Position constraint posture optimization control method, device and equipment of underactuated manipulator and robot

Abstract

The application discloses a position constraint posture optimization control method, device and equipment of an underactuated manipulator and a robot, and relates to the technical field of robots. The method comprises the following steps: obtaining a target pose, a current joint angle and constraint parameters of the underactuated manipulator, wherein the target pose comprises a target position and a target posture, and the constraint parameters comprise a limiting range of each controllable joint of the underactuated manipulator; constructing a constraint optimization problem by taking the joint angle of each controllable joint as a decision variable, minimizing the posture error between the end posture and the target posture as an optimization target, taking the arrival of the end position at the target position as an equality constraint, and taking the limiting range as an inequality constraint; solving the constraint optimization problem to obtain a target joint angle that satisfies the equality constraint and the inequality constraint and has the minimum posture error; and controlling the motion of the underactuated manipulator according to the target joint angle. The application can improve the end posture control precision of the underactuated manipulator.

Description

Technical Field

[0001] This application relates to the field of robotic arm control, and in particular to a method, apparatus, equipment and robot for position constraint posture optimization control of a robotic arm with insufficient degrees of freedom. Background Technology

[0002] In the field of industrial robotics, a six-degree-of-freedom serial robotic arm is the standard configuration for achieving arbitrary position and posture control of the end effector in three-dimensional space. However, in practical applications such as photovoltaic cleaning and construction machinery, due to considerations such as cost and structural reliability, a less-degree-of-freedom serial robotic arm with fewer controllable joints than the target pose degree of freedom is often used. For example, a robotic arm with five controllable joints but lacking one rotational degree of freedom at the end effector, where some joints can be driven by a parallelogram linkage mechanism.

[0003] For robotic arms with insufficient degrees of freedom, since the number of controllable joints is insufficient to simultaneously constrain the position and orientation of the end effector, related technologies typically employ two approaches. One approach uses a position-only inverse kinematics (IK) approach, reducing the inverse kinematics problem to a position constraint solution. While this yields joint angles that meet the position requirements, it completely abandons control over the end effector's orientation, resulting in an arbitrary end effector orientation corresponding to the solution returned by the solver. The other approach, based on the position-only IK approach, uses coordinate transformation to obtain the deviation between the current and target orientations of the end effector. This deviation is then linearly superimposed onto the current angles of the corresponding joints for compensation, and the target pose is gradually approximated through multiple iterations.

[0004] However, since the joints adjusted by attitude compensation also affect the end position, the accuracy of the reached end position will be destroyed after the attitude compensation changes the joint angle. That is, there is a coupling interference between position control and attitude adjustment, which requires multiple iterations to alternately correct the position deviation and attitude deviation. Moreover, the linear superposition compensation method has a large error when the joint axis direction changes with the arm shape, resulting in low end attitude control accuracy of the under-degree-of-freedom robot arm. Summary of the Invention

[0005] This application aims to propose a position constraint attitude optimization control method, device, equipment and robot for a manipulator with insufficient degrees of freedom, which can improve the end-effector attitude control accuracy of the manipulator.

[0006] In a first aspect, embodiments of this application provide a method for position constraint attitude optimization control of a manipulator with insufficient degrees of freedom, comprising the following steps: The target pose, current joint angle, and constraint parameters of the under-degree-of-freedom manipulator are obtained. The target pose includes the target position and the target orientation. The constraint parameters include the limit range of each controllable joint of the under-degree-of-freedom manipulator. Using the joint angles of each controllable joint as decision variables, minimizing the attitude error between the end-effector attitude and the target attitude as the optimization objective, the end-effector position reaching the target position as an equality constraint, and the limiting range as an inequality constraint, a constrained optimization problem is constructed. Solving the constrained optimization problem yields the target joint angle that satisfies both the equality and inequality constraints and minimizes the attitude error. The movement of the under-degree-of-freedom robotic arm is controlled according to the target joint angle.

[0007] According to some embodiments of this application, the under-degree-of-freedom robotic arm includes a target joint driven by a parallelogram linkage mechanism, and the constraint parameters also include the actuator travel range of the target joint; The inequality constraint also includes that the actuator angle of the target joint is within the actuator stroke range, and the actuator angle is determined according to the geometric angle of the target joint and the joint angle of the upstream joint of the target joint, according to a preset transformation relationship.

[0008] According to some embodiments of this application, the optimization objective further includes a sub-objective of minimizing joint motion. The objective function of the constrained optimization problem is the weighted sum of the norm of the attitude error and the joint motion, where the joint motion is the deviation between the decision variable and the current joint angle, and the weighting coefficient corresponding to the norm of the attitude error is greater than the weighting coefficient corresponding to the joint motion.

[0009] According to some embodiments of this application, before solving the constrained optimization problem, the method further includes: Using the current joint angle as the initial seed, perform position-only inverse kinematics solution on the target position to obtain the initial joint angle that satisfies the equality constraint; Solving the constrained optimization problem includes: using the initial joint angle as the initial point, solving the constrained optimization problem.

[0010] According to some embodiments of this application, the step of using the current joint angle as an initial seed to perform position-only inverse kinematics solution on the target position to obtain the initial joint angle that satisfies the equality constraint includes: Multiple sets of bounded random perturbations are applied to the current joint angle to obtain multiple perturbation configurations; Using each of the aforementioned perturbation configurations as initial seeds, the target position is solved by position-only inverse kinematics to obtain multiple initial joint angles that satisfy the aforementioned equality constraints; The step of solving the constrained optimization problem using the initial joint angle as the initial point includes: solving the constrained optimization problem using each of the initial joint angles as the initial point to obtain multiple candidate solutions; and selecting the candidate solution with the smallest objective function value from the multiple candidate solutions as the target joint angle.

[0011] According to some embodiments of this application, solving the constrained optimization problem includes: In each iteration, the constrained optimization problem is locally approximated as a quadratic programming subproblem at the current iteration point, and the search direction is obtained by solving the quadratic programming subproblem. The step size is determined by line search, and the current joint angle is updated according to the search direction and the step size; If the updated current joint angle meets the preset convergence condition, the iteration stops, and the updated current joint angle is determined as the target joint angle.

[0012] According to some embodiments of this application, the attitude error is determined by logarithmic mapping of rotation matrices. The attitude error is a three-dimensional axis-angle vector obtained by logarithmic mapping based on the product of the transpose of the end-effector rotation matrix corresponding to the current joint angle and the target rotation matrix. The step of controlling the movement of the under-degree-of-freedom robotic arm according to the target joint angle includes: converting the target joint angle from a geometric space angle to an actuator space angle; generating a smooth trajectory that satisfies velocity and acceleration constraints according to the actuator space angle; and sending the smooth trajectory to the motion controller of the under-degree-of-freedom robotic arm for execution.

[0013] Secondly, embodiments of this application provide a position constraint attitude optimization control device for a manipulator with insufficient degrees of freedom, comprising: The pose acquisition module is used to acquire the target pose, current joint angle and constraint parameters of the under-degree-of-freedom manipulator. The target pose includes the target position and the target orientation, and the constraint parameters include the limit range of each controllable joint of the under-degree-of-freedom manipulator. The constrained optimization problem construction module is used to construct a constrained optimization problem with the joint angles of each controllable joint as decision variables, the minimization of the attitude error between the end pose and the target pose as the optimization objective, the end position reaching the target position as an equality constraint, and the limit range as an inequality constraint. The constraint optimization problem solving module is used to solve the constraint optimization problem to obtain the target joint angle that satisfies the equality constraints and the inequality constraints and minimizes the attitude error; The motion control module is used to control the movement of the under-degree-of-freedom robotic arm according to the target joint angle.

[0014] Thirdly, embodiments of this application provide an electronic device, the device comprising: a processor and a memory storing computer program instructions; When the processor executes the computer program instructions, it implements the position constraint attitude optimization control method for the under-degree-of-freedom robotic arm as described in the first aspect.

[0015] Fourthly, embodiments of this application provide a robot, including a robot body, a robotic arm disposed on the robot body, and a controller, wherein the robotic arm is a low-degree-of-freedom robotic arm, and the controller is used to operate the method described in the first aspect embodiment.

[0016] The position constraint attitude optimization control method, apparatus, device, and robot of the under-degree-of-freedom robotic arm according to the embodiments of this application have at least the following beneficial effects: In this embodiment, a unified constraint optimization problem is constructed and solved by using the joint angles of each controllable joint as decision variables, minimizing the attitude error between the end-effector attitude and the target attitude as the optimization objective, using the end-effector position reaching the target position as an equality constraint, and using the limit range of each controllable joint as an inequality constraint. This ensures that the end-effector position accuracy is strictly guaranteed by the equality constraints during the solution process, and the end-effector attitude is continuously optimized by the optimization objective during the solution process. Position control and attitude adjustment are mathematically decoupled within the constraint optimization framework. A single solution can simultaneously obtain the joint angles that achieve accurate position and optimal attitude approximation without the need for multiple iterative corrections between position and attitude, or the assumption of a one-to-one linear superposition of joint and attitude components. This improves the end-effector attitude control accuracy of the under-degree-of-freedom robotic arm.

[0017] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0018] The present application will be further described below with reference to the accompanying drawings and embodiments, wherein: Figure 1 A flowchart illustrating an embodiment of the position constraint attitude optimization control method for a manipulator with insufficient degrees of freedom provided in this application; Figure 2 A schematic diagram of the position constraint attitude optimization control device for the under-degree-of-freedom manipulator provided in this application; Figure 3 A schematic diagram of the structure of the electronic device provided in this application. Detailed Implementation

[0019] The features and exemplary embodiments of various aspects of this application will be described in detail below. To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only intended to explain this application and not to limit it. For those skilled in the art, this application can be implemented without some of these specific details. The following description of the embodiments is merely to provide a better understanding of this application by illustrating examples.

[0020] In this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, without necessarily requiring or implying any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus that includes said element.

[0021] Before introducing the technical solutions of the embodiments of this application, the application scenarios and related concepts involved in the embodiments of this application will be explained first.

[0022] A low-degree-of-freedom (DOF) robotic arm refers to a serial robotic arm with fewer controllable joints than the number of degrees of freedom in the end effector's pose. The complete pose of the end effector in three-dimensional space includes three position components and three orientation components, totaling six degrees of freedom. When a robotic arm has only five controllable joints, it cannot simultaneously constrain all six orientation components through inverse kinematics; such a robotic arm is considered a low-DOF robotic arm. For example, in a photovoltaic cleaning scenario, a five-joint hydraulic robotic arm mounted on a mobile chassis has six physical joints. The sixth physical joint lacks controllable motion capability, while the fifth physical joint is driven by a parallelogram linkage mechanism. The robotic arm needs to deliver the cleaning device at the end effector to a designated position on the photovoltaic panel surface and maintain a specified posture of contact with the panel as much as possible.

[0023] A parallelogram linkage mechanism is a transmission mechanism consisting of four links forming a parallelogram. In this mechanism, there is a coupling relationship between the geometric angles of the driven joint and the output angle of the actuator. The actuator angle depends not only on the geometric angle of the joint itself but also on the angle of its upstream joint. For example, for a joint driven by a hydraulic cylinder via a parallelogram linkage mechanism, the stroke range of the hydraulic cylinder is a physically measurable constraint, while the geometric angles used for kinematic solutions need to be calculated based on the hydraulic cylinder output angle and the upstream joint angle.

[0024] Forward kinematics refers to the process of calculating the end effector pose based on the joint angles of the robotic arm; inverse kinematics refers to the process of solving for the joint angles based on the target pose of the end effector; position-only inverse kinematics refers to the inverse kinematics solution method that only uses the end effector position as a constraint and does not impose constraints on the end effector attitude. The Jacobian matrix is ​​a matrix that describes the mapping relationship between the end effector velocity and the joint angular velocity. The position Jacobian matrix describes the mapping from joint angular velocity to end effector linear velocity, while the attitude Jacobian matrix describes the mapping from joint angular velocity to end effector angular velocity.

[0025] To address the technical problems in the background art, embodiments of this application provide a method, apparatus, device, and robot for optimizing the position constraint posture of a robot arm with insufficient degrees of freedom. The method for optimizing the position constraint posture of a robot arm with insufficient degrees of freedom provided in this application embodiment will be described first below.

[0026] Figure 1 This diagram illustrates a flow chart of the position constraint attitude optimization control method for a under-degree-of-freedom robotic arm provided in an embodiment of this application. This method can be applied to an electronic device, which can be a host control device communicating with the robotic arm's motion controller, or it can be integrated within the motion controller. Figure 1 As shown, the method includes the following steps: Step S101: Obtain the target pose, current joint angle, and constraint parameters of the under-degree-of-freedom manipulator. The target pose includes the target position and target orientation, and the constraint parameters include the limit range of each controllable joint of the under-degree-of-freedom manipulator.

[0027] In this step, the target pose refers to the desired pose of the robotic arm's end effector, which can be a six-degree-of-freedom pose description with reference to the robotic arm's base coordinate system. The target position refers to the three-dimensional spatial coordinates of the desired end effector position; for example, in a photovoltaic cleaning scenario, the target position could be the three-dimensional coordinates of a cleaning point on the photovoltaic panel surface. The target orientation refers to the desired three-dimensional orientation of the desired end effector position, such as a perpendicular orientation to the photovoltaic panel surface. The target pose can be generated by the upper-level planning module and received through the communication interface, or it can be input by the operator through a teaching pendant.

[0028] The current joint angle refers to the angle value of each controllable joint of the robotic arm at the current moment, which can be obtained by subscribing to the joint state topic. It should be noted that for joints driven by parallelogram linkage mechanisms, the actuator space angle is directly obtained from the joint state topic. Electronic devices can first convert the actuator space angle into geometric space angle according to the kinematic relationship of the parallelogram linkage mechanism, and then use it as the current joint angle in subsequent calculations.

[0029] Constraint parameters are parameters that limit the feasible range of joint angles. The limit range of each controllable joint refers to the range of angles that each joint is allowed to rotate in terms of mechanical structure. These parameters can be read from the robot model description file (such as the Unified Robot Description Format URDF file) or from mechanical calibration data.

[0030] Step S102: Using the joint angles of each controllable joint as decision variables, minimizing the attitude error between the end-effector attitude and the target attitude as the optimization objective, using the end-effector position reaching the target position as an equality constraint, and using the limit range as an inequality constraint, a constrained optimization problem is constructed.

[0031] In this step, the decision variable refers to the unknown quantity to be solved in the constrained optimization problem, that is, the vector composed of the joint angles of each controllable joint. Taking a robotic arm with five controllable joints as an example, the decision variable is a five-dimensional vector, denoted as θ, that is, θ is equal to the column vector composed of θ1, θ2, θ3, θ4, and θ5, where θ1 to θ5 are the joint angles of the first to fifth controllable joints, respectively.

[0032] Attitude error refers to the rotational deviation between the current attitude and the target attitude of the robotic arm's end effector. In some embodiments, attitude error can be determined by logarithmic mapping of rotation matrices. Specifically, attitude error e(θ) is a three-dimensional axis-angle vector obtained by logarithmic mapping based on the product of the transpose of the end effector rotation matrix corresponding to the current joint angle θ and the target rotation matrix. Its expression is as follows: e(θ) = log(R(θ) · R_target)∨; In the formula, R(θ) is the end-effector rotation matrix corresponding to the joint angle θ, calculated from forward kinematics, and is a 3x3 matrix; R_target is the target rotation matrix corresponding to the target pose; R(θ) Let R(θ) be the transpose of R(θ); log(·)∨ represents a logarithmic mapping of the rotation matrix and taking the axis-angle vector, that is, converting the rotation matrix into a three-dimensional rotation error vector; e(θ) is the three-dimensional attitude error vector. Accordingly, the scalar measure of attitude error can be expressed as E(θ), which is equal to the square of the L2 norm of the attitude error vector e(θ), that is, E(θ) = ‖e(θ)‖², where ‖·‖² represents the square of the L2 norm (i.e., the Euclidean length) of the vector.

[0033] Equality constraints are constraints that must be strictly satisfied during the solution process. In this embodiment, the equality constraint is that the endpoint position reaches the target position, and its expression is: h(θ)=p(θ) p_target = 0; In the formula, h(θ) is the equality constraint function, which is a three-dimensional vector; p(θ) is the end position corresponding to the joint angle θ, calculated by forward kinematics; p_target is the target position; h(θ) equal to zero indicates that the end position has accurately reached the target position.

[0034] Inequality constraints are constraints that allow values ​​to take on a range during the solution process. In the embodiments of this application, the inequality constraints at least include the limit range of each controllable joint, and their expression is: g1(θ):θ_min≤θ≤θ_max; In the formula, g1(θ) is the joint limit inequality constraint; θ_min and θ_max are vectors composed of the lower limit and upper limit of the limit range of each controllable joint, respectively.

[0035] Based on the above optimization objectives and constraints, the constrained optimization problem can be expressed as: minimizeF(θ)=w1·‖e(θ)‖²; subject toh(θ)=p(θ) p_target=0, θ_min≤θ≤θ_max; In the formula, minimize means finding the minimum value of the objective function; subject to means constrained to, that is, the solution process must satisfy the constraints listed below; F(θ) is the objective function; w1 is the weight coefficient corresponding to the attitude error term.

[0036] It should be noted that in this constrained optimization problem, the precise arrival of the end effector position is a hard constraint of equality, guaranteed by the constraint satisfaction mechanism of the optimization solver. That is, any feasible solution output by the solver satisfies the position requirement. The optimization of the end effector attitude is driven by the objective function, meaning that the solver continuously reduces the attitude error while satisfying the constraints. Position control and attitude adjustment are thus mathematically decoupled within the constrained optimization framework. The attitude optimization process does not destroy the already satisfied position accuracy. Therefore, a single solution can simultaneously obtain the joint angles with precise position and optimal attitude, avoiding the coupling interference caused by the step-by-step execution of position control and attitude compensation in related technologies.

[0037] Step S103: Solve the constraint optimization problem to obtain the target joint angle that satisfies both equality and inequality constraints and minimizes the attitude error.

[0038] In this step, the electronic device can use a nonlinear constraint optimization solver to solve the constraint optimization problem constructed in step S102. The target joint angle refers to the angle value of each controllable joint used to control the movement of the robotic arm after the solution is completed. It simultaneously satisfies the position equality constraint and the joint limit inequality constraint, and has the smallest corresponding attitude error among all feasible solutions that satisfy the constraints.

[0039] Step S104: Control the movement of the under-degree-of-freedom robotic arm according to the target joint angle.

[0040] In this step, the electronic device can generate control commands based on the target joint angle and send them to the motion controller of the robotic arm to drive each joint to move to the target joint angle, so that the end effector can accurately reach the target position and approach the target posture in the best way.

[0041] The position-constrained attitude optimization control method for a low-degree-of-freedom manipulator provided in this application constructs and solves a unified constraint optimization problem by using the joint angles of each controllable joint as decision variables, minimizing the attitude error between the end-effector attitude and the target attitude as the optimization objective, using the end-effector position reaching the target position as an equality constraint, and using the limit range of each controllable joint as an inequality constraint. This ensures that the end-effector position accuracy is strictly guaranteed during the solution process by the equality constraints, and the end-effector attitude is continuously optimized during the solution process by the optimization objective. Position control and attitude adjustment are mathematically decoupled within the constraint optimization framework. A single solution can simultaneously obtain the joint angles that achieve accurate position and optimal attitude approximation without the need for multiple iterative corrections between position and attitude, or the assumption of a one-to-one linear superposition of joint and attitude components. This improves the end-effector attitude control accuracy of the low-degree-of-freedom manipulator.

[0042] In some implementations, the under-degree-of-freedom robotic arm includes a target joint driven by a parallelogram linkage mechanism, and the constraint parameters also include the actuator stroke range of the target joint; the inequality constraint also includes the actuator angle of the target joint being within the actuator stroke range, and the actuator angle being determined according to a preset transformation relationship based on the geometric angle of the target joint and the joint angle of the upstream joint of the target joint.

[0043] In this embodiment, the target joint refers to the joint in the robotic arm driven by a parallelogram linkage mechanism, such as the fourth joint in a five-joint hydraulic robotic arm driven by a hydraulic cylinder via a parallelogram linkage. The actuator stroke range refers to the range of angles or displacements that the actuator (e.g., a hydraulic cylinder) driving the target joint is allowed to output in terms of its physical structure; this range can be derived from the physical stroke parameters of the hydraulic cylinder.

[0044] The preset conversion relationship refers to the coupling conversion relationship between the actuator angle of the target joint and its geometric angle, as well as the angle of the upstream joint. Due to the geometric constraints of the parallelogram link, the geometric angle of the target joint depends not only on the actuator output but also on the current angle of the upstream joint. Taking the target joint as the fourth joint as an example, the conversion relationship between its geometric space angle and actuator space angle can be expressed as: θ4_geometric = θ4_actuator θ2 θ3+C_offset θ_virtual; In the formula, θ4_geometric is the geometrical angle of the target joint; θ4_actuator is the actuator angle of the target joint; θ2 and θ3 are the joint angles of the second and third joints upstream of the target joint, respectively; C_offset is the fixed offset constant of the parallelogram linkage mechanism, which can be equal to 13π / 12 radians, approximately 3.403 radians, where π is pi; θ_virtual is the virtual joint angle compensation term of the parallelogram linkage mechanism, used to compensate for virtual degrees of freedom in the linkage mechanism that are not directly measured. Correspondingly, when converting the actuator angle from the geometrical angle, the conversion expression is θ2 + θ3. θ4_geometric C_offset (when ignoring virtual joint angle compensation).

[0045] Based on this, the inequality constraint that the actuator angle of the target joint is within the actuator stroke range can be expressed as: g2(θ):θ4_act_min≤θ2+θ3 θ4 C_offset≤θ4_act_max; In the formula, g2(θ) is the stroke inequality constraint of the parallel link actuator; θ4_act_min and θ4_act_max are the lower limit and upper limit of the actuator stroke range, respectively. For example, the actuator stroke range can be from -1.0 radians to 0.5 radians; θ4 is the geometric angle of the target joint, i.e., the above θ4_geometric.

[0046] In this embodiment, by explicitly adding the parallel link actuator stroke as an inequality constraint to the constraint optimization problem, the solver can perceive the limitation of the actuator stroke during the search for the optimal attitude solution. This avoids the constraint omission caused by parallel link transformation only in the trajectory post-processing stage in related technologies, and ensures that the obtained solution is within the physical feasible domain.

[0047] In some implementations, the optimization objective also includes a sub-objective of minimizing joint motion; the objective function of the constrained optimization problem is a weighted sum of the norm of the posture error and the joint motion, where the joint motion is the deviation between the decision variable and the current joint angle, and the weight coefficient corresponding to the norm of the posture error is greater than the weight coefficient corresponding to the joint motion.

[0048] In this embodiment, the sub-objective of minimizing joint motion refers to the optimization sub-objective that encourages the obtained solution to be close to the current configuration in order to reduce the range of motion of the robotic arm. Joint motion can be measured by the squared L2 norm of the deviation between the decision variable θ and the current joint angle θ_init, i.e., ||θ||. θ_init‖², where θ_init is a vector consisting of the current joint angles. Correspondingly, the objective function can be expressed as: F(θ)=w1·‖e(θ)‖²+w2·‖θ θ_init‖²; In the formula, w1 and w2 are the weighting coefficients corresponding to the attitude error term and the joint motion term, respectively. Since attitude approximation is the main optimization objective of this application, w1 is greater than w2. For example, w1 can be 1.0 and w2 can be 0.05.

[0049] It should be noted that other optimization terms can be flexibly added to the objective function, such as a joint median preference term, which is an optimization term that moves each joint away from its limit to improve the flexibility of subsequent movements. The priority of each optimization term is adjusted by a weight coefficient. In this embodiment, by introducing a sub-objective of minimizing joint motion, the obtained solution can be closer to the current configuration when the posture error is similar, thereby reducing the range of motion of the robotic arm and reducing motion energy consumption and execution time.

[0050] In some implementations, before solving the constrained optimization problem, the method further includes: using the current joint angle as the initial seed, performing position-only inverse kinematics on the target position to obtain the initial joint angle that satisfies the equality constraint; solving the constrained optimization problem includes: using the initial joint angle as the initial point to solve the constrained optimization problem.

[0051] In this embodiment, the initial seed refers to the starting joint angles used when the position-only inverse kinematics solver begins its iterative solution. Position-only inverse kinematics solution refers to inverse kinematics solution with the constraint that the end-effector reaches the target position only; its output is a set of joint angles that enable the end-effector to reach the target position. Initial joint angles refer to the joint angles obtained from the position-only inverse kinematics solution that satisfy the position equality constraint.

[0052] Since inverse kinematics-only solution guarantees that position equality constraints are satisfied, the generated initial joint angles lie within the feasible region of the constrained optimization problem. Using these initial joint angles as the starting point for optimization allows the optimization solution to iterate from within the feasible region, reducing the computational load on the solver to satisfy equality constraints and improving solution efficiency and convergence stability. For example, an electronic device can call the kinematics solver, using the current joint angles as the initial seed, to perform inverse kinematics-only solution on the target position to obtain the initial joint angles, and then use these initial joint angles as the starting point for subsequent optimization solutions.

[0053] In some implementations, using the current joint angle as the initial seed, the target position is solved using position-only inverse kinematics to obtain an initial joint angle that satisfies the equality constraint. This includes: applying multiple sets of bounded random perturbations to the current joint angle to obtain multiple perturbation configurations; using each perturbation configuration as the initial seed, the target position is solved using position-only inverse kinematics to obtain multiple initial joint angles that satisfy the equality constraint; and using the initial joint angle as the initial point, the constrained optimization problem is solved, including: using each initial joint angle as the initial point, the constrained optimization problem is solved to obtain multiple candidate solutions; and the candidate solution with the smallest objective function value is selected from the multiple candidate solutions as the target joint angle.

[0054] In this embodiment, the bounded random perturbation amount refers to a random amount applied to each component of the current joint angle, with an amplitude not exceeding a preset range. That is, the perturbation is not completely randomized, but rather a bounded perturbation within a preset range. Applying the i-th bounded random perturbation amount ε_i to the current joint angle θ_current yields the i-th perturbation configuration. The perturbation configuration refers to the joint angle configuration obtained after perturbation, which serves as the initial seed for the inverse position solution only.

[0055] By solving the position-only inverse kinematics problem using m perturbation configurations as initial seeds, we can obtain m initial joint angles that satisfy the equality constraints but correspond to different arm configurations. These are denoted as the initial point set {θ0^(1), ..., θ0^(m)}, where m is the number of initial points and is a positive integer, for example, m can be 5; θ0^(i) is the i-th initial point, and the superscripts (1) to (m) are the initial point numbers. Since the optimal attitude approximation capability varies under different arm configurations, solving the constraint optimization problem separately from multiple different arm configurations can ensure that different arm configurations are explored, thereby increasing the probability of finding the global optimum.

[0056] A candidate solution refers to the solution obtained after solving the constrained optimization problem at each initial point. The electronic device can perform optimization solutions in parallel for multiple initial points to obtain multiple candidate solutions. The objective function values ​​of each candidate solution are compared, and the candidate solution with the smallest objective function value (i.e., the smallest attitude error) is selected as the target joint angle.

[0057] In some implementations, solving the constrained optimization problem includes: in each iteration, locally approximating the constrained optimization problem as a quadratic programming subproblem at the current iteration point, solving the quadratic programming subproblem to obtain the search direction; determining the step size through line search, and updating the current joint angle according to the search direction and step size; stopping the iteration when the updated current joint angle satisfies the preset convergence condition, and determining the updated current joint angle as the target joint angle.

[0058] In this embodiment, the optimization solution can be obtained using the sequential quadratic programming method. Sequential quadratic programming is an iterative algorithm for solving nonlinear constrained optimization problems. Its basic idea is to locally approximate the original nonlinear problem as a quadratic programming subproblem in each iteration and solve it to obtain the search direction. In the k-th iteration, the current iteration point is denoted as θ_k, and the constructed quadratic programming subproblem can be expressed as: minimize(1 / 2)·d ·H_k·d+ F(θ_k) ·d; subject to h(θ_k) ·d+h(θ_k)=0,g_min≤g(θ_k)+ g(θ_k) ·d≤g_max; In the formula, d represents the search direction to be solved; d H_k is the transpose of d; H_k is the Hessian matrix or its approximation matrix of the objective function in the k-th iteration, which can be obtained, for example, by using the BFGS quasi-Newton approximation. F(θ_k) is the gradient of the objective function at the current iteration point; h(θ_k) is the Jacobian matrix of the equality constraint function at the current iteration point, which is equal to the position Jacobian matrix J_p; g(θ_k) is the value of each inequality constraint function at the current iteration point; g(θ_k) is the Jacobian matrix of the inequality constraint function at the current iteration point; g_min and g_max are the lower and upper bounds of the inequality constraint, respectively.

[0059] The gradient of the objective function with respect to the joint angle can be calculated using the pose Jacobian matrix via the chain rule, and its expression is as follows: F / θ=w1·2·e ·J_e+w2·2·(θ θ_init) ; In the formula, F / θ is the partial derivative of the objective function with respect to the joint angle, i.e., the gradient; e J_e is the transpose of the attitude error vector; J_e is the attitude Jacobian matrix, a 3x5 matrix, where the i-th column represents the rate of change of end-effector attitude caused by a small change in the i-th joint angle; (θ) θ_init) This is the transpose of the joint motion deviation vector. The Jacobian matrix of the equality constraints with respect to joint angles is the position Jacobian matrix, i.e. h / θ = J_p, where the position Jacobian matrix J_p is a 3x5 matrix, and its i-th column represents the rate of change of end-effector position caused by a small change in the i-th joint angle.

[0060] After solving the above quadratic programming subproblem to obtain the search direction d_k, the step size α_k is determined through line search, and the current joint angle is updated according to θ_(k+1) = θ_k + α_k·d_k. Line search refers to the process of finding a step size in the search direction that makes the objective function decrease sufficiently and the constraint violation does not increase.

[0061] The preset convergence condition refers to the condition for determining whether the optimization process can stop. For example, it may include at least one of the following: the change in the objective function is below a first threshold, or the constraint violation is below a second threshold. When the updated current joint angle meets the preset convergence condition, the iteration stops, and the updated current joint angle is determined as the target joint angle. Typically, the sequential quadratic programming method converges after 5 to 15 iterations, with a single solution taking approximately 3 to 10 milliseconds, which meets the requirements of real-time control.

[0062] In some implementations, controlling the motion of the under-degree-of-freedom robotic arm according to the target joint angle includes: converting the target joint angle from a geometric space angle to an actuator space angle; generating a smooth trajectory that satisfies velocity and acceleration constraints based on the actuator space angle; and sending the smooth trajectory to the motion controller of the under-degree-of-freedom robotic arm for execution.

[0063] In this embodiment, geometric space angle refers to the angle in the joint angle space used for kinematic solving; actuator space angle refers to the angle in the angle space that the actual actuator can directly execute. For target joints driven by parallelogram linkage mechanisms, the geometric space angle needs to be converted into actuator space angle according to the aforementioned preset conversion relationship, for example, according to θ4_actuator=θ4_geometric+θ2+θ3. The conversion is performed using C_offset + θ_virtual. For joints not driven by parallel links, their geometric space angles are consistent with the actuator space angles, so no conversion is needed. Since the parallel link constraints are embedded in the kinematic model and included in the optimization process, the conversion from geometric space to actuator space is uniformly performed in the output stage, eliminating the conflict between the conversion steps and the compensation steps in the step-by-step processing of related technologies.

[0064] A smooth trajectory refers to a continuous trajectory from the current joint angle to the target joint angle, where the velocity and acceleration of each joint do not exceed preset limits. For example, it can be generated using fifth-order polynomial interpolation or trapezoidal velocity planning. A motion controller is a control device that directly drives the actuators of each joint of the robotic arm. After the electronic device generates the smooth trajectory, it can send the smooth trajectory to the motion controller for execution via a communication interface (such as the motion interface in the robot's operating system), driving the robotic arm's end effector to accurately reach the target position and approach the target posture in an optimal manner.

[0065] To facilitate understanding of the position constraint attitude optimization control method for a manipulator with insufficient degrees of freedom provided in the embodiments of this application, a specific application example is provided here for illustration.

[0066] This example applies to a photovoltaic power plant cleaning operation scenario. A five-joint hydraulic robotic arm mounted on a mobile chassis has six physical joints, with the sixth joint being uncontrollable and the fourth joint driven by a hydraulic cylinder via a parallelogram linkage mechanism. The robotic arm needs to deliver the end effector cleaning device to a designated position on the photovoltaic panel surface and maintain a prescribed contact posture. The control system includes a kinematics model module, a joint state acquisition module, a position-only inverse kinematics module, a constraint parameter loading module, an optimization problem construction module, a multi-starting point initial point generation module, a nonlinear optimization solution module, and a space transformation and trajectory generation module. The kinematics model module establishes a complete forward and inverse kinematics model containing parallel link constraints; the geometric constraints of the parallel links are directly encoded within the model.

[0067] The control flow in this scenario is as follows.

[0068] The first step is for the control system to receive the target pose, where the target position is the coordinates in the base coordinate system (-1.5m, 2.0m, 1.5m), and the target orientation is the specified orientation in which the cleaning device is attached to the photovoltaic panel. The control system then obtains the current joint angles of the five controllable joints from the joint status topic. Finally, the control system loads constraint parameters from the configuration system, including the physical limit range of each joint and the actuator travel range of the parallel linkage joint. In this example, the actuator travel range is from -1.0 radians to 0.5 radians.

[0069] The second step is to construct a constrained optimization problem for the control system. The objective function is: F=1.0×‖e_orient‖²+0.05×‖θ θ_init‖²; Where e_orient is the attitude error vector, i.e., the aforementioned e(θ); the equality constraint is p(θ) = (negative 1.5 m, 2.0 m, 1.5 m); the inequality constraint is the limit range of each joint and the stroke range of the parallel link actuator.

[0070] The third step is to generate multiple initial points by controlling the system. Five sets of bounded random perturbations are applied to the current joint angle to obtain five perturbation configurations. The position-only inverse kinematics are solved using each perturbation configuration as the initial seed to obtain five initial points that satisfy the position equality constraints but correspond to different arm configurations.

[0071] The fourth step involves the control system performing parallel sequential quadratic programming optimization on the five initial points. Taking the optimal set as an example, the initial points are θ0 = (-1.56 radians, 1.908 radians, 1.645 radians, 0.65 radians, -1.2 radians), with an initial attitude error of 0.35 radians. After 8 iterations (approximately 5 milliseconds), the system converges to the optimal joint angle θ. = (-1.53 ​​radians, 1.89 radians, 1.66 radians, 0.81 radians, -1.34 radians). At this point, the attitude error is reduced to 0.032 radians, the position error is less than 0.001 meters, and both the joint limit constraint and the actuator stroke constraint have passed the check.

[0072] The fifth step involves the control system comparing the attitude errors of the five candidate solutions and selecting the solution with the smallest attitude error (0.032 radians) as the target joint angle. This angle is then converted from a geometric space angle to an actuator space angle, generating a smooth trajectory that satisfies the velocity and acceleration constraints. This trajectory is then sent to the motion controller for execution via the motion interface.

[0073] Through comparative testing, the step-by-step iterative compensation method in related technologies, after three iterations, achieves a position error of less than 0.01 meters, an attitude error of 0.05 radians, and a total time of approximately 6 seconds. In this example, the single-starting-point solution achieves a position error of less than 0.001 meters, an attitude error of 0.04 radians, and a total time of approximately 5 milliseconds. Furthermore, the five-starting-point solution in this example achieves a position error of less than 0.001 meters, an attitude error of 0.032 radians, and a total time of approximately 25 milliseconds. Therefore, compared to the step-by-step iterative method in related technologies, the method in this embodiment has significant advantages in position accuracy, attitude accuracy, and solution time.

[0074] It should be noted that the technical solutions provided in the embodiments of this application can be further extended as follows, and all such extensions fall within the protection scope of this application.

[0075] First, the optimization solver can be replaced with the interior-point method. The interior-point method is more efficient for solving large-scale constrained problems and is suitable for scenarios with many constraints. Second, the attitude error metric can be replaced with quaternion spherical distance to avoid gimbal lock problems that may occur when the axis-angle representation is used at large angles. Third, the calculation of gradients and Hessian matrices can be automatically completed using an automatic differentiation framework to reduce the workload of manual derivation. Fourth, the method of this application can be combined with path planning to perform position constraint attitude optimization at multiple path points along the entire trajectory, rather than only at the endpoint. Fifth, machine learning methods can be combined to train the solution process of the neural network approximate optimization solver to achieve sub-millisecond online solutions. Sixth, the method of this application is not limited to a five-joint configuration and is applicable to serial robotic arms with all joint redundancy or missing joints. It is also applicable to degraded operation scenarios after joint failure. When a joint is locked, the angle of that joint can be fixed to the angle at the time of failure, and the dimension of decision variables can be reduced accordingly to reconstruct the constraint optimization problem. Seventh, the method of this application is applicable to engineering robotic arms with parallel linkages, such as excavators and aerial work platforms, and can also be extended to mobile robotic arm systems, incorporating chassis degrees of freedom into decision variables.

[0076] Based on the position constraint attitude optimization control method for a manipulator with a low degree of freedom provided in the above embodiments, this application also provides a specific implementation of the position constraint attitude optimization control device for a manipulator with a low degree of freedom.

[0077] like Figure 2 As shown, the position constraint attitude optimization control device 200 for a under-degree-of-freedom robotic arm provided in this application embodiment may include: The pose acquisition module 201 is used to acquire the target pose, current joint angle and constraint parameters of the under-degree-of-freedom manipulator. The target pose includes the target position and the target orientation, and the constraint parameters include the limit range of each controllable joint of the under-degree-of-freedom manipulator. The constrained optimization problem construction module 202 is used to construct a constrained optimization problem with the joint angles of each controllable joint as decision variables, the minimization of the attitude error between the end attitude and the target attitude as the optimization objective, the end position reaching the target position as equality constraints, and the limit range as inequality constraints. The constraint optimization problem solving module 203 is used to solve the constraint optimization problem and obtain the target joint angle that satisfies the equality constraints and inequality constraints and minimizes the attitude error. The motion control module 204 is used to control the movement of the under-degree-of-freedom robotic arm according to the target joint angle.

[0078] The position constraint attitude optimization control device 200 of the under-degree-of-freedom manipulator in this application embodiment is used to execute the position constraint attitude optimization control method of the under-degree-of-freedom manipulator in the above embodiment. Its specific processing is the same as that of the position constraint attitude optimization control method of the under-degree-of-freedom manipulator in the above embodiment, and will not be described in detail here.

[0079] Figure 3 A schematic diagram of the hardware structure of the electronic device provided in an embodiment of this application is shown.

[0080] The electronic device may include a processor 301 and a memory 302 storing computer program instructions.

[0081] Specifically, the processor 301 may include a central processing unit (CPU), an application-specific integrated circuit (ASIC), or one or more integrated circuits that can be configured to implement the embodiments of this application.

[0082] Memory 302 may include mass storage for data or instructions. For example, and not limitingly, memory 302 may include a hard disk drive (HDD), floppy disk drive, flash memory, optical disk, magneto-optical disk, magnetic tape, or Universal Serial Bus (USB) drive, or a combination of two or more of these. Where appropriate, memory 302 may include removable or non-removable (or fixed) media. Where appropriate, memory 302 may be internal or external to the integrated gateway disaster recovery device. In a particular embodiment, memory 302 is non-volatile solid-state memory.

[0083] In some embodiments, memory 302 may include read-only memory (ROM), random access memory (RAM), disk storage media device, optical storage media device, flash memory device, electrical, optical, or other physical / tangible memory storage device. Thus, generally, memory includes one or more tangible (non-transitory) computer-readable storage media (e.g., memory devices) encoded with software including computer-executable instructions, and when the software is executed (e.g., by one or more processors), it is operable to perform the operations described with reference to the method according to one aspect of this disclosure.

[0084] The processor 301 reads and executes computer program instructions stored in the memory 302 to implement any of the position constraint attitude optimization control methods for the under-degree-of-freedom robotic arm in the above embodiments.

[0085] In one example, the electronic device may also include a communication interface 303 and a bus 310. For example, Figure 3 As shown, the processor 301, memory 302, and communication interface 303 are connected through bus 310 and complete communication with each other.

[0086] The communication interface 303 is mainly used to realize communication between various modules, devices, units and / or equipment in the embodiments of this application.

[0087] Bus 310 may include hardware, software, or both. For example, and not limitingly, the bus may include an Accelerated Graphics Port (AGP) or other graphics bus, an Enhanced Industry Standard Architecture (EISA) bus, a Front Side Bus (FSB), HyperTransport (HT) interconnect, an Industry Standard Architecture (ISA) bus, an Infinite Bandwidth Interconnect, a Low Pin Count (LPC) bus, a memory bus, a Microchannel Architecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, a PCI-Express (PCI-X) bus, a Serial Advanced Technology Attachment (SATA) bus, a Video Electronics Standards Association Local (VLB) bus, or other suitable buses, or combinations of two or more of these. Where appropriate, bus 310 may include one or more buses. Although specific buses are described and illustrated in embodiments of this application, this application contemplates any suitable bus or interconnect.

[0088] Furthermore, in conjunction with the position constraint attitude optimization control method for the under-degree-of-freedom robotic arm in the above embodiments, this application embodiment can provide a computer storage medium for implementation. This computer storage medium stores computer program instructions; when these computer program instructions are executed by a processor, they implement any of the position constraint attitude optimization control methods for the under-degree-of-freedom robotic arm in the above embodiments.

[0089] This application also relates to a robot, including a robot body, a robotic arm mounted on the robot body, and a controller. The robotic arm is a low-degree-of-freedom robotic arm, and the controller is used to run the position constraint attitude optimization control method of the low-degree-of-freedom robotic arm described in the above embodiments.

[0090] It should be clarified that this application is not limited to the specific configurations and processes described above and shown in the figures. For the sake of brevity, detailed descriptions of known methods are omitted here. In the above embodiments, several specific steps are described and shown as examples. However, the method process of this application is not limited to the specific steps described and shown. Those skilled in the art can make various changes, modifications, and additions, or change the order of steps, after understanding the spirit of this application.

[0091] The functional blocks shown in the above-described structural diagram can be implemented as hardware, software, firmware, or a combination thereof. When implemented in hardware, they can be, for example, electronic circuits, application-specific integrated circuits (ASICs), appropriate firmware, plug-ins, function cards, etc. When implemented in software, the elements of this application are programs or code segments used to perform the required tasks. Programs or code segments can be stored on a machine-readable medium or transmitted over a transmission medium or communication link via data signals carried on a carrier wave. "Machine-readable medium" can include any medium capable of storing or transmitting information. Examples of machine-readable media include electronic circuits, semiconductor memory devices, ROM, flash memory, erasable ROM (EROM), floppy disks, CD-ROMs, optical disks, hard disks, fiber optic media, radio frequency (RF) links, etc. Code segments can be downloaded via computer networks such as the Internet, intranets, etc.

[0092] It should also be noted that the exemplary embodiments mentioned in this application describe methods or systems based on a series of steps or apparatus. However, this application is not limited to the order of the above steps; that is, the steps can be performed in the order mentioned in the embodiments, or in a different order, or several steps can be performed simultaneously.

[0093] The aspects of this disclosure have been described above with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It should be understood that each block in the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that these instructions, executable via the processor of the computer or other programmable data processing apparatus, enable the implementation of the functions / actions specified in one or more blocks of the flowchart illustrations and / or block diagrams. Such a processor can be, but is not limited to, a general-purpose processor, a special-purpose processor, a special application processor, or a field-programmable logic circuit. It is also understood that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can also be implemented by special-purpose hardware performing the specified functions or actions, or can be implemented by a combination of special-purpose hardware and computer instructions.

[0094] The above description is merely a specific implementation of this application. Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, modules, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here. It should be understood that the protection scope of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in this application, and these modifications or substitutions should all be covered within the protection scope of this application.

Claims

1. A method for position-constrained attitude optimization control of a manipulator with insufficient degrees of freedom, characterized in that, Includes the following steps: The target pose, current joint angle, and constraint parameters of the under-degree-of-freedom manipulator are obtained. The target pose includes the target position and the target orientation. The constraint parameters include the limit range of each controllable joint of the under-degree-of-freedom manipulator. Using the joint angles of each controllable joint as decision variables, minimizing the attitude error between the end-effector attitude and the target attitude as the optimization objective, the end-effector position reaching the target position as an equality constraint, and the limiting range as an inequality constraint, a constrained optimization problem is constructed. Solving the constrained optimization problem yields the target joint angle that satisfies both the equality and inequality constraints and minimizes the attitude error. The movement of the under-degree-of-freedom robotic arm is controlled according to the target joint angle.

2. The position constraint attitude optimization control method for a manipulator with insufficient degrees of freedom according to claim 1, characterized in that, The under-degree-of-freedom robotic arm includes a target joint driven by a parallelogram linkage mechanism, and the constraint parameters also include the actuator travel range of the target joint; The inequality constraint also includes that the actuator angle of the target joint is within the actuator stroke range, and the actuator angle is determined according to the geometric angle of the target joint and the joint angle of the upstream joint of the target joint, according to a preset transformation relationship.

3. The position constraint attitude optimization control method for a under-degree-of-freedom robotic arm according to claim 1, characterized in that, The optimization objective also includes the sub-objective of minimizing joint motion. The objective function of the constrained optimization problem is the weighted sum of the norm of the attitude error and the joint motion, where the joint motion is the deviation between the decision variable and the current joint angle, and the weighting coefficient corresponding to the norm of the attitude error is greater than the weighting coefficient corresponding to the joint motion.

4. The position constraint attitude optimization control method for a manipulator with insufficient degrees of freedom according to claim 1, characterized in that, Before solving the constrained optimization problem, the method further includes: Using the current joint angle as the initial seed, perform position-only inverse kinematics solution on the target position to obtain the initial joint angle that satisfies the equality constraint; Solving the constrained optimization problem includes: using the initial joint angle as the initial point, solving the constrained optimization problem.

5. The position constraint attitude optimization control method for a manipulator with insufficient degrees of freedom according to claim 4, characterized in that, The step of using the current joint angle as the initial seed to perform position-only inverse kinematics solution on the target position to obtain the initial joint angle that satisfies the equality constraint includes: Multiple sets of bounded random perturbations are applied to the current joint angle to obtain multiple perturbation configurations; Using each of the aforementioned perturbation configurations as initial seeds, the target position is solved by position-only inverse kinematics to obtain multiple initial joint angles that satisfy the aforementioned equality constraints; The step of solving the constrained optimization problem using the initial joint angle as the initial point includes: solving the constrained optimization problem using each of the initial joint angles as the initial point to obtain multiple candidate solutions; and selecting the candidate solution with the smallest objective function value from the multiple candidate solutions as the target joint angle.

6. The position constraint attitude optimization control method for a manipulator with insufficient degrees of freedom according to claim 1, characterized in that, Solving the constrained optimization problem includes: In each iteration, the constrained optimization problem is locally approximated as a quadratic programming subproblem at the current iteration point, and the search direction is obtained by solving the quadratic programming subproblem. The step size is determined by line search, and the current joint angle is updated according to the search direction and the step size; If the updated current joint angle meets the preset convergence condition, the iteration stops, and the updated current joint angle is determined as the target joint angle.

7. The position constraint attitude optimization control method for a manipulator with insufficient degrees of freedom according to claim 1, characterized in that, The attitude error is determined by logarithmic mapping of the rotation matrix. The attitude error is a three-dimensional axis-angle vector obtained by logarithmic mapping based on the product of the transpose of the end rotation matrix corresponding to the current joint angle and the target rotation matrix. The step of controlling the movement of the under-degree-of-freedom robotic arm according to the target joint angle includes: converting the target joint angle from a geometric space angle to an actuator space angle; A smooth trajectory that satisfies velocity and acceleration constraints is generated based on the actuator's spatial angle, and the smooth trajectory is sent to the motion controller of the under-degree-of-freedom robotic arm for execution.

8. A position constraint attitude optimization control device for a under-degree-of-freedom robotic arm, characterized in that, include: The pose acquisition module is used to acquire the target pose, current joint angle and constraint parameters of the under-degree-of-freedom manipulator. The target pose includes the target position and the target orientation, and the constraint parameters include the limit range of each controllable joint of the under-degree-of-freedom manipulator. The constrained optimization problem construction module is used to construct a constrained optimization problem with the joint angles of each controllable joint as decision variables, the minimization of the attitude error between the end pose and the target pose as the optimization objective, the end position reaching the target position as an equality constraint, and the limit range as an inequality constraint. The constraint optimization problem solving module is used to solve the constraint optimization problem to obtain the target joint angle that satisfies the equality constraints and the inequality constraints and minimizes the attitude error; The motion control module is used to control the movement of the under-degree-of-freedom robotic arm according to the target joint angle.

9. An electronic device, characterized in that, The device includes: a processor and a memory storing computer program instructions; When the processor executes the computer program instructions, it implements the position constraint attitude optimization control method for a manipulator with insufficient degrees of freedom as described in any one of claims 1-7.

10. A robot, characterized in that, The device includes a robot body, a robotic arm mounted on the robot body, and a controller, wherein the robotic arm is a low-degree-of-freedom robotic arm, and the controller is used to run the method described in any one of claims 1 to 7.

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