A method for generating cooperative operation sequences of dual robotic arms for non-target-specific applications

Abstract

This invention relates to the field of robot operation data processing, and particularly to a method for generating a cooperative operation sequence of two robotic arms for non-specific targets. The method includes: acquiring end-effector state feedback data by collecting torque, position, linear velocity, and angular velocity data of the end effector; correcting the nonlinear forcing term of the dynamic motion primitive based on the spatiotemporal deflection characteristics of torque, and correcting the target attraction point based on the virtual work accumulation characteristics; and then substituting the corrected forcing term and the corrected target attraction point into the underlying evolution equation of the dynamic motion primitive to generate a continuous cooperative operation sequence and drive the two robotic arms to complete the handover of a non-specific target, thereby reducing high-frequency oscillations and low-frequency drifts during the handover process of a target with an unknown center of gravity, and improving the stability and load holding reliability of the handover process of the two robotic arms.

Description

Technical Field

[0001] This invention relates to the field of robot operation data processing technology, and in particular to a method for generating cooperative operation sequences of two robotic arms oriented towards non-specific targets. Background Technology

[0002] Collaborative operation of dual robotic arms is a crucial method for intelligent robots to perform complex handling, assembly, sorting, and handover tasks. During collaborative handover, the sending and receiving arms need to transfer the load of the target object within a short time and generate a continuous, smooth, and stable end-effector sequence for the receiving arm. Existing data processing methods for generating robotic arm operation sequences typically employ a dynamic motion primitive model. This model continuously generates the position, velocity, and acceleration states of the robotic arm's end effector using second-order ordinary differential equations incorporating spring-damped structures and nonlinear forcing terms. The target attraction point provides the restoring force for convergence to the predetermined endpoint, while the nonlinear forcing term maintains the spatial geometry of the taught or preset trajectory, enabling the robotic arm to complete collaborative operations along a predetermined path.

[0003] However, in actual dual-arm handover scenarios, the target to be handed over is often not a standard target with known mass distribution and center of gravity position, but rather a non-specific target whose geometry, load distribution, or center of gravity position is not pre-defined. When the handover arm's gripper begins to open, the target load will unidirectionally transfer to the receiving arm in a very short time. If the target's center of gravity deviates from the receiving arm's gripping center, the end of the receiving arm will be subjected to a multi-axis coupled abrupt torque caused by gravity offset. At this time, the nonlinear forcing term in the existing dynamic motion primitive model is still driven by a fixed phase variable, continuously outputting rigid constraint commands to maintain the original spatial trajectory; while the underlying force control or compliance correction needs to adjust the end-effector attitude according to the abrupt torque. The two are prone to numerical conflicts during the acceleration state solution process, causing high-frequency oscillations in the generated continuous operation sequence, which in turn leads to problems such as gripping instability and target micro-slippage at the actual execution end.

[0004] Furthermore, if the nonlinear forcing terms in the dynamic motion primitive model are simply weakened or truncated to suppress high-frequency oscillations, the model tends to degenerate into a spring-damped system dependent on a fixed target attraction point. For non-specific targets with continuous bias loads, the fixed target attraction point can only provide restoring force based on the nominal endpoint, making it difficult to form effective compensation in advance according to the actual bias torque direction and energy accumulation trend. This leads to low-frequency steady-state drift along the bias direction at the end of the connecting arm during the handover transition period, which can cause the lifted arm to drop or even the target to fall off in severe cases. Therefore, how to balance the compliant yielding ability to sudden bias torques and the anti-drift recovery ability to continuous bias loads during the handover process of dual robotic arms with targets of unknown center of gravity has become an urgent problem to be solved in the generation of dual robotic arm cooperative operation sequences. Summary of the Invention

[0005] In view of this, the present invention aims to propose a method for generating cooperative operation sequences of dual robotic arms for non-target-specific operations, in order to solve the problem that existing dynamic motion primitive algorithms are prone to high-frequency oscillations and low-frequency drifts during the handover process of non-target-specific operations.

[0006] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0007] A method for generating cooperative operation sequences of two robotic arms oriented towards a non-target-specific target, the method comprising:

[0008] Step S1: Obtain end-effector state feedback data by collecting and preprocessing multimodal physical state data at the end of the connecting arm during the handover transition period;

[0009] Step S2: By performing spatiotemporal deflection feature mapping on the actual three-dimensional torque vector and torque change rate in the end state feedback data, the adaptive decay factor of the forcing term is obtained and the forcing term is corrected.

[0010] Step S3: By performing virtual work accumulation compensation processing on the end position deviation direction, end three-dimensional actual torque vector and end three-dimensional actual angular velocity vector in the end state feedback data, a dynamic drift compensation vector is obtained and the target attraction point is corrected;

[0011] Step S4: By substituting the modified forcing term and the modified target attraction point into the underlying evolution equation of the dynamic motion primitive, the state is calculated to obtain the single-step cooperative operation state;

[0012] Step S5: By performing numerical integration and inverse kinematic mapping on the single-step cooperative operation state, a continuous cooperative operation sequence is obtained and the dual robotic arms are driven to complete the handover of non-specific targets.

[0013] Furthermore, the acquisition of end-effector state feedback data by collecting and preprocessing multimodal physical state data at the end of the connecting arms during the handover transition period includes:

[0014] When two robotic arms work together to perform a handover task for a non-specific target, the moment when the system control command triggers the handover arm's gripper to open is determined as the start moment of the handover transition period between the two arms.

[0015] During the handover transition period between the two arms, multimodal physical state data of the end of the connecting arm are collected according to a preset sampling period;

[0016] A six-axis torque sensor installed at the flange of the connecting arm end collects three-dimensional torque data of the connecting arm end in Cartesian space, and obtains the actual three-dimensional torque data of the end based on the three-dimensional torque data;

[0017] By reading the encoder position data and encoder speed data of each joint of the connector arm, and combining the forward kinematics model and Jacobian matrix of the connector arm, the end-effector state is calculated to obtain the end-effector three-dimensional actual position data, end-effector three-dimensional actual linear velocity data and end-effector three-dimensional actual angular velocity data.

[0018] Low-pass filtering preprocessing is performed on the actual three-dimensional torque vector, actual three-dimensional position data, actual three-dimensional linear velocity data, and actual three-dimensional angular velocity data of the end-effector to obtain end-effector state feedback data.

[0019] Furthermore, the step of obtaining the adaptive attenuation factor of the forcing term and correcting the forcing term by performing spatiotemporal deflection feature mapping processing on the actual three-dimensional torque vector and torque change rate of the end state feedback data includes:

[0020] By performing instantaneous torsional deflection evaluation on the end-point three-dimensional actual torque vector and torque change rate in the end-point state feedback data, spatiotemporal deflection characteristic data of end-point torque are obtained.

[0021] By performing attenuation mapping on the spatiotemporal deflection feature data of the end moment, an adaptive attenuation factor for the forced term is obtained. Based on the adaptive attenuation factor for the forced term, the original nonlinear forced term is weighted and attenuated to obtain a corrected forced term.

[0022] Furthermore, the instantaneous torsional deflection assessment processing of the end-effector's three-dimensional actual torque vector and torque change rate in the end-effector state feedback data to obtain end-effector spatiotemporal deflection characteristic data includes:

[0023] For any target sampling moment during the transition period of the two arms, extract the three-dimensional actual torque vector of the end corresponding to the target sampling moment from the end state feedback data, and obtain the torque change rate corresponding to the target sampling moment based on the three-dimensional actual torque vector of the end of the adjacent sampling moments;

[0024] The cross product of the actual three-dimensional torque vector at the end of the target sampling time and the torque change rate is performed to obtain the torque space deflection variable at the target sampling time.

[0025] The second-order norm of the torque space deflection magnitude is calculated to obtain the instantaneous torsional deflection assessment corresponding to the target sampling time;

[0026] Based on the instantaneous torsional deflection assessment corresponding to each sampling moment between the start time of the dual-arm handover transition period and the target sampling moment, time accumulation processing is performed to obtain the historical torsional deflection cumulative assessment corresponding to the target sampling moment;

[0027] The second-order norm squared processing is performed on the end three-dimensional actual torque vector corresponding to the target sampling time to obtain the static torque benchmark evaluation corresponding to the target sampling time;

[0028] Based on instantaneous torsional deflection assessment, historical torsional deflection cumulative assessment, and static torque benchmark assessment, spatiotemporal deflection characteristic data of the end moment are obtained.

[0029] Furthermore, the step of obtaining an adaptive attenuation factor for the forced term by performing attenuation mapping processing on the spatiotemporal deflection feature data of the end moment, and then performing weight attenuation processing on the original nonlinear forced term based on the adaptive attenuation factor to obtain a corrected forced term, includes:

[0030] For any target sampling moment during the handover transition period of the two arms, extract the instantaneous torsional deflection assessment, historical torsional deflection cumulative assessment and static torque benchmark assessment corresponding to the target sampling moment from the spatiotemporal deflection characteristic data of the end moment.

[0031] The instantaneous torsional deflection assessment, historical torsional deflection cumulative assessment and static torque benchmark assessment corresponding to the target sampling time are summed to obtain the attenuation mapping benchmark assessment corresponding to the target sampling time.

[0032] The instantaneous torsional deflection assessment corresponding to the target sampling time is used as the numerator, and the attenuation mapping benchmark assessment corresponding to the target sampling time is used as the denominator. Ratio mapping is performed to obtain the adaptive attenuation factor of the forced term corresponding to the target sampling time.

[0033] Obtain the original nonlinear forcing term corresponding to the target sampling time from the dynamic motion primitive model;

[0034] The difference between constant 1 and the adaptive decay factor of the forced term corresponding to the target sampling time is used as the retained weight of the forced term corresponding to the target sampling time;

[0035] The modified forced term corresponding to the target sampling time is obtained by multiplying the weight of the forced term corresponding to the target sampling time with the original nonlinear forced term corresponding to the target sampling time.

[0036] Furthermore, the step of obtaining a dynamic drift compensation vector and correcting the target attraction point by performing virtual work accumulation compensation processing on the end-position deviation direction, the end-three-dimensional actual torque vector, and the end-three-dimensional actual angular velocity vector in the end-position feedback data includes:

[0037] By performing offset displacement direction extraction processing on the current three-dimensional position data of the end point and the initial reference three-dimensional position data at the handover start time in the end point status feedback data, the end point offset displacement direction data is obtained.

[0038] By performing virtual work accumulation and energy benchmark normalization on the end-point three-dimensional actual torque vector, end-point three-dimensional actual angular velocity vector, and end-point three-dimensional actual linear velocity vector in the end-point state feedback data, dynamic drift compensation depth data is obtained.

[0039] By performing spatial compensation vector mapping processing on the end offset displacement direction data and the dynamic drift compensation depth data, a dynamic drift compensation vector is obtained. Then, by performing reverse drift correction processing on the original target attraction point and the dynamic drift compensation vector, a corrected target attraction point is obtained.

[0040] Furthermore, the step of extracting the offset displacement direction data of the end-point by processing the current end-point three-dimensional position data and the initial reference three-dimensional position data at the handover start time from the end-point state feedback data includes:

[0041] Extract the current three-dimensional actual position data of the end point corresponding to the target sampling time from the end point status feedback data, and obtain the initial reference three-dimensional position data corresponding to the start time of the handover transition period between the two arms;

[0042] The difference between the current actual three-dimensional position data of the end point at the target sampling time and the initial reference three-dimensional position data is processed to obtain the end point position deviation vector at the target sampling time.

[0043] Calculate the second norm of the end position deviation vector corresponding to the target sampling time to obtain the magnitude of the end position deviation corresponding to the target sampling time;

[0044] Using the end position deviation vector corresponding to the target sampling time as the numerator and the end position deviation magnitude corresponding to the target sampling time as the denominator, normalization direction extraction processing is performed to obtain the end offset displacement direction data corresponding to the target sampling time.

[0045] Furthermore, the process of obtaining dynamic drift compensation depth data by performing virtual work accumulation and energy benchmark normalization on the end-point three-dimensional actual torque vector, end-point three-dimensional actual angular velocity vector, and end-point three-dimensional actual linear velocity vector in the end-point state feedback data includes:

[0046] For any target sampling moment during the transition period of the two arms, extract the three-dimensional actual torque vector and the three-dimensional actual linear velocity vector of the end from the end state feedback data corresponding to the target sampling moment, and extract the three-dimensional actual torque vector and the three-dimensional actual angular velocity vector of the end corresponding to each sampling moment between the start time of the transition period of the two arms and the target sampling moment.

[0047] For any sampling moment between the start of the transition period between the two arms and the target sampling moment, the actual three-dimensional torque vector at the end of the sampling moment and the actual three-dimensional angular velocity vector at the end of the sampling moment are multiplied by the dot product to obtain the instantaneous virtual work evaluation corresponding to the sampling moment.

[0048] The instantaneous virtual work evaluation corresponding to each sampling moment between the start time of the handover transition period of the two arms and the target sampling time is processed by time accumulation to obtain the virtual work accumulation evaluation corresponding to the target sampling time.

[0049] The second norm of the actual three-dimensional torque vector at the end of the target sampling time is calculated to obtain the torque magnitude at the end of the target sampling time. The second norm of the actual three-dimensional linear velocity vector at the end of the target sampling time is also calculated to obtain the linear velocity magnitude at the end of the target sampling time.

[0050] Multiply the end moment magnitude and the end linear velocity magnitude at the target sampling time, and add the product to the preset minimum constant to obtain the energy normalized benchmark assessment at the target sampling time.

[0051] The virtual work accumulation assessment corresponding to the target sampling time is used as the numerator, and the energy normalized benchmark assessment corresponding to the target sampling time is used as the denominator. The ratio is normalized to obtain the bias energy accumulation depth assessment corresponding to the target sampling time.

[0052] Based on the preset spatial displacement mapping coefficient, the spatial scale mapping process is performed on the bias energy accumulation depth assessment corresponding to the target sampling time to obtain the dynamic drift compensation depth data corresponding to the target sampling time.

[0053] Furthermore, the step of obtaining a dynamic drift compensation vector by performing spatial compensation vector mapping processing on the end offset displacement direction data and the dynamic drift compensation depth data, and obtaining a corrected target attraction point by performing reverse drift correction processing on the original target attraction point and the dynamic drift compensation vector, includes:

[0054] For any target sampling moment during the transition period of the two arms, acquire the end offset displacement direction data and dynamic drift compensation depth data corresponding to the target sampling moment;

[0055] The dynamic drift compensation depth data corresponding to the target sampling time is used as the spatial compensation amplitude, and the end offset displacement direction data corresponding to the target sampling time is used as the spatial compensation direction.

[0056] The spatial compensation direction and spatial compensation amplitude are multiplied and mapped to obtain the dynamic drift compensation vector corresponding to the target sampling time.

[0057] Obtain the original target attraction point corresponding to the target sampling time from the dynamic motion primitive model;

[0058] The original target attraction point at the target sampling time is compared with the dynamic drift compensation vector to obtain the corrected target attraction point at the target sampling time.

[0059] Furthermore, the step of obtaining the single-step cooperative operation state by substituting the modified forcing term and the modified target attraction point into the underlying evolution equation of the dynamic motion primitives for state calculation includes:

[0060] For any target sampling moment during the transition period of the two arms, obtain the correction forcing term, correction target attraction point, current end position state parameter and current end velocity state parameter corresponding to the target sampling moment;

[0061] Obtain the underlying time scaling constant, spring damping system stiffness coefficient, and spring damping system damping coefficient from the dynamic motion primitive model;

[0062] Based on the difference between the corrected target attraction point and the current end position state parameter at the target sampling time, and the stiffness coefficient of the spring damping system, the target convergence recovery term at the target sampling time is obtained.

[0063] Based on the current end velocity state parameter, the underlying time scaling constant, and the damping coefficient of the spring damping system at the target sampling time, obtain the velocity damping suppression term at the target sampling time.

[0064] Based on the target convergence recovery term, velocity damping suppression term and correction forcing term corresponding to the target sampling time, the underlying evolution state of the dynamic motion primitive is calculated to obtain the terminal acceleration state parameter corresponding to the target sampling time.

[0065] The terminal acceleration state parameter corresponding to the target sampling time is used as the single-step cooperative operation state corresponding to the target sampling time.

[0066] Compared with the prior art, the present invention has the following advantages:

[0067] This invention discloses a method for generating cooperative operation sequences of dual robotic arms for non-specific targets. By introducing multimodal physical state feedback, including the end-effector torque, position, linear velocity, and angular velocity, and adaptively correcting the nonlinear forcing term in the dynamic motion primitive based on the spatiotemporal deflection characteristics of the end-effector torque, the dual robotic arms can proactively reduce the rigidity of maintaining the preset trajectory geometry when transferring non-specific targets with unknown mass distribution and center of gravity, based on the actual load abrupt change trend. Therefore, in real-world scenarios where the handover arm grippers open and the target load is instantaneously transferred to the receiving arm, this method effectively avoids the numerical conflict between the forced trajectory constraint and the underlying compliance correction, reduces abrupt fluctuations in acceleration state parameters, suppresses high-frequency oscillations at the end-effector end, and reduces the risk of micro-slippage of the target object between the grippers. Simultaneously, this invention utilizes the virtual work accumulation characteristics formed by the bias torque and end-effector angular velocity, and combines this with the end-effector position deviation direction to dynamically compensate for the target attraction point of the dynamic motion primitive, enabling the sequence generation model to still form restoring force compensation for the bias load even after weakening the rigid forcing term. Therefore, in the process of the arm lifting a target with an unknown center of gravity, low-frequency steady-state drift and falling instability caused by insufficient restoring force at the fixed target attraction point can be avoided. This makes the generated continuous cooperative operation sequence have both compliant yielding ability and anti-bias holding ability, improving the smoothness of the handover process of the two robotic arms to non-specific targets, the reliability of load holding, and the adaptability to actual working conditions. Attached Figure Description

[0068] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0069] Figure 1 This is a flowchart illustrating a method for generating cooperative operation sequences of dual robotic arms oriented towards a non-specific target, as described in an embodiment of the present invention. Detailed Implementation

[0070] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0071] See Figure 1 This is a flowchart of a method for generating cooperative operation sequences of dual robotic arms oriented towards non-specific targets, provided in Embodiment 1 of the present invention. Figure 1 As shown, a method for generating cooperative operation sequences of dual robotic arms oriented towards non-target targets may include:

[0072] Step S1: Collect and preprocess multimodal physical state data of the end of the connecting arm during the handover transition period to obtain end state feedback data.

[0073] First, when the two robotic arms collaboratively perform a non-target handover task, the moment the system control command triggers the opening of the handover arm's gripper is defined as the start time of the handover transition period. During this transition period, multimodal physical state data of the receiving arm's end effector is collected according to a preset sampling period. In this embodiment, the sensor sampling period is set to 1 millisecond for each data acquisition. A six-axis torque sensor located at the flange of the receiving arm's end effector collects three-dimensional torque data of the end effector in Cartesian space, and based on this data, the actual three-dimensional torque data of the end effector is obtained. By reading the encoder position and speed data of each joint of the receiving arm, and combining this with the forward kinematics model and Jacobian matrix of the receiving arm, the end effector state is calculated to obtain the actual three-dimensional position data, actual three-dimensional linear velocity data, and actual three-dimensional angular velocity data of the end effector. Low-pass filtering preprocessing is applied to the actual three-dimensional torque vector, actual three-dimensional position data, actual three-dimensional linear velocity data, and actual three-dimensional angular velocity data of the end effector to obtain end effector state feedback data.

[0074] Thus, the process of acquiring and preprocessing multimodal physical state data of the end arms during the handover transition period has been completed, thereby obtaining end-arm state feedback data.

[0075] Step S2: By performing spatiotemporal deflection feature mapping on the actual three-dimensional torque vector and torque change rate of the end state feedback data, the adaptive decay factor of the forced term is obtained and the forced term is corrected.

[0076] When the two arms are exchanging grippers for a non-specific target with an unknown center of gravity, the core reason for the micro-slippage of the load lies in the defect in the response mechanism of existing sequence generation algorithms to abrupt bias torque. When the handover arm grippers begin to open, the actual weight of the target object instantaneously shifts to the receiving arm. If the center of gravity of the target object deviates from the gripping center of the receiving arm, the end of the receiving arm will be subjected to an unexpected multi-axis abrupt coupling torque. Existing sequence generation algorithms based on dynamic motion primitives are still limited by the nonlinear forcing term driven by their internal time phase variables when dealing with this torque. The significance of this forcing term is to force the system to reproduce the preset nominal trajectory shape in multi-dimensional space. Because this forcing term has extremely high rigidity to spatial constraints, when the underlying force feedback mechanism attempts to output correction commands to overcome the bias torque, it will generate fierce numerical resistance with the forcing term. This conflict between forcibly maintaining the original spatial configuration and the underlying force control compliance correction causes the acceleration state parameters calculated by the system to fluctuate drastically in a short period of time, which in turn triggers high-frequency oscillation output of the end effector, ultimately causing micro-slippage of the target between the grippers. To solve this problem, the rigid constraint that the existing coercive term cannot be adaptively adjusted must be broken. Since relying solely on the threshold of a single dimension of the force sensor cannot accurately reflect the deflection trend of the target force, it is necessary to make judgments based on the spatial evolution of the multi-axis torque at the end of the arm. By extracting the torque vector and its rate of change over time, a feature quantity that can accurately measure the instantaneous torsional deterioration trend is constructed and mapped to a dimensionless attenuation coefficient. Using this coefficient, when the bias torsional trend is detected to be intensifying, the control weight of the nonlinear coercive term in the current generation dimension is actively weakened or even shielded. This allows the system to temporarily abandon rigid tracking of the preset trajectory and instead output a compliant, tentative unloading micro-sequence that conforms to the physical bias trend, fundamentally resolving the conflict between spatial constraints and force control correction.

[0077] In summary, this invention first performs instantaneous torsional deflection assessment on the end-effector's three-dimensional actual torque vector and torque change rate in the end-effector state feedback data to obtain spatiotemporal deflection characteristic data of the end-effector torque. Specifically, for any target sampling moment during the transition period of the two arms, the end-effector's three-dimensional actual torque vector corresponding to the target sampling moment is extracted from the end-effector state feedback data, and the torque change rate corresponding to the target sampling moment is obtained based on the end-effector's three-dimensional actual torque vectors of adjacent sampling moments. A cross product is performed on the end-effector's three-dimensional actual torque vector and torque change rate corresponding to the target sampling moment to obtain the torque spatial deflection magnitude corresponding to the target sampling moment. The second-order norm of the torque spatial deflection magnitude is calculated to obtain the instantaneous torsional deflection assessment corresponding to the target sampling moment. Time accumulation processing is performed on the instantaneous torsional deflection assessments corresponding to each sampling moment between the start of the two-arm transition period and the target sampling moment to obtain the historical torsional deflection cumulative assessment corresponding to the target sampling moment. The second-order norm square processing is performed on the end-effector's three-dimensional actual torque vector corresponding to the target sampling moment to obtain the static torque benchmark assessment corresponding to the target sampling moment. Based on instantaneous torsional deflection assessment, historical torsional deflection cumulative assessment, and static torque benchmark assessment, spatiotemporal deflection characteristic data of the end moment are obtained.

[0078] After acquiring the spatiotemporal deflection feature data of the end moment, the process continues by performing attenuation mapping on the end moment spatiotemporal deflection feature data to obtain the adaptive attenuation factor of the forcing term. Based on the adaptive attenuation factor, the original nonlinear forcing term is weighted and attenuated to obtain the corrected forcing term. Specifically, for any target sampling moment during the transition period between the two arms, the instantaneous torsional deflection assessment, historical torsional deflection cumulative assessment, and static moment benchmark assessment corresponding to the target sampling moment are extracted from the end moment spatiotemporal deflection feature data. The instantaneous torsional deflection assessment, historical torsional deflection cumulative assessment, and static moment benchmark assessment corresponding to the target sampling moment are summed to obtain the attenuation mapping benchmark assessment corresponding to the target sampling moment. The instantaneous torsional deflection assessment corresponding to the target sampling moment is used as the numerator, and the attenuation mapping benchmark assessment corresponding to the target sampling moment is used as the denominator for ratio mapping to obtain the adaptive attenuation factor of the forcing term corresponding to the target sampling moment. The original nonlinear forcing term corresponding to the target sampling moment is obtained from the dynamic motion primitive model. The difference between the constant 1 and the adaptive attenuation factor of the forcing term corresponding to the target sampling moment is used as the retained weight of the forcing term corresponding to the target sampling moment. The modified forced term corresponding to the target sampling time is obtained by multiplying the weight of the forced term corresponding to the target sampling time with the original nonlinear forced term corresponding to the target sampling time.

[0079] In one implementation, assume the first The actual three-dimensional torque vector at the current moment is: ;No. The rate of change of torque at the current moment is The start time of the robotic arm's handover state transition task is... ; Let the variable be a continuous integral variable, then the first... The expression for calculating the adaptive decay factor of the forcing term at each current moment is:

[0080]

[0081] in, Indicates the first The adaptive decay factor of the forcing term at the current moment; Indicates the first The actual three-dimensional torque vector at the end point corresponding to the current moment; Indicates the first The rate of change of torque at the current moment; Indicates the variable during integration time. The actual three-dimensional torque vector at the end of the connecting arm; Indicates the variable during integration time. The first derivative of the actual three-dimensional torque vector at the end of the connecting arm with respect to time; This represents the calculation of the cross product of vectors; This represents the operation of finding the second norm of a vector.

[0082] Furthermore, assume that the original nonlinear forcing term driven by a fixed phase variable is... Then, the expression for calculating the nonlinear forcing term of the actual output after adaptive attenuation correction is:

[0083]

[0084] It should be noted that, in this embodiment, for the two-arm handover task, the algorithm's time step is typically set to 1 millisecond, and the integration time variable... The discretization accumulation step size is consistent with the system sampling period, with an upper time limit. At the current moment, during the non-target-specific transfer phase, existing sequence generation algorithms, in order to ensure the geometry of the end trajectory, use independent phase variables to rigidly drive a constant position constraint command to output. When encountering a target object's center of gravity offset, this rigid constraint not only fails to help counteract the offset force but also causes acceleration output oscillations by hindering necessary spatial clearance, leading to slippage of the object within the gripper. To eliminate this numerical conflict, the aforementioned adaptive decay model functions through a nonlinear spatial mapping of multidimensional torques and their rates of change. The numerator of the formula uses the actual end torque vector at the current moment. Its first rate of change The purpose of performing a cross product and obtaining the second norm is to directly capture the deteriorating torsional component of the bias torque in three-dimensional space, perpendicular to the torque itself and its direction of change. In the precursory period of microslip, the unstable gravitational transfer of the target object not only leads to an increase in force in one dimension but also manifests as a coupled deflection of forces along multiple axes. This cross product term can serve as a highly sensitive indicator of the instantaneous spatial torsional deterioration. Relying solely on instantaneous abrupt changes is highly susceptible to interference from high-frequency noise in sensors, which can cause algorithmic mis-triggering. Furthermore, in extreme slippage conditions, the dramatic increase in instantaneous derivatives can easily lead to numerical divergence in the simple ratio structure. Therefore, the denominator of the formula constructs multiple anti-overflow benchmarks, including the numerator itself. The first term in the denominator directly introduces the same instantaneous torsional deflection feature as the numerator; the second term in the denominator is the sum of the integrals of the cross product outer product magnitude within the handover history window, representing the cumulative torsional fluctuation benchmark experienced by the system since the handover; the third term in the denominator is the square of the current actual torque vector magnitude, serving as a dynamic benchmark to prevent division by zero errors while setting an instantaneous static mechanical threshold. By synchronously introducing the numerator term, which characterizes the instantaneous dynamic deterioration trend, into the denominator, and superimposing it with the historical dynamic evolution and the instantaneous static basis to form an overflow-preventing ratio structure, the attenuation coefficient is strictly constrained within a closed interval of zero to one, preventing numerical divergence caused by extreme abrupt changes. When the transition process is stable, the rate of change of deflection at the numerator is extremely small, the attenuation factor approaches zero, and the system stably outputs the constrained trajectory according to the original forcing term; however, when a torsional abrupt change caused by a centroid offset is detected, the numerator value increases dramatically and dominates the entire fraction, the attenuation factor rapidly approaches one, and through... This mapping logic immediately reduces the weight of the coercive term of the forced constraint target to an extremely low level or even to zero. By weakening the weight of the original nonlinear coercive term, the algorithm spontaneously transforms into a highly compliant pure spring-damped state during this transition period, allowing the end of the arm to make small-amplitude yielding and adaptive attitude adjustment under the action of the target bias force, eliminating the system oscillation and load shedding problems caused by rigidly approaching a fixed geometric space point.

[0085] Thus, the process of obtaining the adaptive decay factor of the forcing term and correcting the forcing term is completed by performing spatiotemporal deflection feature mapping on the actual three-dimensional torque vector and torque change rate of the end state feedback data.

[0086] Step S3: By performing virtual work accumulation compensation processing on the end position deviation direction, end three-dimensional actual torque vector and end three-dimensional actual angular velocity vector in the end state feedback data, a dynamic drift compensation vector is obtained and the target attraction point is corrected.

[0087] Step S2 above, by weakening the coercive term, imparts the necessary compliance to the system, avoiding high-frequency oscillations caused by rigid constraints. When the weight of the coercive term decreases, the algorithm degenerates into a pure spring-damped system at the underlying logic level, allowing the receiving arm to make room. At this time, facing a gravity-biased target, the target's bias torque is equivalent to a continuously acting external bias load. The system can only rely on the previously set fixed target attraction point to generate position restoring force. Since this restoring force is based on the nominal state setting, it is often insufficient to offset the actual bias load, causing the receiving arm to fail to maintain a stable lifting state after the initial room is created, instead experiencing continuous low-frequency steady-state descent drift along the direction of the bias torque. To construct a complete anti-slip and stable lifting mechanism, the system's target restoring force needs to be enhanced simultaneously during the weakening of the coercive term. Conventional position error feedback has a computational lag when dealing with dynamic transfer loads. Therefore, this method extracts the virtual work done by the bias torque on the end-effector's spatial angular velocity during the handover transition period, thereby quantifying the unstable momentum accumulation state inside the target object. By combining the actual small positional deviation direction, a parameterless spatial compensation vector is constructed to dynamically correct the drift of the original target attraction point. By actively adjusting the target point, a restoring force to counteract the bias is provided in advance.

[0088] In summary, this invention first extracts the offset displacement direction data of the end-effector by processing the current three-dimensional position data of the end-effector in the end-effector state feedback data and the initial reference three-dimensional position data at the start of the handover. Specifically, it extracts the current actual three-dimensional position data of the end-effector corresponding to the target sampling time from the end-effector state feedback data and obtains the initial reference three-dimensional position data corresponding to the start of the handover transition period. It then performs difference processing between the current actual three-dimensional position data of the end-effector corresponding to the target sampling time and the initial reference three-dimensional position data to obtain the end-effector position deviation vector corresponding to the target sampling time. Next, it calculates the second-order norm of the end-effector position deviation vector corresponding to the target sampling time to obtain the magnitude of the end-effector position deviation at the target sampling time. Finally, it performs normalized direction extraction processing using the end-effector position deviation vector as the numerator and the magnitude of the end-effector position deviation at the target sampling time as the denominator to obtain the corresponding end-effector offset displacement direction data at the target sampling time.

[0089] After obtaining the end-effector offset displacement direction data, the dynamic drift compensation depth data is obtained by performing virtual work accumulation and energy benchmark normalization on the end-effector state feedback data, specifically, for any target sampling moment during the dual-arm handover transition period, the end-effector three-dimensional actual torque vector and end-effector three-dimensional actual linear velocity vector corresponding to the target sampling moment are extracted from the end-effector state feedback data, and the end-effector three-dimensional actual torque vector and end-effector three-dimensional actual angular velocity vector corresponding to each sampling moment between the start moment of the dual-arm handover transition period and the target sampling moment are extracted. For any sampling moment between the start moment of the dual-arm handover transition period and the target sampling moment, the end-effector three-dimensional actual torque vector and the end-effector three-dimensional actual angular velocity vector corresponding to the sampling moment are multiplied by a dot product to obtain the instantaneous virtual work assessment corresponding to the sampling moment. The instantaneous virtual work assessments corresponding to each sampling moment between the start moment of the dual-arm handover transition period and the target sampling moment are subjected to time accumulation processing to obtain the virtual work accumulation assessment corresponding to the target sampling moment. The second norm of the actual three-dimensional torque vector at the target sampling time is calculated to obtain the torque magnitude at that time. Similarly, the second norm of the actual three-dimensional linear velocity vector at the target sampling time is calculated to obtain the linear velocity magnitude at that time. The torque magnitude and linear velocity magnitude at the target sampling time are multiplied, and the product is added to a preset minimum constant to obtain the energy normalized benchmark assessment at the target sampling time. The virtual work accumulation assessment at the target sampling time is used as the numerator, and the energy normalized benchmark assessment at the target sampling time is used as the denominator; ratio normalization is then performed to obtain the bias energy accumulation depth assessment at the target sampling time. Based on a preset spatial displacement mapping coefficient, the bias energy accumulation depth assessment at the target sampling time is subjected to spatial scale mapping to obtain the dynamic drift compensation depth data at the target sampling time.

[0090] After acquiring the dynamic drift compensation depth data, the final step involves spatial compensation vector mapping between the end-off offset displacement direction data and the dynamic drift compensation depth data to obtain the dynamic drift compensation vector. Then, a reverse drift correction process is performed between the original target attraction point and the dynamic drift compensation vector to obtain the corrected target attraction point. Specifically, for any target sampling moment during the transition period between the two arms, the end-off offset displacement direction data and dynamic drift compensation depth data corresponding to the target sampling moment are acquired. The dynamic drift compensation depth data corresponding to the target sampling moment is used as the spatial compensation amplitude, and the end-off offset displacement direction data corresponding to the target sampling moment is used as the spatial compensation direction. A product mapping process is performed between the spatial compensation direction and the spatial compensation amplitude to obtain the dynamic drift compensation vector corresponding to the target sampling moment. The original target attraction point corresponding to the target sampling moment is obtained from the dynamic motion primitive model. The difference between the original target attraction point corresponding to the target sampling moment and the dynamic drift compensation vector is processed to obtain the corrected target attraction point corresponding to the target sampling moment.

[0091] In one implementation, assume the first The actual three-dimensional position vector of the arm's end at the current moment is: The initial reference three-dimensional position vector of the arm's end at the start of the handover task is: ;No. The actual three-dimensional linear velocity vector of the arm's end effector at the current moment is: ; in the integration time variable The actual three-dimensional angular velocity vector at the end of the arm is The spatial displacement mapping coefficient is Then the first The expression for calculating the dynamic drift compensation vector at the current moment is:

[0092]

[0093] in, Indicates the first The dynamic drift compensation vector at the current moment; Indicates the first The actual three-dimensional position vector of the arm's end at the current moment; This represents the initial reference three-dimensional position vector at the end of the arm at the start of the handover task; Indicates the variable during integration time. The actual three-dimensional torque vector at the end of the connecting arm; Indicates the variable during integration time. The actual three-dimensional angular velocity vector at the end of the arm; Indicates the first The actual three-dimensional linear velocity vector of the arm's end effector at the current moment; This represents the spatial displacement mapping coefficient, used to map the energy evolution ratio to the actual three-dimensional spatial compensation depth, achieving dimensional uniformity. Since the extracted energy ratio is a dimensionless state quantity, the spatial displacement mapping coefficient... Its function is to scale it up proportionally to the actual Cartesian spatial compensation scale. The calibration of this coefficient is based on the equivalent stiffness of the system's underlying spring-damped model: when the system is subjected to a gravitational bias equivalent to the nominal load limit (e.g., 40 Newtons), to excite the underlying model to generate a restoring force sufficient to counteract this load, according to Hooke's Law, the target point needs to generate approximately 40 millimeters of spatial stretching. Therefore, considering the stiffness parameter set in this system (K=1000) and the sensor feedback magnitude, the spatial displacement mapping coefficient in this embodiment... The equivalent conversion gain is calibrated to 1.5, thereby ensuring that the generated spatial compensation depth is physically constrained by the inherent constraints of the nominal load, thus guaranteeing the stability of trajectory generation. This represents a minimal constant used to prevent the denominator from being zero, and is set in the embodiments of the present invention. .

[0094] It should be noted that, in this embodiment of the invention, for the two-arm handover task, the algorithm's time step is typically set to 1 millisecond, and the integration time variable... The discretization accumulation step size is consistent with the system sampling period, with an upper time limit. This refers to the current moment.

[0095] Furthermore, assuming the initial three-dimensional coordinate vector of the target attraction point is set in the algorithm as follows: The expression for calculating the corrected three-dimensional coordinate vector of the target attraction point after dynamic compensation and update is:

[0096]

[0097] It should be noted that, when dealing with the handover and transfer of targets with a center of gravity offset, in order to solve the steady-state drift problem caused by insufficient system restoring force after the weakening of the forcing term, the dynamic drift compensation model constructed above plays a compensating role by analyzing the coupling relationship between physical work and energy reference in real time. The first term of the formula is composed of the deviation vector between the current position and the initial position divided by the second norm of the deviation vector. This term extracts a pure three-dimensional spatial unit direction vector. Its design purpose is to capture the actual small physical drop direction caused by the offset gravity, providing an objective spatial geometric orientation for subsequent compensation. Since relying solely on position deviation for feedback correction will inevitably have a time lag, the second term of the formula constructs a feedforward depth scalar based on energy accumulation. The numerator of the second term is the real-time torque vector within the time window. With angular velocity vector By performing dot product and integration, this structure characterizes the total virtual rotational work done by the bias torque on the end effector during the transition period, serving as an energy measure of the unstable momentum accumulation state within the target object. To enable this work value to have universal adaptive correction capabilities, the denominator of the second term utilizes the product of the second norm of the torque and the second norm of the linear velocity at the current moment to extract an energy basis characterizing the instantaneous translational state of the system. This ratio structure, which uses the accumulated rotational work divided by the instantaneous translational basis, constitutes a depth scalar for evaluating the degree of bias load. Finally, the compensation factor, formed by multiplying the direction vector by the depth scalar, is... It can quantify in real time the physical quantities that the system needs to compensate for in reverse in three-dimensional space. The algorithm's update logic involves actively adjusting the fixed target attraction point in the opposite direction of the offset displacement the instant energy accumulation and a slight displacement are detected. This dynamic spatial offset of the target attraction point causes the degenerate spring-damped model to output a larger convergence restoring force. Without relying on rigidity forcing terms, it accurately counteracts the equivalent downward trend caused by gravity offset, compensates for the algorithm's deficiency in anti-offset restoring force after the model decays forcing terms, and solves the slippage and instability problems during the handover process of non-specific targets.

[0098] Thus, the process of virtual work accumulation compensation is completed by processing the end position deviation direction, end three-dimensional actual torque vector, and end three-dimensional actual angular velocity vector in the end state feedback data to obtain the dynamic drift compensation vector and correct the target attraction point.

[0099] Step S4: By substituting the modified forcing term and the modified target attraction point into the underlying evolution equation of the dynamic motion primitive, the state is calculated to obtain the single-step cooperative operation state.

[0100] In existing technologies, the underlying logic for generating continuous operation sequences based on Dynamic Motion Elements (DMP) utilizes a second-order ordinary differential equation containing a spring-damped structure and a nonlinear forcing term to drive the system state towards the target point. However, as analyzed earlier, the basic equation suffers from instability due to insufficient rigid constraints and anti-bias load when facing non-specific target transitions. Based on the adaptive optimization factors obtained in steps S2 and S3, the inherent invariant parameters of the existing underlying ordinary differential equation are replaced with the dynamically compensated parameters designed above, without compromising its stability. Specifically, the modified forcing term attenuated by spatial deflection characteristics in step S2 replaces the original forcing term to cut off the anti-oscillation caused by rigid spatial approximation. Simultaneously, the modified target attraction point after energy accumulation depth compensation in step S3 replaces the original fixed target attraction point to provide sufficient anti-sag recovery force. By substituting the updated two parameters into the underlying dynamic equations, the most reasonable, bias-compliant, and instability-resistant acceleration command under the current physical feedback can be calculated. Then, the velocity and position states of the sampling period can be obtained by integration, forming a robust single-step cooperative operation sequence.

[0101] Specifically, for any target sampling moment during the transition period between the two arms, the corrected forcing term, corrected target attraction point, current end-effector position state parameter, and current end-effector velocity state parameter corresponding to the target sampling moment are obtained. The underlying time scaling constant, spring-damped system stiffness coefficient, and spring-damped system damping coefficient are obtained from the dynamic motion primitive model. Based on the difference between the corrected target attraction point and the current end-effector position state parameter corresponding to the target sampling moment, and the spring-damped system stiffness coefficient, the target convergence recovery term corresponding to the target sampling moment is obtained. Based on the current end-effector velocity state parameter, the underlying time scaling constant, and the spring-damped system damping coefficient corresponding to the target sampling moment, the velocity damping suppression term corresponding to the target sampling moment is obtained. Based on the target convergence recovery term, velocity damping suppression term, and corrected forcing term corresponding to the target sampling moment, the underlying evolution state of the dynamic motion primitive is calculated to obtain the end-effector acceleration state parameter corresponding to the target sampling moment. The end-effector acceleration state parameter corresponding to the target sampling moment is used as the single-step cooperative operation state corresponding to the target sampling moment.

[0102] In one implementation, it is assumed that the underlying time scaling constant is The stiffness coefficient of the spring-damped system is The damping coefficient of the spring-damped system is The one-dimensional positional state parameter of the arm's end effector generated at the current sampling time is: The one-dimensional velocity state parameter of the arm end generated at the current sampling time is: The current solution output is the one-dimensional acceleration state parameter at the end of the arm. Then the expression for calculating the single-step cooperative operation state at the current moment is:

[0103]

[0104] in, This indicates the current state of a single-step cooperative operation. This represents the stiffness coefficient of the spring-damped system; This represents the modified three-dimensional coordinate vector of the target attraction point; This represents the one-dimensional positional state parameter of the arm's end effector generated at the current sampling moment; This represents the damping coefficient of a spring-damped system; Indicates the underlying time scaling constant; This represents the one-dimensional velocity state parameter of the arm's end effector generated at the current sampling moment; This indicates the correction of the nonlinear forcing term.

[0105] It should be noted that, in this embodiment of the invention, to ensure the convergence stability of the underlying evolution equation of the dynamic motion primitives, the system sets a bottom-level time scaling constant. The value is set to 1; to provide ample reference tension, the stiffness coefficient of the spring-damped system is... The damping coefficient is set to 1000; simultaneously, to achieve the critical damped state of the system and prevent overshoot oscillations caused by improper parameter settings of the algorithm itself, the damping coefficient is... Based on the critical damping formula The value is set to 63.2. By solving the above-mentioned fusion-optimized differential equations, the system can adaptively adjust the parameters of the driving evolution according to the real-time force deflection and work accumulation at the end in each sampling period, thereby completely eliminating the generation of high-frequency excitation and low-frequency divergence at the numerical level.

[0106] Thus, the single-step cooperative operation state is obtained by substituting the modified forcing term and the modified target attraction point into the underlying evolution equation of the dynamic motion primitive to perform state calculation.

[0107] Step S5: By performing numerical integration and inverse kinematic mapping on the single-step cooperative operation state, a continuous cooperative operation sequence is obtained and the dual robotic arms are driven to complete the handover of a non-specific target.

[0108] After acquiring the single-step cooperative operation state corresponding to the target sampling time, the single-step cooperative operation state is used as the end-effector acceleration state parameter of the connector arm within the current sampling period. Based on a preset sampling period, the end-effector acceleration state parameter is subjected to time discretization integration to obtain the end-effector velocity state parameter corresponding to the next sampling time. Then, the end-effector velocity state parameter is integrated to obtain the end-effector position state parameter corresponding to the next sampling time. Thus, within each sampling period, the system can generate single-step position and velocity updates for the connector arm end based on the dynamic calculation results formed by the corrected forcing term and the corrected target attraction point.

[0109] In this embodiment, the numerical integration process can employ Euler integration or other numerical integration methods capable of continuously updating discrete sampled states, such as Runge-Kutta integration. Preferably, when the preset sampling period is 1 millisecond, the system uses Euler integration to progressively integrate the end-effector acceleration and velocity state parameters corresponding to the target sampling time, forming a continuous end-effector position sequence and a continuous end-effector velocity sequence during the handover transition period. The continuous end-effector position sequence and the continuous end-effector velocity sequence together constitute a continuous cooperative operation sequence after adaptive compliance processing and anti-drift compensation.

[0110] Furthermore, through inverse kinematics algorithm, the end position state parameters and end velocity state parameters in the continuous cooperative operation sequence are mapped to the joint angular displacement commands and joint angular velocity commands corresponding to each joint of the receiving arm, and the joint angular displacement commands and joint angular velocity commands are sent to the underlying joint servo actuator of the receiving arm, so that the receiving arm performs end posture adjustment and lifting and holding actions according to the continuous cooperative operation sequence.

[0111] Throughout the entire dual-arm handover transition period, the system cyclically executes steps S1 to S5, causing the adaptive attenuation factor of the forcing term and the dynamic drift compensation vector to be updated in real time with the end-effector state feedback data, and dynamically correcting the continuous cooperative operation sequence as the target load transfer process proceeds. When the handover arm gripper is fully open and the torque fluctuation and position drift at the end of the receiving arm tend to stabilize, the system determines that the load transfer process for the non-specific target is complete, exits the dynamic correction state of the dual-arm handover transition period, and thus drives the dual robotic arms to complete the smooth handover of the non-specific target.

[0112] Thus, by performing numerical integration and inverse kinematic mapping on the single-step cooperative operation state, a continuous cooperative operation sequence is obtained, which drives the two robotic arms to complete the handover of a non-specific target.

[0113] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for generating cooperative operation sequences of dual robotic arms oriented towards non-target-specific operations, characterized in that, The method includes: Step S1: Obtain end-effector state feedback data by collecting and preprocessing multimodal physical state data of the end of the connecting arm during the handover transition period; Step S2: By performing spatiotemporal deflection feature mapping on the actual three-dimensional torque vector and torque change rate in the end state feedback data, the adaptive decay factor of the forcing term is obtained and the forcing term is corrected. Step S3: By performing virtual work accumulation compensation processing on the end position deviation direction, end three-dimensional actual torque vector and end three-dimensional actual angular velocity vector in the end state feedback data, a dynamic drift compensation vector is obtained and the target attraction point is corrected; Step S4: By substituting the modified forcing term and the modified target attraction point into the underlying evolution equation of the dynamic motion primitive, the state is calculated to obtain the single-step cooperative operation state; Step S5: By performing numerical integration and inverse kinematic mapping on the single-step cooperative operation state, a continuous cooperative operation sequence is obtained and the dual robotic arms are driven to complete the handover of non-specific targets.

2. The method for generating a cooperative operation sequence of two robotic arms oriented towards a non-specific target according to claim 1, characterized in that, The process involves collecting and preprocessing multimodal physical state data at the end of the connecting arm during the handover transition period to obtain end-effector state feedback data, including: When two robotic arms work together to perform a handover task for a non-specific target, the moment when the system control command triggers the handover arm's gripper to open is determined as the start moment of the handover transition period between the two arms. During the handover transition period between the two arms, multimodal physical state data of the end of the connecting arm are collected according to a preset sampling period; A six-axis torque sensor installed at the flange of the connecting arm end collects three-dimensional torque data of the connecting arm end in Cartesian space, and obtains the actual three-dimensional torque data of the end based on the three-dimensional torque data; By reading the encoder position data and encoder speed data of each joint of the connector arm, and combining the forward kinematics model and Jacobian matrix of the connector arm, the end-effector state is calculated to obtain the end-effector three-dimensional actual position data, end-effector three-dimensional actual linear velocity data and end-effector three-dimensional actual angular velocity data. Low-pass filtering preprocessing is performed on the actual three-dimensional torque vector, actual three-dimensional position data, actual three-dimensional linear velocity data, and actual three-dimensional angular velocity data of the end-effector to obtain end-effector state feedback data.

3. The method for generating a cooperative operation sequence of two robotic arms oriented towards a non-specific target according to claim 1, characterized in that, The step of obtaining an adaptive attenuation factor for the forcing term and correcting the forcing term by performing spatiotemporal deflection feature mapping processing on the actual three-dimensional torque vector and torque change rate in the end-state feedback data includes: By performing instantaneous torsional deflection evaluation on the end-point three-dimensional actual torque vector and torque change rate in the end-point state feedback data, spatiotemporal deflection characteristic data of end-point torque are obtained. By performing attenuation mapping on the spatiotemporal deflection feature data of the end moment, an adaptive attenuation factor for the forced term is obtained. Based on the adaptive attenuation factor for the forced term, the original nonlinear forced term is weighted and attenuated to obtain a corrected forced term.

4. The method for generating a cooperative operation sequence of two robotic arms oriented towards a non-specific target according to claim 3, characterized in that, The process involves instantaneous torsional deflection assessment of the end-effector's three-dimensional actual torque vector and torque change rate in the end-effector state feedback data to obtain spatiotemporal deflection characteristic data of the end-effector torque, including: For any target sampling moment during the transition period of the two arms, extract the three-dimensional actual torque vector of the end corresponding to the target sampling moment from the end state feedback data, and obtain the torque change rate corresponding to the target sampling moment based on the three-dimensional actual torque vector of the end of the adjacent sampling moments; The cross product of the actual three-dimensional torque vector at the end of the target sampling time and the torque change rate is performed to obtain the torque space deflection at the target sampling time. The second-order norm of the torque space deflection magnitude is calculated to obtain the instantaneous torsional deflection assessment corresponding to the target sampling time; Based on the instantaneous torsional deflection assessment corresponding to each sampling moment between the start time of the dual-arm handover transition period and the target sampling moment, time accumulation processing is performed to obtain the historical torsional deflection cumulative assessment corresponding to the target sampling moment; The second-order norm squared processing is performed on the end three-dimensional actual torque vector corresponding to the target sampling time to obtain the static torque benchmark evaluation corresponding to the target sampling time; Based on instantaneous torsional deflection assessment, historical torsional deflection cumulative assessment, and static torque benchmark assessment, spatiotemporal deflection characteristic data of the end moment are obtained.

5. The method for generating a cooperative operation sequence of two robotic arms oriented towards a non-specific target according to claim 3, characterized in that, The process involves performing attenuation mapping on the spatiotemporal deflection feature data of the end moment to obtain an adaptive attenuation factor for the forced term, and then performing weight attenuation processing on the original nonlinear forced term based on the adaptive attenuation factor to obtain a corrected forced term, including: For any target sampling moment during the handover transition period of the two arms, extract the instantaneous torsional deflection assessment, historical torsional deflection cumulative assessment and static torque benchmark assessment corresponding to the target sampling moment from the spatiotemporal deflection characteristic data of the end moment. The instantaneous torsional deflection assessment, historical torsional deflection cumulative assessment and static torque benchmark assessment corresponding to the target sampling time are summed to obtain the attenuation mapping benchmark assessment corresponding to the target sampling time. The instantaneous torsional deflection assessment corresponding to the target sampling time is used as the numerator, and the attenuation mapping benchmark assessment corresponding to the target sampling time is used as the denominator. Ratio mapping is performed to obtain the adaptive attenuation factor of the forced term corresponding to the target sampling time. Obtain the original nonlinear forcing term corresponding to the target sampling time from the dynamic motion primitive model; The difference between constant 1 and the adaptive decay factor of the forced term corresponding to the target sampling time is used as the retained weight of the forced term corresponding to the target sampling time; The modified forced term corresponding to the target sampling time is obtained by multiplying the weight of the forced term corresponding to the target sampling time with the original nonlinear forced term corresponding to the target sampling time.

6. The method for generating a cooperative operation sequence of two robotic arms oriented towards a non-specific target according to claim 1, characterized in that, The process of obtaining a dynamic drift compensation vector and correcting the target attraction point by performing virtual work accumulation compensation processing on the end position deviation direction, the end three-dimensional actual torque vector, and the end three-dimensional actual angular velocity vector in the end state feedback data includes: By performing offset displacement direction extraction processing on the current three-dimensional position data of the end point and the initial reference three-dimensional position data at the handover start time in the end point status feedback data, the end point offset displacement direction data is obtained. By performing virtual work accumulation and energy benchmark normalization on the end-point three-dimensional actual torque vector, end-point three-dimensional actual angular velocity vector, and end-point three-dimensional actual linear velocity vector in the end-point state feedback data, dynamic drift compensation depth data is obtained. By performing spatial compensation vector mapping processing on the end offset displacement direction data and the dynamic drift compensation depth data, a dynamic drift compensation vector is obtained. Then, by performing reverse drift correction processing on the original target attraction point and the dynamic drift compensation vector, a corrected target attraction point is obtained.

7. The method for generating a cooperative operation sequence of two robotic arms oriented towards a non-specific target according to claim 6, characterized in that, The step of extracting the offset displacement direction data of the end-effector by comparing the current three-dimensional position data of the end-effector with the initial reference three-dimensional position data at the handover start time in the end-effector status feedback data includes: Extract the current three-dimensional actual position data of the end point corresponding to the target sampling time from the end point status feedback data, and obtain the initial reference three-dimensional position data corresponding to the start time of the handover transition period between the two arms; The difference between the current actual three-dimensional position data of the end point at the target sampling time and the initial reference three-dimensional position data is processed to obtain the end point position deviation vector at the target sampling time. Calculate the second norm of the end position deviation vector corresponding to the target sampling time to obtain the magnitude of the end position deviation corresponding to the target sampling time; Using the end position deviation vector corresponding to the target sampling time as the numerator and the end position deviation magnitude corresponding to the target sampling time as the denominator, normalization direction extraction processing is performed to obtain the end offset displacement direction data corresponding to the target sampling time.

8. The method for generating a cooperative operation sequence of two robotic arms oriented towards a non-specific target according to claim 6, characterized in that, The process involves performing virtual work accumulation and energy benchmark normalization on the three-dimensional actual torque vector, three-dimensional actual angular velocity vector, and three-dimensional actual linear velocity vector of the end state feedback data to obtain dynamic drift compensation depth data, including: For any target sampling moment during the transition period of the two arms, extract the three-dimensional actual torque vector and the three-dimensional actual linear velocity vector of the end from the end state feedback data corresponding to the target sampling moment, and extract the three-dimensional actual torque vector and the three-dimensional actual angular velocity vector of the end corresponding to each sampling moment between the start time of the transition period of the two arms and the target sampling moment. For any sampling moment between the start of the transition period between the two arms and the target sampling moment, the actual three-dimensional torque vector at the end of the sampling moment and the actual three-dimensional angular velocity vector at the end of the sampling moment are multiplied by the dot product to obtain the instantaneous virtual work evaluation corresponding to the sampling moment. The instantaneous virtual work evaluation corresponding to each sampling moment between the start time of the handover transition period of the two arms and the target sampling time is processed by time accumulation to obtain the virtual work accumulation evaluation corresponding to the target sampling time. The second norm of the actual three-dimensional torque vector at the end of the target sampling time is calculated to obtain the torque magnitude at the end of the target sampling time. The second norm of the actual three-dimensional linear velocity vector at the end of the target sampling time is also calculated to obtain the linear velocity magnitude at the end of the target sampling time. Multiply the end moment magnitude and the end linear velocity magnitude at the target sampling time, and add the product to the preset minimum constant to obtain the energy normalized benchmark assessment at the target sampling time. The virtual work accumulation assessment corresponding to the target sampling time is used as the numerator, and the energy normalized benchmark assessment corresponding to the target sampling time is used as the denominator. The ratio is normalized to obtain the bias energy accumulation depth assessment corresponding to the target sampling time. Based on the preset spatial displacement mapping coefficient, the spatial scale mapping process is performed on the bias energy accumulation depth assessment corresponding to the target sampling time to obtain the dynamic drift compensation depth data corresponding to the target sampling time.

9. A method for generating a cooperative operation sequence of two robotic arms oriented towards a non-specific target, as described in claim 6, is characterized in that... The process of obtaining a dynamic drift compensation vector by performing spatial compensation vector mapping processing on the end offset displacement direction data and the dynamic drift compensation depth data, and obtaining a corrected target attraction point by performing reverse drift correction processing on the original target attraction point and the dynamic drift compensation vector, includes: For any target sampling moment during the transition period of the two arms, acquire the end offset displacement direction data and dynamic drift compensation depth data corresponding to the target sampling moment; The dynamic drift compensation depth data corresponding to the target sampling time is used as the spatial compensation amplitude, and the end offset displacement direction data corresponding to the target sampling time is used as the spatial compensation direction. The spatial compensation direction and spatial compensation amplitude are multiplied and mapped to obtain the dynamic drift compensation vector corresponding to the target sampling time. Obtain the original target attraction point corresponding to the target sampling time from the dynamic motion primitive model; The original target attraction point at the target sampling time is compared with the dynamic drift compensation vector to obtain the corrected target attraction point at the target sampling time.

10. The method for generating a cooperative operation sequence of two robotic arms oriented towards a non-specific target according to claim 1, characterized in that, The process of substituting the modified forcing term and the modified target attraction point into the underlying evolution equation of the dynamic motion primitive to perform state calculation and obtain the single-step cooperative operation state includes: For any target sampling moment during the transition period of the two arms, obtain the correction forcing term, correction target attraction point, current end position state parameter and current end velocity state parameter corresponding to the target sampling moment; Obtain the underlying time scaling constant, spring damping system stiffness coefficient, and spring damping system damping coefficient from the dynamic motion primitive model; Based on the difference between the corrected target attraction point and the current end position state parameter at the target sampling time, and the stiffness coefficient of the spring damping system, the target convergence recovery term at the target sampling time is obtained. Based on the current end velocity state parameter, the underlying time scaling constant, and the damping coefficient of the spring damping system at the target sampling time, obtain the velocity damping suppression term at the target sampling time. Based on the target convergence recovery term, velocity damping suppression term and correction forcing term corresponding to the target sampling time, the underlying evolution state of the dynamic motion primitive is calculated to obtain the terminal acceleration state parameter corresponding to the target sampling time. The terminal acceleration state parameter corresponding to the target sampling time is used as the single-step cooperative operation state corresponding to the target sampling time.

Images