A constant force grinding method for complex surfaces of a robot based on force feedback

Abstract

The present invention belongs to the field of robotics technology, specifically a constant force grinding method for complex surfaces of a robot based on force feedback. The method comprises the following steps: Step 1, collecting information of a six-dimensional force sensor through a robot controller; Step 2, introducing a fastest differential tracker in the self-disturbance rejection control; Step 3, forming an admittance control model by the robot and the environment to realize the outer loop control of the robot manipulator; Step 4, constructing a non-singular terminal sliding film control law to realize the inner loop control of the robot manipulator, thereby realizing the grinding of the curved workpiece surface. The present invention can improve the force tracking effect of the manipulator in a complex and unknown environment, thereby greatly improving the robot grinding accuracy.

Description

Technical Field

[0001] The invention belongs to the technical field of robots, and in particular to a constant-force grinding method for complex surfaces of a robot based on force feedback. Background Art

[0002] With recent developments, robots have been widely used in many manufacturing industries. Grinding and polishing have become an indispensable process in manufacturing. Traditionally, most grinding processes are performed manually, which requires a high level of operator expertise. Furthermore, manual grinding efficiency decreases over time, and the results are variable. Robots, on the other hand, can perform tasks according to pre-programmed procedures, precisely controlling the position of grinding tools and effectively ensuring product consistency. However, robotic grinding technology also faces challenges. The varying shapes and curvatures of different workpieces increase the complexity and difficulty of machining, leading to significant errors in robot trajectory and force. Therefore, achieving stable tracking of force and position during contact is a key factor in ensuring high-quality workpiece grinding.

[0003] Admittance control establishes a relationship between position and force in a given direction by setting the impedance parameters of the end effector, allowing for simultaneous control of robot motion and contact force. Force control is achieved by adjusting the robot's impedance parameters. However, when the environment geometry and stiffness parameters are uncertain, the steady-state error in the contact force between the robot and the environment is non-zero, resulting in unsatisfactory force tracking. Summary of the Invention

[0004] In order to solve the above technical problems, the present invention provides a constant force grinding method for complex surfaces of a robot based on force feedback, which can improve the force tracking effect of the robotic arm in complex and unknown environments, thereby greatly improving the robot grinding accuracy.

[0005] The technical solution of the present invention is described as follows in conjunction with the accompanying drawings:

[0006] 1. A constant force grinding method for complex surfaces of a robot based on force feedback, comprising the following steps:

[0007] Step 1: Collect information from the six-dimensional force sensor through the robot controller;

[0008] Step 2: Introduce the fastest differential tracker in the active disturbance rejection control;

[0009] Step 3: The robot and the environment form an admittance control model to realize the outer loop control of the robot manipulator;

[0010] Step 4: Construct a non-singular terminal sliding film control law to realize the inner loop control of the robot manipulator, thereby achieving grinding of the curved workpiece surface.

[0011] Furthermore, the specific method of step one is as follows:

[0012] A total of six sets of data, including force and torque under the x, y, and z axes, are collected through the robot controller;

[0013] The collected force and torque are compensated for tool gravity and sensor zero drift, and the six-dimensional force sensor is read through the UDP communication port during the sampling period to measure the actual contact force and torque.

[0014] Furthermore, the six-dimensional force sensor is arranged at the end of the robot to collect force signals when the end tool contacts the workpiece.

[0015] Furthermore, in step 2, the fastest differential tracker in the active disturbance rejection control is expressed as follows:

[0016]

[0017] Function f han (x1,x2,r,h) is defined as follows:

[0018]

[0019] Where v(k) is the desired force; h is the sampling period; x1(k) is the desired force output during the transition process; x2(k) is the differential of the desired force output; sgn(·) is the sign function; fix(·) is the rounding function; the constraint of the control quantity |u|≤r; r is the adjustment factor; sat(·) is the saturation function; x1 is the actual output force; x2 is the first-order derivative of the actual output force; and k0 is the differential gain.

[0020] Furthermore, in step 3, the admittance control model is expressed as follows:

[0021]

[0022] Where ΔF = f e -F d The contact force is the difference between the force of environmental feedback and the expected force; M d is the quality coefficient matrix; B d is the damping coefficient matrix; K d is the stiffness coefficient matrix, which is usually set to an n*n positive definite diagonal matrix, where n is the dimension of the robot workspace; is the expected acceleration; is the actual acceleration; is the expected speed; is the actual speed; X d is the expected position; X r is the actual location;

[0023] Among them, the environmental feedback force f e Simplified to spring model f e =k e (xx e ), the admittance control model is transformed by Laplace, and the final steady-state error is expressed as follows:

[0024]

[0025] Where k e is the environmental stiffness; x e is the environmental position; K d is the stiffness coefficient matrix, set to 0.

[0026] Furthermore, the specific method of step 4 is as follows:

[0027] Based on the admittance control model constructed in step 3, the damping coefficient is compensated as follows:

[0028]

[0029] Where m d is the initial mass coefficient; is the estimated acceleration difference; b d is the initial damping coefficient; Δb is the damping compensation; is the estimated speed difference; Δf=f e -f d ; Δb(t) is the damping compensation; is the estimated position difference; ε=10 -6 Prevent the denominator from being zero; λ is the sampling period; ζ is the update factor; α and β are gain coefficients, and their value range is greater than 0; U limt is the restriction coefficient;

[0030] The system stability conditions are determined by Routh criterion:

[0031]

[0032] When t→∞, f e →f d , that is, the contact force f e Expected force f d tracking;

[0033] The joint angles are introduced into the adaptive sliding mode controller through inverse kinematics to adjust the end motion trajectory of the robot. The robot dynamic model expression is:

[0034]

[0035] Where M(q) is the inertia matrix, which is a symmetric and positive definite n-dimensional square matrix; is the coupling matrix, which is the combined term of Coriolis force and centrifugal force; G(q)∈R n is the n-dimensional gravity column vector; F e ∈R n is the n-dimensional contact force column vector; F f ∈R n is the n-dimensional friction column vector; J T is the transpose of the Jacobian matrix; τ∈R n is the theoretical torque output by the motor under the current joint posture and motion state; q is the n-dimensional column vector of the robot arm joint position; is the n-dimensional column vector of the manipulator joint angular velocity; is the column vector of the n-dimensional robot arm joint angular acceleration; n is the number of robot arm degrees of freedom;

[0036] Design a non-singular terminal sliding surface:

[0037]

[0038] Where e = q d -q,q d is the expected joint position; q is the actual joint position after inverse solution; s=[s1,s2,…,s n ] T ; σ Sliding mode surface slope; σ = diag (σ1, σ2…σ n );e j / k =[e j / k 1,e j / k 2…e j / k n ], j and k are positive odd numbers, and k<j<2k;

[0039] The exponential reaching law is selected as:

[0040]

[0041] Where γ is the reaching law gain, Γ is the compensation coefficient

[0042] Then the non-singular terminal sliding mode control law is:

[0043]

[0044] The non-singular terminal sliding film control law is used as the terminal sliding film controller to achieve position tracking, and the surface of the curved workpiece is polished by a robotic arm.

[0045] The beneficial effects of the present invention are:

[0046] 1) In terms of robot force control, this invention addresses the drawback of inaccurate grinding of complex workpiece surfaces by the robot, and solves the problem of large force / position tracking errors on complex surfaces. By dynamically adjusting the update factor to obtain an adaptive law, the damping coefficient of the admittance control model is compensated, and the contact steady-state force is constrained through terminal sliding mode control. At the same time, the fastest differential tracking controller under the self-disturbance rejection control framework is introduced to design the desired force transformation process, reducing the problem of force overshoot of the robot to the environment in the initial contact stage, effectively reducing the impact of force impact on the workpiece and achieving the expected force tracking effect, with good robustness.

[0047] 2) In terms of robot applications, the constant-force grinding method for complex robot surfaces based on force feedback proposed in the present invention enables the robotic arm to better grind the surface of curved workpieces, providing a more stable and reliable working environment; enables the robotic arm to better adapt to complex environments; and improves the flexibility and stability of the robot tool end, fully proving that the present invention is practical and universal. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0049] Figure 1 This is a principle block diagram of a constant force grinding method for complex surfaces of a robot based on force feedback.

[0050] Figure 2 is the expected force change curve;

[0051] Figure 3 This is the actual force tracking effect of the robot's end in a curved surface environment. DETAILED DESCRIPTION

[0052] The present invention will be further described in detail below with reference to the accompanying drawings and examples. It will be understood that the specific embodiments described herein are intended only to illustrate the present invention and are not intended to limit the present invention. It should also be noted that, for ease of description, the accompanying drawings only illustrate portions relevant to the present invention, not all structures.

[0053] Example 1

[0054] See Figure 1 The embodiment of the present invention provides a constant force grinding method for a complex surface of a robot based on force feedback, wherein the complex surface is a surface with multiple curvatures, comprising the following steps:

[0055] Step 1: Collect information from the six-dimensional force sensor through the robot controller to obtain the contact force at the end of the robot.

[0056] The six-axis force sensor is installed at the end of the robot and collects the force signal when the end tool contacts the workpiece. The robot controller collects six sets of data including the force and torque along the x, y, and z axes.

[0057] The collected force and torque are compensated for tool gravity and sensor zero drift, and the six-dimensional force sensor is read through the UDP communication port during the sampling period to measure the actual contact force and torque.

[0058] Step 2: To prevent the robot from being subjected to sudden force on the workpiece when it first contacts the workpiece, a fastest differential tracker is introduced in the active disturbance rejection control. This is a transition process that uses the desired contact force as input to gradually increase the desired contact force from a step state, thus avoiding the force overshoot problem caused by sudden changes. The details are as follows:

[0059] The fastest differential tracker in active disturbance rejection control is expressed as follows:

[0060]

[0061] Function f han (x1,x2,r,h) is defined as follows:

[0062]

[0063] Where v(k) is the desired force; h is the sampling period; x1(k) is the desired force output during the transition process; x2(k) is the differential of the desired force output; sgn(·) is the sign function; fix(·) is the rounding function; the constraint of the control quantity |u|≤r; r is the adjustment factor; sat(·) is the saturation function; x1 is the actual output force; x2 is the first-order derivative of the actual output force; and k0 is the differential gain.

[0064] Step 3: The robot and the environment form an admittance control model to achieve constant force grinding, i.e., outer loop control of the robot arm. Steps 1 and 2 serve as the input conditions for step 3, i.e., the force difference ΔF in admittance control, as follows:

[0065] The admittance control model is expressed as follows:

[0066]

[0067] Where ΔF = f e -F d The contact force is the difference between the force of environmental feedback and the expected force; M d is the quality coefficient matrix; B d is the damping coefficient matrix; K dis the stiffness coefficient matrix, which is usually set to an n*n positive definite diagonal matrix, where n is the dimension of the robot workspace; is the expected acceleration; is the actual acceleration; is the expected speed; is the actual speed; X d is the expected position; X r is the actual location;

[0068] Among them, the environmental feedback force f e Simplified to spring model f e =k e (xx e ), the admittance control model is transformed by Laplace, and the final steady-state error is expressed as follows:

[0069]

[0070] Where k e is the environmental stiffness; x e is the environmental position; K d is the stiffness coefficient matrix;

[0071] When the environmental stiffness k e and the environment position x e If the value of is known, the reference position trajectory x can be calculated according to the equation r To apply the desired contact force f on the environment d .

[0072] However, in practice, x e and k e The value of is not known in advance. Even if the environment position and environment stiffness are adjusted in real time according to the method of adjusting the reference trajectory, it cannot be guaranteed that the force tracking error is zero or even stable. It can also be seen that the stiffness gain k d Setting it to 0 will satisfy the stiffness k in any case. e and in an unknown environment x e Information is available to ensure accurate tracking.

[0073] Step 4: Construct a non-singular terminal sliding film control law to realize the inner loop control of the robot manipulator, thereby achieving grinding of the curved workpiece surface.

[0074] Based on the admittance control model constructed in step 3, the damping coefficient is compensated as follows:

[0075]

[0076] Where m d is the initial mass coefficient; is the estimated acceleration difference; b dis the initial damping coefficient; Δb is the damping compensation; is the estimated speed difference; Δf=f e -f d ; Δb(t) is the damping compensation; is the estimated position difference; ε=10 -6 Prevent the denominator from being zero; when t=0, η(t)=0; t is the time of the last sampling; λ is the sampling period; ζ is the update factor; α and β are gain coefficients, and their value range is greater than 0; U limt is the restriction coefficient;

[0077] The system stability conditions are determined by Routh criterion:

[0078]

[0079] When t→∞, f e →f d , that is, the contact force f e Expected force f d tracking;

[0080] The joint angles are introduced into the adaptive sliding mode controller through inverse kinematics to adjust the end motion trajectory of the robot. The robot dynamic model expression is:

[0081]

[0082] Where M(q) is the inertia matrix, which is a symmetric and positive definite n-dimensional square matrix; is the coupling matrix, which is the combined term of Coriolis force and centrifugal force; G(q)∈R n is the n-dimensional gravity column vector; F e ∈R n is the n-dimensional contact force column vector; F f ∈R n is the n-dimensional friction force column vector; J T is the transpose of the Jacobian matrix; τ∈R n is the theoretical torque output by the motor under the current joint posture and motion state; q is the n-dimensional column vector of the robot arm joint position; is the n-dimensional column vector of the manipulator joint angular velocity; is the column vector of the n-dimensional robot arm joint angular acceleration; n is the number of robot arm degrees of freedom;

[0083] Design a non-singular terminal sliding surface:

[0084]

[0085] Where e = q d -q,qd is the expected joint position; q is the actual joint position after inverse solution; s=[s1,s2,…,s n ] T ; σ Sliding mode surface slope; σ = diag (σ1, σ2…σ n );e j / k =[e j / k 1,e j / k 2…e j / k n ], j and k are positive odd numbers, and k<j<2k;

[0086] The exponential reaching law is selected as:

[0087]

[0088] Where, γ is the reaching law gain, Γ is the compensation coefficient;

[0089] Then the non-singular terminal sliding mode control law is:

[0090]

[0091] The non-singular terminal sliding film control law is used as the terminal sliding film controller to achieve position tracking, and the surface of the curved workpiece is polished by a robotic arm.

[0092] Example 2

[0093] This embodiment experimentally verifies the constant force grinding method for complex surfaces of a robot based on force feedback proposed in the first embodiment.

[0094] When the end of the robot contacts the surface, the force tracking effect is as follows: Figure 3 As shown in the figure, during grinding, the error between the actual contact force and the expected force is ±0.2N, which meets the constant force tracking requirement.

[0095] Figure 2 Comparison diagram of the expected force before and after processing by the fastest differential tracker.

[0096] The above experimental results show that the constant force grinding method for complex surfaces of robots based on force feedback proposed in the present invention can effectively adapt to the grinding environment of complex curved surface workpieces and has a good tracking effect on position and force.

[0097] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A constant force grinding method for complex surfaces of a robot based on force feedback, characterized in that: The following steps are involved: Step 1: Collect information from the six-dimensional force sensor through the robot controller; Step 2: Introduce the fastest differential tracker in the active disturbance rejection control; Step 3: The robot and the environment form an admittance control model to realize the outer loop control of the robot manipulator; Step 4: Construct a non-singular terminal sliding film control law to realize the inner loop control of the robot manipulator, thereby achieving the grinding of the curved workpiece surface; The specific method of step 4 is as follows: Based on the admittance control model constructed in step 3, the damping coefficient is compensated as follows: Where m d is the initial mass coefficient; is the estimated acceleration difference; b d is the initial damping coefficient; △b is the damping compensation; is the estimated speed difference; △f=f e -f d ;△b(t) is the damping compensation; is the estimated position difference; ε=10 -6 Prevent the denominator from being zero; t is the last sampling time; λ is the sampling period; ζ is the update factor; α and β are gain coefficients, with a value range greater than 0; U limt is the restriction coefficient; The system stability conditions are determined by Routh criterion: When t→∞, f e →f d , that is, the contact force f e Expected force f d tracking; The joint angles are introduced into the adaptive sliding mode controller through inverse kinematics to adjust the end motion trajectory of the robot. The robot dynamic model expression is: Where M(q) is the inertia matrix, which is a symmetric and positive definite n-dimensional square matrix; is the coupling matrix, which is the combined term of Coriolis force and centrifugal force; G(q)∈R n is the n-dimensional gravity column vector; F e ∈R n is the n-dimensional contact force column vector; F f ∈R n is the n-dimensional friction column vector; J Τ is the transpose of the Jacobian matrix; τ∈R n is the theoretical torque output by the motor under the current joint posture and motion state; q is the n-dimensional column vector of the robot arm joint position; is the n-dimensional column vector of the manipulator joint angular velocity; is the column vector of the n-dimensional robot arm joint angular acceleration; n is the number of robot arm degrees of freedom; Design a non-singular terminal sliding surface: Where e = q d -q,q d is the expected joint position; q is the actual joint position after inverse solution; s=[s1,s2,…,s n ] Τ ; σ Sliding mode surface slope; σ = diag (σ1, σ2…σ n );e j / k =[e j / k 1,e j / k 2…e j / k n ], j and k are positive odd numbers, and k <j<2k; The exponential reaching law is selected as: Where, γ is the reaching law gain, Γ is the compensation coefficient; Then the non-singular terminal sliding mode control law is: The non-singular terminal sliding film control law is used as the terminal sliding film controller to achieve position tracking, and the surface of the curved workpiece is polished by a robotic arm.

2. The constant force grinding method for complex surfaces of a robot based on force feedback according to claim 1 is characterized in that: The specific method of step one is as follows: A total of six sets of data, including force and torque under the x, y, and z axes, are collected through the robot controller; The collected force and torque are compensated for tool gravity and sensor zero drift, and the six-dimensional force sensor is read through the UDP communication port during the sampling period to measure the actual contact force and torque.

3. The constant force grinding method for complex surfaces of a robot based on force feedback according to claim 1 is characterized in that: The six-dimensional force sensor is arranged at the end of the robot and collects force signals when the end tool contacts the workpiece.

4. The constant force grinding method for complex surfaces of a robot based on force feedback according to claim 1 is characterized in that: In step 2, the fastest differential tracker in the active disturbance rejection control is expressed as follows: Function f han (x1,x2,r,h) is defined as follows: Where v(k) is the desired force; h is the sampling period; x1(k) is the desired force output during the transition process; x2(k) is the differential of the desired force output; sgn(·) is the sign function; fix(·) is the rounding function; the constraint of the control quantity |u|≤r; r is the adjustment factor; sat(·) is the saturation function; x1 is the actual output force; x2 is the first-order derivative of the actual output force; and k0 is the differential gain.

5. The constant force grinding method for complex surfaces of a robot based on force feedback according to claim 1, characterized in that: In step 3, the admittance control model is expressed as follows: Where, ΔF=F e -F d The contact force is the difference between the force of environmental feedback and the expected force; M d is the quality coefficient matrix; B d is the damping coefficient matrix; K d is the stiffness coefficient matrix, which is usually set to an n*n positive definite diagonal matrix, where n is the dimension of the robot workspace; is the expected acceleration; is the actual acceleration; is the expected speed; is the actual speed; X d is the expected position; X r is the actual location; Among them, the environmental feedback force F e Simplified to spring model F e =k e (xx e ), the admittance control model is transformed by Laplace, and the final steady-state error is expressed as follows: Where k e is the environmental stiffness; x e is the environmental position; K d is the stiffness coefficient matrix, set to 0.

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