55 results about "Lie algebra" patented technology

The invention discloses a low-overlapping-rate point cloud registration method based on topology-metric decoupling, and belongs to the technical field of computer vision and three-dimensional reconstruction, and the method comprises the steps: scanning an object through a three-dimensional laser scanning collection terminal, collecting point clouds at two different angles as a source point cloud and a target point cloud, and achieving high-robustness registration in a difficult scene with an extremely low overlapping rate; according to the method, through the asymmetric association strategy, the zero solution problem under the low overlapping rate is solved through the one-way matching union set, and the recall rate is remarkably increased; meanwhile, through a DGTG geometric pruning and probability manifold optimization mechanism, a voxel quantization error is eliminated by using anisotropic covariance and Lie algebra iteration, a translation error and a rotation error are greatly reduced, and a precision bottleneck caused by voxelization is effectively broken through. According to the method, the existence of a solution can be ensured under the condition that the overlapping rate is extremely low, voxel quantization errors can be eliminated through manifold optimization based on covariance, and high-precision and high-efficiency registration of low-overlapping-rate point clouds is achieved.

The invention discloses a robot fruit grabbing method based on a multi-mode time sequence collaborative prediction algorithm, and aims to solve the problems that the short-time future trajectory is difficult to accurately predict and the grabbing opportunity is difficult to determine due to fruit and branch swinging caused by wind, branch elasticity and platform advancing. According to the method, a multi-modal time sequence is unified through micro-time alignment, uncertainty is quantified, a three-dimensional special Euclidean group and other variable graph converters are constructed, a spiral shaft constraint projection layer is arranged on the edge between the fruit and a fruit stem, and conditional diffusion short-time trajectory prediction of plum algebra parameterization and uncertainty gating triggering are combined; motion planning and closed-loop control of time delay compensation and collision avoidance constraint are executed in a linkage mode, and the technical effects of high-precision short-time three-dimensional pose prediction, grabbing opportunity self-adaptive triggering and high-success-rate stable grabbing are achieved.

The invention relates to the technical field of computer vision, and discloses a precise medicine delivery method and system, and the method effectively strips illumination artifacts through the construction of a local gradient structure tensor field and an anisotropic screening mechanism, remarkably improves the robustness of a visual front end in a light and dark alternating environment, and improves the accuracy of medicine delivery. Rigid body motion constraint and Lie algebra continuous modeling are utilized, high-precision space-time alignment between heterogeneous sensors is realized on the premise that scene depth does not need to be recovered, hardware delay errors are eliminated, a physical-driven probability weight dynamic allocation mechanism is constructed by introducing a multipath scattering index and a structural information entropy flux, and a dynamic space-time alignment algorithm is established. Environment degradation is sensed in real time, the observation weight is adjusted in a self-adaptive mode, the influence of the non-line-of-sight multipath effect and visual texture missing is effectively restrained, high-precision inertial dead reckoning can still be maintained in a blind area where a sensor is in full failure in combination with momentum prior information generated through Schel complement marginalization operation, and the method has the advantages of being high in precision and high in precision. And the navigation continuity and reliability of the distribution robot in a complex scene are ensured.

The invention discloses a modal modeling method for a tendon-driven continuum robot. The method comprises the following steps: carrying out differential modeling on a configuration under a SE (3) Lie group-se (3) Lie algebra framework; the strain field is subjected to spectrum parameterization and is decomposed into active / passive orthogonal subspaces, and an inner product adopts energy weighted Hilbert measurement containing material and section parameters. The active mode is constructed by a linear continuous Jacobian of a tendon path; legendre polynomial expansion is adopted under the collinear layout, and complex Fourier harmonic expansion is adopted under the non-collinear layout; the passive mode is selected according to a spectrum slot position mutual exclusion principle so as to ensure that the passive mode is orthogonal to the active mode in energy and suppress spectrum leakage. Lie group integration and spectral integration are adopted for numerical value realization; newton-Rafson iteration is used in the quasi-static state, and generalized-alpha time integration or Newmark-beta integration is used in the dynamics. The method has high precision and robustness under nonlinear large deformation and multi-tendon coupling conditions, and is suitable for scenes such as software operation, minimally invasive intervention and precise detection.

The invention discloses a data processing method and system based on Lie algebraic dynamics and an entropy modulation mechanism, and relates to the technical field of artificial intelligence and data processing, and the method comprises the steps: constructing a group action operator on a physical manifold, and carrying out the manifold enhancement of input data; the Hilbert subspace decomposition and decoupling of the feature channel are completed in parallel through a learnable decorrelation kernel and tensor contraction operation by using a matrix parallel elastic orbit layer; mapping the features to a symplectic geometric phase space, and introducing an adaptive symplectic respiration operator and a Hamiltonian kinetic equation to carry out physical conservation evolution; constructing a Lie algebra classifier, and determining a data category by calculating a Lie bracket transpose norm of a feature generator and a category base; and guiding model training by using an entropy modulation action quantity loss function containing physical potential energy. The method can solve the problems of poor generalization and weak anti-noise capability of a traditional deep learning model, and can be widely applied to the fields of power equipment monitoring, computer vision, natural language processing and the like.

The invention provides a double-layer safe trainable quantum machine learning method based on polynomial dynamics Lie algebra, and the method comprises the following steps: 1, constructing core variation simulation meeting the constraint of the polynomial dynamics Lie algebra, and guaranteeing the trainability of a model; 2, performing truncated Chebyshev graph coding at an input end, and constructing a rugged loss function landscape by using graph state entanglement and a Chebyshev tower strategy to prevent a snapshot inversion attack; 3, executing dynamic local scrambling at an output end, applying time-varying random local unitary transformation before measurement, and confusing a linear relation between gradient and a snapshot to prevent recovery attack of the snapshot; and 4, measuring and calculating a loss function, and updating parameters. According to the method, an orthogonal decoupling strategy is adopted, a privacy protection mechanism is externally arranged on an input / output interface, and trainability is anchored to core configuration, so that the capability of resisting algebraic attacks is remarkably improved while model convergence is ensured.

The invention discloses an anti-interference multi-label webpage identification method and system under an encrypted traffic condition, and the method comprises the steps: constructing a dynamic association graph through a burst transmission structure of the encrypted traffic, precisely deconstructing aliasing traffic through an entropy weight punishment mechanism and a node aggregation algorithm, and outputting an independent substream sequence; extracting non-stationary time-frequency features for the substreams, fusing the non-stationary time-frequency features with graph topology features extracted based on a graph structure in a tangent space, generating disturbance samples by using an adversarial training environment, adjusting feature weights, and generating composite fingerprints; executing long time sequence modeling on the Lie group manifold by using a Bi-Mama network, reserving a modulation interface, and outputting a preliminary recognition probability; and auditing causal consistency through a webpage loading logic state machine, converting an abnormal state into geodesic line correction in a Lie algebra tangent space, and correcting network parameters on line through a reserved interface. According to the method, the problems that aliasing traffic is difficult to deconstruct, fingerprint robustness is insufficient and an identification result lacks logic consistency constraint are solved.

The invention discloses a dynamic motion primitive coding method and system based on Lie group Lie algebra, and the method comprises the steps: uniformly representing the tail end pose and contact force spinor of a robot in a Lie group form, and constructing a unified mathematical framework; the method comprises the following steps: acquiring a pose and a force spinor sequence through a teaching phase, and converting the force spinor sequence into a virtual pose sequence through scaling mapping; establishing a dynamic motion primitive (DMPs) model based on the Lie group Lie algebra theory, and learning a model weight matrix and a primary function parameter by adopting local weighted regression; and according to the initial and target poses of the new task, generating a smooth trajectory through phase synchronization control and Euler integration, and outputting the smooth trajectory to a robot controller. According to the method, the problems of posture singularity and motion distortion caused by splitting of a posture channel in a traditional DMPs method are solved, the learning fidelity and reproduction stability of the six-degree-of-freedom posture track of the robot are improved, the smoothness and coordination of the whole motion process are guaranteed, and the debugging complexity of a force control system is reduced.

This invention discloses a pose estimation method for industrial parts that integrates neural implicit representation and MGC-SR anti-reflection constraints. The method first acquires RGB-D images and a 3D CAD model of the part to be assembled; it then extracts multimodal features using a pose prediction model based on neural implicit representation and generates an initial 6 DoF pose of the part in the camera coordinate system; it converts the depth image into an observation point cloud using camera intrinsic parameters and performs coarse alignment with the CAD model point cloud in 3D space; it constructs an anti-reflection weighted model (MGC-SR) based on multi-source geometric confidence, and introduces an adaptive weight allocation strategy based on normal consistency and depth confidence to address noise interference in industrial high-reflectivity scenarios. Using Lie group and Lie algebra theory, it iterative fine-tuning minimizes the point cloud registration error in the tangent space, outputting the final high-precision pose. This invention combines the zero-shot generalization of deep learning with the physical accuracy of 3D geometric registration, effectively solving the problems of pose jitter and insufficient accuracy of industrial metal parts in high-reflectivity, low-texture environments, and has high engineering application value.

The application relates to a three-dimensional continuous shape estimation method and system of a flexible robot, wherein the method combines the arc length of the flexible robot and unknown external loads from the environment with a Cosserat elastic rod model and a Cosserat elastic string model to generate a Lie algebra coupled statics model representing a tendon-driven model, models the external loads as Gaussian process noise to construct a prior probability model, obtains a prior probability distribution of the flexible robot in a Lie algebra space, constructs a measurement noise model in the Lie algebra space according to discrete measurement poses captured by a sensor and measurement noise, obtains a predicted measurement value, fuses the prior probability distribution and the predicted measurement value to obtain a posterior shape estimation of the flexible robot, and calculates a continuous three-dimensional shape estimation of the flexible robot and a first credibility of the continuous three-dimensional shape estimation according to the posterior shape estimation and a Gaussian process interpolation method. Therefore, the application realizes accurate perception of the continuous three-dimensional shape of the flexible robot.

The invention discloses a fire source positioning method and system based on combination of thermal imaging and laser ranging, and relates to the field of fire prevention and control. Acquiring a thermal image, an original image and point cloud data of a target area, identifying a fire source candidate area, constructing a cylindrical coordinate system taking one end of a central axis of the fire source candidate area as an original point, and generating a three-dimensional model containing fire source space attitude and obstacle information; adjusting the shooting angle of the thermal imager in combination with the three-dimensional model, and planning a surrounding path containing an effective detection point location; the mobile carrier is controlled to move along the path, and a three-dimensional space constraint matrix is generated; performing Lie algebraic fusion on the thermal imaging signal features and a three-dimensional space constraint matrix in a symplectic geometric space, dynamically adjusting a laser ranging covariance weight through a confrontation recognition model, and mapping the laser ranging covariance weight into a space coordinate of a fire source in a cylindrical coordinate system; and calculating the Riemannian manifold distance between the positioning coordinate and the pre-path data, and when the Riemannian manifold distance exceeds a threshold value, re-sampling the data, updating the model weight and re-positioning. According to the invention, the fire source positioning precision is greatly improved.

The invention discloses a Lie algebra-based variable component subalgorithm layered training method, which comprises the following steps of: optimizing and freezing ZX on a generation element subset G < 1 > = {XX, YY and XY} through a layered activation-freezing training schedule, remarkably relieving a barren plateau, improving trainability, reducing an instantaneous reachable algebra dimension, and increasing gradient variance and optimizing stability; after the switching criterion is met, ZX is introduced and expanded to G2 = {XX, YY, XY, ZX}, and the final expression ability is maintained and recovered; the switching basis is consistent with the dynamic Li algebra structure, and is jointly triggered by gradient statistics and sub-algebra scale indexes, so that the training process is schedulable, explainable and convenient to audit and reproduce.

The application discloses a Lie algebra-based variable quantum algorithm hierarchical training method, through a hierarchical activation-freezing training schedule, first optimization and freezing of ZX on a generating element set G 1 ={XX, YY, XY}, barren plateaus are significantly alleviated and trainability is improved, instantaneous reachable algebraic dimension is reduced, gradient variance is increased and optimization stability is improved; after meeting switching criteria, ZX is introduced to expand to G2={XX, YY, XY, ZX}, and final expression capability is maintained and restored; switching is consistent with dynamic Lie algebra structure, and is jointly triggered by gradient statistics and subalgebra size indexes, so that the training process is schedulable, interpretable, and convenient for auditing and reproduction.

The invention discloses an unmanned aerial vehicle live-action three-dimensional modeling method based on LiDAR assistance, and the method is characterized in that the method comprises the following steps: (1) data collection: employing an IMU + GNSS integrated navigation system to collect the pose data of an unmanned aerial vehicle in real time, carrying out the filtering, intensity value normalization and down-sampling processing of a LiDAR point cloud, and obtaining the pose data of the unmanned aerial vehicle; performing multi-view image feature point extraction and feature point descriptor calculation and matching on the image data; (2) adjusting a conversion matrix through a dynamic weight calculation model; and (3) performing iterative optimization by adopting a nonlinear least square method, converting a registration problem into nonlinear optimization, obtaining an initial conversion matrix from a dynamic weight stage, setting Lie algebra parameterized expression, determining an optimization boundary condition, establishing an iterative optimization process, and gradually and finely adjusting a coordinate conversion relation to enable an overall matching error to be minimum and ensure that a registration error is less than or equal to 0.5 cm. The method has the beneficial effects that the offset of the coordinate system is corrected in real time through the dynamic weight registration algorithm, and the registration error precision is improved by more than three times.

The invention discloses a self-adaptive laser mapping method fusing historical poses and point cloud characteristics, and belongs to the technical field of robot positioning and map construction, and the method comprises the steps: reading point cloud data of a laser radar sensor, and carrying out the preprocessing; modeling the change trend of the obtained historical pose as a Lie algebraic vector field, and constructing a dynamic correction guide field in combination with historical error information; classifying the point cloud into planar points and non-planar points; calculating adaptive weights of different classification points; and respectively establishing point-to-point and point-to-plane residual errors according to point cloud classification, solving the pose of the robot through an adaptive weighted Gauss-Newton optimization method, and updating a local map and a historical pose sequence. According to the method, the historical motion trend and real-time deviation correction are fused, and a geometric feature self-adaptive registration strategy is combined, so that the pose estimation precision and robustness in a complex motion mode and a feature degradation scene are remarkably improved, and an effective solution is provided for reliable navigation of a robot in a GPS denial environment.

The invention relates to a lamp ring-free handle positioning method and system based on Lie group state estimation and dynamic offset calibration, and the method comprises the steps: defining the pose state of a handle based on Lie group SE (3), defining an error state in a corresponding Lie algebra se3 space, and building a system kinetic equation based on error state Kalman filtering; representing a multi-source sensor observation model as an observation function on the Lie group; modeling dynamic offset transformation between the handle and the hand into a time-varying random process, and expanding the state of the time-varying random process into a system state vector for online joint estimation; updating and optimizing the system state vector by using a nonlinear optimization method based on multi-sensor observation to obtain an optimized handle positioning result; the system is implemented based on the method. According to the method, the consistency between the positioning output and the actual physical position of the handle is remarkably improved, the pose jumping phenomenon is effectively eliminated, the immersion and continuity of user experience are improved, and the continuous track which is consistent in time and accurate in space is finally output.

The present application relates to photovoltaic material processing detection technical field, specifically disclose a kind of solar cell panel busbar laser build-up welding defect detection method, comprising: after the pretreatment of busbar laser build-up welding image sample is labeled with defect category, to obtain training set;Extract each covariance matrix in training set to constitute Lie algebra training point set;Lie algebra space point in Lie algebra training point set is clustered in Lie algebra space, and the center point of each category Lie algebra space point is obtained;The Euclidean distance between the Lie algebra test point of the busbar laser build-up welding image to be detected respectively to each category Lie algebra center point is calculated, and the category of the shortest Euclidean distance Lie algebra center point belongs is judged as the category of the busbar laser build-up welding image to be detected.The present application further discloses a kind of solar cell panel busbar laser build-up welding defect detection system.The present application can improve the accuracy and learning efficiency of solar cell panel busbar laser build-up welding defect identification.

The invention belongs to the field of robot motion control and trajectory planning, and particularly relates to a quaternion limited trajectory online re-planning method based on a Lie algebra space, which comprises the following steps of: mapping a current quaternion attitude read by an attitude sensor in real time to the Lie algebra space to obtain rotation vector representation; a trajectory planner is adopted and based on a preset kinematics constraint set, a trajectory with continuous time is planned; target attitude update is monitored in real time, and when a new target quaternion attitude is received, online re-planning is carried out based on a current track state so as to ensure the continuity of the attitude, the angular velocity and the angular acceleration at a switching point; restoring the planned trajectory into a quaternion form through inverse mapping; and performing normalization processing on the recovered quaternion, outputting a quaternion trajectory with continuous time and satisfactory constraint to a trajectory actuator, and ending the current planning cycle. The constraint of the preset maximum angular velocity, angular acceleration and jerk is met in the whole process, and overrun and sudden change are avoided.

This invention proposes a Lie group-based hand-eye calibration method based on optimal transmission theory, comprising the following steps: S1, after the robotic arm performs multiple non-coplanar pose transformations, synchronously acquire the pose data of the actuator end effector and the camera after each pose transformation; S2, map the rotation matrix in the acquired pose data to the Lie algebra space to construct discrete probability distributions of the two sets of pose data; S3, calculate the weights of the pose data based on optimal transmission theory according to the discrete probability distributions of the two sets of pose data; S4, solve the rotation and translation matrices in the hand-eye calibration matrix using weighted averages to obtain the hand-eye calibration matrix. This invention utilizes optimal transmission theory to achieve global consistency optimization of calibration parameters, overcoming the limitations of local optimization in traditional least squares methods, ensuring that the solution results of the rotation matrix and translation vector are not affected by abnormal initial values, maintaining extremely high calibration accuracy even under complex motion trajectories, and completely avoiding systematic failures caused by error accumulation.

The invention relates to the field of music artificial intelligence, and discloses an intelligent music generation algorithm dynamically adapting to environment emotions, which comprises the following steps: acquiring emotional state information of a user in a current environment, and constructing an emotional state function changing along with time for describing an emotional change trend of the user in continuous time; inputting the emotional state function into a pre-trained emotional mapping model to obtain a corresponding music control vector sequence, the control vector sequence being defined in a Lie algebra space of music control parameters; the invention also discloses an intelligent music generation system dynamically adapting to the environmental emotion. The system comprises an emotion recognition module; an emotion mapping module; a track embedding module; a music generation module; and a feedback control module. According to the method, the Lie group trajectory modeling and user emotion feedback fine tuning mechanism is introduced, so that the structural continuity of melody generation and dynamic self-adaption of emotion response are realized.

The application provides a Bessel curve posture interpolation trajectory optimization method, system and computer device, a mapping relationship between a posture trajectory in a Cartesian space and a Lie algebra space tangent vector is established, a Bessel curve interpolation trajectory in the Lie algebra space is constructed, and based on a curvature radius change model and a speed change model of the Bessel curve interpolation trajectory, the smoothness and stability of a multi-section posture interpolation trajectory when a rotation axis changes are improved. Furthermore, based on a Jacobian matrix mapping of a mechanical arm joint space and the Cartesian space, a joint space speed constraint is added, and a joint space maximum angular velocity constraint problem of the mechanical arm is considered to further constrain the Cartesian space speed, bidirectional feedback of the joint space and the Cartesian space is realized, the stability of each joint motion of the mechanical arm is improved, the speed curve of each joint of the mechanical arm is continuous, and the precision of the mechanical arm trajectory tracking is improved.

The invention discloses a class-level object grabbing method based on an equivariant grabbing pose field. The method solves the problems that an existing method is low in reasoning speed, poor in pose generalization and the like. The invention provides an equivariant grabbing pose field which comprises four parts. Firstly, a grabbing pose field is constructed, object shape point cloud serves as a condition, class-level shape features are extracted through a neural network, and mapping from any input pose to an object feasible grabbing pose is learned. Secondly, training a grabbing pose field, quantifying a grabbing pose data set of an object by using L1 norm loss, and supervising the difference between a predicted pose and a grabbing pose true value; then, on the basis of reasoning of a grabbing pose field, grabbing pose prediction is used as guidance for updating a grabbing pose estimated value, and interpolation is carried out in the Lie algebra space; and finally, constructing a grabbing pose field to be equal, so that the network can be generalized to any object pose through the property of the construction instead of data enhancement.

This application discloses a digital predistortion calculation method, apparatus, storage medium, and electronic device. The digital predistortion calculation method includes: acquiring the input signal and corresponding output signal of a power amplifier; determining the nonlinear distortion characteristics of the power amplifier in the amplitude and phase domains based on the input and output signals to identify symmetry breaking modes characterizing the nonlinear distortion characteristics; mapping the symmetry breaking modes to a Lie algebra space, and analyzing the distortion mechanism constituting the symmetry breaking modes based on the Lie algebra space to obtain Lie algebra elements; performing exponential mapping operations on the Lie algebra elements to generate the corresponding symmetry recovery transform function; constructing a performance manifold based on the physical constraints and linearization performance indicators of the power amplifier, and geometrically optimizing the parameters of the symmetry recovery transform function on the performance manifold to generate the target predistortion signal.

The invention discloses a robot track closed-loop detection and pose smoothing method, device and equipment and a medium, and belongs to the field of robot control, and the method comprises the steps: converting a first pose sequence track column in a robot action process into a first Cartesian position vector sequence and a first special orthogonal group rotation matrix sequence; determining a closed-loop region index interval according to the first Cartesian position vector sequence through principal component dimensionality reduction projection; converting the first special orthogonal group rotation matrix sequence into a linear first Lie algebra vector sequence, and performing window average smoothing processing on the first Cartesian position vector sequence and the first Lie algebra vector sequence; the smoothed first Lie algebra vector sequence is restored to the rotation matrix through exponential mapping; and combining the smoothed first Cartesian position vector sequence and the smoothed and reduced first Lie algebra vector sequence to obtain a smoothed second pose trajectory sequence. According to the invention, attitude loss during attitude turning processing can be avoided.

The application provides a kind of metal material defect density measurement method, it is related to the technical field of metal material defect density quantitative analysis regulation material performance.This method includes six steps of establishing original data set, preprocessing original data, judging grain boundary existence, calculating elastic distortion tensor, calculating dislocation density and calculating dislocation density.Compared with the traditional microdefect organization analysis method, this method first introduces Lie algebra mathematical tool to quantitatively analyze the rotation characteristics and structure of dislocation such as Frank vector, breaks through the existing material defect density measurement method and the difficulty in accurately describing and calculating the rotation vector, proposes a differential calculation method for the rotation vector, and quantifies the microdefects such as dislocation and dislocation by combining the EBSD data of the metal material to be measured, which provides an important reference for analyzing the influence of crystal defects such as dislocation on material performance.

The present disclosure relates to the technical field of two-wheeled vehicle systems, and particularly relates to a two-wheeled vehicle state estimation method and device based on a Pinocchio dynamics library and Lie groups, the method comprising: modeling a two-wheeled vehicle based on Lie groups and Lie algebras to construct a motion state; using a Pinocchio dynamics library to obtain a plurality of dynamics parameter matrices of the two-wheeled vehicle in real time to construct a discrete dynamics equation; determining a predicted motion state and a predicted covariance matrix of the two-wheeled vehicle at a next time; according to observation data, using Kalman gain and an observation matrix to perform posterior updating on the predicted motion state and the predicted covariance matrix to determine a posterior motion state and a posterior covariance matrix of the two-wheeled vehicle at the next time. The method provided in the present disclosure obtains dynamics parameter matrices by using a Pinocchio dynamics library, thereby greatly avoiding manual workload, reducing the degree of complexity in the modeling process, improving estimation accuracy, and significantly improving modeling efficiency.

The invention provides a Lie group hand-eye calibration method based on an optimal transmission theory, and the method comprises the following steps: S1, carrying out the multi-time non-coplanar pose transformation of a mechanical arm machine, and synchronously collecting the pose data of the tail end of an actuator and the pose data of a camera after the pose transformation of each time; s2, mapping a rotation matrix in the collected pose data to a Lie algebra space, and constructing discrete probability distribution of the two groups of pose data; s3, according to the discrete probability distribution of the two groups of pose data, calculating the weight of the pose data based on an optimal transmission theory; and S4, weighting and solving a rotation matrix and a translation matrix in the hand-eye calibration matrix to obtain the hand-eye calibration matrix. According to the method, global consistency optimization of calibration parameters is realized by utilizing an optimal transmission theory, local optimization limitation of a traditional least square method is broken through, solving results of a rotation matrix and a translation vector are ensured not to be influenced by abnormal initial values, extremely high calibration precision is still kept under a complex motion track, and the method is suitable for large-scale popularization and application. And systematic failure caused by error accumulation is thoroughly avoided.

The application discloses a wireless speed measurement anti-interference quadrotor unmanned aerial vehicle formation control method, which comprises the following steps: constructing an unmanned cluster system composed of multiple quadrotor unmanned aerial vehicles in a three-dimensional space, and establishing a dynamic model with external disturbance and mass change for each quadrotor unmanned aerial vehicle by using Newton-Euler equation; designing a position loop geometric controller to realize trajectory tracking of each quadrotor unmanned aerial vehicle to a virtual leader and combining with an L1 adaptive control method to resist external disturbance of translational kinematics and mass change of the quadrotor unmanned aerial vehicle; introducing a high-order differentiator to eliminate the requirement of line speed measurement in the formation control of each quadrotor unmanned aerial vehicle, and estimating the first derivative and second derivative of an intermediate control variable u i by using the differentiator; adopting a rotation matrix to represent the attitude of the quadrotor unmanned aerial vehicle, designing a geometric attitude controller on Lie algebra space to realize attitude tracking of the virtual leader, and introducing an L1 adaptive control method to resist external disturbance of rotational kinematics.

This invention discloses a method and system for anti-interference multi-tag webpage recognition under encrypted traffic conditions. The method includes: constructing a dynamic association graph using the burst transmission structure of encrypted traffic; accurately deconstructing aliased traffic and outputting independent sub-stream sequences through an entropy weight penalty mechanism and node aggregation algorithm; extracting non-stationary time-frequency features from the sub-streams and fusing them with graph topological features extracted based on graph structure in the tangent space; generating perturbation samples using an adversarial training environment; adjusting feature weights to generate a composite fingerprint; performing long-term time-series modeling on a Lie group manifold using a Bi-Mamba network and reserving a modulation interface to output a preliminary recognition probability; auditing causal consistency through a webpage loading logic state machine, converting abnormal states into geodesic correction quantities in the Lie algebra tangent space, and correcting network parameters online through the reserved interface. This invention solves the problems of difficult deconstruction of aliased traffic, insufficient fingerprint robustness, and lack of logical consistency constraints in the recognition results.

This application relates to the fields of robot calibration and computer vision, and discloses a robust calibration method for a line laser robot vision system based on model reconstruction. The method includes: fixing a line laser sensor and initializing a hand-eye matrix; installing a freeform surface calibration object on the robot's end effector to acquire surface point clouds and end effector pose data in multiple poses; transforming the point cloud to the robot's end effector coordinate system based on the initial hand-eye matrix to obtain a reconstructed point cloud; searching for the nearest point from the reconstructed point cloud to the calibration object surface and calculating the point-to-surface distance residual; deriving the Jacobian matrix of the residual with respect to the current hand-eye matrix using a Lie algebra right-multiplication perturbation model; establishing an optimization function with residual minimization as the objective and introducing adaptive weights; solving for the hand-eye matrix error vector; and performing manifold updates on the hand-eye matrix until convergence. This application eliminates the dependence on standard parts, removes intermediate fitting errors, and suppresses measurement posture interference through a robust weighting mechanism, thereby improving calibration accuracy and robustness.