Biped robot gait planning method and device for step terrain

Abstract

The invention provides a biped robot gait planning method and device for a step terrain, and belongs to the technical field of robot gait planning, the method comprises the following steps: based on a linear inverted pendulum model, respectively establishing walking modes of an upper step and a lower step of a biped robot; based on a walking mode, mapping the linear inverted pendulum model under the step terrain into a segmented virtual height linear inverted pendulum model under the plane terrain; based on a segmented virtual height linear inverted pendulum model, gait planning of the biped robot under the stepped terrain is achieved through model prediction control. According to the biped robot gait planning method and device for the step terrain, the linear inverted pendulum model with the virtual centroid height is used, the gait mode is established according to the terrain elevation information and the landing point information of the step environment, and the method and device can adapt to the irregular step terrain with the variable height and the variable length; and the gait has good terrain adaptability.

Description

Technical Field

[0001] The present invention relates to the technical field of robot gait planning, and in particular to a method and device for gait planning of a bipedal robot for stepped terrain. Background Art

[0002] Due to the multiple degrees of freedom of bipedal robots, there are frequent mechanical interactions between them and the physical environment during movement, which leads to the high nonlinearity and strong coupling of the mathematical model of their walking process, making it difficult to control. By drawing on the characteristics of human walking, the bipedal robot is abstracted into a simplified physical model, and the walking mode of the bipedal robot is mathematically described, which can effectively simplify the kinematic and dynamic models of the bipedal robot, facilitate motion planning, and reduce the difficulty of control.

[0003] The Linear Inverted Pendulum Model (LIPM) gathers the mass of the whole body of the bipedal robot to a center of mass point, and the center of mass interacts with the ground through an actively retractable massless pendulum. Its characteristic is that the height of the center of mass remains unchanged, so the center of mass dynamic equation becomes linearized during the gait. The stability of the bipedal robot gait can be measured by the zero moment point (ZMP). When it is located in the robot support domain, the robot gait can be considered to be in a stable state. Based on the center of mass dynamic equation of the linear inverted pendulum model, the linear model predictive control (MPC) is introduced, and the real-time rolling optimization solution is used to constrain the robot's zero moment point in the support domain, which can realize the online planning of the bipedal robot gait.

[0004] Traditional predictive control methods based on linear inverted pendulum models are used to implement gait planning of bipedal robots on flat terrains, and cannot be further applied to stepped terrains in the three-dimensional world. However, there are many ups and downs in the actual environment, so the traditional predictive control methods based on linear inverted pendulum models limit the application of bipedal robots in actual environments. Summary of the invention

[0005] The present invention provides a gait planning method and device for a bipedal robot on stepped terrain, so as to solve the defect that a conventional predictive control method based on a linear inverted pendulum model limits the application of the bipedal robot in a practical environment.

[0006] In a first aspect, the present invention provides a biped robot gait planning method for stepped terrain, including: establishing walking patterns for the biped robot to climb up and down steps respectively based on a linear inverted pendulum model; mapping the linear inverted pendulum model under stepped terrain to a segmented virtual height linear inverted pendulum model under planar terrain based on the walking patterns; and realizing gait planning for the biped robot under stepped terrain by using model predictive control based on the segmented virtual height linear inverted pendulum model.

[0007] In a second aspect, the present invention further provides a biped robot gait planning device for stepped terrain, including: A first processing module for establishing walking patterns for the biped robot to climb up and down steps respectively based on a linear inverted pendulum model; A second processing module for mapping the linear inverted pendulum model under stepped terrain to a segmented virtual height linear inverted pendulum model under planar terrain based on the walking patterns; A third processing module for realizing gait planning for the biped robot under stepped terrain by using model predictive control based on the segmented virtual height linear inverted pendulum model.

[0008] In a third aspect, the present invention provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the steps of the biped robot gait planning method for stepped terrain as described in any one of the above are implemented.

[0009] In a fourth aspect, the present invention further provides a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the biped robot gait planning method for stepped terrain as described in any one of the above are implemented.

[0010] In a fifth aspect, the present invention further provides a computer program product, including a computer program, characterized in that when the computer program is executed by a processor, the steps of the biped robot gait planning method for stepped terrain as described in any one of the above are implemented.

[0011] The biped robot gait planning method and device for stepped terrain provided by the present invention have the following beneficial effects compared with the prior art: (1) The present invention uses a linear inverted pendulum model with a virtual center-of-mass height, and the gait pattern established based on the terrain elevation information and foot landing point information of the stepped environment can adapt to irregular stepped terrains with variable heights and lengths, making the gait have better terrain adaptability.

[0012] (2) The linear inverted pendulum model of the virtual centroid height proposed by the present invention mainly realizes the gait planning for the biped robot to walk straight forward; combined with the omnidirectional foot landing point planning and the coordinate transformation matrix, the method proposed by the present invention has the potential to realize omnidirectional walking on a three-dimensional stepped terrain.

[0013] (3) Under the proposed gait pattern, the present invention uses model predictive control to plan the gait trajectories of the biped robot in the forward and vertical directions through an optimization problem, avoiding the kinematic constraints caused by separately optimizing and solving in the two directions, and can shorten the solution time, which is beneficial to the real-time performance of gait planning.

[0014] (4) The stepped terrain gait planning method proposed by the present invention, according to the actual state of the robot, constrains the zero moment point of the robot into the support domain through quadratic optimization solution, ensuring the stability of the walking state of the biped robot and having a certain anti-external force interference performance. Description of the Drawings

[0015] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the drawings required for use in the embodiments or the description of the prior art. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0016] Figure 1 It is a schematic diagram of the walking mode during the up-step process provided by the present invention; Figure 2 It is a schematic diagram of the walking mode during the down-step process provided by the present invention; Figure 3 It is a schematic diagram of the virtual height linear inverted pendulum model provided by the present invention; Figure 4 It is a schematic diagram of the segmented virtual height linear inverted pendulum walking mode provided by the present invention; Figure 5 It is a schematic diagram of the structure of the biped robot gait planning device for stepped terrain provided by the present invention; Figure 6 It is a schematic diagram of the centroid state curve in the sagittal plane when the biped robot of the present invention moves on a stepped terrain; Figure 7 It is a schematic diagram of the centroid state curve in the coronal plane when the biped robot of the present invention moves on a stepped terrain; Figure 8 It is a simulation frame diagram of the biped robot walking in a stepped environment using the gait planning method proposed by the present invention; Figure 9 It is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed implementation manners

[0017] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions in the present invention will be clearly and completely described below with reference to the accompanying drawings in the present invention. Obviously, the described embodiments are some but not all of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present invention without creative efforts shall fall within the protection scope of the present invention.

[0018] It should be noted that in the description of the embodiments of the present invention, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements but also includes other elements not explicitly listed, or further includes elements inherent to such process, method, article or device. Without further limitations, an element defined by the phrase "including one..." does not exclude the existence of additional identical elements in the process, method, article or device including the said element. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0019] The terms "first", "second", etc. in the present application are used to distinguish similar objects and are not used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged under appropriate circumstances so that the embodiments of the present application can be implemented in an order other than those illustrated or described herein, and the objects distinguished by "first", "second", etc. are generally of the same category and do not limit the number of objects. For example, the first object can be one or multiple.

[0020] The following is combined with Figures 1 - 9 Describe the biped robot gait planning method and device for stepped terrain provided by the embodiments of the present invention.

[0021] The biped robot gait planning method for stepped terrain provided by the present invention includes but is not limited to the following steps: Step 101: Based on the linear inverted pendulum model, establish the walking modes of the biped robot for ascending and descending stairs respectively.

[0022] In the coronal plane, inspired by the process of a human ascending and descending stairs, the present invention proposes the walking modes of a biped robot in the ascending and descending stair environments based on the linear inverted pendulum model.

[0023] During the up - stair process, the biped robot first uses the foot on the previous step as the support foot, and the other foot as the swing foot. After stepping the swing foot onto the next step, it then uses the foot on the next step as the support foot to lift the center of mass by the height between two steps. The original support foot on the previous step becomes the swing foot and swings to the step before the previous one, and so on in a cycle. Therefore, based on the linear inverted pendulum model, a walking pattern during the up - stair process is proposed as follows Figure 1 as shown Figure 1 in the schematic diagram of the walking pattern during the up - stair process provided by the present invention: wherein, the dark circle represents the center of mass, the triangle represents the support foot, H i is the height difference between the step where the current support foot is located and the previous step, Θ i is the angle between the line connecting the current landing point and the previous landing point and the horizontal plane, G is the total gravity of the robot, L i is the horizontal distance between the current landing point and the previous landing point, and h is the height of the center of mass under the flat terrain. In this walking pattern, when the support foot is on the i - th step and the swing leg steps towards the (i + 1)-th step, during this process, the center of mass rises by the height H i , moves forward by L i , that is, the angle between the center - of - mass trajectory of the linear inverted pendulum and the horizontal plane at this stage is Θ i , ensuring that the height difference between the center of mass and the support foot at the moment before each switch of the support foot is equal to h.

[0024] The down - stair process is exactly the opposite of the up - stair process. The biped robot first lowers the center of mass by the height difference between two steps, and then uses the foot on the previous step as the support foot, and the other foot as the swing foot. After stepping the swing foot onto the next step down, it then uses the foot on the next step down as the support foot, and so on in a cycle. Therefore, based on the linear inverted pendulum model, a walking pattern during the down - stair process is proposed as follows Figure 2 as shown Figure 2 in the schematic diagram of the walking pattern during the down - stair process provided by the present invention: In this walking pattern, when the support foot is on the i - th step and the swing leg steps onto the (i + 1)-th step down each time, during this process, the center of mass descends by the height H i+1 , moves forward by L i+1 , that is, the angle between the center - of - mass trajectory of the linear inverted pendulum and the horizontal plane at this stage is Θ i+1 , ensuring that the height difference between the center of mass and the support foot at the moment after switching the support foot is equal to h.

[0025] In this walking pattern of going up and down stairs, the line connecting the front and rear support feet of each step and the center - of - mass displacement trajectory in the current stage form a parallelogram, and this parallelogram depends only on the height H between adjacent steps and the stride length L.

[0026] Step 102: Based on the walking pattern, map the linear inverted pendulum model under the stepped terrain into a segmented virtual height linear inverted pendulum model under the planar terrain.

[0027] According to the above walking pattern, it is necessary to generate a smooth centroid trajectory through model predictive control to ensure the stability of the biped robot's movement. The linear inverted pendulum under the stepped terrain has centroid displacements along the horizontal axis (x-axis) and vertical axis (y-axis) (which can be denoted as x and y respectively). At this time, the centroid height changes with time, that is, the mathematical model of the linear inverted pendulum also changes with time, making it inconvenient to directly generate a smooth movement trajectory of the centroid through such a model.

[0028] Taking the above steps as an example, the present invention proposes to rotate the parallelogram formed by the connection line of the front and rear support feet in each step and the centroid displacement trajectory of the current stage by an angle Θ i , that is, perform a coordinate rotation transformation on the linear inverted pendulum model of this stage, and regard the component of gravity GcosΘ i as the equivalent gravity, GsinΘ i and regard it as an external force that horizontally pushes the centroid of the linear inverted pendulum to move in the opposite direction. As shown in Figure 3 , Figure 3 is a schematic diagram of the virtual height linear inverted pendulum model provided by the present invention.

[0029] At this time, the linear inverted pendulum can be regarded as a linear inverted pendulum with a constant centroid height, and this centroid height is called the virtual height : ; wherein, is the horizontal distance between the centroid at the previous moment of switching the support foot and the support foot.

[0030] Under the horizontal external force GsinΘ i the dynamic equation of the linear inverted pendulum model is: ; wherein, is the equivalent gravitational acceleration after coordinate rotation transformation, m is the mass of the centroid of the linear inverted pendulum, τ is the torque at the support foot, x is the centroid displacement in the horizontal axis direction. At this time, the position of the zero moment point of the linear inverted pendulum model is: ; Similarly for going down the steps, rotate the parallelogram formed by the connection line of the front and rear support feet in each step and the centroid displacement trajectory of the current stage by an angle Θ i+1, the virtual height and the position of the zero moment point of the linear inverted pendulum model are respectively: ; ; Performing such a coordinate rotation transformation for each step phase can map the variable-height linear inverted pendulum model under the stepped terrain into a piecewise virtual height linear inverted pendulum model under the planar terrain. Figure 4 is a schematic diagram of the piecewise virtual height linear inverted pendulum walking mode provided by the present invention. As Figure 4 the virtual height of the center of mass remains unchanged for each segment, model predictive control can be used for the center of mass trajectory planning.

[0031] Step 103: Based on the piecewise virtual height linear inverted pendulum model, use model predictive control to achieve the gait planning of the biped robot under the stepped terrain.

[0032] The present invention proposes a walking mode under the stepped terrain and obtains Figure 4 an equivalent piecewise virtual height linear inverted pendulum model. Next, based on this model, model predictive control is used to achieve the gait planning of the robot.

[0033] Assume that the minimum time interval is δ. Then, the state of the robot's center of mass at the k-th moment (the displacement, velocity, acceleration, and the derivative of the acceleration of the center of mass in the horizontal axis direction) is denoted as: , ; The position of the zero moment point is denoted as , and the discretized state transition equation is: ; ; where , respectively represent the virtual height and the equivalent gravitational acceleration of the robot when it is on the i -th step at the k-th moment. The prediction window length of the model predictive control rolling optimization is N (that is, predictive control is performed on the next N δ time). Using the recursive relationship of the state transition equation, the relationship between the ZMP position and the center of mass state in the prediction window can be obtained: ; where , , , , is a Toeplitz matrix of N rows and N columns.

[0034] Establish a quadratic optimization problem, and the cost function is: ; ; where Q and R are constants used to make a trade-off between the ZMP tracking error and the oscillation of the centroid acceleration derivative. is the lower limit of the support area. is the upper limit of the support area.

[0035] When the height of the terrain and the sequence of foothold positions are known, the reference position of the ZMP is known, and then (where , represent the horizontal distance between the current foothold and the previous foothold when the robot is on the i-th step at the k-th moment and the angle between the line connecting the two points and the horizontal plane). Substitute the first element of this sequence into the discretized state transition equation to obtain the optimal centroid state at the next moment. This centroid state is the centroid state in the coordinate system of the piecewise virtual height linear inverted pendulum shown in Figure 4 , and its essence is the vector sum of the centroid states in the x and y axis directions under the stepped terrain. Then decompose it along the x and y axes of the stepped terrain world coordinate system to obtain the centroid state in the stepped terrain world coordinate system shown in Figure 1 : ; So far, the centroid trajectory planning (in the x-axis and y-axis directions) in the sagittal plane has been completed based on the virtual height linear inverted pendulum model predictive control of the present invention. In the coronal plane, the trajectory of the centroid in the z-axis direction can be directly obtained through traditional model predictive control, which will not be elaborated here.

[0036] After completing the centroid trajectory planning, in order to achieve a complete gait planning, next, third-order and fifth-order Bessel curves are respectively used to plan the trajectories of the swing leg in the x and y axis directions in the local coordinate system of the robot, specifically: ; where t is the normalized time coefficient, n is the order of the Bessel curve, A are the control points of the Bessel curve. To avoid the impact with the ground, the positions and velocities of the foot trajectory at the initial and end moments are constrained, and the preset Bessel curve constraint parameters are shown in Table 1: Table 1 Bessel Curve Constraint Parameter Table

[0037] In order to better understand the control method of the embodiment of the present invention, a specific biped robot gait planning example is given below for illustration.

[0038] Using the model and gait planning method provided by the present invention, gait planning is performed for a bipedal robot with a total mass of 90 kg, a thigh length and mass of 0.39 m and 6.7 kg, a calf length and mass of 0.34 m and 5.8 kg, a trunk mass of 65 kg, and a foot length, width and thickness of 0.3 m, 0.2 m and 0.1 m, respectively. The center of mass height when standing still on a flat terrain is , minimum time interval ,A simulation experiment was conducted in Webots to obtain a stable gait under stepped terrain.

[0039] Figure 5 This is a schematic diagram of the centroid height change curve of the bipedal robot provided by the present invention in a stair environment. The blue solid line is the height curve of the stair terrain, the black dotted line is the theoretically optimal centroid height curve obtained by optimization, and the red solid line is the actual curve of the robot centroid height in the simulation experiment. It can be seen that in an environment where the length and height of the stairs change, the centroid height of the robot can be reasonably planned according to the terrain height, and it has a good stair crossing ability.

[0040] Figure 6 is a schematic diagram of the center of mass state curve on the sagittal plane when the biped robot of the present invention moves on a stepped terrain, wherein Z max , Z min , Z real , Z ref They are the upper limit of the support domain, the lower limit of the support domain, the actual ZMP position of the robot, and the reference ZMP position. Between the upper and lower stairs, the robot has a step in place (20 seconds) to switch the gait mode of the upper stairs to the gait mode of the lower stairs. It can be seen that in the process of crossing the stairs, the actual ZMP position of the robot always fluctuates slightly between the ZMP reference positions and is always within the support domain. The forward trajectory of the center of mass is smooth, which reflects that the gait planning method proposed in the present invention has excellent stability in the sagittal plane.

[0041] Figure 7 is a schematic diagram of the center of mass state curve of the coronal plane when the biped robot provided by the present invention moves on a stepped terrain, wherein Z max , Z min , Z real , Z refThey are the upper limit of the support area, the lower limit of the support area, the actual ZMP position of the robot, and the reference ZMP position. It can be seen that during the process of crossing the steps, although the actual ZMP position of the robot fluctuates to a certain extent, it always remains near the reference ZMP position, and the situation of exceeding the support area does not occur. The lateral trajectory of the center of mass is smooth, which reflects that the gait planning method proposed by the present invention has excellent stability performance in the sagittal plane.

[0042] Figure 8 It is a simulation frame diagram of a biped robot walking in a stepped environment using the gait planning method proposed by the present invention.

[0043] On the other hand, the present invention also provides a biped robot gait planning device for stepped terrain, and the device includes: A first processing module, configured to respectively establish walking modes of the biped robot for ascending and descending steps based on a linear inverted pendulum model; A second processing module, configured to map the linear inverted pendulum model under stepped terrain to a segmented virtual height linear inverted pendulum model under planar terrain based on the walking mode; A third processing module, configured to implement gait planning of the biped robot under stepped terrain by using model predictive control based on the segmented virtual height linear inverted pendulum model.

[0044] It should be noted that the biped robot gait planning device for stepped terrain provided by the embodiments of the present invention can execute the biped robot gait planning method for stepped terrain described in any of the above embodiments during specific operation, and this embodiment will not be elaborated herein.

[0045] In summary, compared with the prior art, the biped robot gait planning method and device for stepped terrain provided by the present invention have the following beneficial effects: (1) The present invention uses a linear inverted pendulum model with a virtual center of mass height, and the gait pattern established based on the terrain elevation information and foot landing point information of the stepped environment can adapt to irregular stepped terrains with variable heights and lengths, making the gait have better terrain adaptability.

[0046] (2) The linear inverted pendulum model with the virtual center of mass height proposed by the present invention mainly realizes the gait planning of the biped robot for forward straight walking; combined with the omnidirectional foot landing point planning and the coordinate transformation matrix, the method proposed by the present invention has the potential to realize omnidirectional walking on three-dimensional stepped terrain.

[0047] (3) Under the gait pattern proposed by the present invention, model predictive control is used to plan the gait trajectories of the biped robot in the forward and vertical directions through an optimization problem, avoiding the kinematic constraints caused by separately optimizing and solving in two directions, and can shorten the solution time, which is beneficial to the real-time performance of gait planning.

[0048] (4) The stepped terrain gait planning method proposed by the present invention, according to the actual state of the robot, constrains the zero moment point of the robot into the support domain through quadratic optimization solution, ensuring the stability of the biped robot's walking state and having a certain anti-external force interference performance.

[0049] Figure 9 is a schematic structural diagram of the electronic device provided by the present invention, as Figure 9 shown, the electronic device may include: a processor 910, a communications interface 920, a memory 930, and a communication bus 940. Among them, the processor 910, the communications interface 920, and the memory 930 complete mutual communication through the communication bus 940. The processor 910 can call the logical instructions in the memory 930 to execute the biped robot gait planning method for stepped terrain.

[0050] On the other hand, the present invention also provides a computer program product. The computer program product includes a computer program stored on a non-transitory computer-readable storage medium. The computer program includes program instructions. When the program instructions are executed by a computer, the computer can execute the biped robot gait planning method for stepped terrain provided by the above-mentioned various embodiments. On another aspect, the present invention also provides a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it is implemented to execute the biped robot gait planning method for stepped terrain provided by the above-mentioned various embodiments.

[0051] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on such an understanding, the essence of the above technical solution or the part that contributes to the prior art can be embodied in the form of a software product. The computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., including several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0052] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A biped robot gait planning method for stepped terrain, characterized in that, Including: Based on the linear inverted pendulum model, establish the walking patterns of the biped robot for ascending and descending stairs respectively; Based on the walking patterns, map the linear inverted pendulum model under the stair terrain to a piecewise virtual height linear inverted pendulum model under the planar terrain; Based on the piecewise virtual height linear inverted pendulum model, use model predictive control to achieve gait planning of the biped robot under the stair terrain.

2. The biped robot gait planning method for stepped terrain according to claim 1, characterized in that, Based on the linear inverted pendulum model, establish the walking patterns of the biped robot for ascending and descending stairs respectively, including: The walking pattern for ascending stairs is as follows: during the ascending process, the biped robot first uses the foot on the previous step as the support foot, and the other foot as the swinging foot; after the swinging foot steps onto the next step, then use the foot on the next step as the support foot to lift the center of mass to the height between two steps, and the original support foot on the previous step becomes the swinging foot and swings to the step before the previous one, and so on in a cycle; The walking pattern for descending stairs is as follows: during the descending process, the biped robot first lowers the center of mass by the height difference between two steps, and then uses the foot on the previous step as the support foot, and the other foot as the swinging foot; after the swinging foot steps down to the next step, then use the foot on the next step as the support foot, and so on in a cycle.

3. The biped robot gait planning method for stepped terrain according to claim 2, wherein Also including: Let H i be the height difference between the step where the current support foot is located and the upper step, Θ i be the angle between the line connecting the current landing point and the previous landing point and the horizontal plane, G be the total gravity of the robot, L i be the horizontal distance between the current landing point and the previous landing point, and h be the height of the centroid under the flat terrain; In the walking mode on the upward staircase, when the supporting foot is on the $i$-th step and the swinging leg moves towards the $(i + 1)$-th step, the height $H$ by which the center of mass rises during this process i , and the forward displacement is $L$ i . The angle between the center-of-mass trajectory of the linear inverted pendulum model and the horizontal plane is $\Theta$ i , ensuring that the height difference between the center of mass and the supporting foot is equal to $h$ at the moment immediately before each change of the supporting foot; In the walking mode on the lower staircase, when the supporting foot is on the $i$-th step and the swinging leg steps onto the $(i + 1)$-th step, the height $H$ by which the center of mass drops during this process i+1 , and moves forward by $L$ i+1 , the angle between the center-of-mass trajectory of the linear inverted pendulum center-of-mass model and the horizontal plane is $\Theta$ i+1 , ensuring that the height difference between the center of mass and the supporting foot is equal to $h$ at the moment immediately after switching the supporting foot; In the walking patterns of ascending and descending stairs, the line connecting the front and rear support feet of each step and the trajectory of the center of mass displacement in the current stage form a parallelogram.

4. The biped robot gait planning method for stepped terrain according to claim 3, characterized in that, Based on the walking patterns, map the linear inverted pendulum model under the stair terrain to a piecewise virtual height linear inverted pendulum model under the planar terrain, including: In the walking mode on the staircase, rotate the parallelogram formed by connecting the front and rear support feet in each staircase and the centroid displacement trajectory in the current stage by an angle Θ i , and regard the component of gravity GcosΘ i as the equivalent gravity. GsinΘ i Regard it as the external force that horizontally and reversely pushes the centroid movement of the linear inverted pendulum. Then, the linear inverted pendulum can be regarded as a linear inverted pendulum with a constant centroid height, and the centroid height is called the virtual height : ； Among them, is the horizontal distance between the centroid of the previous moment of the switching support foot and the support foot; Under the horizontal external force GsinΘ i The dynamic equation of the linear inverted pendulum model under the push is as follows: ； Among them, is the equivalent gravitational acceleration after coordinate rotation transformation, m is the mass of the center of mass of the linear inverted pendulum, τ is the torque at the support foot, x is the displacement of the center of mass in the horizontal axis direction; the position of the zero moment point of the linear inverted pendulum model is: ； In the walking mode of the lower staircase, rotate the parallelogram formed by connecting the front and rear support feet in each staircase and the centroid displacement trajectory of the current stage by an angle Θ i+1 , then the virtual height and the position of the zero moment point of the linear inverted pendulum model are respectively: ； ； Perform coordinate rotation transformation on the linear inverted pendulum model of each stepping stage to map the variable height linear inverted pendulum model under the stair terrain to a piecewise virtual height linear inverted pendulum model under the planar terrain.

5. The biped robot gait planning method for stepped terrain according to claim 4, characterized in that Based on the piecewise virtual height linear inverted pendulum model, use model predictive control to achieve gait planning of the biped robot under the stair terrain, including: Let the minimum time interval be δ, and the state of the robot's centroid at the k-th moment is denoted as and ; The position of the zero moment point is denoted as , and the discretized state transition equation is as follows: ； ； Among them, , respectively represent the virtual height and the equivalent gravitational acceleration when the robot is on the i -th step at the k-th moment; the prediction window length of the model predictive control rolling optimization is N. Using the recursive relationship of the state transition equation, the relationship between the ZMP position and the centroid state in the prediction window is obtained: Among them, , , , , is a Toeplitz matrix of N rows and N columns; Establish a quadratic optimization problem, and the cost function is: ； ； where Q and R are constants, is the lower limit of the support domain, is the upper limit of the support domain; When the height of the terrain and the sequence of foothold positions are known, the reference position of the ZMP is known and can be obtained ; where and represent the horizontal distance between the current foothold and the previous foothold when the robot is on the i-th step at the k-th moment, and the angle between the line connecting the two points and the horizontal plane; substituting the first element in this sequence into the discretized state transition equation, the optimal centroid state at the next moment is obtained; Centroid state Perform decomposition in the horizontal and vertical axis directions to obtain the centroid state in the world coordinate system of the stepped terrain; After completing the planning of the center of mass trajectory, use Bezier curves to plan the trajectories of the swinging leg in the horizontal and vertical axes respectively in the local coordinate system of the robot.

6. The biped robot gait planning method for stepped terrain according to claim 5, characterized in that, The Bezier curve is: ； Among them, t is the normalized time coefficient, n is the order of the Bézier curve, and A is the control point of the Bézier curve; Use the preset constraint parameters of the Bezier curve to constrain the positions and velocities of the foot trajectory at the initial and end moments.

7. A biped robot gait planning device for stepped terrain, characterized in that, Including: The first processing module is used to establish the walking patterns of the biped robot for ascending and descending stairs respectively based on the linear inverted pendulum model; The second processing module is used to map the linear inverted pendulum model under the stair terrain to a piecewise virtual height linear inverted pendulum model under the planar terrain based on the walking patterns; The third processing module is used to achieve gait planning of the biped robot under the stair terrain by using model predictive control based on the piecewise virtual height linear inverted pendulum model.

8. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the computer program, it realizes the steps of the biped robot gait planning method for stair terrain as described in any one of claims 1 to 6.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it realizes the steps of the biped robot gait planning method for stair terrain as described in any one of claims 1 to 6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the biped robot gait planning method for stepped terrain according to any one of claims 1 to 6.

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