Walking and diagonal gait motion control method for quadruped robot

Abstract

The present invention relates to a method for controlling the walking and diagonal gait motion of a quadruped robot, which comprises the following steps: step 1: simulating the motion of the quadruped robot by using a low-dimensional point mass model, and establishing a discrete state equation of the motion process in the preview time domain by using a discretization method; step 2: processing the walking and trotting gait of the quadruped robot by using a linear constraint domain, and determining the optimization interval; step 3: establishing a performance index evaluation function of the robot gait motion control model in the preview time domain, and solving the expected footfall and center of mass position of the robot; step 4: realizing the motion control of the quadruped robot according to the expected footfall and center of mass position of the robot. The motion control method proposed by the present invention establishes a discrete state equation in the preview time domain by using a discretization method; maps the gait pattern of the quadruped robot with the gait pattern of the bipedal robot, and introduces a linear constraint domain to process the robot motion; solves the motion control problem of the walking and trotting gait of the robot, and has high robustness.

Description

Technical Field

[0001] The present application relates to the field of robotics, and in particular to a method for controlling walking and diagonal gait motion of a quadruped robot. Background Art

[0002] Quadruped robots are an important branch of robots. Quadruped robots have stronger carrying capacity and better stability than bipedal robots, and simpler structures than hexapod and octapodal robots. However, quadruped robots are typical high-dimensional, nonlinear systems with strong nonlinearity, discrete dynamics and other problems. Therefore, designing a robot gait algorithm to ensure that the robot can move stably on uneven terrain and has strong robustness to external disturbances is the key to gait generation and optimization methods.

[0003] At present, the research on gait planning and stable control algorithms for quadruped robots is mostly focused on gait control methods based on dynamic models, tracking control, and intelligent algorithms. The gait control methods based on dynamic models often require complex trajectory planning and calculation solutions, the gait control methods based on tracking control are slow and have few applicable gait forms, and the gait control methods based on intelligent algorithms require a large amount of sample data training and large amount of calculation. Therefore, a gait generation and optimization method that can plan online, does not simplify or ignore the mutual coupling of the whole body dynamics factors of bipedal robots, has a simple structure, low calculation amount, high robustness, and is suitable for bipedal and quadrupedal robots is needed. Summary of the invention

[0004] In order to overcome the shortcomings of the prior art, the motion control method proposed in the present invention utilizes a low-dimensional point mass model to abstract the dynamics of the entire robot, and predicts the generalized discrete state equation over the entire period of time through a discretization method; the gait pattern of the quadruped robot is mapped to the gait pattern of the biped robot, and a linear constraint domain is introduced to unify the motion gait of the quadruped robot; and the motion control problems of the walking and trotting gaits of the quadruped robot can be solved at the same time.

[0005] To achieve the above purpose, the solution adopted by the present invention is:

[0006] A method for controlling walking and diagonal gait motion of a quadruped robot comprises the following steps:

[0007] Step 1: Use a low-dimensional point mass model to simulate the motion of the quadruped robot and use a discretization method to establish the discrete state equation of the motion process in the preview time domain;

[0008] A low-dimensional point mass model is used to simulate the motion of the quadruped robot, and the point mass model is represented by a state space equation. The point mass model is then converted into a linear inverted pendulum model through linearization, and further converted into a discrete time state space expression. Finally, the discrete time state space model is recursively derived to derive the discrete state equations of the center of mass position, center of mass velocity, center of mass acceleration, center of mass jerk, and center of mass pressure center position.

[0009] Step 2: Process the walking and trotting gait of the quadruped robot through the linear constraint domain to determine the optimization interval;

[0010] The gait pattern of the quadruped robot is mapped to the gait pattern of the biped robot, and the walking and trotting gaits of the quadruped robot are unified through the linear constraint domain; the optimization interval determined according to the linear constraint domain is as follows:

[0011]

[0012] Where: p f0 Indicates the current foothold position; Δx and Δy respectively indicate the pressure center setting range in the horizontal and vertical directions; X cop and Y cop Respectively represent the pressure center of the robot in the horizontal and vertical directions; and Respectively represent the state vector of the robot in the horizontal and vertical directions; p zu and p zs are the control and state coefficient matrices of the robot pressure center, respectively; and They represent the mass center acceleration in the abscissa and ordinate directions respectively;

[0013] Step 3: Establish a performance index evaluation function for the robot gait motion control model in the preview time domain to solve the expected foothold and center of mass position of the robot;

[0014] Based on the irrelevance of the system state variables in the horizontal and vertical directions, the performance index evaluation functions of mass center velocity tracking, pressure center tracking and minimum control input are defined; the performance index evaluation functions in the horizontal and vertical directions in the preview time domain are as follows:

[0015]

[0016] Where: X and Y represent the horizontal and vertical directions respectively; J X / Y represents the performance evaluation index function; ω1 represents the weight coefficient of center of mass velocity tracking; ω2 represents the weight coefficient of pressure center tracking; ω3 represents the weight coefficient of center of mass acceleration tracking; represents the velocity vector of the center of mass at time k+1; represents the expected center of mass velocity state vector at time k+1; X / Y cop (k+1) represents the state vector of the pressure center at time k+1; represents the expected pressure center state vector at time k+1; U X / Y (k) represents the control input vector of the state equation at time k;

[0017] Step 4: Realize the motion control of the quadruped robot according to the expected foothold and center of mass position of the robot;

[0018] Obtain the expected center of mass position and the expected foothold position in step 3, determine the linear predictive control model, and further construct the optimization model of the performance index evaluation function through the regular convex quadratic programming method according to the optimization interval determined in step 2, as shown below:

[0019]

[0020] Where: U p Represents the vector to be optimized in the state equation; U p T represents the transpose of the vector to be optimized of the state equation; H represents the Hessian matrix; f T represents the linear function of the performance index; C represents the inequality coefficient matrix; c represents the inequality setting coefficient; U l and U u Represents the lower and upper limits of the state equation control input vector;

[0021] Among them, the variables to be optimized in the state equation are as follows:

[0022] U p =[U X / Y (k) T P X / Y (k) T ] T ;

[0023] Where: U X / Y (k) represents the control input vector of the state equation; P X / Y (k) represents the foothold position in the preview time domain;

[0024] The motion control of the quadruped robot is realized according to the control input vector of the state equation and the foot position in the preview time domain.

[0025] Preferably, the specific process of deriving the generalized discrete state equation in the entire preview time domain in step 1 is as follows:

[0026] First, the equivalent robot dynamics expression using the low-dimensional point mass model is:

[0027]

[0028] Where: x(t) represents the system state vector of the state equation at time t; represents the first-order derivative of the system state vector at time t; y(t) represents the system state output vector at time t; u(t) represents the state equation control input vector at time t; I represents the unit vector; z com Indicates the center of mass position in the z direction; represents the acceleration of the center of mass in the z direction; g represents the acceleration due to gravity; t represents the time scale;

[0029] Then, the rolling preview time domain is set to NT, and the system rewrites the model into a discrete time state space expression at the kth sampling time interval, as shown below:

[0030]

[0031] In the formula: A represents the system state matrix; B represents the system input variable matrix; C represents the system output variable matrix; x(k) represents the system state vector of the state equation when the discrete time is k; x(k+1) represents the system state vector of the state equation when the discrete time is k+1; u(k) represents the control input vector of the state equation when the discrete time is k; y(k) represents the system state output vector when the discrete time is k.

[0032] The system state matrix, system input variable matrix and system output variable matrix are as follows:

[0033]

[0034] Preferably, the discrete state equations of the center of mass acceleration, center of mass position, center of mass velocity and center of mass acceleration, and center of mass pressure position derived in step 1 are specifically:

[0035] The discrete state equation of the center-of-mass acceleration is as follows:

[0036]

[0037] Where: U(k) represents the control input vector of the state equation at discrete time k; u(k i |k i ) represents k i The state equation control input value at time is the center-of-mass jerk; k i represents the discrete time point of the i-th moment; N represents the length of the preview time domain;

[0038]

[0039] The discrete time state vectors of the center of mass position, center of mass velocity, and center of mass acceleration are as follows:

[0040]

[0041] Where: X[k+1] represents the system state vector at discrete time k+1; x(k i +1|k i ) represents k i System state vector at time +1;

[0042]

[0043] Where: x com and com Respectively represent the centroid position in the horizontal and vertical directions; and Represent the mass center velocity in the horizontal and vertical directions respectively; and Represent the mass center acceleration in the abscissa and ordinate directions respectively;

[0044] The discrete state equation of the center of mass pressure position is as follows:

[0045]

[0046] Where: Y[k+1] represents the system state output vector at discrete time k+1; y(k i +1|k i ) represents k i +1 time system status output value;

[0047] y(k i +1|k i )=[x cop ,y cop ] T ;

[0048] Where: x cop and cop Represent the pressure center position in the horizontal and vertical directions respectively.

[0049] Preferably, the pressure center constraint domain introduced in step 2 is a rectangular constraint domain, which can solve the problem that the movement of the pressure center in one direction will affect the movement in another direction during the model decoupling process.

[0050] Preferably, the control and state coefficient matrix of the robot pressure center in step 2 is specifically:

[0051] The control coefficient matrix of the robot's pressure center is shown below:

[0052]

[0053] Where: T l Indicates the sampling time interval;

[0054] The state coefficient matrix of the robot pressure center is as follows:

[0055]

[0056] Preferably, the specific solution process of the expected foothold position and the expected centroid position in step 3 is as follows:

[0057] Determine the current foothold and the future foothold in the preview time domain to determine the reference pressure center in the preview time domain. The expected foothold is as follows:

[0058]

[0059] Where: V(k+1) represents the foot point selection vector of all sampling moments in the current time domain; Indicates the current landing point; Represents the foot point selection matrix for all sampling moments in the preview time domain; Indicates the location of the footstep in the preview time domain;

[0060] The preview time domain foothold position is as follows:

[0061]

[0062] Where: represents the position of the jth foothold, where j is 1, 2 or 3;

[0063] The expression for the expected position of the center of mass at any time is as follows:

[0064]

[0065] Where: represents the expected landing point position in the horizontal coordinate direction at the i-th moment; ω a represents the first weight coefficient; D represents the function matrix relative to the position; Indicates the center of mass position in the horizontal direction of the end state; Indicates the center of mass position in the horizontal direction of the starting state; T c represents the sampling interval of the expected position of the centroid, Indicates the velocity of the center of mass in the horizontal direction of the starting state; ω b represents the second weight coefficient;

[0066] The method for obtaining the function matrix relative to the position is as follows:

[0067]

[0068] Compared with the prior art, the present invention has the following beneficial effects:

[0069] (1) The motion control method proposed in the present invention uses a low-dimensional point mass model to abstract the dynamics of the entire robot, and uses a discretization method to predict the generalized discrete state equation over the entire period of time; the gait pattern of the quadruped robot is mapped to the gait pattern of the bipedal robot, and a linear constraint domain is introduced to unify the walking and trotting gaits of the quadruped robot; the motion control problems of the walking and trotting gaits of the quadruped robot can be solved simultaneously;

[0070] (2) Compared with the traditional motion gait control method, the method of the present invention has a simple structure. The model predictive control and the foothold adaptation based on the improved reference pressure center make the quadruped robot motion highly robust to external interference, more in line with actual application conditions, and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 This is a control block diagram of a method for controlling walking and diagonal gait motion of a quadruped robot according to an embodiment of the present invention;

[0072] Figure 2 LS gait pattern mapping diagram of a quadruped robot and a biped robot according to an embodiment of the present invention;

[0073] Figure 3 This is a diagonal gait pattern mapping diagram of a quadruped robot and a biped robot according to an embodiment of the present invention;

[0074] Figure 4 It is a motion illustration diagram of the walking gait and diagonal motion gait of the quadruped robot according to an embodiment of the present invention;

[0075] Figure 5 This is a model showing the position of the discrete centroid and the foothold of the sagittal plane in the visual field predicted by the embodiment of the present invention;

[0076] Figure 6 This is a diagram showing the center of mass trajectory and footfall planning results of the Walk gait according to an embodiment of the present invention;

[0077] Figure 7 This is a diagram showing the Trot gait center of mass trajectory and footfall planning result of an embodiment of the present invention;

[0078] Figure 8 This is a diagram showing the anti-interference capability of the technical method of the embodiment of the present invention. DETAILED DESCRIPTION

[0079] Hereinafter, embodiments of the present invention will be described with reference to the drawings.

[0080] The motion control method proposed in the embodiment of the present invention uses a low-dimensional point mass model to abstract the dynamics of the robot as a whole, and uses a discretization method to predict the generalized discrete state equation over the entire period of time; the gait pattern of the quadruped robot is mapped to the gait pattern of the biped robot, and a linear constraint domain is introduced to unify the walking and trotting gait of the quadruped robot; and the motion control problems of the walking and trotting gait of the quadruped robot can be solved simultaneously. Figure 1 The figure shows a control block diagram of the walking and diagonal gait motion control method of a quadruped robot according to an embodiment of the present invention. Compared with the traditional motion gait control method, the method proposed in the embodiment of the present invention has a simple structure, and the model predictive control and foothold adaptation based on the improved reference pressure center make the quadruped robot motion highly robust to external interference, more in line with actual application conditions, and has a broader application prospect.

[0081] The embodiment of the present invention provides a method for controlling walking and diagonal gait motion of a quadruped robot. In order to prove the applicability of the present invention, it is applied to an example, which specifically includes the following steps:

[0082] S1: Use low-dimensional point mass model to simulate the motion of quadruped robot and use discretization method to establish discrete state equation of the motion process in the preview time domain;

[0083] A low-dimensional point mass model is used to simulate the motion of the quadruped robot, and the point mass model is represented by a state-space equation. The point mass model is equivalent to a linear inverted pendulum model through linearization, and further converted into a discrete-time state-space expression. Finally, the discrete-time state-space model is recursively derived to derive the discrete state equations of the center of mass position, center of mass velocity, center of mass acceleration, center of mass jerk and center of mass pressure center position.

[0084] The specific process of deriving the generalized discrete state equation in the entire preview time domain is as follows:

[0085] First, the equivalent robot dynamics expression using the low-dimensional point mass model is:

[0086]

[0087] Where: x(t) represents the system state vector of the state equation at time t; represents the first-order derivative of the system state vector at time t; y(t) represents the system state output vector at time t; u(t) represents the state equation control input vector at time t; I represents the unit vector; z com Indicates the center of mass position in the z direction; represents the acceleration of the center of mass in the z direction; g represents the acceleration due to gravity; and t represents the time scale.

[0088] Then, the rolling preview time domain is set to NT, and the system rewrites the model into a discrete time state space expression at the kth sampling time interval, as shown below:

[0089]

[0090] In the formula: A represents the system state matrix; B represents the system input variable matrix; C represents the system output variable matrix; x(k) represents the system state vector of the state equation when the discrete time is k; x(k+1) represents the system state vector of the state equation when the discrete time is k+1; u(k) represents the control input vector of the state equation when the discrete time is k; y(k) represents the system state output vector when the discrete time is k.

[0091] The discrete state equation of the center-of-mass acceleration is as follows:

[0092]

[0093] Where: U(k) represents the control input vector of the state equation at discrete time k; u(k i |k i ) represents k i The state equation control input value at time is the center-of-mass jerk; k i represents the discrete time point of the i-th moment; N represents the length of the preview time domain.

[0094]

[0095] The discrete time state vectors of the center of mass position, center of mass velocity, and center of mass acceleration are as follows:

[0096]

[0097] Where: X[k+1] represents the system state vector at discrete time k+1; x(k i +1|k i ) represents k i The system state vector at time +1.

[0098]

[0099] Where: x com and com Respectively represent the centroid position in the horizontal and vertical directions; and Represent the mass center velocity in the horizontal and vertical directions respectively; and represent the center of mass acceleration in the horizontal and vertical directions respectively.

[0100] The discrete state equation of the center of mass pressure position is as follows:

[0101]

[0102] Where: Y[k+1] represents the system state output vector at discrete time k+1; y(k i +1|k i ) represents k i +1 time system status output value;

[0103] y(k i +1|k i )=[x cop ,y cop ] T ;

[0104] Where: x cop and cop Represent the pressure center position in the horizontal and vertical directions respectively.

[0105] S2: Process the walking and trotting gait of the quadruped robot through the linear constraint domain to determine the optimization interval;

[0106] The gait pattern of the quadruped robot is mapped to the gait pattern of the biped robot, and the walking and trotting gaits of the quadruped robot are unified through the linear constraint domain; the optimization interval determined according to the linear constraint domain is as follows:

[0107]

[0108] Where: p f0 Indicates the current foothold position; Δx and Δy respectively indicate the pressure center setting range in the horizontal and vertical directions; X cop and Y cop Respectively represent the pressure center of the robot in the horizontal and vertical directions; and Respectively represent the state vector of the robot in the horizontal and vertical directions; p zu and p zs are the control and state coefficient matrices of the robot pressure center, respectively; and They represent the center-of-mass acceleration in the horizontal and vertical directions respectively.

[0109] The introduced pressure center constraint domain is a rectangular constraint domain, which can solve the problem that the movement of the pressure center in one direction will affect the movement in another direction during the model decoupling process.

[0110] The control coefficient matrix of the robot's pressure center is shown below:

[0111]

[0112] Where: T l Indicates the sampling time interval;

[0113] The state coefficient matrix of the robot pressure center is as follows:

[0114]

[0115] like Figure 2 LS gait pattern mapping diagram of the quadruped robot and the biped robot according to the embodiment of the present invention; Figure 3 The figure shows the diagonal gait pattern mapping diagram of the quadruped robot and the biped robot in the embodiment of the present invention; for the quadruped walking gait, the vacancy and landing phases of the right hind leg or left hind leg and the right front leg or left hind leg are similar to the vacancy and landing phases of the virtual right leg or left leg of the biped robot, and the gray shaded area is the quadruped support phase. The diagonal movement gait of the quadruped robot, the movement gait pattern of the quadruped robot can be more intuitively converted into the gait pattern of the biped robot, and then matched with the linear inverted pendulum model.

[0116] Normally, if Figure 4 2 is a diagram illustrating the walking gait and diagonal gait of a quadruped robot according to an embodiment of the present invention; the feasible motion domain of the pressure center constraint of the quadruped robot in the walking gait is relatively large, and the virtual two feet are nonlinearly constrained, and the foot shape corresponding to the landing phase of the virtual two feet changes from triangle 1 to triangle 2. Although the shape of the virtual foot remains unchanged in the diagonal gait, the feasible domain of its pressure center is the straight line segment connecting the two landing feet, which not only has a nonlinear constraint on the feasible domain of the pressure center, but also has a greater restriction on the pressure center constraint domain.

[0117] In order to achieve unified processing of the two gaits, a linear constraint domain is introduced, such as Figure 4 As shown in the rectangular area in , the rectangular linear constraint domain is used as the constraint domain of the pressure center of the diagonal motion gait. By limiting the rectangular constraint domain, the influence of the pressure center movement in one direction on the movement in another direction during the model decoupling process is solved; the preview trajectory deviation caused by the model error is solved by the following capture point theory.

[0118] S3: Establish the performance index evaluation function of the robot gait motion control model in the preview time domain to solve the expected foothold and center of mass position of the robot;

[0119] Based on the irrelevance of the system state variables in the horizontal and vertical directions, the performance index evaluation functions of mass center velocity tracking, pressure center tracking and minimum control input are defined; the performance index evaluation functions in the horizontal and vertical directions in the preview time domain are as follows:

[0120]

[0121] Where: X and Y represent the horizontal and vertical directions respectively; J X / Y represents the performance evaluation index function; ω1 represents the weight coefficient of center of mass velocity tracking; ω2 represents the weight coefficient of pressure center tracking; ω3 represents the weight coefficient of center of mass acceleration tracking; represents the velocity vector of the center of mass at time k+1; represents the expected center of mass velocity state vector at time k+1; X / Y cop (k+1) represents the state vector of the pressure center at time k+1; represents the expected pressure center state vector at time k+1; U X / Y (k) represents the control input vector of the state equation at time k.

[0122] The specific solution process of the expected foot point position and the expected center of mass position is as follows:

[0123] Determine the current foothold and the future foothold in the preview time domain to determine the reference pressure center in the preview time domain. The expected foothold is as follows:

[0124]

[0125] Where: V(k+1) represents the foot point selection vector of all sampling moments in the current time domain; Indicates the current landing point; Represents the foot point selection matrix for all sampling moments in the preview time domain; Indicates the location of the footstep in the preview time domain.

[0126] The preview time domain foothold position is as follows:

[0127]

[0128] Where: Represents the jth foothold position, where j is 1, 2, or 3.

[0129] The expression for the expected position of the center of mass at any time is as follows:

[0130]

[0131] Where: represents the expected landing point position in the horizontal coordinate direction at the i-th moment; ω a represents the first weight coefficient; D represents the function matrix relative to the position; Indicates the center of mass position in the horizontal direction of the end state; Indicates the center of mass position in the horizontal direction of the starting state; T crepresents the sampling interval of the expected position of the centroid, Indicates the velocity of the center of mass in the horizontal direction of the starting state; ω b Represents the second weight coefficient.

[0132] The method for obtaining the function matrix relative to the position is as follows:

[0133]

[0134] like Figure 5 Shown is a model display diagram of the discrete centroid position and foothold of the sagittal plane on the field of view predicted by an embodiment of the present invention.

[0135] S4: Realize the motion control of the quadruped robot according to the robot's desired foothold and center of mass position;

[0136] Obtain the expected center of mass position and the expected foothold position in S3, determine the linear predictive control model, and further construct the optimization model of the performance index evaluation function through the regular convex quadratic programming method according to the optimization interval determined by S2, as shown below:

[0137]

[0138] Where: U p Represents the vector to be optimized in the state equation; U p T represents the transpose of the vector to be optimized of the state equation; H represents the Hessian matrix; f T represents the linear function of the performance index; C represents the inequality coefficient matrix; c represents the inequality setting coefficient; U l and U u Represents the lower and upper limits of the state equation control input vector.

[0139] Among them, the variables to be optimized in the state equation are as follows:

[0140] U p =[U X / Y (k) T P X / Y (k) T ] T ;

[0141] Where: U X / Y (k) represents the control input vector of the state equation; P X / Y (k) represents the footstep position in the preview time domain.

[0142] The motion control of the quadruped robot is realized according to the control input vector of the state equation and the foot position in the preview time domain.

[0143] Finally, the online motion planning algorithm was used to test the walking gait and diagonal motion gait of the quadruped robot, and the planned center of mass trajectory and foothold position were obtained, such as Figure 6 FIG. 1 is a diagram showing the centroid trajectory and footfall planning result of the Walk gait according to an embodiment of the present invention; Figure 7 The figure shows the planning result of the center of mass trajectory and foothold of the Trot gait according to the embodiment of the present invention; by implementing the MPC online motion planning algorithm in the walking gait and diagonal motion gait of the quadruped robot, the quadruped robot can not only plan the center of mass trajectory and foothold as expected, but also adjust the center of mass trajectory and foothold in real time under external disturbances, and has a certain robustness to disturbances. Figure 8 Shown is a diagram demonstrating the anti-interference capability of the technical method of the embodiment of the present invention, proving that the foothold adaptation based on the improved reference pressure center makes the movement of the quadruped robot highly robust to external interference.

[0144] In summary, the calculation results of the quadruped robot walking and diagonal gait motion control method in this case have proved to be very effective.

[0145] (1) The motion control method proposed in the embodiment of the present invention uses a low-dimensional point mass model to abstract the dynamics of the entire robot, and uses a discretization method to predict the generalized discrete state equation over the entire period of time; the gait pattern of the quadruped robot is mapped to the gait pattern of the bipedal robot, and a linear constraint domain is introduced to unify the walking and trotting gaits of the quadruped robot; the motion control problems of the walking and trotting gaits of the quadruped robot can be solved at the same time, and the verification results of the attached figure prove that the method can better complete the motion control process of the robot;

[0146] (2) Compared with the traditional motion gait control method, the method introduced in the embodiment of the present invention has a simpler structure and better model prediction control effect. The accompanying drawings prove that the foothold adaptation based on the improved reference pressure center makes the movement of the quadruped robot highly robust to external interference, which is more in line with actual application conditions and has broad application prospects.

[0147] The embodiments described above are only descriptions of the preferred implementation modes of the present invention, and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for controlling walking and diagonal gait motion of a quadruped robot, characterized in that: It includes the following steps: Step 1: Use a low-dimensional point mass model to simulate the motion of the quadruped robot and use a discretization method to establish the discrete state equation of the motion process in the preview time domain; A low-dimensional point mass model is used to simulate the motion of the quadruped robot, and the point mass model is represented by a state space equation. The point mass model is then converted into a linear inverted pendulum model through linearization, and further converted into a discrete time state space expression. Finally, the discrete time state space model is recursively derived to derive the discrete state equations of the center of mass position, center of mass velocity, center of mass acceleration, center of mass jerk, and center of mass pressure center position. Step 2: Process the walking and trotting gait of the quadruped robot through the linear constraint domain to determine the optimization interval; The gait pattern of the quadruped robot is mapped to the gait pattern of the biped robot, and the walking and trotting gaits of the quadruped robot are unified through the linear constraint domain; the optimization interval determined according to the linear constraint domain is as follows: Where: p f0 Indicates the current foothold position; Δx and Δy respectively indicate the pressure center setting range in the horizontal and vertical directions; X cop and Y cop Respectively represent the pressure center of the robot in the horizontal and vertical directions; and Respectively represent the state vector of the robot in the horizontal and vertical directions; p zu and p zs are the control and state coefficient matrices of the robot pressure center, respectively; and They represent the mass center acceleration in the abscissa and ordinate directions respectively; Step 3: Establish a performance index evaluation function for the robot gait motion control model in the preview time domain to solve the expected foothold and center of mass position of the robot; Based on the irrelevance of the system state variables in the horizontal and vertical directions, the performance index evaluation functions of mass center velocity tracking, pressure center tracking and minimum control input are defined; the performance index evaluation functions in the horizontal and vertical directions in the preview time domain are as follows: Where: X and Y represent the horizontal and vertical directions respectively; J X / Y represents the performance evaluation index function; ω1 represents the weight coefficient of center of mass velocity tracking; ω2 represents the weight coefficient of pressure center tracking; ω3 represents the weight coefficient of center of mass acceleration tracking; represents the velocity vector of the center of mass at time k+1; represents the expected center of mass velocity state vector at time k+1; X / Y cop (k+1) represents the state vector of the pressure center at time k+1; represents the expected pressure center state vector at time k+1; U X / Y (k) represents the control input vector of the state equation at time k; Step 4: Realize the motion control of the quadruped robot according to the expected foothold and center of mass position of the robot; Obtain the expected center of mass position and the expected foothold position in step 3, determine the linear predictive control model, and further construct the optimization model of the performance index evaluation function through the regular convex quadratic programming method according to the optimization interval determined in step 2, as shown below: Where: U p Represents the vector to be optimized in the state equation; U p T represents the transpose of the vector to be optimized of the state equation; H represents the Hessian matrix; f T represents the linear function of the performance index; C represents the inequality coefficient matrix; c represents the inequality setting coefficient; U l and U u Represents the lower and upper limits of the state equation control input vector; Among them, the variables to be optimized in the state equation are as follows: IN p =[U X / Y (k) T P X / Y (k) T ] T ; Where: P X / Y (k) represents the foothold position in the preview time domain; The motion control of the quadruped robot is realized according to the control input vector of the state equation and the foot position in the preview time domain.

2. The method for controlling walking and diagonal gait motion of a quadruped robot according to claim 1, characterized in that: The specific process of deriving the generalized discrete state equation in the entire preview time domain in step 1 is as follows: First, the equivalent robot dynamics expression using the low-dimensional point mass model is: Where: x(t) represents the system state vector of the state equation at time t; represents the first-order derivative of the system state vector at time t; y(t) represents the system state output vector at time t; u(t) represents the state equation control input vector at time t; I represents the unit vector; z com Indicates the centroid position in the z direction; represents the acceleration of the center of mass in the z direction; g represents the acceleration due to gravity; t represents the time scale; Then, the rolling preview time domain is set to NT, and the system rewrites the model into a discrete time state space expression at the kth sampling time interval, as shown below: In the formula: A represents the system state matrix; B represents the system input variable matrix; C represents the system output variable matrix; x(k) represents the system state vector of the state equation when the discrete time is k; x(k+1) represents the system state vector of the state equation when the discrete time is k+1; u(k) represents the control input vector of the state equation when the discrete time is k; y(k) represents the system state output vector when the discrete time is k.

3. The method for controlling walking and diagonal gait motion of a quadruped robot according to claim 1, characterized in that: The discrete state equations of the center of mass acceleration, center of mass position, center of mass velocity and center of mass acceleration, and center of mass pressure center position derived in step 1 are specifically: The discrete state equation of the center-of-mass acceleration is as follows: Where: U(k) represents the control input vector of the state equation at discrete time k; u(k i |k i ) represents k i The state equation control input value at time is the center-of-mass jerk; k i represents the discrete time point of the i-th moment; N represents the length of the preview time domain; The discrete time state vectors of the center of mass position, center of mass velocity, and center of mass acceleration are as follows: Where: X[k+1] represents the system state vector at discrete time k+1; x(k i +1|k i ) represents k i System state vector at time +1; Where: x com and com Respectively represent the centroid position in the horizontal and vertical directions; and Represent the mass center velocity in the horizontal and vertical directions respectively; and Represent the mass center acceleration in the abscissa and ordinate directions respectively; The discrete state equation of the center of mass pressure position is as follows: Where: Y[k+1] represents the system state output vector at discrete time k+1; y(k i +1|k i ) represents k i +1 time system status output value; and(k) i +1|k i )=[x cop ,and cop ] T ; Where: x cop and cop Represent the pressure center position in the horizontal and vertical directions respectively.

4. The method for controlling walking and diagonal gait motion of a quadruped robot according to claim 1, characterized in that: The pressure center constraint domain introduced in step 2 is a rectangular constraint domain, which can solve the problem that the movement of the pressure center in one direction will affect the movement in another direction during the model decoupling process.

5. The method for controlling walking and diagonal gait motion of a quadruped robot according to claim 1, characterized in that: The control and state coefficient matrix of the robot pressure center in step 2 is specifically: The control coefficient matrix of the robot's pressure center is shown below: Where: T l Indicates the sampling time interval; The state coefficient matrix of the robot pressure center is as follows:

6. A method for controlling walking and diagonal gait motion of a quadruped robot according to claim 1, characterized in that: The specific solution process of the expected foothold position and the expected center of mass position in step 3 is as follows: Determine the current foothold and the future foothold in the preview time domain to determine the reference pressure center in the preview time domain. The expected foothold is as follows: Where: V(k+1) represents the foot point selection vector of all sampling moments in the current time domain; Indicates the current landing point; Represents the foot point selection matrix for all sampling moments in the preview time domain; Indicates the location of the footstep in the preview time domain; The preview time domain foothold position is as follows: Where: represents the position of the jth foothold, where j is 1, 2 or 3; The expression for the expected position of the center of mass at any time is as follows: Where: represents the expected landing point position in the horizontal coordinate direction at the i-th moment; ω a represents the first weight coefficient; D represents the function matrix relative to the position; Indicates the center of mass position in the horizontal direction of the end state; Indicates the center of mass position in the horizontal direction of the starting state; T c represents the sampling interval of the expected position of the centroid, Indicates the velocity of the center of mass in the horizontal direction of the starting state; ω b represents the second weight coefficient; The method for obtaining the function matrix relative to the position is as follows:

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