Composite control method for man-machine collaborative transportation in constraint task space based on multi-task priority, cascade ESO and ECBF

Abstract

The invention provides a compound control method for man-machine collaborative transportation in a constraint task space based on multi-task priority, cascade ESO and ECBF. The compound control method comprises the steps that a joint space dynamics model, a kinematics model and a null-space velocity kinematics model of a redundant robot are established; on the basis of a null space projection method, a multi-task priority decoupling controller is designed according to the priority sequence of end effector direction control, end effector position control and null space compliance control; the multi-task priority decoupling controller comprises an end effector direction stabilization controller, an end effector position compliance controller and a null space task compliance controller; and designing a two-stage cascaded ESO, and designing an index control barrier function based on the two-stage cascaded ESO to obtain an end effector position compliance controller.

Description

Technical Field

[0001] The present invention relates to the field of human-machine collaborative transportation. Specifically, it relates to a composite control method for human-machine collaborative transportation in a constrained task space based on multi-task priority, cascaded ESO, and ECBF. Background Art

[0002] Human-machine collaborative transportation in a task space constrained environment focuses on the optimization problem of robots and humans collaborating to complete material handling in complex scenarios. By integrating dynamic environment perception and real-time path planning technologies, the system can achieve efficient obstacle avoidance in narrow or dynamic obstacle areas; combining human motion intention prediction and adaptive impedance control to build a compliant interaction mechanism to ensure collaborative safety and operation fluency. This technology breaks through the traditional rigid collaboration mode of industrial robots and uses multi-modal sensors and intelligent decision-making algorithms to significantly improve the transportation efficiency in scenarios such as warehousing logistics and intelligent manufacturing, providing an innovative solution for human-machine co-fusion operations under space constraints.

[0003] In human-machine collaborative transportation with a constrained task space, ensuring that the end effector (such as a robotic arm gripper) always remains within a safe range is the core requirement for ensuring the safety and efficiency of human-machine collaboration. Because once the end effector exceeds the preset safety area, it may accidentally collide with the operator due to a deviation in the motion trajectory or dynamic changes in the environment, resulting in serious injuries; or it may impact surrounding equipment, shelves, or precision workpieces, causing high-cost economic losses or production interruptions.

[0004] In existing human-robot collaborative transportation with limited task space, commonly used methods include artificial potential field (APF), barrier Lyapunov function (BLF), and control barrier function (CBF). APF defines a potential function to represent the repulsive force from unsafe areas. However, due to neglecting system dynamics, it may cause the robot to enter unsafe areas. BLF and CBF explain the system dynamics and theoretically keep the robot within the safe area. However, the BLF scheme is too strict, only considering system states within the safe area and having strict requirements for initial conditions and reference trajectories. CBF considers the entire state space and defines a constraint function. If the nominal controller keeps the constraint function positive, it is used; otherwise, the system seamlessly switches to the constraint controller to prevent the robot from exceeding the safe area. Therefore, CBF has received increasing attention from researchers in recent years. Nguyen et al. introduced the exponential control barrier function (ECBF) to implement state constraints in high-order systems. Subsequently, ECBF has been applied in different fields. However, it should be noted that the performance of the ECBF method for state constraints depends on the accuracy of the system model. In a pHRC system based on multi-task priorities, the robot faces model uncertainties, external disturbances, and interference from high-priority tasks to low-priority tasks. These uncertainties pose challenges to imposing strict state constraints on traditional ECBF methods.

[0005] To solve the above existing problems, people have been seeking an ideal technical solution. Summary of the Invention

[0006] The object of the present invention is to address the deficiencies of the prior art and thus provide a composite control method and device for human-robot collaborative transportation in a constrained task space based on multi-task priorities, cascaded ESO, and ECBF.

[0007] To achieve the above object, the technical solution adopted by the present invention is as follows: A composite control method for human-robot collaborative transportation in a constrained task space based on multi-task priorities, cascaded ESO, and ECBF, characterized by comprising the following steps:

[0008] Establish the joint space dynamics model, kinematic model, and null space velocity kinematic model of the redundant robot;

[0009] Based on the null space projection method, design a multi-task priority decoupling controller in the order of priority: end effector direction control, end effector position control, null space compliant control;

[0010] Design a two-stage cascaded ESO, where the first-stage ESO obtains the disturbance torque based on the joint space dynamics model, and the second-stage ESO obtains the disturbance estimation error based on the end effector position task dynamics;

[0011] Design an exponential control barrier function based on a second - level cascade ESO, and obtain a compliant controller that can constrain the position of the end - effector based on the exponential control barrier function and the nominal controller.

[0012] The present invention has prominent substantive features and significant progress compared with the prior art. Specifically, the present invention proposes a composite control framework based on multi - task, cascaded extended state observer (ESO) and control barrier function (CBF). The framework aims to ensure the stability of the posture of the transported object and enable the robot end - effector to always comply with human movements within a safe range. First, a multi - task priority scheme based on null - space projection is adopted, and controllers are designed in the order of priority: end - effector attitude stabilization, position impedance control, and null - space compliance control, ensuring that the attitude control performance is not affected by other tasks. Next, a cascaded ESO is designed to estimate system model uncertainties, external disturbances, and the interference of high - priority tasks on low - priority tasks. Then, a CBF is designed based on the cascaded ESO to ensure that the position of the end - effector is always within a safe range.

[0013] Compared with traditional controllers without a priority structure, this method significantly improves the stability of the end - effector direction control. Compared with control schemes without CBF, it successfully restricts the movement of the end - effector within the restricted task space. In addition, compared with traditional CBF schemes without disturbance estimation, this method improves the performance of the algorithm. Brief Description of the Drawings

[0014] Figure 1 is a schematic flow chart of the present invention.

[0015] Figure 2 is a principle block diagram of the present invention. Detailed Embodiment

[0016] The extended state observer (ESO) has wide applicability because it can estimate states and compound uncertainties using only position measurements, while simplifying the tuning process. However, it is more effective for fixed or slowly changing disturbances, while the multi - task - priority - based pHRC involves highly time - varying uncertainties. The cascaded ESO has shown excellent performance in estimating such changes. Therefore, combining the cascaded ESO with ECBF can enhance the state - constraint performance in complex uncertain systems. This application integrates multi - task priority, cascaded ESO, and ECBF to ensure the stability of the posture of the transported object and enable the robot end - effector to always comply with human movements within a safe range. And before the applicant's research, no previous research has explored applying the cascaded ESO to ECBF or integrating cESO - ECBF into multi - task - priority - based pHRC to handle state constraints.

[0017] The following is a detailed description of the technical solution of the present invention through specific embodiments in combination with Figure 1 and Figure 2 , as follows:

[0018] Embodiment 1

[0019] The composite control method based on multi-task priority, cascaded extended state observer (ESO) and exponential control barrier function (ECBF) proposed in this embodiment includes the following steps:

[0020] Step 1: Establish the joint space dynamics model, kinematic model, and null space velocity kinematic model of the redundant robot;

[0021] The expression of the joint space dynamics model of the redundant robot is:

[0022]

[0023] In the formula, respectively represent the joint position, velocity, and acceleration, M(q) ∈ R n×n is the inertia matrix, is the Coriolis matrix, G(q) ∈ R n is the gravity torque, τ ∈ R n is the control torque, is the Jacobian matrix corresponding to the end effector position, is the external force applied to the end effector obtained by the force sensor, τ d is the disturbance torque including unknown load, model error, and external torque applied to the robot body, n is the number of joints of the robot, m p is the dimension of the end effector position;

[0024] The expression of the robot kinematic model is:

[0025]

[0026] In the above formula, is the quaternion form of the end effector direction matrix R e η e is the scalar part, is the vector part, is the position of the end effector, and are the rotational and translational velocities of the end effector, ψ k (·) is the forward kinematics, is the Jacobian matrix corresponding to the end effector direction;

[0027] The expression of the null space velocity kinematic model is:

[0028]

[0029] Hypothesis 1: There are no singular configurations in the motion process of the robot, and it satisfies

[0030] The velocity in the augmented task space is

[0031]

[0032] Under Hypothesis 1, J aug is a full-rank matrix.

[0033] Step 2: Based on the null space projection method, design a multi-task priority decoupling controller according to the priority order: end effector direction control, end effector position control, null space compliance control, to ensure that the attitude control performance is not affected by other tasks.

[0034] Step 2.1: To ensure that the end effector direction control is not affected by other tasks, make the following adjustment to the Jacobian matrix corresponding to the end effector position:

[0035]

[0036] where is the inertia-weighted pseudo-inverse of J r the inertia-weighted pseudo-inverse of J is the inertia-weighted pseudo-inverse of J r is the identity matrix, I ∈ R n×n is the identity matrix, is the velocity of the second-level task in the priority structure, which will be affected by w;

[0037] Based on the adjusted Jacobian matrix, obtain the augmented Jacobian matrices of each level of task

[0038]

[0039] Under the conditions of Hypothesis 1 in Step 1, is a full-rank matrix, and then the relationship between and can be obtained, where is a lower triangular block matrix, specifically as follows:

[0040]

[0041] Step 2.2: Based on the augmented Jacobian matrices of each level of task, obtain the inertia-decoupled task space dynamics model:

[0042]

[0043] where, is an interference item from the first-priority task,

[0044] Step 2.3, design the multi-task priority decoupling controller as:

[0045]

[0046] where is the estimated value of τ d subsequently estimated by the first stage of the cascaded ESO, F ctrl,r and F ctrl,p are the orientation and position controllers of the end effector, F ctrl,z is the null-space compliance controller.

[0047] Step 2.4, after substituting the multi-task priority decoupling controller into the inertial decoupled task-space dynamics model, the dynamics models of each level of tasks are obtained;

[0048]

[0049]

[0050] wherein, is the estimation error.

[0051] Step 2.5, based on the dynamics models of each level of tasks obtained above, design the corresponding controllers respectively: the end effector orientation stabilization controller, the end effector position compliance controller, and the null-space task compliance controller;

[0052] It should be noted that the position of the end effector should be constrained within the safe area. Therefore, the position compliance controller designed in this embodiment is the nominal controller. Subsequently, an exponential control barrier function is further designed to ensure that the position of the robot end effector is constrained within the safe area while being as close as possible to the nominal controller, thereby realizing the compliant behavior within the safe area.

[0053] The control design of each level of tasks is as follows:

[0054]

[0055]

[0056] wherein, is the estimated value of, subsequently obtained by the second stage of the cascaded ESO estimation, F ctrl,p,no is the nominal controller for realizing position compliance, is the control gain of the orientation controller, K d,z ∈R n×n , is the control gain of the null-space compliance control, ε de is the direction error matrix the vector part in the quaternion form of, R d is the reference direction of the end effector for keeping the tray horizontal; q d is the joint reference position, which is usually used to maintain the maximum operability of the robot.

[0057] Step 3: Design a second-order cascaded ESO. Among them, the first-order ESO obtains the disturbance torque based on the joint-space dynamic model, and the second-order ESO obtains the disturbance estimation error based on the end-effector position task dynamics to estimate the system model uncertainty, external disturbance, and the interference of high-priority tasks on low-priority tasks.

[0058] Design the first-order ESO:

[0059] Define the extended state vector and Then the joint-space dynamics can be transformed into the state-space form

[0060]

[0061] Then, design the first-order ESO as follows

[0062]

[0063] where and are and the estimations of, the observer gains w q is the bandwidth of the observer, which is used to adjust the performance of the first-order ESO. The larger the bandwidth, the smaller the observer error, but it will amplify the noise in the system and may cause the instability of the system. Therefore, the size of the bandwidth needs to be balanced between the observation performance and the system stability.

[0064] Then further obtain Here, the upper bound of the disturbance estimation error is defined as

[0065] Then, design the second-order ESO:

[0066] Define the extended state vector and Then the dynamics corresponding to the end-effector position task can be transformed into the state-space form

[0067]

[0068] Then, design the second-order ESO as follows

[0069]

[0070] where and are and estimates, and the observer gain is the bandwidth of the observer, which is used to adjust the performance of the second-stage ESO. The larger the bandwidth, the smaller the observer error, but it will amplify the noise in the system and may cause system instability. Therefore, the size of the bandwidth needs to be balanced between the observation performance and system stability.

[0071] Then, further obtain Here, the upper bound of the disturbance estimation error is defined as

[0072] It can be seen that the role of the second-stage ESO is to estimate the estimation error of the first-stage ESO and the interference of the first-priority task on the second-priority task, and the interference estimated by the second-stage ESO will be used to design the end-effector position controller and the exponential control barrier function in step 4.

[0073] Step 4: Design an exponential control barrier function based on the two-stage cascaded ESO to obtain a set of controllers that ensure that the position of the robot end-effector is always within the safety set. Then, based on the exponential control barrier function and the nominal controller, obtain a compliant controller that can constrain the position of the end-effector to ensure that the position of the end-effector is always within the safe range.

[0074] Define the safety set C that constrains the position of the robot end-effector

[0075]

[0076] where h max (x p ) = x max,p - x p , h min (x p ) = x p - x min,p are constraint functions, and here is a constant and satisfies

[0077] The first derivative of the constraint function is

[0078]

[0079] The second derivative of the constraint function is

[0080]

[0081]

[0082] Definition 1 (Disturbance Estimation-based Exponential Control Barrier Function (DE-ECBF)) Consider the nonlinear system where \(u\) is the control input, \(f(x)\) and \(g(x)\) are known system models, and \(d(t)\) is an unknown external disturbance; a function \(h(x)\) of relative degree \(r (r > 1)\) is called a DE-ECBF if there exists \(K\in\mathbb{R}\) r and

[0083]

[0084] where is the upper bound of the disturbance estimation error, satisfying Define the set The following lemma guarantees that \(h(x)\) is non-negative.

[0085] Lemma 1: For a function \(h(x)\) of relative degree \(r (r > 1)\) satisfying the DE-ECBF condition, any locally Lipschitz controller \(u\in\mathcal{K}\) h (x) can ensure that \(h(x)>0\) for all \(t > 0\).

[0086] According to Definition 1, the allowable set of the controller \(u\) ctrl,p can be obtained and is defined as follows:

[0087]

[0088] Then, use quadratic programming QP to determine the minimum regulatory control force required to maintain the safety condition:

[0089]

[0090] Compared with traditional controllers without a priority structure, this method significantly improves the stability of the end effector orientation control. Compared with control schemes without CBF, it successfully restricts the movement of the end effector within the restricted task space. In addition, compared with traditional CBF schemes without disturbance estimation, this method improves the performance of the algorithm.

[0091] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that: it is still possible to modify the specific implementation manners of the present invention or perform equivalent replacements on some technical features; without departing from the spirit of the technical solutions of the present invention, they should all be covered within the scope of the technical solutions claimed by the present invention.

Claims

1. A composite control method for human-robot collaborative transportation in a constrained task space based on multi-task priority, cascaded ESO, and ECBF, characterized in that It includes the following steps: Establish the joint space dynamics model, kinematics model, and null space velocity kinematics model of the redundant robot; Based on the null space projection method, design a multi-task priority decoupling controller according to the priority order: end effector orientation control, end effector position control, null space compliance control; Design a second-order cascaded ESO. Among them, the first-order ESO obtains the disturbance torque based on the joint space dynamics model, and the second-order ESO obtains the perturbation estimation error based on the end effector position task dynamics; Design an exponential control barrier function based on the second-order cascaded ESO, and obtain a compliance controller that can constrain the end effector position based on the exponential control barrier function and the nominal controller.

2. The composite control method for human-machine collaborative transportation in a constrained task space based on multi-task priority and cascaded ESO according to claim 1, characterized in that, The expression of the redundant robot joint space dynamics model is: wherein, represent the joint position, velocity, and acceleration respectively, M(q) ∈ R n×n is the inertia matrix, is the Coriolis matrix, G(q) ∈ R n is the gravity torque, τ ∈ R n is the control torque, is the Jacobian matrix corresponding to the end effector position, is the external force applied to the end effector obtained by the force sensor, τ d is the disturbance torque, including unknown loads, model errors, and external torques applied to the robot body, n is the number of joints of the robot, m p is the dimension of the end effector position; The expression of the robot kinematics model is: In the above formula, is the quaternion form of the end effector orientation matrix R e , where η e is the scalar part, is the vector part, is the position of the end effector, and are the rotational and translational velocities of the end effector, ψ k (·) is the forward kinematics, is the Jacobian matrix corresponding to the end effector orientation; The expression of the null space velocity kinematics model is: Hypothesis 1: There is no singular configuration in the motion process of the robot, and it satisfies The velocity in the augmented task space is Under Hypothesis 1, J aug is a full-rank matrix.

3. The composite control method for human-machine collaborative transportation in a constrained task space based on multi-task priority, cascaded ESO, and ECBF according to claim 2, wherein, Based on the null space projection method, design a multi-task priority decoupling controller according to the priority order: end effector orientation control, end effector position control, null space compliance control, including: Adjust the Jacobian matrix corresponding to the end effector position to obtain the augmented Jacobian matrix of each task; Based on the augmented Jacobian matrix of each task, obtain the inertia-decoupled task space dynamics model; Design a multi-task priority decoupling controller: where is the estimate of τ d , F ctrl,r and F ctrl,p are the orientation controller and position controller of the end effector, and F ctrl,z is the null space compliance controller; After substituting the multi-task priority decoupling controller into the inertia-decoupled task space dynamics model, obtain the dynamics model of each task; Based on the dynamics model of each task obtained above, design the corresponding controllers respectively: end effector orientation stabilization controller, end effector position compliance controller, null space task compliance controller; Among them, is 's estimated value, F ctrl,p,no is the nominal controller for implementing position compliance, is the control gain of the orientation controller, K d,z ∈R n×n , is the control gain of the null-space compliance control, ε de is the orientation error matrix 's vector part in the quaternion form, R d is the reference orientation of the end effector; q d is the joint reference position.

4. The composite control method for human-machine collaborative transportation in a constrained task space based on multi-task priority, cascaded ESO, and ECBF according to claim 3, characterized in that The design steps of the second-order cascaded ESO are: Define the expanded state vector and z q3 = Δ = M -1 τ d , then the joint space dynamics can be transformed into the state space form Design the first-order ESO as the following structure: where and are the estimates of z q1 , z q2 and z q3 , and the observer gain K q1 = 3w q , w q is the bandwidth of the observer; Obtain the interference torque based on the first-level ESO wherein Define the extended state vector and Then the dynamics corresponding to the end - effector position task can be transformed into the state - space form: Design the second-order ESO as the following structure: Among them and are and estimates of, the observer gain is the bandwidth of the observer; Obtained based on the first-level ESO Among them, 5. The composite control method for human-machine collaborative transportation in a constrained task space based on multi-task priority, cascaded ESO, and ECBF according to claim 4, characterized in that, Design an exponential control barrier function based on the second-order cascaded ESO, and obtain a compliance controller that can constrain the end effector position based on the exponential control barrier function and the nominal controller, including: Define the safety set C that constrains the end effector position of the robot as: where h max (x p ) = x max,p - x p , h min (x p ) = x p - x min,p is a constraint function, where is a constant and satisfies The first-order differential of the constraint function is: The second-order differential of the constraint function is: Definition 1: Consider the nonlinear system where u is the control input, f(x) and g(x) are known system models, and d(t) is an unknown external disturbance; a function h(x) of relative degree r (r > 1) is called a DE-ECBF if there exists K ∈ R r and then where is the upper bound of the disturbance estimation error, satisfying Define the set The following lemma ensures that h(x) is non-negative; Lemma 1: For a function \(h(x)\) with relative degree \(r (r > 1)\) satisfying the DE - ECBF condition, any locally Lipschitz controller \(u\in\mathcal{K}\) h (x) can ensure that \(h(x)>0\) holds for all \(t > 0\); According to Definition 1, the admissible set of the controller u ctrl,p can be obtained and is defined as follows: Then, use QP to determine the minimum adjustment control force required to maintain the safety condition:

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