Hydraulic mechanical arm global energy consumption optimization method fused with dynamic time domain planning

Abstract

The invention provides a hydraulic mechanical arm global energy consumption optimization method fused with dynamic time domain planning, which comprises the following steps of: according to a plurality of pre-scaling time periods divided by pre-scaling duration time of a reference track of a hydraulic mechanical arm, a plurality of post-scaling time periods divided by post-scaling duration time and a time change rate corresponding to a pre-scaling track first-order derivative; constructing a multi-layer two-dimensional configuration layer; reverse iteration is carried out on the multiple two-dimensional configuration layers, and the minimum operation cost of each two-dimensional configuration layer and the optimal control quantity corresponding to the minimum operation cost are obtained; and according to the optimal control quantity of each two-dimensional configuration layer, forward iteration is conducted on each two-dimensional configuration layer, and a hydraulic mechanical arm movement track fused with dynamic time planning is obtained. According to the method, under the conditions that the tail end track is not affected and all constraints are met, the movement track of the hydraulic mechanical arm can be scaled in the time dimension, the system energy consumption is reduced, and the operation efficiency is improved.

Description

Technical Field

[0001] The present invention belongs to the field of lasers, and particularly relates to a global energy consumption optimization method for a hydraulic manipulator integrating dynamic time-domain planning. Background Art

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

[0003] The problem of optimal energy consumption redundancy decomposition for hydraulic manipulators is non-convex. Conventional direct optimization methods are prone to generating local optimal solutions rather than global optimal solutions. Although using multiple initial values for repeated calculations can exclude the interference of local optimal solutions, it will cause waste of time and resources. At the same time, factors such as valve opening and closing and asymmetric cylinder areas lead to non-continuous and non-smooth characteristics in the energy consumption problem of hydraulic manipulators. Optimization methods based on gradients are difficult to directly solve this problem. Existing research on global energy consumption optimization of hydraulic manipulators only utilizes the degrees of freedom in the joint dimension to optimize the system energy consumption, but does not further optimize the energy consumption in the time dimension. Summary of the Invention

[0004] The present invention provides a global energy consumption optimization method for a hydraulic manipulator integrating dynamic time-domain planning to solve the problem that existing research on global energy consumption optimization of hydraulic manipulators only utilizes the degrees of freedom in the joint dimension to optimize the system energy consumption, but does not further optimize the energy consumption in the time dimension.

[0005] According to the first aspect of the embodiments of the present invention, a global energy consumption optimization method for a hydraulic manipulator integrating dynamic time-domain planning is provided, including the following steps:

[0006] Step S100: Divide the duration s of the reference trajectory of the hydraulic manipulator into multiple pre-scaling time periods; scale the reference trajectory to obtain a scaled trajectory, divide the duration t of the scaled trajectory into multiple post-scaling time periods; obtain the first derivative of the duration s and the first derivative is discretely divided into multiple time change 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 combinations of each time point discretely divided in the corresponding post-scaling time period and each time change rate. Scale each pre-scaling time period respectively, and use the obtained durations after scaling as the control variables in the control variable set U. Initialize the operating costs after combining each set of state variables X with each control variable in the control variable set U.

[0008] Step S200: Perform backward iteration on this multi-layer two-dimensional configuration layer. For each state variable in the set of state variables X corresponding to each two-dimensional configuration layer, combine this state variable with each control variable in the control variable set U respectively. For each combination, calculate the system dynamics under this combination, the minimum operating cost of this system dynamics, and the energy consumption characteristic parameter model of the hydraulic manipulator under the action of this combination. Evaluate the operating cost of the hydraulic manipulator under the action of this combination according to the calculated minimum operating cost of this system dynamics and the energy consumption characteristic parameter model. Determine the minimum operating cost among the operating costs calculated for each two-dimensional configuration layer, and use 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 this system dynamics is related to the initial operating cost of backward iterating the previous two-dimensional configuration layer.

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

[0010] Optionally, step S100 specifically includes:

[0011] Step S110: Uniformly divide the duration s of the reference trajectory of the hydraulic manipulator into N t time periods. Each time period is a pre-scaling time period, and N t is an integer greater than 1.

[0012] Step S120: Scale this reference trajectory to obtain a scaled trajectory, and uniformly divide the duration t of this scaled trajectory into N t time periods. Each time period is a post-scaling time period.

[0013] Step S130: Obtain the first derivative of this duration s with respect to time and discretely divide this first derivative into N v time change rates. N v is an integer greater than 1.

[0014] Step S140: For the i-th two-dimensional configuration layer, discretely divide the i-th scaled time period in sequence to obtain N t time points, and use these N t time points as the first-dimensional data of the i-th two-dimensional configuration layer, and each time change rate as the second-dimensional data of the i-th configuration layer, so that the i-th configuration layer forms an N t ×N v two-dimensional discrete network, where the combination of each time point and each time change rate constitutes each state variable in the state variable set X corresponding to the i-th two-dimensional configuration layer, and i is an integer greater than 0 and less than or equal to N t ;

[0015] Step S150: Scale each pre-scaled time period, and use the obtained durations after scaling as the control variables in the control variable set U, and initialize the operating costs after combining each state variable set X with each control variable in the control variable set U.

[0016] Optionally, in the step S200:

[0017] For each combination, first calculate the joint angular velocity, joint angular acceleration of the hydraulic manipulator before and after scaling, the oil supply pressure of the load-sensitive system after scaling, and the total flow rate of the hydraulic system. According to the joint angular velocity and joint angular acceleration before and after scaling, determine whether to calculate the system dynamics and operating costs under this combination. If so, calculate the system dynamics according to this combination. When the system dynamics is to reverse iterate the state variables of the upper two-dimensional configuration layer, use the minimum operating cost among the operating costs calculated for the reverse iteration of the upper two-dimensional configuration layer in the previous iteration as the minimum operating cost of this system dynamics;

[0018] When the system dynamics is not to reverse iterate the state variables of the upper two-dimensional configuration layer, use the minimum operating cost among the operating costs calculated for the reverse iteration of the upper two-dimensional configuration layer in the previous iteration, the state variable corresponding to this minimum operating cost, the initial operating cost of the upper two-dimensional configuration layer, and the system dynamics, and use the linear interpolation method to determine the minimum operating cost of this system dynamics;

[0019] According to the parameters in the calculation process of the oil supply pressure of the load-sensitive system after scaling and the total flow rate of the hydraulic system, calculate the energy consumption characteristic parameter model of the hydraulic manipulator under this combination.

[0020] Optionally, the step S200 specifically includes:

[0021] 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 in the control variable set U k , determine the hydraulic robotic arm joint angles, joint angular velocities, and joint angular accelerations before and after scaling under the action of the state variable x i,j and the control variable u k , where i, j, and k are all integers greater than 0, and the initial value of i is N t -1, N t is the number of time periods before and after scaling, and the initial values of j and k are both 1;

[0022] Step S220, calculate the oil supply pressure of the scaled load-sensitive system and the total flow rate of the hydraulic system under the action of the state variable x i,j and the control variable u k ;

[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 before and after scaling both meet the convention, then calculate the system dynamics based on the hydraulic robotic arm configuration, and evaluate the operation cost of the hydraulic robotic arm under the action of the state variable x i,j and the control variable u k according to the minimum operation cost corresponding to the system dynamics, the energy consumption characteristic model of the hydraulic robotic arm, the oil supply pressure of the scaled load-sensitive system, and the parameters in the calculation process of the total flow rate of the hydraulic system, and execute Step S240; otherwise, execute Step S240;

[0024] Step S240, determine whether k is equal to N t , if so, execute Step S250, otherwise, k++, and return to execute Step S210;

[0025] Step S250, determine whether j is equal to N t ×N v , if so, execute Step S260; otherwise, j++, and return to execute Step S210, N v is the number of time change rates, which is an integer greater than 1;

[0026] Step S260, determine whether i is equal to 1, if so, execute Step S270; otherwise, i--, and return to execute Step S210;

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

[0028] Optionally, the Step S210 specifically includes:

[0029] Differentiate the joint angle q of the hydraulic manipulator with respect to time r (s) with respect to time for the first order and the second order to obtain the joint angular velocity before scaling and the joint angular acceleration

[0030] Determine the joint angle q, joint angular velocity s (t), and joint angular acceleration of the scaled hydraulic manipulator according to the following formula and joint angular acceleration

[0031]

[0032] where represents the first derivative of the duration s with respect to time, represents the second derivative of the duration s with respect to time.

[0033] Optionally, the step S220 specifically includes

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

[0035]

[0036]

[0037]

[0038]

[0039]

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

[0041] Step S222: Obtain the supply oil pressure p h of each joint in the scaled load-sensing system according to the relationship between the oil cylinder output force F in and the supply oil pressure p 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 are vectors related to the oil cylinder output force, the oil cylinder working area, and the pressure margin Δp ls set for the load-sensing system respectively;

[0048] Step S223: Determine the maximum supply oil pressure p in,im = max{p in,1 , …, p in,n}, and calculate the supply oil pressure p ls,s of the scaled load-sensing system according to the following formula:

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

[0050] Step S224: Considering the leakage loss caused by the supply oil pressure p ls,s , calculate the total flow rate Q s of the scaled hydraulic system according to the following formula:

[0051] In the formula, represents the total flow rate of the hydraulic system before scaling, that is, in the time coordinate system corresponding to the reference trajectory, and the expression is as follows:​​

[0052]

[0053] wherein, r i represents the moment arm transformation mapping corresponding to the robotic arm joint i; A a,i and A b,i respectively represent the areas of the rodless chamber and the rod chamber of the hydraulic cylinder corresponding to the joint i; H i (*) is a step function, which is defined as

[0054]

[0055] Optionally, the step S230 specifically includes:

[0056] Step S231, based on the configuration of the hydraulic robotic arm, calculate the system dynamics x i+1 :

[0057]

[0058] where Δ s represents the duration of each time period before scaling;

[0059] Step S232, determine whether the system dynamics x i+1 is a state variable in the state variable set X corresponding to the (i + 1)-th layer two-dimensional configuration layer. If so, use the minimum operating cost among the various operating costs calculated for the (i + 1)-th layer two-dimensional configuration layer in the previous iteration as the minimum operating cost corresponding to the system dynamics x i+1 Otherwise, determine the minimum operating cost among the various operating costs calculated for the (i + 1)-th layer two-dimensional configuration layer in the previous iteration and the state variable corresponding to this minimum operating cost, and determine the initial operating cost after combining the state variable set X and the control variable u of the (i + 1)-th layer two-dimensional configuration layer. According to the determined state variable and the system dynamics x k , perform linear interpolation on the determined minimum operating cost and the initial operating cost to obtain the minimum operating cost corresponding to the system dynamics x i+1 i+1

[0060] Step S233, based on the minimum operating cost evaluate the operating cost J i,j of the hydraulic robotic arm under the action of the state variable x k and the control variable u k (x ij , u k ) according to the following formula:

[0061] ​​

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

[0063]

[0064] In the formula, s i represents the time period before scaling corresponding to the i-th two-dimensional configuration layer, represents the first derivative of the time period s i before scaling, and b1, b2, b3, b4, b5, b6, b7, a q , a p1 and a p2 are combined terms related to the manipulator configuration and are calculated respectively according to 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] Wherein, a 1,im ~a 4,im respectively represent the im-th component corresponding to a1~a4 in the calculation process of the oil supply pressure of the load-sensitive system after scaling, and im is the sequence number of the maximum oil supply pressure p in,im in the oil supply pressure vector corresponding to each joint; k p1 and k p2 respectively represent the leakage coefficients of the system; represents the total flow rate of the hydraulic system before scaling, that is, in the time coordinate system corresponding to the reference trajectory; Δp ls represents the pressure margin set by the load-sensitive system.

[0078] Optionally, the step S300 specifically includes:

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

[0080]

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

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

[0083] The beneficial effects of the present invention are as follows:

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

[0085] 2. Based on the optimal energy consumption trajectory obtained by redundancy decomposition, the present invention further optimizes the energy consumption by time scaling to obtain the trajectory with the optimal energy consumption in both the joint and time dimensions, which is of great significance for realizing the reduction of the energy consumption of the hydraulic manipulator. Description of the Drawings

[0086] Figure 1 is a flowchart of an embodiment of the global energy consumption optimization method for a hydraulic manipulator integrating dynamic time domain programming according to the present invention;

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

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

[0089] Figure 4 is a comparison diagram of the trajectories and system flow rates of experiments using the method of the present invention and traditional methods;

[0090] Figure 5 is a curve diagram of joint angles, speeds, and accelerations of experiments using the present invention. Detailed Embodiments

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

[0092] In the description of the present invention, unless otherwise specified and limited, it should be noted that the term "connection" should be understood in a broad sense. For example, it can be a mechanical connection or an electrical connection, or it can be the communication inside two components. It can be directly connected or indirectly connected through an intermediate medium. For those of ordinary skill in the art, the specific meaning of the above terms can be understood according to specific situations.

[0093] See Figure 1 , which is a flowchart of an embodiment of the global energy consumption optimization method for a hydraulic manipulator integrating dynamic time domain programming according to the present invention. CombiningFigure 2 As shown, the method may include the following steps:

[0094] Step S100: Divide the duration s of the reference trajectory of the hydraulic manipulator into multiple pre-scaling time periods; scale the reference trajectory to obtain a scaled trajectory, divide the duration t of the scaled trajectory into multiple post-scaling time periods; obtain the first derivative of the duration s and the first derivative is discretely divided into multiple time change rates;

[0095] 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 combinations of each time point discretely divided from the corresponding post-scaling time period and each time change rate; use the durations after scaling of each pre-scaling time period as the control variables in the control variable set U, initialize the operating costs after combining each set of state variables X 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: Uniformly divide the duration s of the reference trajectory of the hydraulic manipulator into N t time periods, each time period is a pre-scaling time period, and N t is an integer greater than 1. Among them, according to the required calculation accuracy and calculation amount, input N t to uniformly divide the duration s into N t time periods, and the reference trajectory can be the energy consumption optimal trajectory of the oil hydraulic manipulator obtained by energy consumption redundancy decomposition. The durations of each pre-scaling time period are the same as Δ s which can be the same. The present invention uses the energy consumption optimal trajectory of the oil hydraulic manipulator as the reference trajectory and performs dynamic time domain planning for the energy consumption optimal trajectory, which can further reduce the energy consumption of the movement trajectory of the hydraulic manipulator.

[0097] Step S120: Scale the reference trajectory to obtain a scaled trajectory, and uniformly divide the duration t of the scaled trajectory into N t time periods, and each time period is a post-scaling time period.

[0098] Step S130: Obtain the first derivative of the duration s with respect to time and the first derivative is discretely divided into N v time change rates, and N v is an integer greater than 1;

[0099] Step S140: For the i-th two-dimensional configuration layer, discretely divide the i-th scaled time period in sequence to obtain N t time points. Take these N t time points as the first-dimensional data of the i-th two-dimensional configuration layer, and take each time change rate as the second-dimensional data of the i-th configuration layer, so that the i-th configuration layer forms a two-dimensional discrete network of N t ×N v . Each combination of each time point and each time change rate constitutes each state variable in the corresponding state variable set X of the i-th two-dimensional configuration layer. i is an integer greater than 0 and less than or equal to N t . Among them, multiple two-dimensional configuration layers can be used to represent the state transition process of the hydraulic manipulator in time series, and they are all two-dimensional discrete grids.

[0100] Step S150: Scale each pre-scaled time period respectively, take the obtained durations after scaling as the control variables in the control variable set U, and initialize the operating costs after combining each state variable set X with each control variable in the control variable set U.

[0101] Step S200: Perform backward iteration on the multi-layer two-dimensional configuration layer: For each state variable in the corresponding state variable set X of each two-dimensional configuration layer, combine the state variable with each control variable in the control variable set U respectively. For each combination, calculate the system dynamics under this combination, the minimum operating cost of this system dynamics, and the energy consumption characteristic parameter model of the hydraulic manipulator under the action of this combination. According to the calculated minimum operating cost of this system dynamics and the energy consumption characteristic parameter model, evaluate the operating cost of the hydraulic manipulator under the action of this combination; determine the minimum operating cost among the operating costs 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 this system dynamics is related to the initial operating cost of backward iterating the previous two-dimensional configuration layer, and execute Step S300.

[0102] In the said Step S200: For each combination, first, the joint angular velocity, joint angular acceleration of the hydraulic manipulator before and after scaling, and the oil supply pressure of the load-sensitive system and the total flow rate of the hydraulic system after scaling can be calculated. According to the joint angular velocity and joint angular acceleration before and after scaling, determine whether to calculate the system dynamics and operating cost under this combination. If so, calculate the system dynamics according to this combination. When this system dynamics is the state variable of backward iterating the previous two-dimensional configuration layer, take the minimum operating cost among the operating costs calculated for backward iterating the previous two-dimensional configuration layer in the previous iteration as the minimum operating cost of this system dynamics;

[0103] When the system dynamics do not reverse-iterate the state variables of the upper two-dimensional configuration layer, based on the minimum operating cost of each operating cost calculated for the reverse-iteration of the upper two-dimensional configuration layer in the previous iteration, the state variables corresponding to the minimum operating cost, the initial operating cost of the upper two-dimensional configuration layer, and the system dynamics, the linear interpolation method is used to determine the minimum operating cost of the system dynamics;

[0104] According to the parameters in the calculation process of the scaled load-sensitive system supply pressure and the total hydraulic system flow rate, an energy consumption characteristic parameter model of the hydraulic manipulator under this combined action is calculated.

[0105] In this embodiment, the 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 in the control variable set U k , and determine the joint angles, joint angular velocities, and joint angular accelerations of the hydraulic manipulator before and after scaling under the action of the state variable x i,j and the control variable u k , where i, j, and k are all integers greater than 0, the initial value of i is N t -1, N t is the number of time periods before and after scaling, the initial values of j and k are both 1, and step S220 is executed.

[0107] Step S220: Calculate the supply pressure of the scaled load-sensitive system and the total flow rate of the hydraulic system under the action of the state variable x i,j and the control variable u k , and execute step S230.

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

[0109] Step S240: Determine whether k is equal to N t , if so, execute step S250, otherwise, k++, and return to execute step S210;

[0110] Step S250: Determine whether j is equal to Nt ×N v If so, execute step S260; otherwise, j++, return to execute step S210, N v is the number of time change rates, which is an integer greater than 1;

[0111] Step S260, determine whether i is equal to 1. If so, execute step S270; otherwise, i--, return to execute step S210;

[0112] Step S270, determine the minimum operating cost of each 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 of the corresponding two-dimensional configuration layer.

[0113] Among them, the step S210 may specifically include:

[0114] Respectively perform the first-order differentiation of the hydraulic manipulator joint angle q r (s) with respect to time and the second-order differentiation to obtain the joint angular velocity before scaling and the joint angular acceleration

[0115] Determine the scaled hydraulic manipulator joint angle q s (t), joint angular velocity and joint angular acceleration

[0116]

[0117] where represents the first-order derivative of the duration s with respect to time, represents the second-order derivative of the duration s with respect to time.

[0118] The step S220 may specifically include:

[0119] Step S221, calculate the output force F of the oil cylinder corresponding to each joint under the action of the state variable x i,j and the control variable u k according to the following formula: h :

[0120]

[0121]

[0122]

[0123]

[0124]

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

[0126] Step S222, according to the relationship between the cylinder output force F h and the oil supply pressure p in , obtain the oil supply pressure p in of each joint in the scaled load sensing system:

[0127]

[0128] a1 = HAk1

[0129] a2 = HAk2

[0130] a3 = HAk4

[0131] a4 = HAk3 + Hp c

[0132] wherein, H, A, and p c are respectively vectors related to the cylinder output force, the cylinder working area, and the pressure margin Δp ls set by the load sensing system, and the expressions are as follows respectively:

[0133]

[0134]

[0135] ​​

[0136] Wherein, A a,i and A b,i represent the effective areas of the rod chamber and the non-rod chamber of the linear hydraulic cylinder of the 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}, and calculate the oil supply pressure p of the scaled load-sensitive system according to the following formula ls,s :

[0138] Wherein, a 1,im ~a 4,im respectively represent the corresponding im-th components in the vectors a1~a4, and im is the serial number of the maximum oil supply pressure p in,im .

[0139] Step S224: Considering the leakage loss caused by the oil supply pressure p ls,s , calculate the total flow rate Q of the scaled hydraulic system according to the following formula s :

[0140] Wherein, represents the total flow rate of the hydraulic system before scaling in the time coordinate system corresponding to the reference trajectory, and the expression is as follows:

[0141]

[0142] Wherein, r i represents the force arm transformation mapping corresponding to the robotic arm joint i; A a,i and A b,i respectively represent the areas of the non-rod chamber and the rod chamber of the hydraulic cylinder corresponding to the joint i; H i (*) is a step function, which is defined as

[0143]

[0144] The said step S230 may specifically include:

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

[0146]

[0147] Wherein, Δ s represents the duration of each period before scaling;

[0148] Step S232: Determine whether the system dynamics x i+1 is a state variable in the state variable set X corresponding to the (i + 1)-th layer two-dimensional configuration layer. If so, take the minimum operating cost among the various operating costs calculated for the (i + 1)-th layer two-dimensional configuration layer in the previous iteration as the minimum operating cost corresponding to the system dynamics x i+1 Otherwise, determine the minimum operating cost among the various operating costs calculated for the (i + 1)-th layer two-dimensional configuration layer in the previous iteration and the state variable corresponding to this minimum operating cost, and determine the state variable set X and the control variable u of the (i + 1)-th layer two-dimensional configuration layer. Combine the initial operating costs. According to the determined state variable and the system dynamics x k , perform linear interpolation on the determined minimum operating cost and the initial operating cost to obtain the minimum operating cost corresponding to the system dynamics x i+1 i+1

[0149] Step S233: Based on the minimum operating cost , evaluate the operating cost J i,j of the hydraulic manipulator under the action of the state variable x k and the control variable u k using the following formula ij k :

[0150]

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

[0152]

[0153] In the formula, s i represents the time period before scaling corresponding to the i-th layer two-dimensional configuration layer, represents the first derivative of the time period s i before scaling, and b1, b2, b3, b4, b5, b6, b7, a q , a p1 and a p2 ​​​It is a combined term related to the configuration of the robotic arm and is calculated according to the following formulas respectively:

[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 respectively represent the i_m-th component corresponding to the vectors a1 to a4 in the calculation process of the oil supply pressure of the load-sensitive system after scaling. i_m is the serial number of the maximum oil supply pressure p in,im in the oil supply pressure vector corresponding to each joint; k p1 and k p2 respectively represent the leakage coefficients of the system; represents the total flow rate of the hydraulic system before scaling, that is, under the time coordinate system corresponding to the reference trajectory; Δp ls represents the pressure margin set by the load-sensitive system.

[0167] Step S300: Set the initial state of the hydraulic manipulator, 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 manipulator.

[0168] The step S300 may specifically include:

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

[0170]

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

[0172] Taking Figure 3 the three-degree-of-freedom hydraulic manipulator driven by the load-sensitive system shown as the experimental object, the method of the present invention and the traditional DP algorithm are used to optimize the energy consumption of the same elliptical trajectory. During the experiment, the system flow rate, energy consumption, calculation time, and execution time are as Figure 4 shown. Among them, C1 represents the method of the present invention, C2 represents the traditional method, and C3 represents the method without planning. From Figure 4It can be seen that, compared with the traditional DP algorithm, the total energy consumption of the hydraulic manipulator following the trajectory planning of the method of the present invention is reduced from 19.8973 kJ to 14.7412 kJ, and the energy-saving efficiency is increased from 34.98% to 44.73%. At the same time, the trajectory running time is reduced from the original 30 s to 10.575 s. In addition, the joint angles, speeds, and accelerations in the experiment of the method of the present invention are respectively as Figure 5 (a) to (i) show. From Figure 5 it can be seen that the trajectory planned by 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 the system energy consumption and improve the operation efficiency by scaling the motion trajectory of the hydraulic manipulator in the time dimension without affecting the end trajectory and satisfying all constraints. In addition, based on the energy consumption-optimal trajectory obtained by redundant decomposition, the present invention further optimizes the energy consumption by time scaling to obtain a trajectory with optimal energy consumption in both the joint and time dimensions, which is of great significance for realizing the energy consumption reduction of the hydraulic manipulator.

[0174] Those skilled in the art will readily conceive of other embodiments of the present invention after considering the specification and practicing the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the present invention, which follow the general principles of the present invention and include known common knowledge or conventional technical means in the technical field not disclosed by the present invention. The specification and examples are only to be considered as exemplary, and the true scope and spirit of the present invention are pointed out by the following claims.

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

Claims

1. A global energy consumption optimization method for a hydraulic manipulator integrating dynamic time-domain programming, characterized in that, It includes the following steps: Step S100: Divide the duration s of the reference trajectory of the hydraulic manipulator into multiple pre-scaling time periods; Scale the reference trajectory to obtain a scaled trajectory, divide the duration t of the scaled trajectory into multiple scaled time periods; obtain the first derivative of the duration s and the first derivative is discretely divided into multiple time change 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 combinations of each time point discretely divided in the corresponding post-scaling time period and each time change rate. Scale each pre-scaling time period respectively, and use the obtained durations after scaling as the control variables in the control variable set U. Initialize the operating cost after combining each set of state variables X 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 set of state variables 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 under this combination, the minimum operating cost of the system dynamics, and the energy consumption characteristic parameter model of the hydraulic manipulator under the action of this combination. Evaluate the operating cost of the hydraulic manipulator under the action of this combination according to the calculated minimum operating cost of the system dynamics and the energy consumption characteristic parameter model. Determine the minimum operating cost among the operating costs calculated for each two-dimensional configuration layer, and use 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 reverse-iterating the previous two-dimensional configuration layer; Step S300: Set the initial state of the hydraulic manipulator, and based on the optimal control variables of each two-dimensional configuration layer, perform forward iteration on each two-dimensional configuration layer to obtain the motion trajectory of the hydraulic manipulator.

2. The global energy consumption optimization method of the hydraulic manipulator integrating dynamic time-domain planning according to claim 1, characterized in that The specific content of step S100 includes: Step S110: Uniformly divide the duration s of the reference trajectory of the hydraulic manipulator into N t time periods, each of which is a time period before scaling, and N t 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 N t time segments, each of which is a scaled time segment; Step S130: Obtain the first derivative of the duration s with respect to time And use this first derivative To discretely divide it into N v Time change rates, where N v Is an integer greater than 1; Step S140: For the i-th two-dimensional configuration layer, discretely divide the i-th scaled time period in sequence to obtain N t time points. Use these N t time points as the first-dimensional data of the i-th two-dimensional configuration layer, and use each time change rate as the second-dimensional data of the i-th configuration layer, so that the i-th configuration layer forms an N t ×N v two-dimensional discrete network. The combination of each time point and each time change rate respectively constitutes each state variable in the set X of state variables corresponding to the i-th two-dimensional configuration layer. Here, i is an integer greater than 0 and less than or equal to N t . Step S150: Scale each pre-scaling time period, and use the obtained durations after scaling as the control variables in the control variable set U. Initialize the operating cost after combining each set of state variables X with each control variable in the control variable set U.

3. The global energy consumption optimization method of the hydraulic manipulator integrating dynamic time-domain planning according to claim 1, characterized in that In step S200: For each combination, first calculate the joint angular velocity, joint angular acceleration of the hydraulic manipulator before and after scaling, the oil supply pressure of the load-sensitive system after scaling, and the total flow rate of the hydraulic system. According to the joint angular velocity and joint angular acceleration before and after scaling, determine whether to calculate the system dynamics and operating cost under this combination. If so, calculate the system dynamics according to this combination. When the system dynamics is the state variable of reverse-iterating the previous two-dimensional configuration layer, use the minimum operating cost among the operating costs calculated for reverse-iterating the previous two-dimensional configuration layer in the previous iteration as the minimum operating cost of the system dynamics; When the system dynamics do not reverse-iterate the state variables of the upper two-dimensional configuration layer, based on the minimum operating cost of each operating cost calculated for the reverse-iteration of the upper two-dimensional configuration layer in the previous iteration, the state variables corresponding to the minimum operating cost, the initial operating cost of the upper two-dimensional configuration layer, and the system dynamics, the linear interpolation method is used to determine the minimum operating cost of the system dynamics; According to the parameters in the calculation process of the scaled load-sensitive system supply oil pressure and the total hydraulic system flow rate, the energy consumption characteristic parameter model of the hydraulic manipulator under this combined action is calculated.

4. The global energy consumption optimization method of the hydraulic manipulator integrating dynamic time-domain planning according to claim 1 or 3, characterized in that, The specific steps of step S200 include: 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 k in the control variable set U, and determine the joint angles, joint angular velocities, and joint angular accelerations of the hydraulic manipulator before and after scaling under the action of the state variable x i,j and the control variable u k , where i, j, and k are all integers greater than 0, and the initial value of i is N t - 1, N t is the number of time periods before and after scaling, and the initial values of j and k are both 1; Step S220, calculate the oil supply pressure of the scaled load-sensitive system and the total flow rate of the hydraulic system under the action of the state variable x i,j and the control variable u k ; Step S230: Determine whether the joint angular velocity and joint angular acceleration meet the convention. If both the joint angular velocity and joint angular acceleration meet the convention before and after scaling, calculate the system dynamics based on the configuration of the hydraulic manipulator, and calculate the parameters of the process according to the minimum operating cost corresponding to the system dynamics, the energy consumption characteristic model of the hydraulic manipulator, the supply oil pressure of the load-sensing system after scaling, and the total flow rate of the hydraulic system, and evaluate the operating cost of the hydraulic manipulator under the state variable x i,j and the control variable u k When acting, execute step S240; otherwise, execute step S240; Step S240: Determine whether k is equal to N t , if so, execute Step S250; otherwise, increment k by 1 and return to execute Step S210; Step S250: Determine whether j is equal to N t ×N v , if yes, execute Step S260; otherwise, j++, return to execute Step S210, N v is the number of time change rates, which is an integer greater than 1; Step S260, determine whether i is equal to 1. If so, execute step S270; otherwise, i--, and return to execute step S210; Step S270, determine the minimum operating cost of each 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 of the corresponding two-dimensional configuration layer.

5. The global energy consumption optimization method of the hydraulic manipulator integrating dynamic time-domain planning according to claim 4, characterized in that, The specific steps of step S210 include: Differentiate the joint angle q of the hydraulic manipulator with respect to time r (s) for the first order and the second order to obtain the joint angular velocity before scaling and the joint angular acceleration Determine the joint angle q of the scaled hydraulic robotic arm according to the following formula s (t), joint angular velocity and joint angular acceleration where represents the first derivative of the duration s with respect to time, represents the second derivative of the duration s with respect to time.

6. The global energy consumption optimization method of the hydraulic manipulator integrating dynamic time-domain planning according to claim 4, characterized in that The specific steps of step S220 include: Step S221. Calculate the output force F of the oil cylinder corresponding to each joint under the action of the state variable x i,j and the control variable u k according to the following formula: h : In the formula, represents the first derivative of the duration s of the reference trajectory with respect to time, represents the second derivative of the duration s of the reference trajectory with respect to time, R(q r ) = diag(r1 r2 … r n ) is the force arm transformation matrix of the hydraulic manipulator, M(q r ), and G(q r ) respectively represent the inertia matrix, the Coriolis force and centrifugal force matrix, and the gravity vector of the hydraulic manipulator, represents the joint angular velocity before scaling, represents the joint angular acceleration before scaling, J is the Jacobian matrix, F t is the end force, f c = [f c.1 , …, f c.n T and f v = [f v.1 , …, f v.n T are respectively the Coulomb friction coefficient and the viscous friction coefficient vector;​​ Step S222: According to the output force F of the oil cylinder h and the oil supply pressure p in , obtain the oil supply pressure p of each joint in the scaled load sensing system in : a1 = HAk1 a2 = HAk2 a3 = HAk4 a4 = HAk3 + Hp c Wherein, H, A, and p c are vectors related to the output force of the oil cylinder, the working area of the oil cylinder, and the pressure margin Δp set by the load sensing system ls respectively; Step S223: Determine the maximum oil supply pressure p in the oil supply pressure vectors corresponding to each joint in,im = max{p in,1 , …, p in,n}, and calculate the oil supply pressure p of the scaled load sensing system according to the following formula ls,s : where a 1,im ~a 4,im respectively represent the corresponding im-th component in vectors a1~a4, and im is the serial number of the maximum fuel supply pressure p in,im ; Step S224: Consider the fuel supply pressure p ls,s Due to the leakage loss caused, calculate the total flow rate Q of the scaled hydraulic system according to the following formula s : In the formula, represents the total flow rate of the hydraulic system before scaling in the time coordinate system corresponding to the reference trajectory, and the expression is as follows: where r i represents the force arm transformation mapping corresponding to the robotic arm joint i; A a,i and A b,i respectively represent the areas of the rodless chamber and the rod chamber of the hydraulic cylinder corresponding to joint i; H i (*) is a step function, which is defined as:

7. The global energy consumption optimization method of a hydraulic manipulator integrating dynamic time-domain planning according to claim 4, characterized in that The specific steps of step S230 include: Step S231: Based on the configuration of the hydraulic robotic arm, calculate the system dynamics x according to the following formula i+1 :[[]]END]] where Δ s represents the duration of each time period before scaling; Step S232: Determine the system dynamics x i+1 Is it a state variable in the state variable set X corresponding to the i+1th two-dimensional configuration layer? If so, the minimum operating cost of each operating cost calculated for the i+1th two-dimensional configuration layer in the previous iteration is taken as the minimum operating cost of the system dynamic x i+1 Corresponding minimum operating cost Otherwise, determine the minimum operating cost of each operating cost calculated for the i+1th two-dimensional configuration layer in the previous iteration and the state variable corresponding to the minimum operating cost, and determine the state variable set X and control variable u of the i+1th two-dimensional configuration layer k The combined initial operating cost is determined based on the state variables and system dynamics x i+1 , perform linear interpolation on the determined minimum operating cost and initial operating cost to obtain the system dynamic x i+1 Corresponding minimum operating cost Step S233, based on the minimum operating cost Evaluate the operating cost J of the hydraulic manipulator under the state variable x i,j and the control variable u k according to the following formula k (x ij , u k ): E k (x ij , u k ) represents the energy consumption characteristic parameter model of the hydraulic manipulator under the action of the state variable x i,j and the control variable u k , and E k (x ij , u k ) = P k (x ij , u k ) · u k ; where s i represents the time period before scaling corresponding to the two-dimensional configuration layer of the i-th layer, represents the time period s before scaling i the first derivative of, b1, b2, b3, b4, b5, b6, b7, a q , a p1 and a p2 are combined terms related to the manipulator configuration and are calculated respectively according to the following formulas: b2 = a 1,im a 2,im k p1 + a 1,im a q b 31 = a 1,im a p1 + a 1,im k p1 a p2 + a 2,im a q b 32 = 2a 1,im a 3,im k p1 b 41 = a q a p2 + a 2,im a p1 b 42 = a 2,im a 3,im k p1 + a 3,im a q b6 = a 3,im k p1 a p2 +a 3,im a q1 b7 = a p1 a p2 a p1 = a 4,im k p1 + Δp ls k p1 + k p2 a p2 = a 4,im + Δp ls Among them, a 1,im ~a 4,im respectively represent the im-th component corresponding to a1 to a4 in the calculation process of the oil supply pressure of the load-sensitive system after scaling, where im is the serial number of the maximum oil supply pressure p in,im in the oil supply pressure vector corresponding to each joint; k p1 and k p2 respectively represent the leakage coefficients of the system; represents the total flow rate of the hydraulic system before scaling, that is, under the time coordinate system corresponding to the reference trajectory; Δp ls represents the pressure margin set for the load-sensitive system.

8. The global energy consumption optimization method of the hydraulic manipulator integrating dynamic time-domain planning according to claim 1, characterized in that The specific steps of step S300 include: Set the initial state x0 of the hydraulic manipulator, and perform forward iteration on each two-dimensional configuration layer according to the following formula: where x i+1,j represents the j-th state variable in the (i + 1)-th two-dimensional configuration layer, and x i,j represents the j-th state variable in the i-th two-dimensional configuration layer, represents the optimal control variable of the i-th two-dimensional configuration layer, and Δ s represents the duration of each time period before scaling.

9. The global energy consumption optimization method of the hydraulic manipulator integrating dynamic time-domain planning according to claim 1, characterized in that, In step S100, the reference trajectory is the optimal energy consumption trajectory of the oil hydraulic manipulator obtained by energy consumption redundancy decomposition.

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