A Global Energy Consumption Optimization Method for Hydraulic Robotic Arms Integrating Dynamic Time-Domain Programming

Abstract

This invention provides a global energy consumption optimization method for a hydraulic robotic arm that integrates dynamic time-domain programming. It constructs a multi-layered two-dimensional configuration layer based on multiple pre-scaling time periods (divided into pre-scaling time periods), multiple post-scaling time periods (divided into post-scaling time periods), and the time change rate corresponding to the first derivative of the pre-scaling trajectory. The method then performs inverse iteration on these multi-layered two-dimensional configuration layers to obtain the minimum operating cost and the optimal control quantity corresponding to the minimum operating cost for each layer. Based on the optimal control quantity of each layer, the method performs forward iteration on each layer to obtain the hydraulic robotic arm motion trajectory integrated with dynamic time programming. This invention can reduce system energy consumption and improve operational efficiency by scaling the motion trajectory of the hydraulic robotic arm in the time dimension without affecting the end effector trajectory and while satisfying all constraints.

Description

Technical Field

[0001] This invention belongs to the field of lasers, specifically relating to a global energy consumption optimization method for hydraulic robotic arms that integrates dynamic time-domain programming. Background Technology

[0002] Redundant hydraulic robotic arms play a crucial role in fields such as construction, mining, and forestry due to their high power density, strong impact resistance, and the flexibility afforded by redundant degrees of freedom. Since the motion states of each joint and the dynamic characteristics of the hydraulic system directly affect the energy consumption of the hydraulic robotic arm, optimizing its motion trajectory by considering energy efficiency can limit energy loss during task execution and improve system efficiency.

[0003] The optimal redundancy decomposition problem for the energy consumption of hydraulic robotic arms is non-convex, and conventional direct optimization methods are prone to producing local optima rather than global optima. While repeated calculations with multiple initial values ​​can eliminate interference from local optima, they also waste time and resources. Furthermore, factors such as valve opening and closing and cylinder area asymmetry contribute to the discontinuous and non-smooth nature of the energy consumption problem in hydraulic robotic arms, making gradient-based optimization methods difficult to apply directly. Existing research on global energy consumption optimization for hydraulic robotic arms only utilizes the joint-dimensional degrees of freedom to optimize system energy consumption, without further optimizing energy consumption in the time dimension. Summary of the Invention

[0004] This invention provides a global energy consumption optimization method for hydraulic robotic arms that integrates dynamic time-domain programming, in order to solve the problem that existing global energy consumption optimization studies for hydraulic robotic arms only utilize the joint dimension to optimize system energy consumption, but do not further optimize energy consumption in the time dimension.

[0005] According to a first aspect of the present invention, a method for global energy consumption optimization of a hydraulic robotic arm integrating dynamic time-domain programming is provided, comprising the following steps:

[0006] Step S100: Divide the duration s of the hydraulic robotic arm reference trajectory into multiple pre-scaling time intervals; scale the reference trajectory to obtain a scaled trajectory, and divide the duration t of the scaled trajectory into multiple post-scaling time intervals; calculate the first derivative of the duration s. and the first derivative Discretely divide the time-varying rate into multiple time-varying rates;

[0007] Construct multi-layer two-dimensional configuration layers corresponding to different pre-scaling time periods. Each two-dimensional configuration layer is used to represent a set of state variables X. The state variables in the corresponding set of state variables X are the combination of each time point of the corresponding scaled time period and each time change rate. Scale each pre-scaling time period and use each duration obtained after scaling as the control variables in the control variable set U. Initialize the running cost of each set of state variables X combined with each control variable in the control variable set U.

[0008] Step S200: Perform reverse iteration on the multi-layer two-dimensional configuration layer: For each state variable in the state variable set X corresponding to each two-dimensional configuration layer, combine the state variable with each control variable in the control variable set U. For each combination, calculate the system dynamics, the minimum operating cost of the system dynamics, and the energy consumption characteristic parameter model of the hydraulic manipulator under the action of the combination. Based on the calculated minimum operating cost of the system dynamics and the energy consumption characteristic parameter model, evaluate the operating cost of the hydraulic manipulator under the action of the combination. Determine the minimum operating cost of each operating cost calculated for each two-dimensional configuration layer, and take the optimal control variable corresponding to each minimum operating cost as the optimal control variable of the corresponding two-dimensional configuration layer. The determination of the minimum operating cost of the system dynamics is related to the initial operating cost of the previous two-dimensional configuration layer in reverse iteration.

[0009] Step S300: Set the initial state of the hydraulic robotic arm, and perform forward iteration on each two-dimensional configuration layer based on the optimal control variables of each layer to obtain the motion trajectory of the hydraulic robotic arm.

[0010] Optionally, step S100 specifically includes:

[0011] Step S110: Divide the duration s of the hydraulic robotic arm reference trajectory evenly into N. t There are N time periods, each of which is the original time period before scaling. t It is an integer greater than 1;

[0012] Step S120: Scale the reference trajectory to obtain a scaled trajectory, and divide the duration t of the scaled trajectory evenly into N. t There are several time periods, each of which is a scaled-down version of the time period.

[0013] Step S130: Calculate the first derivative of the duration s with respect to time. and the first derivative Discretely divide N v The rate of change over time, N v It is an integer greater than 1;

[0014] Step S140: For the i-th two-dimensional configuration layer, the i-th scaled time period is discretized sequentially to obtain N. t At each time point, the N t Each time point is used as the first dimension data of the i-th two-dimensional configuration layer, and each time change rate is used as the second dimension data of the i-th configuration layer, thus forming N from the i-th configuration layer. t ×N v A two-dimensional discrete network, wherein each time point and its combination with various time rates of change constitute the state variables in the state variable set X corresponding to the i-th two-dimensional configuration layer, where i is greater than 0 and less than or equal to N. t Integers;

[0015] Step S150: Scale each time period before scaling, and use each duration obtained after scaling as a control variable in the control variable set U. Initialize the running cost of each state variable set X after combining it with each control variable in the control variable set U.

[0016] Optionally, in step S200:

[0017] For each combination, the joint angular velocity and angular acceleration of the hydraulic manipulator before and after scaling, as well as the oil supply pressure of the load-sensitive system and the total flow of the hydraulic system after scaling, can be calculated first. Based on the joint angular velocity and angular acceleration before and after scaling, it is determined whether to calculate the system dynamics and operating costs under the action of this combination. If so, the system dynamics are calculated based on this combination. When the system dynamics are the state variables of the reverse iteration of the upper two-dimensional configuration layer, the minimum operating cost of each operating cost calculated in the previous iteration for the reverse iteration of the upper two-dimensional configuration layer is taken as the minimum operating cost of the system dynamics.

[0018] When the system dynamics are not the state variables of the reverse iteration of the previous two-dimensional configuration layer, the minimum operating cost of the system dynamics is determined by linear interpolation based on the minimum operating cost of each operating cost calculated in the previous iteration for the reverse iteration of the previous two-dimensional configuration layer, the state variable corresponding to the minimum operating cost, the initial operating cost of the previous two-dimensional configuration layer, and the system dynamics.

[0019] Based on the parameters calculated during the scaling process of the oil supply pressure of the load-sensitive system and the total flow of the hydraulic system, the energy consumption characteristic parameter model of the hydraulic robotic arm under this combined action is calculated.

[0020] Optionally, step S200 specifically includes:

[0021] Step S210: For the i-th two-dimensional configuration layer, select its j-th state variable x. i,jAnd select the k-th control variable u from the set of control variables U. k Determine the state variable x i,j and control variable u k Under the influence of scaling, the joint angles, joint angular velocities, and joint angular accelerations of the hydraulic robotic arm before and after scaling are calculated, where i, j, and k are all integers greater than 0, and the initial value of i is N. t -1, N t The initial values ​​of j and k are 1, representing the number of time periods before and after scaling.

[0022] Step S220: Calculate the state variable x i,j and control variable u k Under the influence of scaling, the oil supply pressure of the load-sensitive system and the total flow rate of the hydraulic system are adjusted.

[0023] Step S230: Determine whether the joint angular velocity and joint angular acceleration meet the convention: If the joint angular velocity and joint angular acceleration meet the convention both before and after scaling, then based on the dynamic calculation of the hydraulic manipulator configuration system, and according to the minimum operating cost corresponding to the system dynamics, the energy consumption characteristic model of the hydraulic manipulator, the parameters of the oil supply pressure of the load-sensitive system after scaling, and the total flow of the hydraulic system, evaluate the hydraulic manipulator in the state variable x. i,j and control variable u k If the operating cost under the action is determined, proceed to step S240; otherwise, proceed to step S240.

[0024] Step S240: Determine if k equals N t If yes, proceed to step S250; otherwise, increment k and return to step S210.

[0025] Step S250: Determine if j is equal to N t ×N v If yes, proceed to step S260; otherwise, increment j and return to step S210. v The number of rates of change over time, which is an integer greater than 1;

[0026] Step S260: Determine if i is equal to 1. If yes, proceed to step S270; otherwise, decrement i and return to step S210.

[0027] Step S270: Determine the minimum operating cost calculated for each two-dimensional configuration layer, and use the optimal control variable corresponding to each minimum operating cost as the optimal control variable for the corresponding two-dimensional configuration layer.

[0028] Optionally, step S210 specifically includes:

[0029] The joint angle q of the hydraulic robotic arm was respectively... r (s) Perform the first-order differential with respect to time and second-order differential Obtain the joint angular velocity before scaling and joint angular acceleration

[0030] The scaled hydraulic robotic arm joint angle q is determined using the following formula. s (t), joint angular velocity and joint angular acceleration

[0031]

[0032] in This represents the first derivative of the duration *s* with respect to time. This represents the second derivative of the duration s with respect to time.

[0033] Optionally, step S220 specifically includes:

[0034] Step S221: Calculate the state variable x according to the following formula. i,j and control variable u k Under the action, the hydraulic cylinder output force F corresponding to each joint h :

[0035]

[0036]

[0037]

[0038]

[0039]

[0040] In the formula, This represents the first derivative of the duration *s* of the reference trajectory with respect to time. R(q) represents the second derivative of the duration s of the reference trajectory with respect to time. r = diag(r1 r2 … r) n M(q) is the lever arm transformation matrix of the hydraulic manipulator. r ), and G(q) r Let represent the inertia matrix, Coriolis force and centrifugal force matrix, and gravity vector of the hydraulic robotic arm, respectively. This represents the joint angular velocity before scaling. Represents the joint angular acceleration before scaling, J is the Jacobian matrix, and F tf is the end force. c =[f c.1 ,…,f c.n ] T and f v =[f v.1 ,…,f v.n ] T These are the vectors of the Coulomb friction coefficient and the viscous friction coefficient, respectively;

[0041] Step S222: Based on the output force F of the hydraulic cylinder h With oil supply pressure p in The relationship is used to obtain the oil supply pressure p of each joint in the scaled load-sensitive system. in :

[0042]

[0043] a1=HAk1

[0044] a2=HAk2

[0045] a3=HAk4

[0046] a4=HAk3+Hp c

[0047] In the formula, H, A and p c The pressure margin Δp is set for the cylinder output force, cylinder working area, and load-sensitive system, respectively. ls Related vectors;

[0048] Step S223: Determine the maximum oil supply pressure p in the oil supply pressure vector corresponding to each joint. in,im =max{p in,1 ,…,p in,n The oil supply pressure p of the scaled load-sensitive system is calculated using the following formula. ls,s :

[0049] In the formula, a 1,im ~a 4,im These represent the im-th components of vectors a1 to a4, where im is the maximum oil supply pressure p. in,im The serial number;

[0050] Step S224, Consider the oil supply pressure p ls,s The leakage loss is calculated using the following formula to determine the total flow rate Q of the scaled hydraulic system. s :

[0051] In the formula, The total flow rate of the hydraulic system before scaling is expressed as follows, within the time coordinate system corresponding to the reference trajectory:

[0052]

[0053] In the formula, r i A represents the lever arm transformation mapping corresponding to joint i of the robotic arm; a,i and A b,i H represents the area of ​​the rodless chamber and the rod chamber of the hydraulic cylinder corresponding to joint i, respectively; i (*) is the step function, defined as

[0054]

[0055] Optionally, step S230 specifically includes:

[0056] Step S231: Based on the hydraulic robotic arm configuration, calculate the system dynamics x according to the following formula. i+1 :

[0057]

[0058] Where Δ s This indicates the duration of each time period before scaling;

[0059] Step S232: Determine the dynamics of the system x i+1 Is it a state variable in the state variable set X corresponding to the (i+1)th two-dimensional configuration layer? If so, then take the minimum operating cost calculated for each operating cost for the (i+1)th two-dimensional configuration layer in the previous iteration as the dynamic value of the system x. i+1 Corresponding minimum operating cost Otherwise, determine the minimum operating cost calculated for each operating cost of the (i+1)th two-dimensional configuration layer in the previous iteration, as well as the corresponding state variable, and determine the state variable set X and control variable u of the (i+1)th two-dimensional configuration layer. k The initial operating cost after combination depends on the determined state variables and system dynamics x. i+1 Linear interpolation is performed on the determined minimum operating cost and initial operating cost to obtain the dynamic value x of the system. i+1 Corresponding minimum operating cost

[0060] Step S233: Based on minimum operating cost The hydraulic robotic arm in state variable x can be evaluated using the following formula. i,j and control variable u k Operating cost J under the action k (x ij ,u k ):

[0061]

[0062] E k (x ij ,u k ) represents the state variable x of the hydraulic robotic arm. i,j and control variable u k Energy consumption characteristic parameter model under action, E k (x ij ,u k ) = P k (x ij ,u k )·u k ;

[0063]

[0064] In the formula, s i This represents the time period before scaling for the i-th two-dimensional configuration layer. Indicates the time period s before scaling. i The first derivatives, b1, b2, b3, b4, b5, b6, b7, a q a p1 and a p2 These are combination terms related to the robotic arm configuration, calculated using the following formulas:

[0065]

[0066] b2 = a 1,im a 2,im k p1 +a 1,im a q

[0067] b 31 =a 1,im a p1 +a 1,im k p1 a p2 +a 2,im a q

[0068] b 32 =2a 1,im a 3,im k p1

[0069] b 41 =a q a p2 +a 2,im a p1

[0070] b 42 =a 2,im a 3,im kp1 +a 3,ima q

[0071]

[0072] b6 = a 3,im k p1 a p2 +a 3,im ap1

[0073] b7 = a p1 a p2

[0074]

[0075] a p1 =a 4,im k p1 +Δp ls k p1 +k p2

[0076] a p2 =a 4,im +Δp ls

[0077] Among them, a 1,im ~a 4,im These represent the im-th component of vectors a1 to a4 during the calculation of the oil supply pressure in the scaled load-sensitive system, where im is the maximum oil supply pressure p in the oil supply pressure vector corresponding to each joint. in,im The serial number; k p1 and k p2 These represent the system leakage coefficients; This represents the total flow rate of the hydraulic system before scaling, within the time coordinate system corresponding to the reference trajectory; Δp ls This indicates the pressure margin set for a load-sensitive system.

[0078] Optionally, step S300 specifically includes:

[0079] Set the initial state x0 of the hydraulic robotic arm, and perform forward iteration on each two-dimensional configuration layer according to the following formula:

[0080]

[0081] In the formula, x i+1,j Let x represent the j-th state variable in the (i+1)-th two-dimensional configuration layer. i,j This represents the j-th state variable in the i-th two-dimensional configuration layer. Let Δ represent the optimal control variable of the i-th two-dimensional configuration layer. s This indicates the duration of each time period before scaling.

[0082] Optionally, in step S100, the reference trajectory is the optimal energy consumption trajectory of the hydraulic robotic arm obtained by energy redundancy decomposition.

[0083] The beneficial effects of this invention are:

[0084] 1. The method of the present invention can reduce system energy consumption and improve work efficiency by scaling the motion trajectory of the hydraulic robotic arm in the time dimension without affecting the end trajectory and satisfying all constraints.

[0085] 2. Based on the energy-optimal trajectory obtained by redundancy decomposition, this invention further optimizes energy consumption by time scaling, resulting in a trajectory with optimal energy consumption in both the joint and time dimensions. This is of great significance for reducing the energy consumption of hydraulic robotic arms. Attached Figure Description

[0086] Figure 1 This is a flowchart of an embodiment of the global energy consumption optimization method for hydraulic robotic arms that integrates dynamic time-domain programming according to the present invention;

[0087] Figure 2 This is a schematic diagram of the structure of the multi-layer two-dimensional configuration layer of the present invention;

[0088] Figure 3 This is a schematic diagram of the experimental system of the present invention;

[0089] Figure 4 A comparison diagram of the trajectory and system flow rate of experiments conducted using the method of this invention and conventional methods;

[0090] Figure 5 The graph shows the joint angle, velocity, and acceleration curves used in experiments conducted using this invention. Detailed Implementation

[0091] To enable those skilled in the art to better understand the technical solutions in the embodiments of the present invention, and to make the above-mentioned objectives, features and advantages of the embodiments of the present invention more apparent and understandable, the technical solutions in the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0092] In the description of this invention, unless otherwise specified and limited, it should be noted that the term "connection" should be interpreted broadly. For example, it can be a mechanical connection or an electrical connection, or it can be a connection between two internal components. It can be a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above term according to the specific circumstances.

[0093] See Figure 1 This is a flowchart of an embodiment of the global energy consumption optimization method for hydraulic robotic arms that integrates dynamic time-domain programming, as described in this invention. Combined with... Figure 2 As shown, the method may include the following steps:

[0094] Step S100: Divide the duration s of the hydraulic robotic arm reference trajectory into multiple pre-scaling time intervals; scale the reference trajectory to obtain a scaled trajectory, and divide the duration t of the scaled trajectory into multiple post-scaling time intervals; calculate the first derivative of the duration s. and the first derivative Discretely divide the time-varying rate into multiple time-varying rates;

[0095] Construct multi-layered two-dimensional configuration layers corresponding to different pre-scaling time periods. Each two-dimensional configuration layer represents a state variable set X, where the state variables in the state variable set X are combinations of each time point discretely divided into the corresponding scaled time period and various time change rates. Scale the duration of each pre-scaling time period and use it as a control variable in the control variable set U. Initialize the operating cost of each state variable set X combined with each control variable in the control variable set U, and execute step S200. In this embodiment, step S100 may specifically include:

[0096] Step S110: Divide the duration s of the hydraulic robotic arm reference trajectory evenly into N. t There are N time periods, each of which is the original time period before scaling. t N is an integer greater than 1. The input N can be any number of integers, depending on the required computational precision and complexity. t To uniformly divide the duration s into N t Each time period is defined as a reference trajectory, which can be the energy-optimal trajectory of the hydraulic robotic arm obtained by energy redundancy decomposition. The duration of each time period before scaling is the same as Δ. s They can be the same. This invention uses the energy-optimal trajectory of the hydraulic robotic arm as a reference trajectory and performs dynamic time-domain planning on the energy-optimal trajectory, which can further reduce the energy consumption of the hydraulic robotic arm's motion trajectory.

[0097] Step S120: Scale the reference trajectory to obtain a scaled trajectory, and divide the duration t of the scaled trajectory evenly into N. t There are several time periods, each of which is a scaled-down version.

[0098] Step S130: Calculate the first derivative of the duration s with respect to time. and the first derivative Discretely divide N v The rate of change over time, N v It is an integer greater than 1;

[0099] Step S140: For the i-th two-dimensional configuration layer, the i-th scaled time period is discretized sequentially to obtain N. t At each time point, the N t Each time point is used as the first dimension data of the i-th two-dimensional configuration layer, and each time change rate is used as the second dimension data of the i-th configuration layer, thus forming N from the i-th configuration layer. t ×N v A two-dimensional discrete network, wherein each time point and its combination with various time rates of change constitute the state variables in the state variable set X corresponding to the i-th two-dimensional configuration layer, where i is greater than 0 and less than or equal to N. t Integers. Among them, the multi-layer two-dimensional configuration layer can be used to represent the temporal state transition process of the hydraulic manipulator, and all of them are two-dimensional discrete meshes.

[0100] Step S150: Scale each time period before scaling, and use each duration obtained after scaling as a control variable in the control variable set U. Initialize the running cost of each state variable set X after combining it with each control variable in the control variable set U.

[0101] Step S200: Perform reverse iteration on the multi-layer two-dimensional configuration layer: For each state variable in the state variable set X corresponding to each two-dimensional configuration layer, combine the state variable with each control variable in the control variable set U. For each combination, calculate the system dynamics, the minimum operating cost of the system dynamics, and the energy consumption characteristic parameter model of the hydraulic manipulator under the action of the combination. Based on the calculated minimum operating cost of the system dynamics and the energy consumption characteristic parameter model, evaluate the operating cost of the hydraulic manipulator under the action of the combination. Determine the minimum operating cost of each operating cost calculated for each two-dimensional configuration layer, and take the optimal control variable corresponding to each minimum operating cost as the optimal control variable of the corresponding two-dimensional configuration layer. The determination of the minimum operating cost of the system dynamics is related to the initial operating cost of the previous two-dimensional configuration layer in reverse iteration. Execute step S300.

[0102] In step S200: For each combination, the joint angular velocity and joint angular acceleration of the hydraulic manipulator before and after scaling, as well as the oil supply pressure of the load-sensitive system and the total flow of the hydraulic system after scaling, can be calculated first. Based on the joint angular velocity and joint angular acceleration before and after scaling, it is determined whether to calculate the system dynamics and operating costs under the action of the combination. If so, the system dynamics are calculated based on the combination. When the system dynamics are the state variables of the reverse iteration of the upper two-dimensional configuration layer, the minimum operating cost of each operating cost calculated for the reverse iteration of the upper two-dimensional configuration layer in the previous iteration is taken as the minimum operating cost of the system dynamics.

[0103] When the system dynamics are not the state variables of the reverse iteration of the previous two-dimensional configuration layer, the minimum operating cost of the system dynamics is determined by linear interpolation based on the minimum operating cost of each operating cost calculated in the previous iteration for the reverse iteration of the previous two-dimensional configuration layer, the state variable corresponding to the minimum operating cost, the initial operating cost of the previous two-dimensional configuration layer, and the system dynamics.

[0104] Based on the parameters calculated during the scaling process of the oil supply pressure of the load-sensitive system and the total flow of the hydraulic system, the energy consumption characteristic parameter model of the hydraulic robotic arm under this combined action is calculated.

[0105] In this embodiment, step S200 may specifically include:

[0106] Step S210: For the i-th two-dimensional configuration layer, select its j-th state variable x. i,j And select the k-th control variable u from the set of control variables U. k Determine the state variable x i,j and control variable u k Under the influence of scaling, the joint angles, joint angular velocities, and joint angular accelerations of the hydraulic robotic arm before and after scaling are calculated, where i, j, and k are all integers greater than 0, and the initial value of i is N. t -1, N t The initial values ​​of j and k are both 1, representing the number of time periods before and after scaling. Then, proceed to step S220.

[0107] Step S220: Calculate the state variable x i,j and control variable u k Under the action of scaling, the oil supply pressure of the load-sensitive system and the total flow of the hydraulic system are adjusted, and step S230 is executed.

[0108] Step S230: Determine whether the joint angular velocity and joint angular acceleration meet the convention: If the joint angular velocity and joint angular acceleration meet the convention both before and after scaling, then based on the dynamic calculation of the hydraulic manipulator configuration system, and according to the minimum operating cost corresponding to the system dynamics, the energy consumption characteristic model of the hydraulic manipulator, the parameters of the oil supply pressure of the load-sensitive system after scaling, and the total flow of the hydraulic system, evaluate the hydraulic manipulator in the state variable x. i,j and control variable u k If the operating cost under the action is determined, proceed to step S240; otherwise, proceed to step S240.

[0109] Step S240: Determine if k equals N t If yes, proceed to step S250; otherwise, increment k and return to step S210.

[0110] Step S250: Determine if j is equal to Nt ×N v If yes, proceed to step S260; otherwise, increment j and return to step S210. v The number of rates of change over time, which is an integer greater than 1;

[0111] Step S260: Determine if i is equal to 1. If yes, proceed to step S270; otherwise, decrement i and return to step S210.

[0112] Step S270: Determine the minimum operating cost calculated for each two-dimensional configuration layer, and use the optimal control variable corresponding to each minimum operating cost as the optimal control variable for the corresponding two-dimensional configuration layer.

[0113] Specifically, step S210 may include:

[0114] The joint angle q of the hydraulic robotic arm was respectively... r (s) Perform the first-order differential with respect to time and second-order differential Obtain the joint angular velocity before scaling and joint angular acceleration

[0115] The scaled hydraulic robotic arm joint angle q is determined using the following formula. s (t), joint angular velocity and joint angular acceleration

[0116]

[0117] in This represents the first derivative of the duration *s* with respect to time. This represents the second derivative of the duration s with respect to time.

[0118] Step S220 may specifically include:

[0119] Step S221: Calculate the state variable x according to the following formula. i,j and control variable u k Under the action, the hydraulic cylinder output force F corresponding to each joint h :

[0120]

[0121]

[0122]

[0123]

[0124]

[0125] In the formula, This represents the first derivative of the duration *s* of the reference trajectory with respect to time. R(q) represents the second derivative of the duration s of the reference trajectory with respect to time. r = diag(r1 r2 … r) n M(q) is the lever arm transformation matrix of the hydraulic manipulator. r ), and G(q) r Let represent the inertia matrix, Coriolis force and centrifugal force matrix, and gravity vector of the hydraulic robotic arm, respectively. This represents the joint angular velocity before scaling. Represents the joint angular acceleration before scaling, J is the Jacobian matrix, and F t f is the end force. c =[f c.1 ,…,f c.n ] T and f v =[f v.1 ,…,f v.n ] T These are the vectors of the Coulomb friction coefficient and the viscous friction coefficient, respectively;

[0126] Step S222: Based on the output force F of the hydraulic cylinder h With oil supply pressure p in The relationship is used to obtain the oil supply pressure p of each joint in the scaled load-sensitive system. in :

[0127]

[0128] a1=HAk1

[0129] a2=HAk2

[0130] a3=HAk4

[0131] a4=HAk3+Hp c

[0132] In the formula, H, A and p c The pressure margin Δp is set for the cylinder output force, cylinder working area, and load-sensitive system, respectively. ls The relevant vectors and their expressions are as follows:

[0133]

[0134]

[0135]

[0136] In the formula, A a,i and A b,i This represents the working area of ​​the rod-side and rodless chambers of the linear cylinder driving joint i.

[0137] Step S223: Determine the maximum oil supply pressure p in the oil supply pressure vector corresponding to each joint. in,im =max{p in,1 ,…,p in,n The oil supply pressure p of the scaled load-sensitive system is calculated using the following formula. ls,s :

[0138] In the formula, a 1,im ~a 4,im These represent the im-th components of vectors a1 to a4, where im is the maximum oil supply pressure p. in,im The serial number;

[0139] Step S224, Consider the oil supply pressure p ls,s The leakage loss is calculated using the following formula to determine the total flow rate Q of the scaled hydraulic system. s :

[0140] In the formula, The total flow rate of the hydraulic system before scaling is expressed as follows, within the time coordinate system corresponding to the reference trajectory:

[0141]

[0142] In the formula, r i A represents the lever arm transformation mapping corresponding to joint i of the robotic arm; a,i and A b,i H represents the area of ​​the rodless chamber and the rod chamber of the hydraulic cylinder corresponding to joint i, respectively; i (*) is the step function, defined as

[0143]

[0144] Step S230 may specifically include:

[0145] Step S231: Based on the hydraulic robotic arm configuration, calculate the system dynamics x according to the following formula. i+1 :

[0146]

[0147] Where Δ s This indicates the duration of each time period before scaling;

[0148] Step S232: Determine the dynamics of the system x i+1 Is it a state variable in the state variable set X corresponding to the (i+1)th two-dimensional configuration layer? If so, then take the minimum operating cost calculated for each operating cost for the (i+1)th two-dimensional configuration layer in the previous iteration as the dynamic value of the system x. i+1 Corresponding minimum operating cost Otherwise, determine the minimum operating cost calculated for each operating cost of the (i+1)th two-dimensional configuration layer in the previous iteration, as well as the corresponding state variable, and determine the state variable set X and control variable u of the (i+1)th two-dimensional configuration layer. k The initial operating cost after combination depends on the determined state variables and system dynamics x. i+1 Linear interpolation is performed on the determined minimum operating cost and initial operating cost to obtain the dynamic value x of the system. i+1 Corresponding minimum operating cost

[0149] Step S233: Based on minimum operating cost The hydraulic robotic arm in state variable x can be evaluated using the following formula. i,j and control variable u k Operating cost J under the action k (x ij ,u k ):

[0150]

[0151] E k (x ij ,u k ) represents the state variable x of the hydraulic robotic arm. i,j and control variable u k Energy consumption characteristic parameter model under action, E k (x ij ,u k ) = P k (x ij ,u k )·u k ;

[0152]

[0153] In the formula, s i This represents the time period before scaling for the i-th two-dimensional configuration layer. Indicates the time period s before scaling. i The first derivatives, b1, b2, b3, b4, b5, b6, b7, a q a p1 and a p2These are combination terms related to the robotic arm configuration, calculated using the following formulas:

[0154]

[0155] b2 = a 1,im a 2,im k p1 +a 1,im a q

[0156] b 31 =a 1,im a p1 +a 1,im k p1 a p2 +a 2,im a q

[0157] b 32 =2a 1,im a 3,im k p1

[0158] b 41 =a q a p2 +a 2,im a p1

[0159] b 42 =a 2,im a 3,im k p1 +a 3,im a q

[0160]

[0161] b6 = a 3,im k p1 a p2 +a 3,im a p1

[0162] b7 = a p1 a p2

[0163]

[0164] a p1 =a 4,im k p1 +Δp ls k p1 +k p2

[0165] a p2 =a4,im +Δp ls

[0166] Among them, a 1,im ~a 4,im These represent the im-th component of vectors a1 to a4 during the calculation of the oil supply pressure in the scaled load-sensitive system, where im is the maximum oil supply pressure p in the oil supply pressure vector corresponding to each joint. in,im The serial number; k p1 and k p2 These represent the system leakage coefficients; This represents the total flow rate of the hydraulic system before scaling, within the time coordinate system corresponding to the reference trajectory; Δp ls This indicates the pressure margin set for a load-sensitive system.

[0167] Step S300: Set the initial state of the hydraulic robotic arm, and perform forward iteration on each two-dimensional configuration layer based on the optimal control variables of each layer to obtain the motion trajectory of the hydraulic robotic arm.

[0168] Step S300 may specifically include:

[0169] Set the initial state x0 of the hydraulic robotic arm, and perform forward iteration on each two-dimensional configuration layer according to the following formula:

[0170]

[0171] In the formula, x i+1,j Let x represent the j-th state variable in the (i+1)-th two-dimensional configuration layer. i,j This represents the j-th state variable in the i-th two-dimensional configuration layer. Let Δ represent the optimal control variable of the i-th two-dimensional configuration layer. s This indicates the duration of each time period before scaling. After obtaining the motion trajectory of the hydraulic robotic arm, the trajectories of each joint can be input to the motion controller of the hydraulic robotic arm, so that the motion controller outputs servo valve voltage to control the movement of the redundant hydraulic robotic arm.

[0172] by Figure 3 The load-sensitive system-driven three-degree-of-freedom hydraulic manipulator shown is used as the experimental object. The method of this invention and the traditional DP algorithm are used to optimize energy consumption for the same elliptical trajectory. During the experiment, the system flow rate, energy consumption, computation time, and execution time are as follows: Figure 4 As shown. Wherein, C1 represents the method of this invention, C2 represents the conventional method, and C3 represents the method without prior planning. Figure 4As can be seen, compared with the traditional DP algorithm, the total energy consumption of the hydraulic robotic arm after trajectory planning using the method of this invention is reduced from 19.8973kJ to 14.7412kJ, and the energy efficiency is increased from 34.98% to 44.73%. Simultaneously, the trajectory running time is reduced from 30s to 10.575s. Furthermore, the joint angles, velocities, and accelerations in the experiment using the method of this invention are as follows: Figure 5 As shown in (a) to (i). From Figure 5 It can be seen that the trajectory planned using this method only scales the trajectory running time without changing other conditions.

[0173] As can be seen from the above embodiments, the method of the present invention can reduce system energy consumption and improve work efficiency by scaling the motion trajectory of the hydraulic robotic arm in the time dimension without affecting the end effector trajectory and satisfying all constraints. Furthermore, based on the energy-optimal trajectory obtained using redundancy decomposition, the present invention further optimizes energy consumption by utilizing time scaling, obtaining a trajectory with optimal energy consumption in both the joint and time dimensions, which is of great significance for reducing the energy consumption of hydraulic robotic arms.

[0174] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the following claims.

[0175] It should be understood that the present invention is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is defined solely by the appended claims.

Claims

1. A global energy consumption optimization method for a hydraulic robotic arm integrating dynamic time-domain programming, characterized in that, Includes the following steps: Step S100: Divide the duration s of the hydraulic robotic arm reference trajectory into multiple pre-scaling time periods; The reference trajectory is scaled to obtain a scaled trajectory, and the duration t of the scaled trajectory is divided into multiple scaled time intervals; the first derivative of the duration s is calculated. and the first derivative Discretely divide the time-varying rate into multiple time-varying rates; Construct multi-layer two-dimensional configuration layers corresponding to different pre-scaling time periods. Each two-dimensional configuration layer is used to represent a set of state variables X. The state variables in the corresponding set of state variables X are the combination of each time point of the corresponding scaled time period and each time change rate. Scale each pre-scaling time period and use each duration obtained after scaling as the control variables in the control variable set U. Initialize the running cost of each set of state variables X combined with each control variable in the control variable set U. Step S200: Perform reverse iteration on the multi-layer two-dimensional configuration layer: For each state variable in the state variable set X corresponding to each two-dimensional configuration layer, combine the state variable with each control variable in the control variable set U. For each combination, calculate the system dynamics, the minimum operating cost of the system dynamics, and the energy consumption characteristic parameter model of the hydraulic manipulator under the action of the combination. Based on the calculated minimum operating cost of the system dynamics and the energy consumption characteristic parameter model, evaluate the operating cost of the hydraulic manipulator under the action of the combination. Determine the minimum operating cost of each operating cost calculated for each two-dimensional configuration layer, and take the optimal control variable corresponding to each minimum operating cost as the optimal control variable of the corresponding two-dimensional configuration layer. The determination of the minimum operating cost of the system dynamics is related to the initial operating cost of the previous two-dimensional configuration layer in reverse iteration. Step S300: Set the initial state of the hydraulic robotic arm, and perform forward iteration on each two-dimensional configuration layer based on the optimal control variables of each layer to obtain the motion trajectory of the hydraulic robotic arm. Step S100 specifically includes: Step S110: Divide the duration s of the hydraulic robotic arm reference trajectory evenly into... There are several time periods, each of which is the original time period before scaling. It is an integer greater than 1; Step S120: Scale the reference trajectory to obtain a scaled trajectory, and evenly divide the duration t of the scaled trajectory into... There are several time periods, each of which is a scaled-down version of the time period. Step S130: Calculate the first derivative of the duration s with respect to time. and the first derivative Discretely divided Rate of change over time It is an integer greater than 1; Step S140: For the i-th two-dimensional configuration layer, the i-th scaled time period is discretized sequentially to obtain... At this point in time, the Each time point is used as the first dimension data of the i-th two-dimensional configuration layer, and each time change rate is used as the second dimension data of the i-th two-dimensional configuration layer, thus forming the i-th two-dimensional configuration layer. A two-dimensional discrete network, wherein each time point and its combination with various time rates of change constitute the state variables in the state variable set X corresponding to the i-th two-dimensional configuration layer, where i is greater than 0 and less than or equal to 0. Integers; Step S150: Scale each time period before scaling, and use each duration obtained after scaling as a control variable in the control variable set U. Initialize the running cost of each state variable set X after combining it with each control variable in the control variable set U.

2. The global energy consumption optimization method for hydraulic robotic arms based on dynamic time-domain programming as described in claim 1, characterized in that, In step S200: For each combination, first calculate the joint angular velocity and joint angular acceleration of the hydraulic manipulator before and after scaling, as well as the oil supply pressure of the load-sensitive system and the total flow of the hydraulic system after scaling. Based on the joint angular velocity and joint angular acceleration before and after scaling, determine whether to calculate the system dynamics and operating costs under the action of this combination. If so, calculate the system dynamics based on this combination. When the system dynamics are the state variables of the reverse iteration of the previous two-dimensional configuration layer, take the minimum operating cost of each operating cost calculated for the reverse iteration of the previous two-dimensional configuration layer in the previous iteration as the minimum operating cost of the system dynamics. When the system dynamics are not the state variables of the reverse iteration of the previous two-dimensional configuration layer, the minimum operating cost of the system dynamics is determined by linear interpolation based on the minimum operating cost of each operating cost calculated in the previous iteration for the reverse iteration of the previous two-dimensional configuration layer, the state variable corresponding to the minimum operating cost, the initial operating cost of the previous two-dimensional configuration layer, and the system dynamics. Based on the parameters calculated during the scaling process of the oil supply pressure of the load-sensitive system and the total flow of the hydraulic system, the energy consumption characteristic parameter model of the hydraulic robotic arm under this combined action is calculated.

3. The global energy consumption optimization method for a hydraulic robotic arm based on dynamic time-domain programming according to claim 1 or 2, characterized in that, Step S200 specifically includes: Step S210: For the i-th two-dimensional configuration layer, select its j-th state variable. And select the k-th control variable from the set of control variables U. Determine the state variable and control variables Under the influence of scaling, the joint angles, joint angular velocities, and joint angular accelerations of the hydraulic robotic arm before and after scaling are calculated, where i, j, and k are all integers greater than 0, and the initial value of i is... , The initial values ​​of j and k are 1, representing the number of time periods before and after scaling. Step S220: Calculate the state variables and control variables Under the influence of scaling, the oil supply pressure of the load-sensitive system and the total flow rate of the hydraulic system are adjusted. Step S230: Determine whether the joint angular velocity and joint angular acceleration meet the convention: If the joint angular velocity and joint angular acceleration meet the convention both before and after scaling, then based on the dynamic calculation of the hydraulic manipulator configuration system, according to the minimum operating cost corresponding to the system dynamics, the energy consumption characteristic model of the hydraulic manipulator, the oil supply pressure of the load-sensitive system after scaling, and the parameters of the total flow rate of the hydraulic system, evaluate the hydraulic manipulator in terms of state variables. and control variables If the operating cost under the action is determined, proceed to step S240; otherwise, proceed to step S260. Step S240: Determine if k is equal to If yes, proceed to step S250; otherwise, increment k and return to step S210. Step S250: Determine if j is equal to If yes, proceed to step S260; otherwise, increment j and return to step S210. The number of rates of change over time, which is an integer greater than 1; Step S260: Determine if i is equal to 1. If yes, proceed to step S270; otherwise, decrement i and return to step S210. Step S270: Determine the minimum operating cost calculated for each two-dimensional configuration layer, and use the optimal control variable corresponding to each minimum operating cost as the optimal control variable for the corresponding two-dimensional configuration layer.

4. The global energy consumption optimization method for hydraulic robotic arms based on dynamic time-domain programming as described in claim 3, characterized in that, Step S210 specifically includes: The joint angles of the hydraulic robotic arm were respectively... Perform the first derivative with respect to time and second-order differential Obtain the joint angular velocity before scaling. and joint angular acceleration ; Determine the scaled hydraulic robotic arm joint angles using the following formula. Joint angular velocity and joint angular acceleration : in This represents the first derivative of the duration *s* with respect to time. This represents the second derivative of the duration s with respect to time.

5. The global energy consumption optimization method for hydraulic robotic arms based on dynamic time-domain programming as described in claim 3, characterized in that, Step S220 specifically includes: Step S221: Calculate the state variables according to the following formula. and control variables Under the action, the hydraulic cylinders corresponding to each joint output force : In the formula, This represents the first derivative of the duration *s* of the reference trajectory with respect to time. This represents the second derivative of the duration *s* of the reference trajectory with respect to time. It is the lever arm transformation matrix of the hydraulic robotic arm. , and Let these represent the inertia matrix, Coriolis force and centrifugal force matrices, and gravity vector of the hydraulic robotic arm, respectively. This represents the joint angular velocity before scaling. This represents the joint angular acceleration before scaling. For Jacobian matrices, For the end force, and These are the vectors of the Coulomb friction coefficient and the viscous friction coefficient, respectively; Step S222: Based on the output force of the hydraulic cylinder With oil supply pressure The relationship is used to obtain the oil supply pressure of each joint in the scaled load-sensitive system. : In the formula, , and The pressure margins are set for the cylinder output force, cylinder working area, and load-sensitive system, respectively. Related vectors; Step S223: Determine the maximum oil supply pressure in the oil supply pressure vector corresponding to each joint. The oil supply pressure of the scaled load-sensitive system is calculated using the following formula. : In the formula, ~ Representing vectors respectively ~ The corresponding number in One portion, For maximum oil supply pressure The serial number; Step S224, Consider the oil supply pressure The resulting leakage loss is calculated using the following formula to determine the total flow rate of the scaled hydraulic system. : , and These represent the system leakage coefficients; In the formula, The total flow rate of the hydraulic system before scaling is expressed as follows, within the time coordinate system corresponding to the reference trajectory: In the formula, Represents the joints of the robotic arm The corresponding lever arm transformation mapping; These represent the areas of the rodless chamber and the rod chamber of the hydraulic cylinder corresponding to joint i, respectively; The step function is defined as follows: 。 6. The global energy consumption optimization method for hydraulic robotic arms based on dynamic time-domain programming according to claim 3, characterized in that, Step S230 specifically includes: Step S231: Based on the hydraulic robotic arm configuration, calculate the system dynamics according to the following formula. : in This indicates the duration of each time period before scaling; Step S232: Determine the dynamics of the system. Is it a state variable in the state variable set X corresponding to the (i+1)th two-dimensional configuration layer? If so, then take the minimum operating cost calculated for each operating cost for the (i+1)th two-dimensional configuration layer in the previous iteration as the dynamic value of the system. Corresponding minimum operating cost Otherwise, determine the minimum operating cost calculated for each operating cost of the (i+1)th two-dimensional configuration layer in the previous iteration, as well as the corresponding state variables, and determine the state variable set X and control variables of the (i+1)th two-dimensional configuration layer. The initial operating cost after combination depends on the determined state variables and system dynamics. Linear interpolation is performed on the determined minimum operating cost and initial operating cost to obtain the dynamic value of the system. Corresponding minimum operating cost ; Step S233: Based on minimum operating cost The hydraulic robotic arm is evaluated in terms of state variables according to the following formula. and control variables Operating costs under the influence : Indicates the state variables of the hydraulic robotic arm. and control variables Energy consumption characteristic parameter model under action, ; In the formula, This represents the time period before scaling for the i-th two-dimensional configuration layer. Indicates the time period before scaling. The first derivative, , , , , , , , , and These are combination terms related to the robotic arm configuration, calculated using the following formulas: in, ~ These represent the vectors used in the calculation of the oil supply pressure of the scaled load-sensitive system. ~ The corresponding number in One portion, The maximum oil supply pressure in the oil supply pressure vector corresponding to each joint. The serial number; and These represent the system leakage coefficients; This represents the total flow rate of the hydraulic system before scaling, within the time coordinate system corresponding to the reference trajectory. This indicates the pressure margin set for a load-sensitive system.

7. The global energy consumption optimization method for hydraulic robotic arms based on dynamic time-domain programming as described in claim 1, characterized in that, Step S300 specifically includes: Setting the initial state of the hydraulic robotic arm The two-dimensional configuration layers are iterated forward according to the following formula: In the formula, This represents the j-th state variable in the (i+1)-th two-dimensional configuration layer. This represents the j-th state variable in the i-th two-dimensional configuration layer. Denotes the optimal control variables for the i-th two-dimensional configuration layer. This indicates the duration of each time period before scaling.

8. The global energy consumption optimization method for a hydraulic robotic arm based on dynamic time-domain programming as described in claim 1, characterized in that, In step S100, the reference trajectory is the optimal energy consumption trajectory of the hydraulic robotic arm obtained by energy redundancy decomposition.

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