A method for implementing high-speed matrix cascade multiplication calculation for robotic arm control

Abstract

The present invention discloses a method for realizing high-speed matrix cascade multiplication calculation for manipulator control, comprising: determining any two adjacent matrices #imgabs0# and #imgabs1#, wherein M k and N k Indicates the number of rows and columns of the k-th matrix #imgabs2#, M k‑1 and N k‑1 represents the number of rows and columns of the k-1th matrix #imgabs3#, k=0,1,2,...,S-1, S≥1 and S∈Z + ; Perform equivalent order reduction processing on the matrix #imgabs4# and #imgabs5# of the matrix sparse features, and determine the matrix order after equivalent order reduction; determine the optimal order of matrix multiplication according to the determined matrix order after equivalent order reduction; according to the determined optimal order of matrix multiplication, convert the cascade matrix multiplication into parallel dot product calculation, obtain the calculation result and output it. The present invention aims to solve the problem that in the process of manipulator control, the traditional processor is difficult to calculate in real time when facing a large number of matrix multiplications of kinematics forward and inverse solutions.

Description

Technical Field

[0001] The invention belongs to the technical field of robot arm control, and in particular relates to a method for realizing high-speed matrix cascade multiplication calculation of robot arm control. Background Art

[0002] In the control calculation of robotic arms, especially morphologically reconfigurable robotic arms, more than 90% of the control calculation time is concentrated on matrix multiplication operations. With the development of robot intelligence, refined and complex operations require increasingly real-time calculations of kinematic forward and inverse solutions. The traditional matrix calculation processing flow alone can no longer meet the requirements of high-performance computing.

[0003] There are currently two main methods for accelerating matrix operations: one is to design dedicated matrix calculation digital logic to achieve calculation acceleration, but this implementation method occupies huge hardware resources and is difficult to implement variable and flexible matrix calculation modes, especially for specific computing scenarios, such as homogeneous matrix calculations in the forward solution calculation process of a robotic arm, and it is difficult to use the sparse characteristics of the matrix itself to reduce the amount of calculation; the other is to directly improve the system computing efficiency by improving the matrix fast algorithm, such as Stressen and Cannon matrix fast multiplication, combined with multi-core parallel computing, but the improvement of the matrix fast algorithm has an upper limit, and the implementation of parallel multi-core computing mainly focuses on the parallelization of matrix data blocks, without considering the optimization of the calculation process for cascaded matrix multiplication and addition operations. Summary of the invention

[0004] The technology of the present invention solves the problem: Overcoming the shortcomings of the prior art, providing a method for implementing high-speed matrix cascade multiplication calculation for robot arm control, aiming to solve the problem that traditional processors are difficult to calculate in real time when faced with a large number of matrix multiplications for kinematic forward and inverse solutions during robot arm control.

[0005] In order to solve the above technical problems, the present invention discloses a method for realizing high-speed matrix cascade multiplication calculation for controlling a robot arm, comprising:

[0006] Determine any two adjacent matrices and Among them, M k and N k Represents the kth matrix The number of rows and columns, M k-1 and N k-1 Represents the k-1th matrix The number of rows and columns, k = 0, 1, 2, ..., S-1, S ≥ 1 and S ∈ Z + ;

[0007] For the matrix and Perform equivalent rank reduction processing on the sparse features of the matrix and determine the matrix order after the equivalent rank reduction;

[0008] Determine the optimal order of matrix multiplication according to the determined equivalent reduced-order matrix order;

[0009] According to the determined optimal order of matrix multiplication, the cascade matrix multiplication is converted into parallel dot product calculation, and the calculation result is obtained and output.

[0010] In the above-mentioned high-speed matrix cascade multiplication calculation implementation method for manipulator control, the matrix Denotes the S matrices Γ used for continuous multiplication (k,k+1) , Γ (k,k+1) Represents the homogeneous transformation matrix between the adjacent degree-of-freedom joint coordinate systems of the S-degree-of-freedom space manipulator.

[0011] In the above-mentioned high-speed matrix cascade multiplication calculation implementation method for manipulator control, Γ (k,k+1) It is expressed as follows:

[0012]

[0013] in, represents the translation change between two adjacent joint coordinate systems, ξ (k,k+1) Represents the rotation change between two adjacent joint coordinate systems.

[0014] In the above-mentioned high-speed matrix cascade multiplication calculation implementation method for robot arm control,

[0015]

[0016] Among them, θ k+1 Represents the rotation angle of the k+1th joint of the robot around its axis.

[0017] In the above-mentioned high-speed matrix cascade multiplication calculation implementation method for manipulator control, the homogeneous transformation matrix Γ of the entire end position of the S-degree-of-freedom space manipulator is (0,S) And the matrix multiplication result Y M×N They are respectively expressed as follows:

[0018]

[0019]

[0020] In the above-mentioned high-speed matrix cascade multiplication calculation implementation method for robot arm control, for the matrix and Perform equivalent rank reduction processing on the sparse features of the matrix and determine the matrix order after equivalent rank reduction, including:

[0021] Pair Matrix and Divide into four blocks and get the matrix The corresponding four-block matrix and matrix The corresponding four-block matrix;

[0022] Perform block multiplication calculation on each block matrix, and detect the number of zero row vectors on each multiplied matrix, and detect the number of zero column vectors on each multiplied matrix;

[0023] The order of the matrix after equivalent order reduction is determined according to the detection results of the number of zero row vectors of each multiplied matrix and the detection results of the number of zero column vectors of each multiplication matrix.

[0024] In the above-mentioned high-speed matrix cascade multiplication calculation implementation method for robot arm control, the matrix is ​​calculated by the following formula: and Divide into four blocks:

[0025]

[0026]

[0027] in, Representation Matrix Medium 0 to (M k / 2)-1 row, 0 to (N k / 2)-1 column of data, Representation Matrix Medium 0 to (M k / 2)-1 row, (N k / 2) to N k -1 column of data, Representation Matrix Medium k / 2) to M k -1 row, 0 to (N k / 2)-1 column of data, Representation Matrix Medium k / 2) to M k -1 row, (N k / 2) to N k -1 column of data; Representation Matrix Medium 0 to (M k-1 / 2)-1 row, 0 to (N k-1 / 2)-1 column of data, Representation Matrix Medium 0 to (M k-1 / 2)-1 row, (N k-1 / 2) to N k-1 -1 column of data, Representation Matrix Medium k-1 / 2) to M k-1-1 row, 0 to (N k-1 / 2)-1 column of data, Representation Matrix Medium k-1 / 2) to M k-1 -1 row, (N k-1 / 2) to N k-1 -1 column of data.

[0028] In the above-mentioned high-speed matrix cascade multiplication calculation implementation method for robot arm control, the block multiplication calculation is performed on each block matrix through the following formula to obtain the block multiplication calculation result:

[0029]

[0030] Among them, A, B, C, and D are four intermediate quantities, and they are:

[0031]

[0032] In the above-mentioned high-speed matrix cascade multiplication calculation implementation method for manipulator control, the equivalent reduced-order matrix order Q is determined by the following formula: k :

[0033]

[0034] Among them, λ (k-1,v) Represents the detection result of the number of zero row vectors of each multiplied matrix, γ (k,v) Represents the detection result of the number of zero column vectors in each multiplication matrix, v∈[LU,RU,LD,RD].

[0035] In the above-mentioned high-speed matrix cascade multiplication calculation implementation method for robot arm control, the optimal matrix multiplication order m(i,k) is determined by the following formula:

[0036]

[0037] The present invention has the following advantages:

[0038] (1) The present invention discloses a method for realizing high-speed matrix cascade multiplication calculation for robot arm control. According to matrix partitioning and statistics of matrix sparse characteristics, the optimal multiplication order of cascade matrices is planned, and the inherent multiplication process is adjusted to reduce the amount of calculation, so as to solve the problem that traditional processors are difficult to calculate in real time when facing a large number of matrix multiplications for kinematic forward and inverse solutions during robot arm control.

[0039] (2) The present invention discloses a method for realizing high-speed matrix cascade multiplication calculation for robot arm control, which can allocate matrix multiplication tasks according to finite vector multiplication and addition resources to maximize resource utilization.

[0040] (3) The present invention discloses a method for realizing high-speed matrix cascade multiplication calculation for robot arm control, which can effectively utilize the block zero vectors of the homogeneous matrix in the robot arm control calculation process and reduce the amount of cascade multiplication calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a flowchart of the steps of a method for implementing high-speed matrix cascade multiplication calculation for robot control in an embodiment of the present invention;

[0042] Figure 2 is a schematic structural diagram of a multi-degree-of-freedom spatial robotic arm in an embodiment of the present invention;

[0043] Figure 3 It is a schematic diagram of equivalent reduced-order calculation based on the sparse characteristics of block matrices in a method for realizing high-speed matrix cascade multiplication calculation for robot control in an embodiment of the present invention;

[0044] Figure 4 It is a calculation flow chart of a method for realizing high-speed matrix cascade multiplication calculation for controlling a robot arm in an embodiment of the present invention;

[0045] Figure 5 It is a hardware design block diagram of parallel dot product calculation in a method for realizing high-speed matrix cascade multiplication calculation for robot control in an embodiment of the present invention;

[0046] Figure 6 It is a hardware design block diagram of a dot product calculation unit in a method for realizing high-speed matrix cascade multiplication calculation for robot control in an embodiment of the present invention;

[0047] Figure 7 This is an example diagram of a homogeneous matrix positive solution cascade multiplication calculation process in a method for realizing high-speed matrix cascade multiplication calculation for robot arm control in an embodiment of the present invention;

[0048] Figure 8 This is an example diagram of the optimal order of homogeneous matrix positive solution cascade multiplication in a method for realizing high-speed matrix cascade multiplication calculation for robot arm control in an embodiment of the present invention;

[0049] Fig. 9 This is an example diagram of task allocation of matrix multiplication dot product calculation unit groups in a method for implementing high-speed matrix cascade multiplication calculation for robot arm control in an embodiment of the present invention. DETAILED DESCRIPTION

[0050] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments disclosed in the present invention will be further described in detail below with reference to the accompanying drawings.

[0051] One of the core ideas of the present invention is to disclose a method for realizing high-speed matrix cascade multiplication calculation for robot arm control, including three parts: equivalent order reduction calculation, optimal order calculation and parallel dot product calculation. Among them, the equivalent order reduction calculation is implemented by counting the zero vectors of the block matrix to remove unnecessary multiplication and accumulation operations in the matrix with a large number of zero vectors. When the row vector in the multiplied matrix or the column vector in the multiplication matrix is ​​0, the multiplication and accumulation operation of the vector is considered unnecessary. The optimal order calculation is calculated based on the equivalent reduced order matrix obtained to obtain the optimal multiplication order. Through the parallel dot product calculation, the efficiency of the effective vector dot product calculation is improved, thereby improving the calculation speed of the matrix cascade multiplication.

[0052] like Figure 1 In this embodiment, the robot arm controls the high-speed matrix cascade multiplication calculation implementation method, including:

[0053] Step 1: Determine any two adjacent matrices and

[0054] In this embodiment, if Figure 2 , the coordinate systems of two adjacent joints of the multi-DOF spatial manipulator are F k and F k+1 , the k+1th joint of the multi-DOF manipulator rotates around its axis θ k+1 After that, the joint coordinate system F k+1 Relative to the joint coordinate system F k The rotation matrix can be expressed as:

[0055]

[0056] Among them, ξ (k,k+1) Represents the rotation change between two adjacent joint coordinate systems, that is, the joint coordinate system F k+1 Relative to the joint coordinate system F k The rotation matrix of .

[0057] The end pose homogeneous transformation matrix can be used to calculate the position and velocity transformation relationship from the base to the end. The end pose homogeneous transformation matrix of the multi-DOF spatial manipulator can be expressed as follows:

[0058]

[0059] Among them, Γ (0,S) represents the homogeneous transformation matrix of the end position of the whole arm in S-degree-of-freedom space, Γ (k,k+1) Represents the homogeneous transformation matrix between the adjacent degree-of-freedom joint coordinate systems of the S-degree-of-freedom space manipulator.

[0060] Furthermore, Γ (k,k+1) It is expressed as follows:

[0061]

[0062] in, represents the translation change between two adjacent joint coordinate systems, It is a 1X3 translation matrix.

[0063] For the dynamic path planning process, Γ (0,S) The value of needs to be calculated in real time according to the changes in joint angle telemetry, which is the key to the kinematics forward and inverse solution calculations. (0,S) The calculation process of is a typical matrix cascade multiplication process, so Redefine as follows:

[0064]

[0065] Among them, Y M×N Represents the result of matrix multiplication, matrix Denotes the S matrices Γ used for continuous multiplication (k,k+1) , M k and N k Represents the kth matrix The number of rows and columns, M k-1 and N k-1 Represents the k-1th matrix The number of rows and columns, k = 0, 1, 2, ..., S-1, S ≥ 1 and S ∈ Z + .

[0066] Step 2, for the matrix and Perform equivalent rank reduction processing on the sparse features of the matrix and determine the matrix order after equivalent rank reduction.

[0067] In this embodiment, if Figure 3 As shown in the figure, the equivalent reduction steps of the matrix sparse features based on the block matrix are as follows:

[0068] For matrices, any two adjacent matrices and The computational effort of multiplication is In matrix calculations, especially in the process of robot control calculations, the matrix and There is often sparsity. Considering that the matrix calculation dimension of the robot arm control calculation process is generally no more than 10, the matrix and Divide into four blocks and get the matrix The corresponding four-block matrix and matrix The corresponding four-block matrix:

[0069]

[0070]

[0071] in, Representation Matrix Medium 0 to (M k / 2)-1 row, 0 to (N k / 2)-1 column of data, Representation Matrix Medium 0 to (M k / 2)-1 row, (N k / 2) to N k -1 column of data, Representation Matrix Medium k / 2) to M k -1 row, 0 to (N k / 2)-1 column of data, Representation Matrix Medium k / 2) to M k -1 row, (N k / 2) to N k -1 column of data; Representation Matrix Medium 0 to (M k-1 / 2)-1 row, 0 to (N k-1 / 2)-1 column of data, Representation Matrix Medium 0 to (M k-1 / 2)-1 row, (N k-1 / 2) to N k-1 -1 column of data, Representation Matrix Medium k-1 / 2) to M k-1 -1 row, 0 to (N k-1 / 2)-1 column of data, Representation Matrix Medium k-1 / 2) to M k-1 -1 row, (N k-1 / 2) to N k-1 -1 column of data.

[0072] Perform block multiplication calculations on each block matrix to obtain the block multiplication calculation results

[0073]

[0074] Among them, A, B, C, and D are four intermediate quantities, and they are:

[0075]

[0076] Consider the matrix after block v∈[LU,RU,LD,RD], when it is a zero matrix or a unit matrix, the amount of matrix multiplication is 0, let the proportion of some rows and columns be β (w,v) (β (w,v) ∈[0,1],w=k-1,k), then the amount of calculation for the adjacent matrix multiplication of the four blocks is:

[0077]

[0078] If the zero value part of the multiplied matrix occupies λ rows (λ∈Z + ,λ≤M k-1 / 2), the zero value part of the multiplication matrix occupies the γ columns (γ∈Z + ,γ≤N k / 2), then β (w,v) The numerical calculation is as follows:

[0079]

[0080] Then we have:

[0081]

[0082] According to the above formula, after counting the zero vectors of the sparse matrix, the column count of the multiplied matrix and the row count of the multiplied matrix can be equivalent to:

[0083]

[0084] Therefore, the number of zero row vectors of each multiplied matrix can be detected, and the number of zero column vectors of each multiplication matrix can be detected; then, according to the detection results of the number of zero row vectors of each multiplied matrix and the number of zero column vectors of each multiplication matrix, the matrix order Q after equivalent reduction is determined. k :

[0085]

[0086] Among them, λ (k-1,v) Represents the detection result of the number of zero row vectors of each multiplied matrix, γ (k,v) Represents the detection result of the number of zero column vectors in each multiplication matrix.

[0087] Step 3: Determine the optimal order of matrix multiplication according to the determined equivalent reduced-order matrix order.

[0088] In this embodiment, the optimal matrix multiplication order m(i, k) can be determined by the following formula:

[0089]

[0090] Step 4: According to the determined optimal order of matrix multiplication, the cascade matrix multiplication is converted into parallel dot product calculation, and the calculation result is obtained and output.

[0091] In this embodiment, for matrix cascade multiplication calculation, as Figure 4 As shown, the high-speed matrix cascade multiplication calculation process includes the following steps:

[0092] a) Wait for the matrix multiplication cascade calculation to start.

[0093] b) Yes and Divide into four blocks and get and

[0094] c) Perform block multiplication on each block matrix, and detect the number of zero row vectors of each multiplied matrix to obtain λ (k-1,v) , detect the number of zero column vectors of each multiplication matrix to obtain γ (k,v) .

[0095] d) Determine the matrix order Q after equivalent reduction k :

[0096]

[0097] e) Determine the optimal order of matrix multiplication m(i,k):

[0098]

[0099] f) Convert the cascaded matrix multiplication into parallel dot product calculations.

[0100] like Figure 5 As shown, the control system mainly includes a central controller and a joint controller. The central controller is connected to multiple joint controllers via a 1553B bus. The central controller mainly includes a CPU module, a bus interface module, and a parallel dot product calculation module. In each control cycle, the joint controller reads the telemetry information such as the position and speed of the joint, which is received by the bus interface module through the 1553B bus after framing, and is handed over to the bus interface processing unit in the CPU module for parsing to form a standard protocol data frame; the standard protocol data frame is sent to the telemetry and remote control processing unit for parsing to obtain the position and speed information required for the forward and inverse solutions of kinematics, forming a data frame. and take out The non-zero calculation vector in is sent to the data cache of the parallel dot product calculation module; the scheduling calculation unit allocates matrices to each dot product calculation module according to the optimal order of matrix multiplication m(i,k). Read the corresponding non-zero calculation vectors from the data cache in turn, store them in each dot product calculation unit DPU, start each DPU calculation, and get the result The telemetry and remote control processing unit takes out the calculation results from the data cache, transmits them to the bus interface processing unit, and sends them to the 1553B bus through the bus interface module. After receiving the control speed and position information sent by the bus, each joint controller generates a pulse width modulation signal and sends it to the joint, completing the entire single control cycle.

[0101] Furthermore, the scheduling calculation unit controls the data cache through the cache read and write control signal DPU_WrRd and the cache address access signal DPU_Addr, and sends the read data sent to the selector MUX_O to the dot product calculation unit group as a selection signal by DPU_Sel_O according to the need of reading and writing, and the result output by the dot product calculation unit group passes through the selector MUX_I and is sent to the data cache by DPU_Sel_I as a selection signal. The scheduling calculation unit enables and controls the parameters of the click calculation unit group according to its output state.

[0102] like Figure 6 As shown, the dot product calculation unit includes FIFO, gate MUX, multiplier, adder, and comparator. The two calculation vectors 1 and 2 are input into FIFO1 and FIFO2 respectively. The data of the two FIFOs are controlled by the enable signals Mux_en1 and Mux_en2 of the gates MUX1 and 2 to control the output time, and the output results enter the multiplier at the same time; the multiplication result is input into the accumulator, and the number of accumulations m and the number of rows of the multiplied matrix M k Through the comparator comparison, if the accumulated number reaches M k The result is output to FIFO3, which outputs the final dot product result. The external interface and the internal calculation module are divided into two clock domains. Specifically, high-speed matrix cascade multiplication and Non-zero vectors and The dot product calculation unit receives two external input vectors to FIFO1 and FIFO2: input vector 1 and input vector 2. Input vectors 1 and 2 are the row vector and column vector of adjacent matrices respectively. The two vectors are dot-producted, and each element is multiplied in turn and summed up. The final summation result The data stored in FIFO3 is read out by the scheduling calculation unit, indicating that the dot product calculation of the row vector and column vector of two adjacent matrices is completed. k -1-1],γ∈Z+,

[0103] In an embodiment of the present invention, high-speed matrix cascade multiplication calculation includes equivalent order reduction calculation, optimal order calculation and parallel dot product calculation. Among them, the equivalent order reduction calculation is implemented to remove unnecessary multiplication and accumulation operations in a matrix with a large number of zero vectors. When the row vector in the multiplied matrix or the column vector in the multiplication matrix is ​​0, the multiplication and accumulation operation of the vector is considered unnecessary, thereby saving time and improving performance. Figure 7 This is an example of the calculation process of the cascade multiplication method for the positive solution of homogeneous matrices. In the calculation process, six homogeneous 4X4 matrices X 4X4 (k) (k=0,1,…,5) performs multiplication operation on X 4X4 (3) and X 4X4 (4) Perform statistics and perform equivalent order reduction. First, the 4X4 matrix is ​​divided into 4 blocks according to formula (3) to obtain a 2X2 matrix representation of the multiplication result; then, statistics are performed on each 2X2 matrix to calculate the zero-value map of the block matrix vector and its parameters; finally, the matrix order after equivalent order reduction is calculated. According to the above formula, it can be calculated as follows Figure 8 The optimal order for cascaded multiplications is shown.

[0104] Furthermore, when there are 5 parallel dot product calculation units, Fig. 9 Given a matrix X 4X4 (3) and X 4X4 (4) The distribution of each non-zero vector in each dot product calculation unit during the multiplication process, where the dot product calculations of the first five vectors are distributed in five calculation units, and after the calculations are completed, the dot product calculations of the last four vectors are distributed in the first four vector dot product calculation units.

[0105] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

[0106] The contents not described in detail in the specification of the present invention belong to the common knowledge of the professionals in this field.

Claims

1. A method for realizing high-speed matrix cascade multiplication calculation for controlling a robot arm, characterized in that: include: Determine any two adjacent matrices and Among them, M k and N k Represents the kth matrix The number of rows and columns, M k-1 and N k-1 Represents the k-1th matrix The number of rows and columns, k = 0, 1, 2, ..., S-1, S ≥ 1 and S ∈ Z + ; For the matrix and Perform equivalent rank reduction processing on the sparse features of the matrix and determine the matrix order after the equivalent rank reduction; Determine the optimal order of matrix multiplication according to the determined equivalent reduced-order matrix order; According to the determined optimal order of matrix multiplication, the cascade matrix multiplication is converted into parallel dot product calculation, and the calculation result is obtained and output; For the matrix and Perform equivalent rank reduction processing on the sparse features of the matrix and determine the matrix order after equivalent rank reduction, including: Pair Matrix and Divide into four blocks and get the matrix The corresponding four-block matrix and matrix The corresponding four-block matrix; Perform block multiplication calculation on each block matrix, and detect the number of zero row vectors on each multiplied matrix, and detect the number of zero column vectors on each multiplied matrix; Determine the matrix order after equivalent reduction according to the detection results of the number of zero row vectors of each multiplied matrix and the detection results of the number of zero column vectors of each multiplication matrix; The matrix is ​​transformed by the following formula and Divide into four blocks: in, Representation Matrix Medium 0 to (M k / 2)-1 row, 0 to (N k / 2)-1 column of data, Representation Matrix Medium 0 to (M k / 2)-1 row, (N k / 2) to N k -1 column of data, Representation Matrix Medium k / 2) to M k -1 row, 0 to (N k / 2)-1 column of data, Representation Matrix Medium k / 2) to M k -1 row, (N k / 2) to N k -1 column of data; Representation Matrix Medium 0 to (M k-1 / 2)-1 row, 0 to (N k-1 / 2)-1 column of data, Representation Matrix Medium 0 to (M k-1 / 2)-1 row, (N k-1 / 2) to N k-1 -1 column of data, Representation Matrix Medium k-1 / 2) to M k-1 -1 row, 0 to (N k-1 / 2)-1 column of data, Representation Matrix Medium k-1 / 2) to M k-1 -1 row, (N k-1 / 2) to N k-1 -1 column of data; The matrix order Q after equivalent reduction is determined by the following formula k : Among them, λ (k-1,v) Represents the detection result of the number of zero row vectors of each multiplied matrix, γ (k,v) Represents the detection result of the number of zero column vectors of each multiplication matrix, v∈[LU,RU,LD,RD]; The optimal order of matrix multiplication m(i,k) is determined by the following formula:

2. The method for realizing high-speed matrix cascade multiplication calculation for controlling a robot arm according to claim 1, characterized in that: matrix Denotes the S matrices Γ used for continuous multiplication (k,k+1) , Γ (k,k+1) Represents the homogeneous transformation matrix between the adjacent degree-of-freedom joint coordinate systems of the S-degree-of-freedom space manipulator.

3. The method for realizing high-speed matrix cascade multiplication calculation for controlling a robot arm according to claim 2, characterized in that: Γ (k,k+1) It is expressed as follows: in, represents the translation change between two adjacent joint coordinate systems, ξ (k,k+1) Represents the rotation change between two adjacent joint coordinate systems.

4. The method for realizing high-speed matrix cascade multiplication calculation for controlling a robot arm according to claim 3, characterized in that: Among them, θ k+1 Represents the rotation angle of the k+1th joint of the robot around its axis.

5. The method for realizing high-speed matrix cascade multiplication calculation for controlling a robot arm according to claim 1, characterized in that: Homogeneous transformation matrix Γ of the end position of the whole arm in S-degree-of-freedom space manipulator (0,S) And the matrix multiplication result Y M×N They are respectively expressed as follows:

6. The method for realizing high-speed matrix cascade multiplication calculation for controlling a robot arm according to claim 1, characterized in that: Through the following formula, block multiplication calculation is performed on each block matrix to obtain the block multiplication calculation result Among them, A, B, C, and D are four intermediate quantities, and they are:

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