose of the UAV corresponding to the i-th path node of the k-th UAV; k represents the UAV number.
4. A method for UAV pose-coupled path planning based on dual quaternions according to claim 1 or 3, characterized in that, The number of path nodes N is adjusted based on the path curvature or environmental complexity, using the following formula: (12)； in, Number of basic path nodes; As an indicator of environmental complexity; This is the adjustment coefficient.
5. The method for UAV pose coupling path planning based on dual quaternions according to claim 1, characterized in that, objective function Represented as: ， in, For path smoothing, For obstacle avoidance, For flight dynamics constraints, , , These are the weighting coefficients for each sub-item.
6. The method for UAV pose coupling path planning based on dual quaternions according to claim 5, characterized in that, During path planning, the weighting coefficients are dynamically adjusted based on obstacle density. (11)； in, represents the dynamic weight parameter of the i-th sub-item of the objective function. The number of sub-items in the objective function.
7. The method for UAV pose coupling path planning based on dual quaternions according to claim 1, characterized in that, Flight constraints include altitude constraints, attitude change constraints, and obstacle avoidance constraints; The altitude constraint is to ensure that the drone's flight altitude satisfies the following expression: (8)； in, This represents the flight altitude of the i-th path node; and These represent the minimum and maximum permitted flight altitudes, respectively. The attitude change constraint is to ensure that the attitude changes between adjacent path nodes satisfy the following expression: (9)； in, Indicates the maximum permissible range of attitude changes; The obstacle avoidance constraint is to ensure that the safe distance between the UAV path nodes and obstacles in the environment during the path planning process satisfies the following expression: (10)； in, Indicates the distance from the path node to the obstacle; This is the safe distance threshold.
8. The method for UAV pose coupling path planning based on dual quaternions according to claim 7, characterized in that, For multi-drone collaborative mission scenarios, the objective function of the dual quaternion optimization model is... Further including collision avoidance constraints between drones, the safe distance constraint for collision avoidance constraints between drones is: (14)； in, This indicates the position of the k-th drone at the i-th path node; This indicates the position of the j-th drone at the i-th path node; This refers to the minimum safe distance between drones.
9. The method for UAV pose coupling path planning based on dual quaternions according to claim 1, characterized in that, The expression for the motion vector is: (3)； in, Represents the rotation vector. Represents the translation vector; Motion Operator The expression is: (4)； (5)； in, For the unit dual quaternion space; Let it be the motion vector space; This represents the rotation vector extracted from the unit quaternion. This represents the translation vector extracted from the dual quaternion; Unit dual quaternion operator The expression is: (6)； (7)； in, Represented by motion vectors The unit dual quaternion generated by the mapping, For mappings that generate unit quaternions from rotation vectors, This is the pure quaternion form corresponding to the translation vector. Denotes the dual unit, used to distinguish between the real and dual parts in a dual quaternion, satisfying and .
10. The method for UAV pose-coupled path planning based on dual quaternions according to claim 1, characterized in that, The method also includes: sensing environmental changes in real time during the flight of the UAV along the planned trajectory; when the detected environmental changes exceed a predetermined threshold, the remaining unflighted paths are replanned locally, with the current pose of the UAV as the new starting point.