A robot control method for bone grinding
By introducing a composite control framework of instrument-bone tissue interaction force model and interference observer, the problem of low trajectory tracking accuracy during orthopedic robot grinding was solved, and efficient and stable control of the robot in complex environments was achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- BEIJING UNIV OF POSTS & TELECOMM
- Filing Date
- 2026-03-04
- Publication Date
- 2026-06-09
Smart Images
Figure CN122163322A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a robot control method for bone grinding, belonging to the field of robotic bone grinding. Background Technology
[0002] With the gradual application of robotics in clinical orthopedic surgery, robot-assisted surgery is increasingly demonstrating its great potential in improving surgical precision, reducing trauma risks, and improving patient outcomes. However, the mechanical properties of bone tissue are complex and vary from person to person. The grinding process inevitably involves nonlinear dynamics, uncertainties, and external disturbances, which places higher demands on the control strategies of the robotic system. How to achieve high efficiency, stability, and controllability in the grinding process while ensuring surgical safety remains a core scientific problem that urgently needs to be solved.
[0003] To address the aforementioned challenges, this study focuses on the control of orthopedic robot grinding, systematically conducting theoretical modeling, algorithm design, and experimental verification. An interaction force model between the instrument and bone tissue is introduced, and based on this, a composite control framework combining feedforward control and a disturbance observer is proposed. Feedforward control effectively compensates for the grinding action under a known mechanical model, while the disturbance observer enhances the system's robustness to unknown disturbances and modeling errors. The combination of these two approaches not only improves the robot's adaptability in complex surgical environments but also provides a new solution for ensuring the smoothness and predictability of the grinding process. In conclusion, research on a robot control method for bone grinding has significant theoretical research value. Summary of the Invention
[0004] In view of this, the present invention provides a robot control method for bone grinding, which improves the trajectory tracking accuracy of the robot in complex grinding environments.
[0005] This invention provides a robot control method for bone grinding, comprising:
[0006] Based on the obtained interaction force model between the device and bone tissue, a robot trajectory tracking controller based on the feedback of the interaction force between the device and bone tissue is established to meet the compensation of the modelable interaction force between the device and bone tissue.
[0007] Based on the obtained unknown disturbance observation model, a robot trajectory tracking controller based on a nonlinear disturbance observer is established to improve the trajectory tracking accuracy of the robot in complex grinding environments.
[0008] In the above method, the step of establishing a robot trajectory tracking controller based on the obtained instrument-bone tissue interaction force model to meet the modelable instrument-bone tissue interaction force compensation includes:
[0009] Based on the interaction force between instruments and bone tissue during orthopedic surgery, it can be expressed as:
[0010]
[0011] in, This is the grinding force coefficient. Bone tissue density, Bone tissue density, Main spindle speed , and These are the exponential coefficients for bone density, speed, and rotational speed, respectively.
[0012] Therefore, based on the mapping relationship between the interaction force between the device and bone tissue and the robot joint, the feedforward term of the robotic arm... Designed as follows:
[0013]
[0014] in, For the transpose of the robot's Jacobian matrix, This refers to the interaction force between the end effector and the bone tissue.
[0015] Based on the PD feedback control law:
[0016]
[0017] Wherein, the tracking error is , , It is a symmetric positive definite gain matrix.
[0018] in accordance with The dynamic equations of the multi-degree-of-freedom robotic arm are:
[0019]
[0020] in, The positive definite inertial matrix of order 1. For centrifugal and Coriolis force terms, For gravity, This is the control input for the robotic arm.
[0021] Therefore, the grinding force feedforward PD composite control law adopted is as follows:
[0022]
[0023] in, It is a positive definite inertial matrix. For centrifugal and Coriolis force terms, This is the gravity term.
[0024] Therefore, a robot trajectory tracking controller based on the feedforward of the interaction force between the device and bone tissue is established to meet the modelable compensation of the interaction force between the device and bone tissue.
[0025] In the above method, the step of establishing a robot trajectory tracking controller based on a nonlinear disturbance observer according to the obtained unknown disturbance observation model to improve the trajectory tracking accuracy of the robot in complex grinding environments includes:
[0026] The robot dynamics equations incorporating nonlinear perturbation terms are as follows:
[0027]
[0028] in, The joint angle vector. For the estimated inertia matrix, For the estimated centrifugal and Coriolis force terms, For the estimated gravity term, To control the torque, For grinding unknown nonlinear disturbance torque.
[0029] Therefore, the nonlinear disturbance observer is designed as follows:
[0030]
[0031] in, The time derivative of the estimated grinding disturbance torque. This is the observer gain matrix, used to adjust the convergence speed and stability of the observer.
[0032] According to the definition of interference observer error for:
[0033]
[0034] make
[0035]
[0036] We can obtain,
[0037]
[0038] The aforementioned interference observer has a drawback: it requires measuring acceleration values. However, accurately measuring acceleration in a robotic system is difficult. Deriving acceleration signals from noise-contaminated velocity signals is not a suitable approach. Therefore, the interference observer is modified so that it does not require acceleration measurement. To this end, an auxiliary variable is defined. for:
[0039]
[0040] Where, vector The modified observer gain matrix can be used to determine the outcome. Sure:
[0041]
[0042] We can obtain:
[0043]
[0044] Therefore, the improved interference observer does not need to perform acceleration measurements, because the term It has been eliminated. Based on the above analysis, the following form was adopted:
[0045]
[0046] To complete the design of the nonlinear disturbance observer, it is necessary to determine the vector. and .
[0047]
[0048]
[0049] in, Since it is an invertible matrix, it can be found using linear matrix inequalities.
[0050]
[0051] As can be seen from the above technical solutions, the present invention has the following beneficial effects:
[0052] In the technical solution of this invention, a robot control method for bone grinding is obtained; based on the obtained interaction force model between the instrument and bone tissue, a robot trajectory tracking controller based on the feedforward of the interaction force between the instrument and bone tissue is established to meet the compensation of the modelable interaction force between the instrument and bone tissue; based on the obtained unknown disturbance observation model, a robot trajectory tracking controller based on a nonlinear disturbance observer is established to improve the trajectory tracking accuracy of the robot in complex grinding environments. Attached Figure Description
[0053] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort or labor.
[0054] Figure 1This is a schematic diagram of the robot control method for bone grinding provided in this invention example;
[0055] Figure 2 is a schematic diagram of the trajectory tracking of each joint during the robot grinding process provided in the example of the present invention. (a) End-effector trajectory tracking with nonlinear interference observer, (b) End-effector unknown tracking, (c) End-effector unknown tracking error, (d) Joint velocity tracking, and (e) Joint torque. Specific Implementation
[0056] To better understand the technical solution of the present invention, the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
[0057] It should be understood that the described embodiments are merely some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.
[0058] This invention provides a robot control method for bone grinding; please refer to [the relevant documentation]. Figure 1 This is a schematic diagram of the robot control method for bone grinding provided by the present invention. Without being limited to the preceding description, the robot control method for bone grinding is applicable to the field of orthopedic surgery and provides precise control accuracy for robotic bone grinding. The method includes the following steps:
[0059] Step 101: Based on the obtained interaction force model between the device and bone tissue, establish a robot trajectory tracking controller based on the feedforward of the interaction force between the device and bone tissue to meet the compensation of the modelable interaction force between the device and bone tissue.
[0060] Based on the interaction force between instruments and bone tissue during orthopedic surgery, it can be expressed as:
[0061]
[0062] in, This is the grinding force coefficient. Bone tissue density, Bone tissue density, Main spindle speed , and These are the exponential coefficients for bone density, speed, and rotational speed, respectively.
[0063] Therefore, based on the mapping relationship between the interaction force between the device and bone tissue and the robot joint, the feedforward term of the robotic arm... Designed as follows:
[0064]
[0065] in, For the transpose of the robot's Jacobian matrix, This refers to the interaction force between the end effector and the bone tissue.
[0066] Based on the PD feedback control law:
[0067]
[0068] Wherein, the tracking error is , , It is a symmetric positive definite gain matrix.
[0069] in accordance with The dynamic equations of the multi-degree-of-freedom robotic arm are:
[0070]
[0071] in, The positive definite inertial matrix of order 1. For centrifugal and Coriolis force terms, For gravity, This is the control input for the robotic arm.
[0072] Therefore, the grinding force feedforward PD composite control law adopted is as follows:
[0073]
[0074] in, It is a positive definite inertial matrix. For centrifugal and Coriolis force terms, This is the gravity term.
[0075] in accordance with The grinding force generated by the free-range instrument and bone tissue The control equations for the robotic arm are:
[0076]
[0077] Therefore, the control equation for the orthopedic machine can be obtained as follows:
[0078]
[0079] Available:
[0080]
[0081] The error between the device and bone tissue interaction force compensation term and the actual value is... We can obtain:
[0082]
[0083] To analyze the stability of the system, the Lyapunov function is selected as follows:
[0084]
[0085] in accordance with and The positive definiteness of knowledge, The expression is globally positive definite. For Taking the derivative, we get:
[0086]
[0087] Based on utilization Oblique symmetry ,but
[0088]
[0089] Therefore,
[0090]
[0091] in, (The two terms cancel each other out), resulting in:
[0092] Case 1: Ideal feedforward and no disturbance
[0093] If the device and the feedforward of the interaction force accurately cancel out the external force, that is ,but:
[0094]
[0095] in accordance with Bounded and Furthermore, by the LaSalle invariant set theorem, we can conclude that the trajectory tracking error converges asymptotically.
[0096] Scenario 2: Disturbance For bounded disturbances ( )
[0097] in accordance with Non-zero and bounded, using the Cauchy-Schwarz and Young's inequalities:
[0098]
[0099] Therefore, substituting the above formula into... have to:
[0100]
[0101] Therefore, when When bounded, systematic error Ultimately bounded, and the steady-state boundary is related to the disturbance amplitude. Proportional. By increasing , It can reduce the final error neighborhood, but it is necessary to weigh issues such as actual actuator saturation and noise amplification.
[0102] Scenario 3: Disturbance decay over time
[0103] in accordance with Asymptotic convergence can be achieved by decaying over time; a common approach is to design a perturbation observer (DOB) or an adaptive law, such that... It is estimated and compensated in the closed loop, eventually restoring the convergence property of case A.
[0104] Step 102: Based on the obtained unknown disturbance observation model, establish a robot trajectory tracking controller based on a nonlinear disturbance observer to improve the trajectory tracking accuracy of the robot in a complex grinding environment.
[0105] The robot dynamics equations incorporating nonlinear perturbation terms are as follows:
[0106]
[0107] in, The joint angle vector. For the estimated inertia matrix, For the estimated centrifugal and Coriolis force terms, For the estimated gravity term, To control the torque, For grinding unknown nonlinear disturbance torque.
[0108] Therefore, the nonlinear disturbance observer is designed as follows:
[0109]
[0110] in, The time derivative of the estimated grinding disturbance torque. This is the observer gain matrix, used to adjust the convergence speed and stability of the observer.
[0111] According to the definition of interference observer error for:
[0112]
[0113] make
[0114]
[0115] We can obtain,
[0116]
[0117] The aforementioned interference observer has a drawback: it requires measuring acceleration values. However, accurately measuring acceleration in a robotic system is difficult. Deriving acceleration signals from noise-contaminated velocity signals is not a suitable approach. Therefore, the interference observer is modified so that it does not require acceleration measurement. To this end, an auxiliary variable is defined. for:
[0118]
[0119] Where, vector The modified observer gain matrix can be used to determine the outcome. Sure:
[0120]
[0121] We can obtain:
[0122]
[0123] Therefore, the improved interference observer does not need to perform acceleration measurements, because the term It has been eliminated. Based on the above analysis, the following form was adopted:
[0124]
[0125] To complete the design of the nonlinear disturbance observer, it is necessary to determine the vector. and .
[0126]
[0127]
[0128] in, Since it is an invertible matrix, it can be found using linear matrix inequalities.
[0129]
[0130] Therefore, the Lyapunov function is designed as follows:
[0131]
[0132] in, If it is a positive definite matrix, then For positive definiteness, .
[0133] We can obtain,
[0134]
[0135] Based on the observer, we can obtain
[0136]
[0137] The observation error equation can be obtained as follows:
[0138]
[0139] thus,
[0140]
[0141] thus,
[0142]
[0143] Construct the following inequality:
[0144]
[0145] in, It is a symmetric positive definite matrix.
[0146]
[0147] Therefore, the disturbance observer converges exponentially, and the convergence accuracy depends on the parameters. value, The larger the value, the faster the convergence speed and the higher the accuracy.
[0148] Therefore, it is evident that the formula contains nonlinear terms and must be converted into a linear matrix inequality to solve it. Let ,Will and Multiply by the formula respectively On the left and right sides,
[0149]
[0150] because ,but Then the sufficient condition for the above equation to hold is:
[0151]
[0152] According to Schur's complement theorem: Assume If it is a positive definite matrix, then Equivalent to Therefore, the above formula is:
[0153]
[0154] Whether the solution to the inequality is valid depends on and value, The smaller, The smaller the value, the easier it is to obtain an effective solution.
[0155] Therefore, the experimental results show, as shown in Figure 2, that the trajectory tracking position error at the end point is within 10. -4 The magnitude (maximum error in the Y-axis direction is 5.78 × 10⁻⁶) -4 The accuracy (m) is reduced by a factor of 10 compared to the trajectory tracking position error at the end point under model uncertainty and external disturbances. The maximum velocity tracking error for each joint is [5.4, 3.1, 3.8, 27, 11.5, 27.5] × 10⁻⁶. -5 The value in rad / s has a significant impact on the velocity tracking of joints 4, 5, and 6, with the maximum joint velocity tracking error being 27.5 × 10⁻⁶. -5 The torque of joint 2 is rad / s. The torque of joint 2 has a significant impact on the output torque of joints 2 and 3. The torque range of joint 2 is [-27.07, -25.54] N, with a change of 1.53 N. The torque range of joint 3 is [-29.22, -29.08], with a change of 0.14 N. Compared to the model uncertainty and external disturbances, the change in torque of joint 3 is reduced by 11.36 N, and the change in torque of joint 4 is reduced by 8.87 N.
Claims
1. A robot control method for bone grinding, characterized in that, The method includes: Based on the obtained interaction force model between the device and bone tissue, a robot trajectory tracking controller based on the feedback of the interaction force between the device and bone tissue is established to meet the compensation of the modelable interaction force between the device and bone tissue. Based on the obtained unknown disturbance observation model, a robot trajectory tracking controller based on a nonlinear disturbance observer is established to improve the trajectory tracking accuracy of the robot in complex grinding environments.
2. The method according to claim 1, characterized in that, Based on the obtained instrument-bone tissue interaction force model, a robot trajectory tracking controller based on instrument-bone tissue interaction force feedforward is established to meet the compensation of modelable instrument-bone tissue interaction force, including: Based on the interaction force between instruments and bone tissue during orthopedic surgery, it can be expressed as: in, This is the grinding force coefficient. Bone tissue density, Bone tissue density, Main spindle speed , and These are the exponential coefficients for bone mineral density, speed, and rotational speed, respectively. Therefore, based on the mapping relationship between the interaction force between the device and bone tissue and the robot joint, the feedforward term of the robotic arm... Designed as follows: in, For the transpose of the robot's Jacobian matrix, The interaction force between the end effector and bone tissue; Based on the PD feedback control law: Wherein, the tracking error is , , It is a symmetric positive definite gain matrix; in accordance with The dynamic equations of the multi-degree-of-freedom robotic arm are: in, The positive definite inertial matrix of order 1. For centrifugal and Coriolis force terms, For gravity, For the control input of the robotic arm; Therefore, the grinding force feedforward PD composite control law adopted is as follows: in, It is a positive definite inertial matrix. For centrifugal and Coriolis force terms, This is the term related to gravity. Therefore, a robot trajectory tracking controller based on the feedforward of the interaction force between the device and bone tissue is established to meet the modelable compensation of the interaction force between the device and bone tissue.
3. The method according to claim 1, characterized in that, Based on the obtained unknown disturbance observation model, a robot trajectory tracking controller based on a nonlinear disturbance observer is established to improve the trajectory tracking accuracy of the robot in complex grinding environments, including: The robot dynamics equations incorporating nonlinear perturbation terms are as follows: in, The joint angle vector. For the estimated inertia matrix, For the estimated centrifugal and Coriolis force terms, For the estimated gravity term, To control the torque, For grinding unknown nonlinear disturbance torque; Therefore, the nonlinear disturbance observer is designed as follows: in, The time derivative of the estimated grinding disturbance torque. This is the observer gain matrix, used to adjust the convergence speed and stability of the observer; According to the definition of interference observer error for: make We can obtain, The aforementioned interference observer has a drawback: it requires measuring acceleration values. However, accurately measuring acceleration in a robotic system is difficult. Deriving acceleration signals from noise-contaminated velocity signals is not a suitable approach. Therefore, the interference observer is modified so that it does not require acceleration measurement. To this end, an auxiliary variable is defined. for: Where, vector The modified observer gain matrix can be used to determine the outcome. Sure: We can obtain: Therefore, the improved interference observer does not need to perform acceleration measurements, because the term It has been eliminated. Based on the above analysis, the following form was adopted: To complete the design of the nonlinear disturbance observer, it is necessary to determine the vector. and : in, Since it is an invertible matrix, it can be found using linear matrix inequalities: