A mobile control method for a legged robot

Abstract

The present invention discloses a method for controlling the movement of a legged robot, which comprises the following steps: obtaining target parameters of the legged robot, and establishing a hybrid angular momentum linear inverted pendulum model based on the target parameters; performing periodic gait analysis based on a phase plane diagram of the hybrid angular momentum linear inverted pendulum model to obtain periodic gait characteristics; determining a step length control rate based on the periodic gait characteristics, and controlling the movement of the legged robot according to the step length control rate. In the present invention, the theoretical ideas of the hybrid linear inverted pendulum model and the angular momentum linear inverted pendulum model are integrated to construct a hybrid angular momentum linear inverted pendulum model, which can narrow the gap between the model and the real system and realize a rich range of movement gaits.

Description

Technical Field

[0001] The present invention relates to the field of robot technology, and in particular to a movement control method of a legged robot. Background Art

[0002] With the rapid development of science and technology, robotics technology has been widely used in various fields, such as industrial manufacturing, medical health, service industry, etc. As an important branch of robotics technology, legged robots have shown great application potential in complex environments due to their unique mobility and flexibility.

[0003] However, due to the motion characteristics of the inverted pendulum, the legged motion of the legged robot faces a series of challenges, such as strong nonlinearity of system dynamics, high control real-time requirements, and discrete interaction between the foot and the ground. In practical applications, the reduced-order model plays an important role in legged motion control. The reduced-order model greatly saves the cost of control calculation by simplifying the robot system, ignoring the inertia of the body and the mass of the legs and only considering the motion law of the body's center of mass.

[0004] As the most basic of these reduced-order models, the Linear Inverted Pendulum model is widely used in legged motion control, especially bipedal motion control. In recent years, many extensions have been generated based on the Linear Inverted Pendulum model, among which the Hybrid Linear Inverted Pendulum model and the Angular Momentum Linear Inverted Pendulum model have attracted much attention. However, the above-mentioned linear inverted pendulum models all have shortcomings, such as: the existing hybrid linear inverted pendulum model does not consider the change of the system's angular momentum and is quite different from the real system, and the existing Angular Momentum Linear Inverted Pendulum model does not consider the double-support gait and lacks gait richness. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a movement control method of a legged robot to solve the problem that the reduced-order model of the existing legged robot is quite different from the real system and lacks gait richness.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is: a movement control method of a legged robot, which comprises the following steps:

[0007] S1: obtaining target parameters of the legged robot, and establishing a hybrid angular momentum linear inverted pendulum model based on the target parameters;

[0008] S2: performing periodic gait analysis based on the phase plane diagram of the hybrid angular momentum linear inverted pendulum model to obtain periodic gait characteristics;

[0009] S3: Determine a step length control rate based on the periodic gait characteristics to control the movement of the legged robot according to the step length control rate.

[0010] Furthermore, in the movement control method of the legged robot described in the present invention, in step S1, the target parameters include: system parameters and expected gait parameters of the legged robot; wherein, the system parameters include gravitational acceleration and system mass, and the expected gait parameters include expected center of mass movement height.

[0011] Furthermore, in the movement control method of the legged robot described in the present invention, in step S1, a hybrid angular momentum linear inverted pendulum model is established based on the target parameters, comprising the following steps:

[0012] Based on the target parameters, constructing a first system dynamics equation of the legged robot in a single-support stage and a second system dynamics equation of the legged robot in a double-support stage respectively;

[0013] Based on the principle of conservation of angular momentum, a first state transfer equation for switching from the single support stage to the double support stage is obtained, and a second state transfer equation for switching from the double support stage to the single support is obtained.

[0014] Furthermore, in the movement control method of the legged robot described in the present invention, in step S1, the first system dynamics equation is:

[0015]

[0016] The second system dynamics equation is:

[0017]

[0018] in, represents the displacement of the center of mass in the moving direction during the single support stage; represents the angular momentum of the center of mass relative to the supporting leg end during the single support phase; represents the first-order differential of the displacement of the center of mass in the moving direction during the single support stage; It represents the first-order differential of the angular momentum of the center of mass relative to the supporting leg end during the single support phase; represents the first-order differential of the displacement of the center of mass in the moving direction during the double support stage; represents the first-order differential of the displacement of the center of mass in the moving direction at the initial moment of the double support stage; represents the first-order differential of the angular momentum of the center of mass relative to the supporting leg end during the double support phase; represents the system mass of the legged robot, represents the acceleration due to gravity, H Indicates the expected center of mass movement height.

[0019] Furthermore, in the movement control method of the legged robot described in the present invention, in step S1, the first state transfer equation is:

[0020]

[0021] The second state transfer equation is:

[0022]

[0023] in, represents the first state transfer equation, represents the second state transfer equation, where SSP represents the single support stage and DSP represents the double support stage; Indicates i The displacement of the center of mass in the moving direction at the initial moment of the double support stage; Indicates i The displacement of the center of mass in the moving direction at the end of the single support phase; Indicates i The angular momentum of the center of mass relative to the supporting leg end at the initial moment of the double support phase of the step; Indicates i The angular momentum of the center of mass relative to the supporting leg end at the end of the single support phase of the step; Indicates i+ 1. Displacement of the center of mass in the moving direction at the initial moment of the single support stage; Indicates i The displacement of the center of mass in the moving direction at the end of the double support phase; Indicates i+ 1. The angular momentum of the center of mass relative to the supporting leg end at the initial moment of the single support phase; Indicates i The angular momentum of the center of mass relative to the supporting leg end at the end of the double support phase, For the i The actual step length of the step.

[0024] Furthermore, in the movement control method of the legged robot described in the present invention, in step S2, the following steps are included:

[0025] Based on the phase plane diagram, performing one-step cycle gait analysis to obtain one-step cycle gait features;

[0026] Based on the phase plane diagram, a two-step periodic gait analysis is performed to obtain two-step periodic gait features.

[0027] Furthermore, in the movement control method of the legged robot described in the present invention, in step S3, the following steps are included:

[0028] In the case of a one-step cycle gait, based on the one-step cycle gait characteristics, a first expected step length is obtained and a first step length control rate is determined.

[0029] Furthermore, in the movement control method of the legged robot of the present invention, in step S3, the first expected step length is:

[0030]

[0031] in, represents the first expected step length; Indicates the end time of the single support stage L The expected value of L represents the angular momentum of the center of mass relative to the supporting leg end; represents the slope of the end state line; Indicates the duration of the double support phase; m represents the system mass of the legged robot; H Indicates the expected center of mass movement height.

[0032] Furthermore, in the movement control method of the legged robot described in the present invention, in step S3, the following steps are included:

[0033] In the case of a two-step cycle gait, obtaining a second expected step length and a third expected step length based on the two-step cycle gait characteristics;

[0034] A second step size control rate corresponding to the second desired step size is determined, and a third step size control rate corresponding to the third desired step size is determined.

[0035] Furthermore, in the movement control method of the legged robot described in the present invention, the method further includes the following steps:

[0036] A plurality of groups of optional gains are obtained, and a target gain is selected from the plurality of groups of optional gains; and the step length control rate corrects the foothold based on the target gain.

[0037] The beneficial effects of the present invention are as follows: the present invention integrates the theoretical ideas of the hybrid linear inverted pendulum model and the angular momentum linear inverted pendulum model to construct a hybrid angular momentum linear inverted pendulum model. On the one hand, compared with the hybrid linear inverted pendulum model, the hybrid angular momentum linear inverted pendulum model in the present invention can better filter the influence of angular momentum disturbance on the accuracy of the model, thereby improving the mobile control effect of the controller generated based on the model on the legged robot, and narrowing the gap between the model and the real system. On the other hand, compared with the angular momentum linear inverted pendulum model, the hybrid angular momentum linear inverted pendulum model in the present invention has a double support stage, which can form a richer robot walking gait to cope with more complex terrain environments. In addition, the present invention designs the step length control rate based on the dynamic characteristics of the hybrid angular momentum linear inverted pendulum model, which can achieve rapid and stable convergence of the system state under disturbance. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 A flowchart of the steps of the mobile control method according to the present invention in one embodiment;

[0039] Figure 2 It is a schematic diagram of a hybrid angular momentum linear inverted pendulum model in the first embodiment of the movement control method of the present invention;

[0040] Figure 3 It is a schematic diagram of the change of the system state of a one-step periodic gait in the phase plane diagram of the movement control method of the present invention in the first embodiment;

[0041] Figure 4 The convergence of the movement control method of the present invention after the one-step period gait in the first embodiment is disturbed and the first set of gains is selected in the step length control rate;

[0042] Figure 5 This is the convergence condition of the movement control method described in the present invention after a one-step period gait in the first embodiment is disturbed and the second set of gains is selected in the step length control rate. DETAILED DESCRIPTION

[0043] In order to explain the technical content, achieved objectives and effects of the present invention in detail, the following is an explanation in combination with the implementation modes and the accompanying drawings.

[0044] Legged motion has a series of challenges due to its inverted pendulum motion characteristics, such as strong nonlinearity of system dynamics, high control real-time requirements, and discrete interaction between the foot and the ground. Reduced-order models play an important role in legged motion control. Such models simplify the robot system, ignore the inertia of the body and the mass of the legs, and only consider the motion law of the body's center of mass, which greatly saves the cost of control calculation. As the most basic of these reduced-order models, the Linear Inverted Pendulum (LIP) model is widely used in legged motion control, especially bipedal motion control. This model is a planar model consisting of a mass representing the robot body and a massless straight rod representing the robot's supporting leg. One end of the straight rod is connected to the mass, and the other end generates a ground reaction force by contacting the ground to achieve controllable motion of the mass in the sagittal plane. This model usually assumes that the leg rod can be extended and retracted along the length direction, thereby achieving linear motion of the mass at a fixed height along the horizontal direction.

[0045] In recent years, many extension works have been produced based on the linear inverted pendulum model, among which the most concerned ones include the hybrid linear inverted pendulum (H-LIP) model and the angular momentum linear inverted pendulum (ALIP) model. The hybrid linear inverted pendulum model breaks through the limitation of the linear inverted pendulum model that only considers the single support phase (SSP) and adds the double support phase (DSP). Based on the analysis of the phase plane diagram of the single support phase, one-step cycle gait and two-step cycle gait are derived, and they are combined and used in the motion description and control of the legged robot in the sagittal and coronal planes. At the same time, the model can also generate the expected foothold in real time according to the change of the system state to ensure that the center of mass motion converges to the expected trajectory, and achieve stable convergence of the center of mass velocity and position under disturbance.

[0046] However, the hybrid linear inverted pendulum model cannot get rid of the limitations of the linear inverted pendulum model. The linear inverted pendulum model has many challenges in real robot applications because it ignores the change in angular momentum of the body. Based on this, the angular momentum linear inverted pendulum model is derived from the Euler equation, and its superiority in angular momentum disturbance filtering is proved by comparative analysis with the linear inverted pendulum model. Specifically, the model transforms the second state variable, the center of mass velocity, in the linear inverted pendulum model into the angular momentum of the center of mass relative to the end point of the foot touching the ground. Compared with the linear inverted pendulum model, although the model still ignores the change in angular momentum of the body relative to the center of mass, this transformation makes the model closer to the motion description of the real robot system without destroying the linear characteristics of the model. Furthermore, through the control idea of ​​looking one step ahead, the angular momentum linear inverted pendulum model can use the change of the foot landing point to achieve stable convergence of the center of mass velocity. However, the current angular momentum linear inverted pendulum model only considers the single-support leg case and instantaneous supporting leg switching, and lacks discussion of the double-support case, which is not conducive to improving gait diversity and needs further improvement.

[0047] In view of the fact that the existing hybrid linear inverted pendulum model does not consider the change of system angular momentum and deviates far from the real system, and the existing angular momentum linear inverted pendulum model does not consider the double support gait and lacks gait richness, the purpose of the present invention is to: (1) integrate the theoretical ideas of the hybrid linear inverted pendulum model and the angular momentum linear inverted pendulum model, construct a hybrid angular momentum linear inverted pendulum model, and narrow the gap between the model and the real system by considering the change of system angular momentum while maintaining the linear characteristics of the model, and realize rich mobile gaits through the double support stage. (2) Design a motion controller based on the dynamic characteristics of the model to achieve fast and stable convergence of the system state under disturbance.

[0048] Please refer to Figures 1 to 5 The present invention provides a legged robot movement control method based on a hybrid angular momentum linear inverted pendulum model. The movement control method comprises the steps of establishing a hybrid angular momentum linear inverted pendulum model, analyzing a periodic gait based on a phase plane diagram of the hybrid angular momentum linear inverted pendulum model, and designing a step length control rate for maintaining the periodic gait. Specifically, the movement control method comprises the following steps:

[0049] Step S1: obtaining target parameters of the legged robot, and establishing a hybrid angular momentum linear inverted pendulum model based on the target parameters;

[0050] Step S2: performing periodic gait analysis based on the phase plane diagram of the hybrid angular momentum linear inverted pendulum model to obtain periodic gait features;

[0051] Step S3: Based on the periodic gait characteristics, determine the step length control rate to control the movement of the legged robot.

[0052] From the above description, it can be seen that the beneficial effects of the present invention are: the present invention integrates the theoretical ideas of the hybrid linear inverted pendulum model and the angular momentum linear inverted pendulum model to construct a hybrid angular momentum linear inverted pendulum model. Under the premise of maintaining the linear characteristics of the model, the gap between the model and the real system is narrowed by considering the change of the system angular momentum, and a rich mobile gait is achieved through the double support stage. Specifically: (1) Compared with the hybrid linear inverted pendulum model, the hybrid angular momentum linear inverted pendulum model in the present invention can better filter the influence of angular momentum disturbance on the accuracy of the model, thereby improving the mobile control effect of the controller generated based on the model on the legged robot and narrowing the gap between the model and the real system. At the same time, based on the dynamic characteristics of the hybrid angular momentum linear inverted pendulum model, a motion controller is designed (such as designing the step length control rate) to achieve rapid and stable convergence of the system state under disturbance. (2) Compared with the angular momentum linear inverted pendulum model, the hybrid angular momentum linear inverted pendulum model in the present invention has a double support stage, which can form a richer robot walking gait to cope with more complex terrain environments.

[0053] The following combination Figure 1 , each step in steps S1 to S3 and other optional steps are described in detail.

[0054] Step S1, obtaining the target parameters of the legged robot, and establishing a hybrid angular momentum linear inverted pendulum model based on the target parameters of the legged robot. The target parameters include the system parameters and expected gait parameters of the legged robot, the system parameters include gravitational acceleration and system mass, and the expected gait parameters include the expected center of mass movement height. It should be noted that the present invention simplifies the legged robot into a body mass point with all system mass and a massless supporting leg rod, constructs a hybrid angular momentum linear inverted pendulum model that characterizes the system dynamics, realizes the horizontal movement of the system center of mass at the desired height, and allows the single support stage and the double support stage to occur alternately, forming a rich gait.

[0055] In practical applications, the gravitational acceleration, system mass and expected center of mass movement height of the legged robot are first obtained. m represents the system quality of the robot, represents the acceleration due to gravity, H represents the expected center of mass movement height, x represents the displacement of the center of mass in the moving direction, L represents the angular momentum of the center of mass relative to the supporting leg end, with the lower left subscript s Indicates the single support stage, the lower left corner mark D represents the double support stage, TRepresents the duration of the support phase. On this basis, based on the acquired gravitational acceleration, system mass, and expected center of mass movement height of the legged robot, a hybrid angular momentum linear inverted pendulum model is established, and the hybrid angular momentum linear inverted pendulum model includes a single support phase and a double support phase. In the present invention, the hybrid angular momentum linear inverted pendulum model can be characterized by the following equations: the first system dynamics equation in the single support phase; the second system dynamics equation in the double support phase; the first state transfer equation for the system to switch from the single support phase to the double support phase; and the second state transfer equation for the system to switch from the double support phase to the single support phase, wherein:

[0056] The first system dynamic equation corresponding to the single support stage is the same as the existing angular momentum linear inverted pendulum model, that is:

[0057]

[0058] The double support stage system maintains a constant center of mass velocity and angular momentum, and the corresponding second system dynamics equation is:

[0059]

[0060] in, represents the displacement of the center of mass in the moving direction during the single support stage; represents the angular momentum of the center of mass relative to the supporting leg end during the single support phase; represents the first-order differential of the displacement of the center of mass in the moving direction during the single support stage; It represents the first-order differential of the angular momentum of the center of mass relative to the supporting leg end during the single support phase; represents the first-order differential of the displacement of the center of mass in the moving direction during the double support stage; represents the first-order differential of the displacement of the center of mass in the moving direction at the initial moment of the double support stage; represents the first-order differential of the angular momentum of the center of mass relative to the supporting leg end during the double support phase; represents the system mass of the legged robot, represents the acceleration due to gravity, H Indicates the expected center of mass movement height.

[0061] Afterwards, based on the first system dynamics equation, a first analytical solution expression corresponding to the first system dynamics equation is obtained, and based on the second system dynamics equation, a second analytical solution expression corresponding to the second system dynamics equation is obtained; wherein the first analytical solution expression is:

[0062]

[0063] The second analytical solution expression is:

[0064]

[0065] Among them, SSP represents the single support stage; DSP represents the double support stage; t Indicates time; Indicates the single support stage x Based on time variables t The function of x represents the displacement of the center of mass in the moving direction; represents the displacement of the center of mass in the moving direction at the initial moment of the single support stage; represents the time of the initial moment of the single support phase; It represents the angular momentum of the center of mass relative to the supporting leg end at the initial moment of the single support stage; Indicates the single support stage L Based on time variables t The function of L represents the angular momentum of the center of mass relative to the supporting leg end; represents the hyperbolic cosine function; represents the hyperbolic sine function; Indicates the double support stage x Based on time variables t The function of x represents the displacement of the center of mass in the moving direction; represents the displacement of the center of mass in the moving direction at the initial moment of the double support stage; represents the angular momentum of the center of mass relative to the supporting leg end at the initial moment of the double support stage; represents the time of the initial moment of the double support phase; Indicates the double support stage L Based on time variables t The function of L represents the angular momentum of the center of mass relative to the supporting leg end; is the intermediate variable, ; m represents the quality of the robot system, It should be noted that the first analytical solution expression and the second analytical solution expression are another expression of the single and double support stages of the proposed hybrid angular momentum linear inverted pendulum model, which can be used to subsequently derive periodic gait characteristics and step length control rate. and The value of can be obtained based on the above first analytical solution expression and the second analytical solution expression. At the same time, the expression of the corresponding expected step length can also be derived using the above first analytical solution expression and the second analytical solution expression.

[0066] Therefore, based on the principle of conservation of angular momentum, the first state transfer equation for the system to switch from the single support stage to the double support stage is:

[0067]

[0068] The second state transition equation for the system to switch from the double support stage to the single support stage is:

[0069]

[0070] Among them, SSP represents the single support stage; DSP represents the double support stage; Indicates i The displacement of the center of mass in the moving direction at the initial moment of the double support stage; Indicates i The displacement of the center of mass in the moving direction at the end of the single support phase; Indicates i The angular momentum of the center of mass relative to the supporting leg end at the initial moment of the double support phase of the step; Indicates i The angular momentum of the center of mass relative to the supporting leg end at the end of the single support phase of the step; Indicates i+ 1. Displacement of the center of mass in the moving direction at the initial moment of the single support stage; Indicates i The displacement of the center of mass in the moving direction at the end of the double support phase; Indicates i+ 1. The angular momentum of the center of mass relative to the supporting leg end at the initial moment of the single support phase; Indicates i The angular momentum of the center of mass relative to the supporting leg end at the end of the double support phase, For the i The actual step length of the step. In the subsequent description, if the lower right subscript indicating the number of steps is omitted, it means that all variables are for the same step. The above-mentioned principle of conservation of angular momentum means that when a system (such as a legged robot) is not subjected to external torque or the sum of the external torques is zero, the angular momentum of the system remains unchanged.

[0071] Step S2, performing periodic gait analysis based on the phase plane diagram of the hybrid angular momentum linear inverted pendulum model to obtain periodic gait features.

[0072] Ideal legged motion is usually a cycle of periodic gaits. Finding periodic gaits is important for the stable control of legged motion. The mixed angular momentum linear inverted pendulum model is a staged second-order linear system. The phase plane diagram, as an important tool for analyzing second-order linear systems, can reveal the law of system state changes, assist in finding periodic gaits, and provide guidance for the design of corresponding controllers.

[0073] The hybrid angular momentum linear inverted pendulum model proposed in the present invention mainly focuses on the phase plane diagram of the single support stage because the system state changes in the double support stage are relatively simple. In the present invention, the phase plane diagram of the single support stage can be constructed based on the first system dynamics equation obtained in the above step S1, so that the periodic gait analysis can be performed based on the phase plane diagram of the single support stage to obtain the corresponding periodic gait characteristics. The first system dynamics equation corresponding to the single support stage is a linear autonomous system. According to its eigenvalue The corresponding eigenvector is For the convenience of expression, , is an intermediate variable with no specific physical meaning. Therefore, the phase plane diagram of the single support stage shows the characteristics of a saddle point, which is separated by two eigenvector lines. It is divided into four areas: up, down, left and right.

[0074] The periodic gait analysis of the present invention mainly focuses on one-step periodic gait and two-step periodic gait.

[0075] Based on the phase plane diagram of the single support stage, a periodic gait analysis is performed on the one-step periodic gait, and the specific analysis is as follows: For the one-step periodic gait, since the angular momentum of the double support stage remains unchanged, it must have the characteristic that the angular momentum is equal at the beginning and end of the single support stage. Therefore, a horizontal angular momentum line can be drawn on the phase plane diagram of the single support stage to represent the angular momentum value of the double support stage. For this type of periodic gait, the system state must start from a point on the straight line, leave the straight line under the action of system dynamics, and return to another point on the straight line through the flow of the phase plane diagram as the end state of the single support stage. In the subsequent double support stage, the system will maintain the size of the angular momentum and only change the horizontal displacement, that is, continue to move forward along the horizontal angular momentum line until the next single support stage begins, and the system state instantly switches to the initial state of the gait.

[0076] Based on the above-mentioned periodic gait analysis of the phase plane diagram of the single support stage, in order to find a suitable initial system state for a one-step periodic gait, the present invention uses , according to the first system dynamics equation, we can get:

[0077]

[0078] in, is the duration of the single support phase; It represents the angular momentum of the center of mass relative to the supporting leg end at the end of the single support phase; The time indicating the end of the single support phase; The time representing the initial moment of the single support phase.

[0079] make ,in The slope of the end state line indicates that the one-step gait characteristics can be inferred, which are as follows: The initial state of the system Located at the initial state line Similarly, the end state of the single support stage can also be obtained At the end state line It should be pointed out that due to Therefore, the initial state line and the final state line are always sandwiched between the two eigenvector lines in the upper and lower regions of the phase plane, that is, the initial and final states of the system in a one-step periodic gait must be located in the upper or lower region of the phase plane at the same time.

[0080] Based on the phase plane diagram of the single support stage, the two-step periodic gait is analyzed. The specific analysis is as follows: For the two-step periodic gait, two horizontal lines can be drawn on the phase plane diagram of the single support stage to represent the different angular momentum values ​​of the two double support stages in one cycle. In order to maintain generality, one of the lines is defined as angular momentum line 1 and the other as angular momentum line 2. For this type of periodic gait, the system state starts from a point on angular momentum line 1, leaves the line in the first single support stage and reaches a point on angular momentum line 2 through the flow of the phase plane diagram, and then goes along angular momentum line 2 to another point on the line during the first double support stage, which is the starting point of the second step. In the second single support stage, the system state leaves angular momentum line 2 again and returns to a point on angular momentum line 1 through the flow of the phase plane diagram, and finally goes through the second double support stage and returns to the starting point of the first step along angular momentum line 1, completing a two-step periodic gait. For this type of gait, the single support phase of each step must occur in an upper, lower, left, or right area in the phase plane, but the two single support phases in the same cycle can occur in different areas respectively. Therefore, a rich two-step periodic gait can be obtained through permutations and combinations.

[0081] Therefore, based on the above two-step cycle gait analysis of the phase plane diagram of the single support stage, for the single support stage of the first step in the two-step cycle gait (i.e., the first single support stage), the present invention uses , and according to the first system dynamics equation we can get:

[0082]

[0083] in, Based on the angular momentum lines 1 and 2 on the phase plane diagram This special case of axisymmetric setup, is a bias, indicating that there are countless possibilities for angular momentum line 2 relative to angular momentum line 1. and It can be inferred that in the single support phase of the first step of the two-step cycle gait, the two-step cycle gait characteristics can be as follows: The initial state of the first step of the system Located at the initial state line Similarly, we can get the final state of the first step of the system At the end state line It should be pointed out that The special case of this is applicable to standing still with an average speed of zero.

[0084] It should be noted that represents the hyperbolic tangent function; represents the first single support phase in the two-step gait at the initial moment L ; represents the first single support phase in the two-step gait at the end time L ; represents the duration of the first single-support phase in a two-step gait cycle; represents the first single support phase in the two-step gait at the initial moment x ; represents the first single support phase in the two-step gait at the end time x ; represents the slope of the end state line of the first step in a two-step cycle gait; It is an intermediate variable and has no clear physical meaning.

[0085] For the single support phase of the second step in the two-step cycle gait (i.e., the second single support phase), the system also has the initial state Located at the initial state line Up, end state At the end state line In order to narrow the scope of investigation and simplify the control, the duration of the single support phase is set to be equal, that is, Therefore, based on the angular momentum line 1 , angular momentum line 2 As well as the first and second system dynamics equations and the first and second state transfer equations, we can get:

[0086]

[0087] That is, in order to make the duration of the single support phase in the two-step cycle gait equal, the system state changes in the two single support phases need to be about L In this case, we can make , so in the single support phase of the second step in the two-step cycle gait, the two-step cycle gait characteristics can be as follows: the initial state line and the end state line of each step of the system are and It should be pointed out that due to and The initial state of the first step of the system can be located in the upper and lower parts or the left and right areas of the phase plane, forming two types of two-step periodic gaits with slightly different styles.

[0088] It should be noted that represents the second single support phase in the two-step gait at the initial moment x ; represents the second single support phase in the two-step gait at the end time x ; represents the slope of the end state line of any step after unification in the two-step cycle gait; represents the slope of the end state line of the second step in a two-step cycle gait; represents the second single support phase in the two-step gait at the initial moment L ; represents the second single support phase in the two-step gait at the end time L ; Represents the duration of the second single-stance phase in a two-step gait cycle.

[0089] Step S3, based on the periodic gait characteristics, determine the step length control rate, so as to control the movement of the legged robot based on the step length control rate. In practical applications, the step length control rate will be designed based on the periodic gait characteristics in step S2 to ensure that the system state can quickly and stably converge back to the periodic gait after deviating from the periodic gait.

[0090] For a one-step cycle gait, based on the above one-step cycle gait characteristics, its expected step length (i.e., the first expected step length) can be obtained as:

[0091]

[0092] in, represents the duration of the double support phase, represents the expected step length in a one-step gait (i.e., the first expected step length); Indicates the end time of the single support stage L Expected value; Represents the slope of the end state line.

[0093] Correspondingly, based on the first desired step length, the designed first step length control rate is:

[0094]

[0095] in, represents the step length control rate under one-step gait (i.e., the first step length control rate), and represents the state error at the end of the single support stage, and For the control gain (i.e., gain), based on the above one-step cycle gait characteristics and the first step length control rate, it can be deduced that:

[0096]

[0097] The above expression represents the transfer relationship between the error of the system state at the end of the i+1th step and the error of the system state at the end of the ith step. The error should converge (tend to zero) to ensure the stability of the system periodic gait, that is, the matrix on the right side of the equal sign is all zeros. However, it is impossible to achieve all zeros in practice, so there are two sets of gain values, that is, to ensure that there are at least three zeros and the absolute value of the other non-zero term is less than 1 to ensure convergence.

[0098] It should be noted that represents the displacement of the center of mass in the moving direction at the end of the i-th single support stage; Indicates the end time of the single support stage x Expected value; Indicates i The angular momentum of the center of mass relative to the supporting leg end at the end of the single support phase of the step; Indicates the end time of the single support stage L Expected value; It represents the error between the displacement of the center of mass in the moving direction at the end of the i+1th single support stage and the expected value; It represents the error between the angular momentum of the center of mass relative to the supporting leg end and the expected value at the end of the i+1th single support phase.

[0099] In order to make the above expression and tend to zero, let and (i.e. the first set of gains), and then the transfer equation of the system state error after the first set of gains is obtained:

[0100]

[0101] According to the above formula, it can be inferred that after the first step length control rate selects the first set of gains (that is, selects the first set of gains as the target gains) to correct the foothold, the convergence effect is as follows: can converge to a periodic gait after one step, while because It needs to converge gradually to a periodic gait, that is, the position of the first step converges and the speed converges gradually.

[0102] You can also and (i.e. the second set of gains), and then the transfer equation of the system state error after the second set of gains is obtained:

[0103]

[0104] According to the above formula, it can be inferred that after the first step length control rate selects the second set of gains (that is, selects the second set of gains as the target gains) to correct the foothold, the convergence effect is as follows: can converge to a periodic gait after two steps, while It can converge to a periodic gait after one step, that is, the speed converges in the first step and the position converges in the second step.

[0105] For the two-step cycle gait, based on the two-step cycle gait characteristics corresponding to the single support phase of the first step in the above two-step cycle gait, the expected step length of the first step (i.e., the second expected step length) can be obtained as:

[0106]

[0107] Based on the two-step cycle gait characteristics corresponding to the single support phase of the second step in the above two-step cycle gait, the expected step length of the second step (i.e., the third expected step length) is:

[0108]

[0109] Similarly, based on the second desired step length, the step length control rate of the first step (i.e., the second step length control rate) is designed as:

[0110]

[0111] And based on the third expected step length, the step length control rate of the second step (i.e., the third step length control rate) can be determined as:

[0112]

[0113] Based on the above second step control rate and third step control rate, the convergence of the first and second steps in the two-step periodic gait can be deduced, where the transfer relationship between the system state error of the second step in the i-th cycle and the system state error of the first step in the i-th cycle is:

[0114] Among them, the transfer relationship between the system state error of the first step in the i+1th cycle and the system state error of the second step in the i-th cycle is:

[0115]

[0116] Then, two sets of optional gains and corresponding convergence effects that are the same as those of the one-step periodic gait are obtained; and due to symmetry, the values ​​of the control gains in the two-step periodic gait do not change with the odd and even steps in the same cycle.

[0117] Specifically, the two sets of optional gains for the two-step periodic gait and the corresponding convergence effects are as follows:

[0118] The first group gain is and , when the first set of gains is selected as the target gains, the transfer equation corresponding to the system state error is:

[0119]

[0120] According to the above formula, it can be inferred that after the step length control rate in the two-step periodic gait (including the second step length control rate and the third step length control rate) selects the first set of gains to correct the foothold in the current step, the convergence effect is as follows: can converge to a periodic gait after one step, while because It needs to converge gradually to a periodic gait, that is, the first step position converges and the speed converges gradually;

[0121] Among them, the second group gain is and , when the second set of gains is selected as the target gains, the transfer equation corresponding to the system state error is:

[0122]

[0123] According to the above formula, it can be inferred that after the step length control rate in the two-step periodic gait (including the second step length control rate and the third step length control rate) selects the second set of gains to correct the foothold in the current step, the convergence effect is as follows: can converge to a periodic gait after two steps, while It can converge to a periodic gait after one step, that is, the speed converges in the first step and the position converges in the second step.

[0124] It should be noted that the above is the expected step length of the first step in a two-step gait; is the expected step length of the second step in a two-step cycle gait; is the step length control rate of the first step in the two-step cycle gait, is the step length control rate of the second step in the two-step cycle gait; represents the first single support phase in the two-step gait at the end time L Expected value; represents the second single support phase in the two-step gait at the end time L Expected value; It represents the error between the displacement of the center of mass in the moving direction at the end of the first single support phase of the i-th cycle in the two-step cycle gait and the expected value; It represents the error between the displacement of the center of mass in the moving direction and the expected value at the end of the second single support phase of the i-th cycle in the two-step cycle gait; It represents the error between the angular momentum of the center of mass relative to the supporting leg end and the expected value at the end of the first single support phase of the i-th cycle in the two-step gait; It represents the error between the angular momentum of the center of mass relative to the supporting leg end and the expected value at the end of the second single support phase of the i-th cycle in the two-step cycle gait; It represents the error between the displacement of the center of mass in the moving direction and the expected value at the end of the first single support phase of the i+1th cycle in the two-step cycle gait; It represents the error between the angular momentum of the center of mass relative to the supporting leg end and the expected value at the end of the first single support phase of the i+1th cycle in the two-step cycle gait; represents the first step in a two-step gait Gain; represents the first step in a two-step gait Gain; represents the second step in a two-step cycle gait Gain; represents the second step in a two-step cycle gait Gain.

[0125] In summary, the present invention proposes a method for controlling the movement of a legged robot, aiming to improve the performance of the legged robot in fast and stable convergence to a periodic gait after being disturbed under rich gaits through a hybrid angular momentum linear inverted pendulum model. In addition, it should be pointed out that: (1) The present invention is based on horizontal ground and is also applicable to terrains where adjacent contact points are not on the same horizontal plane, such as rugged roads, slopes, steps, etc., after making corresponding modifications. (2) The present invention is applicable to the situation where different types of legged robot platforms such as bipeds, quadrupeds, and hexapods move through two equivalent virtual legs. It is only necessary to equate multiple legs that touch the ground in the same phase to one virtual leg. (3) The hybrid angular momentum linear inverted pendulum model proposed in the present invention is applicable to the center of mass motion control of the legged robot in two typical two-dimensional planes, the sagittal plane and the coronal plane, as well as the center of mass motion control in any two-dimensional plane linearly related to these two planes. (4) The present invention requires real-time knowledge of the relative position and velocity of the robot's center of mass relative to the supporting leg end. These system state quantities can be obtained through various onboard sensors and state estimation algorithms. (5) The present invention proposes the characteristics of the dynamic phase plane diagram of the one-step periodic gait and the two-step periodic gait based on the hybrid angular momentum linear inverted pendulum model, as well as the corresponding expected step length calculation method. (6) The present invention proposes a step length control rate based on the hybrid angular momentum linear inverted pendulum model, which changes the actual step length by updating the next footfall point in real time, thereby achieving rapid and stable convergence of the system state under disturbance. (7) The step length control rate proposed in the present invention simultaneously considers the state errors of position and velocity (angular momentum), and has a better convergence speed than the forward-looking one-step control method based on the angular momentum linear inverted pendulum model and the optimal control gain method based on the hybrid linear inverted pendulum model, because the former only considers the state error of angular momentum, while the latter can actually only achieve asymptotic convergence. In addition, the step length control rate proposed in the present invention has multiple sets of optional gains, which can be selected and used as needed.

[0126] Please refer to Figures 1 to 5 , Embodiment 1 of the present invention is: This embodiment realizes the horizontal movement of the mixed angular momentum linear inverted pendulum model along the front-back direction in the sagittal plane through a one-step periodic gait, aiming to realize the forward and backward movement of the legged robot, as follows:

[0127] (1) The schematic diagram of the mixed angular momentum linear inverted pendulum model is as follows Figure 2 The model consists of a body mass point and two massless straight legs. The mass of the mass point is m , at a height of H The horizontal direction is x Axis direction, forward is positive; vertical direction is zAxis direction, upward is positive. Movement is divided into single support phase and double support phase, where single and double support refers to the number of legs touching the ground at the same time. Single and double support phases are performed alternately, and the switching between phases is completed instantly, thus achieving continuous movement of the system.

[0128] (2) Figure 3 The figure shows the phase plane diagram of a biped robot in the single support stage and the system state change trajectory of a typical one-step gait cycle. , , , There are two straight lines on the phase plane, which are the initial state line and the final state line of the system. The system state starts from the initial state line, flows along the solid line ① in the phase plane, goes through the single support stage to reach the final state line, and then enters the double support stage, flows along the solid line ① parallel to the axis, and finally flows along the solid line ① at the end of the double support stage. Figure 3 The dotted line in the figure switches back to the initial state line instantly, ending the current cycle.

[0129] (3) Figure 4 The figure shows the convergence effect of a one-step periodic gait after the system state is disturbed, using the step length control rate proposed in the present invention to select the first set of gains in the current step to start the foot point correction, that is, the first step position convergence and speed asymptotic convergence. Figure 5 The figure shows the convergence effect of a one-step periodic gait after the system state is disturbed, using the step length control rate proposed in the present invention to select the second set of gains in the current step to start the foot point correction, that is, the first step speed convergence and the second step position convergence.

[0130] The second embodiment of the present invention is: This embodiment realizes the horizontal movement of the mixed angular momentum linear inverted pendulum model along the left and right directions in the coronal plane through a one-step periodic gait, aiming to realize the left and right movement of the legged robot with crossed legs. Compared with the first embodiment, the difference lies in the coronal plane control for bipedal movement.

[0131] Embodiment three of the present invention is: This embodiment utilizes a two-step periodic gait to realize horizontal movement of a mixed angular momentum linear inverted pendulum model in the front-to-back direction in the sagittal plane, aiming to realize the legged robot walking in place or forward and backward without crossing its legs. Compared with embodiment one, the difference is that a two-step periodic gait is used in the sagittal plane.

[0132] Embodiment 4 of the present invention is: This embodiment utilizes a two-step periodic gait to realize horizontal swinging of a mixed angular momentum linear inverted pendulum model along the left and right directions in the coronal plane, aiming to realize the legged robot's stepping on the spot or moving left and right without crossing the legs. Compared with embodiment 1, the difference is that a two-step periodic gait is used in the coronal plane.

[0133] Embodiment five of the present invention is: This embodiment combines the use of a one-step cycle gait and a two-step cycle gait to respectively realize the movement of a mixed angular momentum linear inverted pendulum model in the sagittal plane and the coronal plane along the front-to-back and left-to-right directions, aiming to realize rich moving gaits of a legged robot. Compared with embodiment one, the difference is that a one-step cycle gait and a two-step cycle gait are comprehensively used in the sagittal plane and the coronal plane.

[0134] Embodiment six of the present invention is: This embodiment applies the movement control based on the mixed angular momentum linear inverted pendulum model to a quadruped robot. Compared with embodiment one, the difference lies in that two groups of supporting legs need to be formed during the movement of the quadruped robot. The supporting legs in the same group are in the same phase and work together to form a virtual supporting leg to achieve single support. The two virtual legs formed by the two groups of supporting legs achieve double support.

[0135] Embodiment seven of the present invention is: This embodiment applies the movement control based on the mixed angular momentum linear inverted pendulum model to a hexapod robot. Compared with embodiment one, the difference lies in that two groups of supporting legs need to be formed during the movement of the hexapod robot. The supporting legs in the same group have the same phase and work together to form a virtual supporting leg to achieve single support. The two virtual legs formed by the two groups of supporting legs achieve double support.

[0136] In summary, the present invention provides a method for controlling the movement of a legged robot: (1) The theoretical ideas of the hybrid linear inverted pendulum model and the angular momentum linear inverted pendulum model are integrated to construct a hybrid angular momentum linear inverted pendulum model. Under the premise of maintaining the linear characteristics of the model, the gap between the model and the real system is narrowed by considering the change of the system angular momentum, and a rich movement gait is achieved through the double support stage. On this basis, a motion controller is designed based on the dynamic characteristics of the hybrid angular momentum linear inverted pendulum model to achieve rapid and stable convergence of the system state under disturbance. (2) The hybrid angular momentum linear inverted pendulum model in the present invention is derived based on the angular momentum linear inverted pendulum model. Compared with the hybrid linear inverted pendulum model, although both are reduced-order models and are highly simplified versions of the real robot system, the angular momentum linear inverted pendulum model can better filter the influence of angular momentum disturbance on the accuracy of the model, thereby improving the movement control effect of the controller generated based on the hybrid angular momentum linear inverted pendulum model on the legged robot. (3) The hybrid angular momentum linear inverted pendulum model in the present invention is derived based on the hybrid linear inverted pendulum model. Compared with the angular momentum linear inverted pendulum model, it has a double support stage, and further provides a control method for a one-step periodic gait and a two-step periodic gait, which can form a richer robot walking gait to cope with a more complex terrain environment. (4) The step length control rate proposed in the present invention considers the state errors of position and velocity (angular momentum) at the same time. Compared with the forward-looking one-step control method based on the angular momentum linear inverted pendulum model and the optimal control gain method based on the hybrid linear inverted pendulum model, the convergence speed is better, because the former only considers the state error of angular momentum, while the latter can only achieve asymptotic convergence. In addition, the step length control rate proposed in the present invention has multiple sets of optional gains, which can be selected and used as needed. (5) The present invention aims to improve the performance of legged robots in fast and stable convergence to periodic gaits after being disturbed under rich gaits through the hybrid angular momentum linear inverted pendulum model. The present invention simplifies the legged robot into a body mass point with all system mass and a massless supporting leg rod, constructs a hybrid angular momentum linear inverted pendulum model that characterizes the system dynamics, realizes the horizontal movement of the system center of mass at a desired height, and allows single support and double support stages to occur alternately, forming a rich gait. In addition, the present invention proposes a step length control rate based on the hybrid angular momentum linear inverted pendulum model, which changes the actual step length by updating the next footfall point in real time, thereby achieving rapid and stable convergence of the system state under disturbance.

[0137] The above descriptions are merely embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent transformations made using the contents of the present invention's specification and drawings, or directly or indirectly applied in related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A method for controlling movement of a legged robot, characterized in that: The following steps are involved: S1: obtaining target parameters of the legged robot, and establishing a hybrid angular momentum linear inverted pendulum model based on the target parameters; S2: performing periodic gait analysis based on the phase plane diagram of the hybrid angular momentum linear inverted pendulum model to obtain periodic gait features, wherein the periodic gait features include one-step periodic gait features and two-step periodic gait features; S3: determining a step length control rate based on the periodic gait characteristics, so as to control the movement of the legged robot according to the step length control rate; In step S1, a hybrid angular momentum linear inverted pendulum model is established based on the target parameters, including the following steps: Based on the target parameters, constructing a first system dynamics equation of the legged robot in a single-support stage and a second system dynamics equation of the legged robot in a double-support stage respectively; Based on the principle of conservation of angular momentum, a first state transfer equation for switching from the single support stage to the double support stage is obtained, and a second state transfer equation for switching from the double support stage to the single support stage is obtained; In step S2, the following steps are included: based on the phase plane diagram, performing a one-step cycle gait analysis to obtain a one-step cycle gait feature; based on the phase plane diagram, performing a two-step cycle gait analysis to obtain a two-step cycle gait feature; In step S3, the following steps are included: in the case of a one-step cycle gait, based on the one-step cycle gait feature, obtaining a first expected step length and determining a first step length control rate; The first expected step length is: in, represents the first expected step length; represents the slope of the end state line; Indicates the duration of the double support phase; m represents the system mass of the legged robot; H Indicates the expected center of mass movement height.

2. The movement control method of the legged robot according to claim 1, characterized in that: In step S1, the target parameters include: system parameters and expected gait parameters of the legged robot; wherein the system parameters include gravitational acceleration and system mass, and the expected gait parameters include expected center of mass movement height.

3. The movement control method of the legged robot according to claim 1, characterized in that: In step S1, the first system dynamics equation is: The second system dynamics equation is: in, represents the displacement of the center of mass in the moving direction during the single support stage; represents the angular momentum of the center of mass relative to the supporting leg end during the single support phase; represents the first-order differential of the displacement of the center of mass in the moving direction during the single-support stage; It represents the first-order differential of the angular momentum of the center of mass relative to the supporting leg end during the single support phase; represents the first-order differential of the displacement of the center of mass in the moving direction during the double support stage; represents the first-order differential of the displacement of the center of mass in the moving direction at the initial moment of the double support stage; represents the first-order differential of the angular momentum of the center of mass relative to the supporting leg end during the double support phase; represents the system mass of the legged robot, represents the acceleration due to gravity, H Indicates the expected center of mass movement height.

4. The movement control method of the legged robot according to claim 1, characterized in that: In step S1, the first state transfer equation is: The second state transfer equation is: in, represents the first state transfer equation, represents the second state transfer equation, where SSP represents the single support stage and DSP represents the double support stage; Indicates i The displacement of the center of mass in the moving direction at the initial moment of the double support stage; Indicates i The displacement of the center of mass in the moving direction at the end of the single support phase; Indicates i The angular momentum of the center of mass relative to the supporting leg end at the initial moment of the double support phase of the step; Indicates i The angular momentum of the center of mass relative to the supporting leg end at the end of the single support phase of the step; Indicates i+ 1. Displacement of the center of mass in the moving direction at the initial moment of the single support stage; Indicates i The displacement of the center of mass in the moving direction at the end of the double support phase; Indicates i+ 1. The angular momentum of the center of mass relative to the supporting leg end at the initial moment of the single support phase; Indicates i The angular momentum of the center of mass relative to the supporting leg end at the end of the double support phase, For the i The actual step length of the step.

5. The movement control method of the legged robot according to claim 1, characterized in that: In step S3, the following steps are included: In the case of a two-step cycle gait, obtaining a second expected step length and a third expected step length based on the two-step cycle gait characteristics; A second step size control rate corresponding to the second desired step size is determined, and a third step size control rate corresponding to the third desired step size is determined.

6. The movement control method of the legged robot according to claim 1, characterized in that: The method further comprises the following steps: A plurality of groups of optional gains are obtained, and a target gain is selected from the plurality of groups of optional gains; and the step length control rate corrects the foothold based on the target gain.

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