A robust preset performance control method for a dexterous two-fingered hand robot

Abstract

The present invention discloses a robust preset performance control method for a dexterous two-finger-arm hand robot, which relates to the field of motion planning and control of a two-finger-arm hand robot system, and mainly comprises the following parts: firstly, according to the kinetic energy and potential energy of the system, a unified dynamic model of the two-finger-arm hand robot is established based on the Lagrange equation; secondly, based on the system dynamics model, a low-complexity robust preset performance controller with relaxed controllability conditions is designed, and motion control is realized through the system joints; finally, the performance of the robust preset performance controller is evaluated, and the control results are analyzed to ensure the reliability and effectiveness of the controller.

Description

Technical Field

[0001] The present invention relates to the field of automatic control, and in particular to a low-complexity robust preset performance control method with relaxed controllability conditions, and in particular to a robust preset performance control scheme for a robot arm-hand system with external interference and model uncertainty. Background Art

[0002] In the past decade, robotic arm-hand systems have been widely used in various fields, from automated assembly on industrial production lines to minimally invasive surgery in healthcare, logistics handling, aircraft and spacecraft maintenance to the military field. Therefore, robotic arm-hand systems have received increasing attention from researchers and scholars. The design of robotic arms and multi-finger dexterous hand controllers has been widely studied.

[0003] However, most of the current research on robotic arms and dexterous hands is conducted separately, that is, it usually focuses on the movement of the robotic arm or the multi-fingered dexterous hand, rather than the combination of the two. Therefore, the robotic arm and the dexterous hand have their own control schemes. However, in some complex manipulation tasks, it may be necessary to coordinate the use of both capabilities. Since the hand and arm need to cooperate to achieve the same goal, it is expected to control them as a whole system. At this time, there will be two controllers controlling the robotic arm and the dexterous hand in the arm-hand system respectively. At present, there are relatively few studies on the unified control of the robotic arm-hand system.

[0004] At the same time, for multi-input and multi-output systems such as robot arm-hand systems, the control input gain matrix is ​​often complex or even unknown, so it is necessary to set controllability conditions for the specific system. In the early years, some controllability conditions were proposed, but these conditions were relatively conservative, which limited the control applications of more robot arm-hand systems that could have been considered.

[0005] To solve the above problems, the present invention conducts detailed modeling of the overall system consisting of a robotic arm and a multi-fingered hand, expands it to have model uncertainty, introduces a more relaxed controllability condition, and on this basis develops a more general controller with low structural complexity, low computational cost and fast response speed. Summary of the invention

[0006] For the above problems, the present invention provides an innovative, low-complexity robust preset performance control method with relaxed controllability conditions, aiming to solve the challenge of accurately tracking the desired trajectory of the robot arm-hand system in the face of unknown external disturbances and model uncertainties. First, the method comprehensively and uniformly models the two-finger arm-hand robot system, deeply analyzes the various components of the system, and carefully considers the possible external disturbances and model uncertainties. The key to this step is to accurately grasp the actual working environment of the two-finger arm-hand robot system to establish an arm-hand integrated mathematical model to provide a solid foundation for subsequent control design. Secondly, based on the information obtained in the modeling stage, the present invention adopts a robust preset performance control strategy to ensure that the two-finger arm-hand robot system can achieve efficient tracking of the desired trajectory in a complex and uncertain environment. Among them, the important technology is the relaxation of the controllability conditions. Through flexible control means, the system can better adapt to different working conditions and tolerate external disturbances to a certain extent, thereby improving the robustness of the system. It is worth mentioning that while achieving robustness, the method realizes effective control of the preset performance of the two-finger arm-hand robot system through the precise design of performance control. The core of this technology is to make full use of advanced control theories and methods to ensure that the system can perform tasks stably and reliably in various complex environments, thus highlighting the unique contribution of the present invention in improving the performance of the dual-finger arm hand robot system.

[0007] In order to achieve the above-mentioned improvements and innovations, the present invention adopts the following technical solutions: The two-finger arm hand robot is a specially designed robot structure with a flexible arm and two-finger fingers, and its overall structure includes a robot arm and a mechanical finger. The robot arm is the main part of the whole system, responsible for supporting and positioning the mechanical finger. The robot arm is usually composed of three joints and connecting rods to provide multi-degree-of-freedom movement. Its design purpose is to achieve high flexibility and accuracy in different working scenarios. The mechanical finger is located at the end of the robot arm and has two degrees of freedom. It is a key component for performing various operation tasks. The two-finger arm hand robot adopts a two-finger design, and the two fingers can work together to achieve more complex and diverse operations. The installation of the mechanical finger adopts a high-precision joint connection to ensure that the finger can accurately follow the movement of the arm. In the modeling process, it is necessary to consider knowledge of multiple aspects such as mechanics, dynamics, and control theory to establish an accurate mathematical model. The Lagrangian method is a method for establishing dynamic equations in a motion system. It is based on the generalized coordinates and generalized velocity of the system, defines the Lagrangian function of the system, and then applies the Euler-Lagrangian equation to derive the system's equation of motion. When establishing the Lagrangian model of the two-finger arm-hand system, it is necessary to determine the system's degrees of freedom and generalized coordinates. The degrees of freedom are the number of joints that can move independently in the system, and the generalized coordinates are the variables used to describe the position of the system. The specific steps are as follows: Step 1: Based on the kinematics of the connecting rods, the speed and position of each connecting rod are obtained to obtain the kinetic energy and potential energy of the system; the speed of each connecting rod is obtained through the position of each connecting rod of the arm-hand robot system relative to the base coordinate, and the kinetic energy of each connecting rod is obtained through the kinetic energy formula, and the kinetic energy of the arm-hand system is obtained by summing up; Step 2: Combining the kinetic energy and potential energy of the system, the dynamic model of the arm-hand system is obtained using the Lagrange equation; Step 3: Based on the dynamic model of the system, a low-complexity robust preset performance controller with relaxed controllability conditions is designed, and the stability of the controller is proved through mathematical analysis and reasoning; Step 4: Each joint of the two-finger arm-hand system is controlled by the controller, thereby controlling the movement of the entire system, and the control results are analyzed. It is found that the control error is within the specified performance function, thereby verifying the effectiveness and reliability of the controller.

[0008] Step 1: Based on the kinematics of the connecting rod, the speed and position of each connecting rod are obtained to obtain the kinetic energy and potential energy of the system, which can be specifically expressed as:

[0009] The structure of the robot arm system is as follows Figure 1 As shown in the figure, the system consists of a 3-joint robotic arm and a pair of 2-joint robotic fingers with hemispherical fingertips. 11 ,q 12 ,q 13 are the three joint angles of the robot arm, l 11 ,l 12 ,l 13is the connecting rod length of the robot arm; q 14 ,q 15 is the joint angle of the first robotic finger, l 14 ,l 15 is the length of the connecting rod of the first robot finger; q 21 ,q 22 is the joint angle of the second robotic finger, l 21 ,l 22 is the length of the connecting rod of the second mechanical finger. Assume that the arm-hand robot is a rigid structure, friction is not considered, and its motion is limited to a two-dimensional horizontal plane, so there is no influence of gravity. Then the two hemispherical fingertips can be expressed as

[0010]

[0011]

[0012]

[0013]

[0014] Then the kinetic energy of the connecting rod at the ends of the two fingers can be expressed as

[0015] Kinetic energy of the connecting rod at the end of the first finger

[0016] Kinetic energy of the connecting rod at the end of the second finger

[0017] Where m 15 、m 22 Represent the mass of the connecting rod at the end of the first and second fingers respectively; the above method can be used to obtain the expression of the kinetic energy generated by other joints, and further obtain the total kinetic energy of the system as:

[0018] K=K 01 +K 02 +K e +K w +K 13 +K 14 +K 21

[0019] Among them, K e , K w , K 13 , K 14 , K 21 They represent the kinetic energy generated by the other five joints. Because the influence of gravity is ignored, the Lagrange equation of the robot arm-hand system can be written as follows:

[0020] L=K

[0021] Step 2: Combine the kinetic energy and potential energy of the system and use the Lagrange equation to establish the dynamic model of the two-finger arm robot system:

[0022]

[0023] Among them, u i represents the torque generated by each joint. It can be further written as:

[0024]

[0025] Among them, H(q) is a 7×7 inertia matrix, which is positive definite and symmetric. is a skew-symmetric matrix, q=(q 11 ,q 12 ,q 13 ,q 14 ,q 15 ,q 21 ,q 22 ) T is the joint angle, u=(u 11 ,u 12 ,u 13 ,u 14 ,u 15 ,u 21 ,u 22 ) T is the input torque of the two-finger arm robot.

[0026] Step 3: Based on the system's dynamic model, a low-complexity robust preset performance controller with relaxed controllability conditions is designed, and the stability of the controller is proved through mathematical analysis and reasoning. The specific description is:

[0027] The output tracking error ε1 and the virtual tracking error ε2 are defined as:

[0028] ε1=qq d

[0029]

[0030] Among them, q d is the expected joint trajectory of the two-finger arm robot system, and α1 is the virtual controller. Define e i =[e i,11 ,e i,12 ,e i,13 ,e i,14 ,e i,15 ,e i,21 ,e i,22 ] T , v i =[v i,11 ,v i,12 ,vi,13 ,v i,14 ,v i,15 ,v i,21 ,v i,22 ] T Among them, v i,j =v(e i,j ), Then the virtual controller α1 and the actual controller u are designed as:

[0031]

[0032]

[0033] Afterwards, mathematical reasoning of stability analysis proves that all signals in the closed-loop robot arm-hand system are globally and eventually uniformly bounded, and the output of the two-finger arm-hand robot system asymptotically tracks the expected output. The specific description is:

[0034] In order to achieve ε i We will prove that That is, Ω0 is an invariant set of e(t). Let's discuss two cases separately:

[0035] i) If but

[0036] ii) If but

[0037] Among them, t m = inf{t>0|e max (t)=σ0} is the first violation of e max (t)<σ0. Then, we use contradiction to prove Consider the following Lyapunov function:

[0038]

[0039] Derivative, using Λ1,β1, The diagonal properties and extreme value theory finally yield:

[0040]

[0041] in, is a positive constant, and Similarly, consider the following Lyapunov function:

[0042]

[0043] The same processing as above is performed, and the derivatives of the two Lyapunov functions are analyzed respectively. By utilizing the transfer of boundedness, it can be concluded that all internal signals of the closed-loop system are bounded.

[0044] Step 4: The controller is used to control each joint of the two-finger arm hand system, thereby controlling the movement of the entire system, and the control results are analyzed. It is found that the control error is within the specified performance function, thereby verifying the effectiveness and reliability of the controller.

[0045] The advantages of the present invention are: first, a unified modeling is performed for the robot two-finger arm hand, so that the robot arm and the multi-finger hand can be controlled as a whole system; second, a set of robust preset performance control schemes are designed to control the arm-hand system. The controller does not rely on an accurate system model and therefore has strong flexibility and adaptability. In addition, the control scheme is not complicated, saving computing costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to make the purpose, technical solution and advantages of the present invention clearer, the present invention will be further described below with reference to the accompanying drawings.

[0047] Figure 1 It is a schematic diagram of the structure of the dual-fingered arm hand robot system of the present invention;

[0048] Figure 2 It is a schematic diagram of a simulation object of the present invention;

[0049] Figure 3 It is a schematic diagram of the tracking errors of each joint of the dual-finger arm hand robot system of the present invention and the given preset performance function limits;

[0050] Figure 4 It is a schematic diagram of the input torque of each joint of the dual-finger arm hand robot system of the present invention. DETAILED DESCRIPTION

[0051] The simulation verification effect of the present invention will be described below with reference to the accompanying drawings in the specification to make its technical content clearer and easier to understand.

[0052] Figure 2 The two-finger-arm hand robot system of the present invention is shown as consisting of a multi-joint connected driving mechanism, a 3-DOF robotic arm, and two 2-DOF fingers. The shoulder joint is used as the basic coordinate system, and the fingertips of each finger are the basis for the implementation of the end, providing a simulation model of a robust preset performance control method.

[0053] Figure 3The above is a schematic diagram of the changes in the error of each joint of the two-finger arm robot system in tracking the expected trajectory and the given preset performance function boundary after the robust preset performance control method of the present invention is adopted. It can be found that the tracking error of each joint gradually converges to zero after 6 seconds, and is always within the boundary of the two performance functions. The control convergence speed and steady-state tracking error are small enough, and the control target is successfully achieved.

[0054] Figure 4 The figure shows the change of input torque of each joint of the two-finger arm robot system. Under the robust preset performance control method, the input torque drives the joint to move as expected. It can be found that the amplitude of the input torque of each joint is relatively small, which illustrates the effectiveness and superiority of the control method.

[0055] The present invention provides a snake-like robot control method, which mainly comprises the following steps:

[0056] Step 1: Based on the kinematics of the links, the speed and position of each link are obtained to obtain the kinetic energy and potential energy of the system. Specifically, the speed of each link is obtained by the position of each link of the arm-hand robot system relative to the base coordinates, and the kinetic energy of each link is obtained by the kinetic energy formula. The sum is used to obtain the kinetic energy of the arm-hand system. Since gravity is ignored, the potential energy of the system is zero.

[0057] Step 2: Combining the kinetic energy and potential energy of the system, the Lagrange equation is used to establish the dynamic model of the two-fingered arm-hand system.

[0058] Step 3: Based on the system's dynamic model, a low-complexity robust preset performance controller with relaxed controllability conditions is designed, and the stability of the controller is proved through mathematical analysis and reasoning.

[0059] Step 4: The controller is used to control each joint of the two-finger arm hand system, thereby controlling the movement of the entire system, and the control results are analyzed. It is found that the control error is within the specified performance function, thereby verifying the effectiveness and reliability of the controller.

[0060] The dynamic model of the dual-finger arm robot system is established by adopting a general multi-link rigid body structure. The motion state of the multi-link structure satisfies the mechanical structure constraints. The dynamic model is established according to the Lagrange equation Its inertia matrix H(q) is a 7×7 positive definite symmetric matrix, u=(u 11 ,u 12 ,u 13 ,u 14 ,u 15 ,u 21 ,u 22 ) T is the joint input torque.

[0061] The designed low-complexity robust preset performance controller and virtual controller with relaxed controllability conditions are Where N(ε) is the Nussbaum function with an update rate of

[0062] The control method proposed in this paper is based on the simulation experiment of a multi-link two-finger arm hand system. After adding the robust preset performance control method, the tracking error curve and input torque curve of each joint of the system are output, which verifies that the control method has a good control effect on the two-finger arm hand robot system with an incompletely accurate model. Figure 3 It can be found that after applying the control input of the present invention to each joint of the two-finger arm robot system, the tracking error between each joint and the desired trajectory gradually converges to zero after 6 seconds and always remains within the boundaries of the two performance functions. The control convergence speed and steady-state tracking error are small enough, and the control target is successfully achieved. Figure 4 It can be found that the input torque amplitude of each joint is small, which shows the effectiveness and superiority of the control method. In addition, the controller structure complexity of this scheme is low, which reduces the calculation cost.

[0063] Although the above description has gradually described the illustrative specific embodiments of the present invention so that those skilled in the art can understand it, the present invention is not limited to the scope of the specific embodiments. Those skilled in the art can make various changes or modifications within the scope of the claims, as long as the various changes are within the spirit and scope of the present invention as defined and determined by the attached claims.

Claims

1. A robust preset performance control method for a dexterous two-finger arm hand robot, characterized in that: The method comprises the following steps: Step 1: based on the kinematics of the connecting rods, the speed and position of each connecting rod are obtained to obtain the kinetic energy and potential energy of the system; the speed of each connecting rod is obtained by the position of each connecting rod of the arm-hand robot system relative to the base coordinate, the kinetic energy of each connecting rod is obtained by the kinetic energy formula, and the kinetic energy of the arm-hand system is obtained by summing up; Step 2: combining the kinetic energy and potential energy of the system, the dynamic model of the arm-hand system is obtained by using the Lagrange equation; Step 3: based on the dynamic model of the system, a low-complexity robust preset performance controller with relaxed controllability conditions is designed; Step 4: each joint of the two-finger arm-hand system is controlled by the controller, so as to control the movement of the entire system, and the control result is analyzed; Step 1: Based on the kinematics of the connecting rod, the speed and position of each connecting rod are obtained to obtain the kinetic energy and potential energy of the system, which can be specifically expressed as: The robot arm-hand system consists of a 3-joint robotic arm and a pair of 2-joint robotic fingers with hemispherical fingertips; 11 ,q 12 ,q 13 are the three joint angles of the robot arm, l 11 ,l 12 ,l 13 is the connecting rod length of the robot arm; q 14 ,q 15 is the joint angle of the first robotic finger, l 14 ,l 15 is the length of the connecting rod of the first robot finger; q 21 ,q 22 is the joint angle of the second robotic finger, l 21 ,l 22 is the length of the connecting rod of the second mechanical finger; the arm-hand robot is a rigid structure, friction is not considered and its movement is limited to a two-dimensional horizontal plane. The two hemispherical fingertips are represented as x 01 =l 11 so what 11 +l 12 cos(q 11 +q 12 )+l 13 cos(q 11 +q 12 +q 13 )+l 14 cos(q 11 +q 12 +q 13 +q 14 )+l 15 cos(q 11 +q 12 +q 13 +q 14 +q 15 ) and 01 =l 11 sinq 11 +l 12 sin(q 11 +q 12 )+l 13 sin(q 11 +q 12 +q 13 )+l 14 sin(q 11 +q 12 +q 13 +q 14 )+l 15 sin(q 11 +q 12 +q 13 +q 14 +q 15 ) x 02 =l 11 so what 11 +l 12 cos(q 11 +q 12 )+l 21 cos(q 11 +q 12 +q 13 +q 21 )+l 22 cos(q 11 +q 12 +q 13 +q 21 +q 22 ) y 02 =l 11 sinq 11 +l 12 sin(q 11 +q 12 )+l 21 sin(q 11 +q 12 +q 13 +q 21 )+l 22 sin(q 11 +q 12 +q 13 +q 21 +q 22 ) The kinetic energy of the connecting rods at the ends of the two fingers is expressed as: Kinetic energy of the connecting rod at the end of the first finger Kinetic energy of the connecting rod at the end of the second finger Where m 15 、m 22 denote the masses of the connecting rods at the ends of the first and second fingers, respectively; The expressions of kinetic energy generated by other joints are obtained, and the total kinetic energy of the system is obtained as: K=K 01 +K 02 +K e +K w +K 13 +K 14 +K 21 Among them, K e , K w , K 13 , K 14 , K 21 Respectively represent the kinetic energy generated by the other five joints; the Lagrange equation of the robot arm-hand system is written in the following form: L=K.

2. The robust preset performance control method of a dexterous two-finger arm hand robot according to claim 1 is characterized in that: Step 2: Combine the kinetic energy and potential energy of the system and use the Lagrange equation to establish the dynamic model of the two-finger arm robot system: Among them, u i represents the torque generated by each joint; further written as: Among them, H(q) is a 7×7 inertia matrix, is a skew-symmetric matrix, q=(q 11 ,q 12 ,q 13 ,q 14 ,q 15 ,q 21 ,q 22 ) T is the joint angle, u=(u 11 ,u 12 ,u 13 ,u 14 ,u 15 ,u 21 ,u 22 ) T is the input torque of the two-finger arm robot.

Images