Servo hydraulic stretch pad time optimal trajectory calculation method, system and medium

Abstract

The present application discloses a method, system and medium for calculating the time optimal trajectory of a servo hydraulic stretching pad, which mainly relates to the technical field of servo hydraulic stretching pads, and is used to solve the problem that the existing traditional pre-acceleration design usually ignores the complex dynamic characteristics and kinematic constraints of the system, resulting in the inability to fully exert the system performance; the time optimality is not considered, and the efficiency of the pre-acceleration stage is low. It includes: dividing the stretching displacement distance into four displacement distances on average; obtaining the control vertex for reaching the initial position and the end point of each displacement distance; substituting the time value of each end point as the control vertex into the preset quintic B-spline expression to obtain the motion trajectory, and then obtain the speed and acceleration; when the speed and acceleration meet the preset dynamic constraints and the preset kinematic constraints, otherwise enter through the preset depth Q network to update the specific values ​​of each control vertex in the preset quintic spline curve.

Description

Technical Field

[0001] The present application relates to the field of servo hydraulic technology, and in particular to a method, system and medium for calculating the optimal time trajectory of a servo hydraulic stretching pad. Background Art

[0002] The servo hydraulic stretch pad is an advanced hydraulic transmission and control device, which is widely used in the stamping process of metal sheets, especially in the fields that require high precision and complex shape forming, such as the manufacturing process of automobile covers, aerospace parts and household appliance shells. With the continuous development of modern industry, the requirements for the stretching efficiency of the servo hydraulic stretch pad are getting higher and higher. The working process of the servo hydraulic stretch pad can be regarded as the slider driving the upper punch vertically downward to contact and build pressure with the servo hydraulic stretch pad to stretch the sheet metal.

[0003] The existing servo hydraulic stretch pad uses pre-acceleration technology. When the press slide has not yet contacted the stretch pad, the stretch pad starts and slides down smoothly at the set speed. The servo hydraulic stretch pad accurately contacts the slide at the preset pre-acceleration end point, which improves the smoothness and accuracy of the production process. By adjusting the pre-acceleration parameters, the system can adapt to different process requirements.

[0004] However, the above traditional pre-acceleration design usually ignores the complex dynamic characteristics and kinematic constraints of the system, resulting in the inability to fully utilize the system performance; in addition, time optimization is not considered, and the pre-acceleration stage is inefficient. Summary of the invention

[0005] In view of the above-mentioned deficiencies in the prior art, the present application provides a method, system and medium for calculating the time optimal trajectory of a servo hydraulic stretching pad, so as to solve the problem that the traditional pre-acceleration design usually ignores the complex dynamic characteristics and kinematic constraints of the system, resulting in the inability to fully exert the system performance, and does not consider the time optimality, resulting in low efficiency in the pre-acceleration stage.

[0006] In the first aspect, the present application provides a method for calculating the optimal time trajectory of a servo hydraulic stretching pad, the method comprising: S1, obtaining the stretching displacement distance of the servo hydraulic stretching pad from a preset starting point vertically downward to a preset end point in contact with a slider, and dividing the stretching displacement distance into four displacement distances on average; S2, randomly generating the time used for each displacement segment, and then obtaining the control vertices for reaching the initial position and the end point of each displacement distance; S3, substituting the time value of each end point as the control vertex into a preset quintic B-spline expression to obtain a motion trajectory, and then obtaining the speed and acceleration; S4, when the speed and acceleration meet the preset dynamic constraints and the preset kinematic constraints, enter S5, otherwise enter S2; S5, through a preset deep Q network, solve the preset quintic spline curve, and update the specific values ​​of each control vertex in the preset quintic spline curve.

[0007] Furthermore, the time taken to pass through each displacement segment is randomly generated, and then the control vertex reaching the initial position and the end point of each displacement segment is obtained, specifically including: randomly generating the time taken to pass through each displacement segment: t1, t2, t3, t4; obtaining the segment value of each displacement segment from the end point to the initial position: L1, L2, L3, L4; determining the control vertex of the initial position to be (0,0), the control vertex of the first displacement segment from the end point to be (t1, L1), the control vertex of the second displacement segment from the end point to be (t1+t2, L2), the control vertex of the third displacement segment from the end point to be (t1+t2+t3, L3), and the control vertex of the fourth displacement segment from the end point to be (t1+t2+t3+t4, L4).

[0008] Furthermore, the time value of each end point is substituted into the preset quintic B-spline expression as the control vertex to obtain the motion trajectory, and then obtain the speed and acceleration, specifically including: through the formula:

[0009]

[0010] Where u represents the preset node vector { , , ,......, }, where m represents a preset constant, and m-1 is greater than 4; represents the motion trajectory, represents the i-th control vertex starting from the initial position, and the value range of i is [0,4]. Represents the preset basis function of the preset quintic B-spline expression; obtain The first derivative of is used as the velocity; get The second derivative of is taken as acceleration.

[0011] Further, satisfying the preset dynamic constraint condition and the preset kinematic constraint condition specifically includes: when the speed is within the preset speed range and the acceleration is within the preset acceleration range, determining that the preset dynamic constraint formula is satisfied; determining whether the acceleration satisfies the preset dynamic constraint formula:

[0012]

[0013] N

[0014] Among them, A represents the effective area of ​​the rodless cavity, Indicates the load pressure, represents the total mass of the load and the piston rod converted to the piston, y represents the acceleration, Indicates the internal friction of the edge holding cylinder. It represents the total external force acting on the piston except the driving force. represents the motor's moment of inertia, Indicates the motor rotation angle, Indicates the motor output torque, represents the motor friction; where, , , , , , , are the values ​​corresponding to the current speed and acceleration obtained by the preset fitting software; A, , N is a preset constant.

[0015] Furthermore, by using a preset deep Q network, a preset quintic spline curve is solved, and specific values ​​of each control vertex in the preset quintic spline curve are updated, specifically including:

[0016]

[0017]

[0018]

[0019] Among them, Q() represents the preset deep Q network, represents the preset learning rate, s represents the current control vertex, a represents the time used for the segment displacement distance corresponding to the current control vertex, r() represents the preset adjustment function, Indicates the preset adjustment parameters, represents the previous control vertex, Indicates the time used for the previous displacement distance, L(W) represents the preset loss function, represents the preset objective function, Represents a preset parameter, and the preset parameter belongs to a preset parameter set; Indicates the previous preset parameter of a preset parameter in the preset parameter set.

[0020] In the second aspect, the present application provides a servo hydraulic stretching pad time optimal trajectory calculation system, the system includes: a bisection module, used to obtain the stretching displacement distance of the servo hydraulic stretching pad from a preset starting point vertically downward to a preset end point in contact with a slider, and divide the stretching displacement distance into four displacement distances on average; a vertex acquisition module, used to randomly generate the time used to pass each displacement segment, and then obtain the control vertex reaching the initial position and the end point of each displacement distance; a speed acquisition module, used to substitute the time value of each end point as the control vertex into a preset quintic B-spline expression, obtain the motion trajectory, and then obtain the speed and acceleration; a constraint determination module, used to enter the update numerical module when the speed and acceleration meet the preset dynamic constraints and the preset kinematic constraints, otherwise enter the vertex acquisition module; the update numerical module is used to solve the preset quintic spline curve through a preset deep Q network, and update the specific values ​​of each control vertex in the preset quintic spline curve.

[0021] Furthermore, the vertex acquisition module includes a vertex acquisition unit, which is used to randomly generate the time used for each displacement segment: t1, t2, t3, t4; obtain the segment value of each displacement segment from the end point to the initial position: L1, L2, L3, L4; determine that the control vertex of the initial position is (0,0), the control vertex of the first displacement segment from the end point is (t1, L1), the control vertex of the second displacement segment from the end point is (t1+t2, L2), the control vertex of the third displacement segment from the end point is (t1+t2+t3, L3), and the control vertex of the fourth displacement segment from the end point is (t1+t2+t3+t4, L4).

[0022] Further, the speed acquisition module includes a speed acquisition unit, which is used to obtain the speed through the formula:

[0023]

[0024] Where u represents the preset node vector { , , ,......, }, where m represents a preset constant, and m-1 is greater than 4; represents the motion trajectory, represents the i-th control vertex starting from the initial position, and the value range of i is [0,4]. Represents the preset basis function of the preset quintic B-spline expression; obtain The first derivative of is used as the velocity; get The second derivative of is taken as acceleration.

[0025] Further, the constraint determination module includes a constraint determination unit, which is used to determine whether a preset dynamic constraint formula is satisfied when the speed is within a preset speed range and the acceleration is within a preset acceleration range; and determine whether the acceleration satisfies the preset dynamic constraint formula:

[0026]

[0027] N

[0028] Among them, A represents the effective area of ​​the rodless cavity, Indicates the load pressure, represents the total mass of the load and the piston rod converted to the piston, y represents the acceleration, Indicates the internal friction of the edge holding cylinder. It represents the total external force acting on the piston except the driving force. represents the motor's moment of inertia, Indicates the motor rotation angle, Indicates the motor output torque, represents the motor friction; where, , , , , , , are the values ​​corresponding to the current speed and acceleration obtained by the preset fitting software; A, , N is a preset constant.

[0029] In a third aspect, the present application provides a non-volatile computer storage medium having computer instructions stored thereon, which, when executed, implement a method for calculating a time optimal trajectory of a servo hydraulic stretching pad as described in any one of the above items.

[0030] Those skilled in the art can understand that the present application has at least the following beneficial effects:

[0031] This application takes into account the kinematic characteristics of the pre-acceleration stage and satisfies the preset kinematic constraint formula, which can make the motion trajectory smoother and more accurate. Considering the preset dynamic constraint formula of the pre-acceleration stage, the performance is brought into play and the time is optimized while satisfying the preset dynamic constraint formula. The quintic B-spline curve model has good continuity and ensures a smooth transition of position, velocity, and acceleration. And only a single time variable t needs to be optimized, which reduces the difficulty of the optimization problem. The deep Q network algorithm is introduced to solve the optimal time. The deep Q network has the ability to handle nonlinear problems, which can solve the optimal time faster. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Some embodiments of the present disclosure are described below with reference to the accompanying drawings, in which:

[0033] Figure 1 It is a flow chart of a method for calculating the optimal time trajectory of a servo hydraulic stretching pad provided in an embodiment of the present application.

[0034] Figure 2 It is a schematic diagram of the internal structure of a servo hydraulic stretching pad time optimal trajectory calculation system provided in an embodiment of the present application. DETAILED DESCRIPTION

[0035] It should be understood by those skilled in the art that the embodiments described below are only preferred embodiments of the present disclosure, and do not mean that the present disclosure can only be implemented through the preferred embodiments. The preferred embodiments are only used to explain the technical principles of the present disclosure, and are not used to limit the protection scope of the present disclosure. Based on the preferred embodiments provided by the present disclosure, all other embodiments obtained by ordinary technicians in this field without creative work should still fall within the protection scope of the present disclosure.

[0036] It should also be noted that the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, commodity or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, commodity or device. In the absence of more restrictions, the elements defined by the sentence "comprises a ..." do not exclude the existence of other identical elements in the process, method, commodity or device including the elements.

[0037] The technical solution proposed in the embodiments of the present application is described in detail below with reference to the accompanying drawings.

[0038] The present application embodiment provides a method for calculating the optimal time trajectory of a servo hydraulic stretching pad, such as Figure 1 As shown, the method provided in the embodiment of the present application mainly includes the following steps:

[0039] S1, obtaining the stretching displacement distance of the servo hydraulic stretching pad from a preset starting point vertically downward to a preset end point in contact with the slider, and evenly dividing the stretching displacement distance into four displacement distances.

[0040] S2 randomly generates the time taken to pass through each displacement stage, and then obtains the control vertex reaching the initial position and the end point of each displacement stage.

[0041] As an example, this step may be specifically as follows:

[0042] The time used for each displacement is randomly generated: t1, t2, t3, t4; the segment value of each displacement segment from the end point to the initial position is obtained: L1, L2, L3, L4; the control vertex of the initial position is determined to be (0,0), the control vertex of the first displacement segment from the end point is (t1, L1), the control vertex of the second displacement segment from the end point is (t1+t2, L2), the control vertex of the third displacement segment from the end point is (t1+t2+t3, L3), and the control vertex of the fourth displacement segment from the end point is (t1+t2+t3+t4, L4).

[0043] S3, substituting the time value of each end point of each segment as a control vertex into a preset quintic B-spline expression to obtain a motion trajectory, and then obtain the velocity and acceleration.

[0044] As an example, this step may be specifically as follows:

[0045] By formula:

[0046]

[0047] Where u represents the preset node vector { , , ,......, }, where m represents a preset constant, and m-1 is greater than 4; represents the motion trajectory, represents the i-th control vertex starting from the initial position, and the value range of i is [0,4]. Represents the preset basis function of the preset quintic B-spline expression; obtain The first derivative of is used as the velocity; get The second derivative of is taken as acceleration.

[0048] S4: When the velocity and acceleration meet the preset dynamic constraint conditions and the preset kinematic constraint conditions, enter S5; otherwise, enter S2.

[0049] As an example, satisfying the preset dynamic constraint condition and the preset kinematic constraint condition may specifically be:

[0050] When the speed is within the preset speed range and the acceleration is within the preset acceleration range, it is determined that the preset dynamic constraint formula is satisfied; it is determined whether the acceleration satisfies the preset dynamic constraint formula:

[0051]

[0052] N

[0053] Among them, A represents the effective area of ​​the rodless cavity, Indicates the load pressure, represents the total mass of the load and the piston rod converted to the piston, y represents the acceleration, Indicates the internal friction of the edge holding cylinder. It represents the total external force acting on the piston except the driving force. represents the motor's moment of inertia, Indicates the motor rotation angle, Indicates the motor output torque, represents the motor friction; where, , , , , , , are the values ​​corresponding to the current speed and acceleration obtained by the preset fitting software; A, , N is a preset constant.

[0054] S5, solving the preset quintic spline curve through the preset deep Q network, and updating the specific value of each control vertex in the preset quintic spline curve.

[0055] As an example, this step may be specifically as follows:

[0056]

[0057]

[0058]

[0059] Among them, Q() represents the preset deep Q network, represents the preset learning rate, s represents the current control vertex, a represents the time used for the segment displacement distance corresponding to the current control vertex, r() represents the preset adjustment function, Indicates the preset adjustment parameters, represents the previous control vertex, Indicates the time used for the previous displacement distance, L(W) represents the preset loss function, represents the preset objective function, Represents a preset parameter, and the preset parameter belongs to a preset parameter set; Indicates the previous preset parameter of a preset parameter in the preset parameter set.

[0060] besides, Figure 2 A servo hydraulic stretching pad time optimal trajectory calculation system is provided in the embodiment of the present application. Figure 2 As shown, the system provided in the embodiment of the present application mainly includes:

[0061] The bisection module 210 is used to obtain the stretching displacement distance of the servo hydraulic stretching pad from a preset starting point vertically downward to a preset end point in contact with the slider, and to evenly divide the stretching displacement distance into four displacement distances.

[0062] The vertex acquisition module 220 is used to randomly generate the time taken to pass each displacement segment, and then obtain the control vertex that reaches the initial position and the end point of each displacement segment.

[0063] The vertex acquisition module 220 includes a vertex acquisition unit, which is used to randomly generate the time used for each displacement segment: t1, t2, t3, t4; obtain the segment value of each displacement segment from the end point to the initial position: L1, L2, L3, L4; determine that the control vertex of the initial position is (0,0), the control vertex of the first displacement segment from the end point is (t1, L1), the control vertex of the second displacement segment from the end point is (t1+t2, L2), the control vertex of the third displacement segment from the end point is (t1+t2+t3, L3), and the control vertex of the fourth displacement segment from the end point is (t1+t2+t3+t4, L4).

[0064] The speed acquisition module 230 is used to substitute the time value of each end point of each segment as a control vertex into a preset quintic B-spline expression to obtain a motion trajectory, and then obtain speed and acceleration.

[0065] The speed acquisition module 230 includes a speed acquisition unit, which is used to obtain the speed through the formula:

[0066]

[0067] Where u represents the preset node vector { , , ,......, }, where m represents a preset constant, and m-1 is greater than 4; represents the motion trajectory, represents the i-th control vertex starting from the initial position, and the value range of i is [0,4]. Represents the preset basis function of the preset quintic B-spline expression; obtain The first derivative of is used as the velocity; get The second derivative of is taken as acceleration.

[0068] The constraint determination module 240 is used to enter the value updating module when the velocity and acceleration meet the preset dynamic constraint conditions and the preset kinematic constraint conditions, and enter the vertex obtaining module otherwise.

[0069] The constraint determination module 240 includes a constraint determination unit for determining whether a preset dynamic constraint formula is satisfied when the speed is within a preset speed range and the acceleration is within a preset acceleration range; and determining whether the acceleration satisfies the preset dynamic constraint formula:

[0070]

[0071] N

[0072] Among them, A represents the effective area of ​​the rodless cavity, Indicates the load pressure, represents the total mass of the load and the piston rod converted to the piston, y represents the acceleration, Indicates the internal friction of the edge holding cylinder. It represents the total external force acting on the piston except the driving force. represents the motor's moment of inertia, Indicates the motor rotation angle, Indicates the motor output torque, represents the motor friction; where, , , , , , , are the values ​​corresponding to the current speed and acceleration obtained by the preset fitting software; A, , N is a preset constant.

[0073] The updating value module 250 is used to solve the preset quintic spline curve through the preset deep Q network, and update the specific value of each control vertex in the preset quintic spline curve.

[0074] In addition, an embodiment of the present application further provides a non-volatile computer storage medium on which executable instructions are stored. When the executable instructions are executed, a method for calculating the optimal time trajectory of a servo hydraulic stretching pad as described above is implemented.

[0075] So far, the technical solutions of the present disclosure have been described in combination with the above multiple embodiments, but it is easy for those skilled in the art to understand that the protection scope of the present disclosure is not limited to these specific embodiments. Without departing from the technical principles of the present disclosure, those skilled in the art can split and combine the technical solutions in the above-mentioned various embodiments, and can also make equivalent changes or replacements to the relevant technical features. Any changes, equivalent replacements, improvements, etc. made within the technical concept and / or technical principle of the present disclosure will fall within the protection scope of the present disclosure.

Claims

1. A method for calculating the optimal time trajectory of a servo hydraulic stretching pad, characterized in that: The method comprises: S1, obtaining the stretching displacement distance of the servo hydraulic stretching pad from a preset starting point vertically downward to a preset end point in contact with the slider, and dividing the stretching displacement distance into four displacement distances on average; S2, randomly generates the time taken to pass through each displacement segment, and then obtains the control vertex that reaches the initial position and the end point of each displacement segment; S3, substituting the time value of each end point of each segment as a control vertex into a preset quintic B-spline expression to obtain a motion trajectory, and then obtain the velocity and acceleration; S4, when the velocity and acceleration meet the preset dynamic constraint conditions and the preset kinematic constraint conditions, enter S5, otherwise enter S2; Among them, the preset dynamic constraints and preset kinematic constraints are met, specifically including: When the speed is within the preset speed range and the acceleration is within the preset acceleration range, determining that the preset dynamic constraint formula is satisfied; Determine whether the acceleration satisfies the preset dynamic constraint formula: N Among them, A represents the effective area of ​​the rodless cavity, Indicates the load pressure, represents the total mass of the load and the piston rod converted to the piston, y represents the acceleration, Indicates the internal friction of the edge holding cylinder. It represents the total external force acting on the piston except the driving force. represents the motor's moment of inertia, Indicates the motor rotation angle, Indicates the motor output torque, Indicates motor friction; in, , , , , , , are the values ​​corresponding to the current speed and acceleration obtained by the preset fitting software; A, , N is a preset constant; S5, solving the preset quintic spline curve through the preset deep Q network, and updating the specific value of each control vertex in the preset quintic spline curve.

2. The method for calculating the optimal time trajectory of a servo hydraulic stretching pad according to claim 1, characterized in that: The time taken to pass each displacement is randomly generated, and then the control vertex reaching the initial position and the end point of each displacement is obtained, including: Randomly generate the time used to pass each displacement segment: t1, t2, t3, t4; Get the segment value of each segment displacement from the end point to the initial position: L1, L2, L3, L4; The control vertex of the initial position is determined to be (0,0), the control vertex of the first displacement distance to the end point is (t1, L1), the control vertex of the second displacement distance to the end point is (t1+t2, L2), the control vertex of the third displacement distance to the end point is (t1+t2+t3, L3), and the control vertex of the fourth displacement distance to the end point is (t1+t2+t3+t4, L4).

3. The method for calculating the optimal time trajectory of a servo hydraulic stretching pad according to claim 1, characterized in that: Substitute the time value of each end point as the control vertex into the preset quintic B-spline expression to obtain the motion trajectory, and then obtain the speed and acceleration, including: By formula: Where u represents the preset node vector { , , ,......, }, where m represents a preset constant, and m-1 is greater than 4; represents the motion trajectory, represents the i-th control vertex starting from the initial position, and the value range of i is [0,4]. represents a preset basis function of a preset quintic B-spline expression; Get The first derivative of is used as the velocity; get The second derivative of is taken as acceleration.

4. The method for calculating the optimal time trajectory of a servo hydraulic stretching pad according to claim 1, characterized in that: Through the preset deep Q network, the preset quintic spline curve is solved, and the specific values ​​of each control vertex in the preset quintic spline curve are updated, including: Among them, Q() represents the preset deep Q network, represents the preset learning rate, s represents the current control vertex, a represents the time used for the segment displacement distance corresponding to the current control vertex, r() represents the preset adjustment function, Indicates the preset adjustment parameters, represents the previous control vertex, Indicates the time used for the previous displacement distance, L(W) represents the preset loss function, represents the preset objective function, Represents a preset parameter, and the preset parameter belongs to a preset parameter set; Indicates the previous preset parameter of a preset parameter in the preset parameter set.

5. A servo hydraulic stretching pad time optimal trajectory calculation system, characterized in that: The system comprises: A bisection module is used to obtain the stretching displacement distance of the servo hydraulic stretching pad from a preset starting point vertically downward to a preset end point in contact with the slider, and to evenly divide the stretching displacement distance into four displacement distances; The vertex acquisition module is used to randomly generate the time taken to pass each displacement segment, and then obtain the control vertex reaching the initial position and the end point of each displacement segment; The speed acquisition module is used to substitute the time value of each segment end point as the control vertex into the preset quintic B-spline expression to obtain the motion trajectory, and then obtain the speed and acceleration; The constraint determination module is used to enter the value update module when the velocity and acceleration meet the preset dynamic constraint conditions and the preset kinematic constraint conditions, otherwise enter the vertex acquisition module; The constraint determination module includes a constraint determination unit. Used to determine that a preset dynamic constraint formula is satisfied when the speed is within a preset speed range and the acceleration is within a preset acceleration range; Determine whether the acceleration satisfies the preset dynamic constraint formula: N Among them, A represents the effective area of ​​the rodless cavity, Indicates the load pressure, represents the total mass of the load and the piston rod converted to the piston, y represents the acceleration, Indicates the internal friction of the edge holding cylinder. It represents the total external force acting on the piston except the driving force. represents the motor's moment of inertia, Indicates the motor rotation angle, Indicates the motor output torque, Indicates motor friction; in, , , , , , , are the values ​​corresponding to the current speed and acceleration obtained by the preset fitting software; A, , N is a preset constant; The numerical update module is used to solve the preset quintic spline curve through the preset deep Q network and update the specific values ​​of each control vertex in the preset quintic spline curve.

6. The servo hydraulic stretching pad time optimal trajectory calculation system according to claim 5, characterized in that: The vertex acquisition module includes a vertex acquisition unit, Used to randomly generate the time used for each displacement: t1, t2, t3, t4; Get the segment value of each segment displacement from the end point to the initial position: L1, L2, L3, L4; The control vertex of the initial position is determined to be (0,0), the control vertex of the first displacement distance to the end point is (t1, L1), the control vertex of the second displacement distance to the end point is (t1+t2, L2), the control vertex of the third displacement distance to the end point is (t1+t2+t3, L3), and the control vertex of the fourth displacement distance to the end point is (t1+t2+t3+t4, L4).

7. The servo hydraulic stretching pad time optimal trajectory calculation system according to claim 5, characterized in that: The speed acquisition module includes a speed acquisition unit, Used by the formula: Where u represents the preset node vector { , , ,......, }, where m represents a preset constant, and m-1 is greater than 4; represents the motion trajectory, represents the i-th control vertex starting from the initial position, and the value range of i is [0,4]. represents a preset basis function of a preset quintic B-spline expression; Get The first derivative of is used as the velocity; get The second derivative of is taken as acceleration.

8. A non-volatile computer storage medium, characterized in that: Computer instructions are stored thereon, and when the computer instructions are executed, a method for calculating the optimal time trajectory of a servo hydraulic stretching pad as described in any one of claims 1 to 4 is implemented.

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