CN113805601A - Biped robot stair climbing gait planning method based on cooperative control - Google Patents
Biped robot stair climbing gait planning method based on cooperative control Download PDFInfo
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Abstract
The invention relates to the technical field of humanoid robot motion rules, and discloses a biped robot stair climbing gait planning method based on cooperative control, which comprises the following steps: s10: establishing a kinematic model of a first robot and a second robot for conveying objects according to a preset D-H parameter method; s20: and planning a first preset gait track of the first robot through cubic polynomial interpolation, obtaining the angle of the knee joint of the first robot based on a preset algorithm, and controlling the first robot to finish a first preset gait motion. The method plans the gait of stair climbing of the two robots by utilizing the cubic polynomial interpolation to obtain the time-related tracks of hip joints and ankle joints of the robots, obtains the motion rule of each joint in the complete gait cycle, and realizes that the two robots cooperate to stably convey objects to finish stair climbing.
Description
Technical Field
The invention relates to the field of humanoid robot motion rules, in particular to a biped robot stair climbing gait planning method based on cooperative control.
Background
With the development of artificial intelligence technology, the research of cooperation of a plurality of robots is more and more extensive, and the robot has related application in the fields of rescue action, warehouse cooperation, football match and the like. The idea of using robots to accomplish complex and cumbersome tasks and being able to harmoniously co-exist with humans in the same environment is becoming more mature. Meanwhile, in order to further improve the quality and speed of industrial production and reduce the risk of accidents in cooperation between human users and robots, the cooperation between the robots and the robots is regarded as an ideal solution.
A biped robot is a robot that mimics the structural features of a human being, with the ultimate goal of achieving similar motion behavior as a human being. At present, many biped robots capable of walking movement have been successfully developed at home and abroad, such as ATLAS and Petman of boston power company in the united states, HRP of AIST in japan, ASIMO of honda company in japan, KHR of AKIST in korea, an open source robot iCub in europe, HIT and GoRoBoT of harbin industrial university in china, KDW of defense science and technology university, BHR of beijing physics and university, THBIP of qinghua university, and the like. Although the biped robots can realize stable walking movement, the walking energy efficiency is low, the cruising ability is poor, and the biped robots are difficult to move to practical application. Indeed, human gait becomes very efficient over hundreds of years of natural evolution, and published data indicate that human gait is 25 times as energy efficient as that of the ATLAS robot and 16 times as efficient as that of the ASIMO robot. The scientific principle behind human energy-efficient gait lies in the rational planning of the motion phases and the coordinated movement of the joints.
Disclosure of Invention
The invention aims to provide a biped robot stair climbing gait planning method based on cooperative control, which can realize dynamic walking of two robots in a stair environment on the premise of keeping the stability of the two robots.
The planning method specifically comprises the following technical scheme:
a biped robot stair climbing gait planning method based on cooperative control comprises the following steps:
s10: establishing a kinematic model of a first robot and a second robot for conveying objects according to a preset D-H parameter method;
s20: planning a first preset gait track of the first robot through cubic polynomial interpolation, obtaining the angle of the knee joint of the first robot based on a preset algorithm, and controlling the first robot to finish a first preset gait motion;
s30: after the first robot finishes the first preset gait motion, the gravity center of the first robot after finishing the first preset gait motion is reduced by adjusting the angle of the knee joint of the first robot;
s40: planning a second preset gait track of the second robot according to the terminal speed of the movement of the conveyed object and the cubic polynomial interpolation value, and controlling the second robot to finish second preset gait motion;
s50: after the second robot finishes the second preset gait motion, the first robot is enabled to restore the upright state by adjusting the angle of the knee joint of the first robot, and the first preset gait motion and the second preset gait motion are repeated to carry out the gait track of the next step.
Further, the kinematic model includes a positive kinematic model and an inverse kinematic model.
Further, a positive kinematic model is established for the leg of the first robot according to a preset D-H parameter method, a world coordinate system sigma W is established at the center position of the right ankle joint of the first robot, and a homogeneous transformation matrix T of the motion of the right leg of the first robot is obtained as follows:
further, when the local coordinate system of the left ankle joint of the second robot is Σ α, the homogeneous transformation coordinates with respect to the world coordinate system Σ W are:
further, an inverse kinematics model is established for the leg of the first robot according to a preset D-H parameter method, inverse kinematics solution is carried out on joint coordinates of the ankle joint and joint coordinates of the hip joint through a geometric method, and the hip joint position vector in an ankle joint coordinate system is obtained as follows:
wherein the joint coordinate of the ankle joint is (P)0，R0) The hip joint coordinates are (P)4，R4) The center of the ankle joint is the origin of a world coordinate system sigma W;
the distance between the ankle joint and the hip joint obtained by using the pythagorean theorem is as follows:
according to the cosine theorem:
L2＝Lknee 2+Lhip 2-2LkneeLhipcos(π-θ3)
obtaining the angle theta of the knee joint3Comprises the following steps:
further, the trajectory expression of the hip joint of the first robot is as follows:
wherein, [ y ]hs，zhs]TAs the initial position of the hip joint of the first robot, [ v ]yhs，vzhs]TIs the initial velocity of the first robot hip joint, [ yhe，zhe]TFor the end position of the hip joint of the first robot, [ v ]yhe，vzhe]TThe gait cycle is T, the step length is Ls, the middle moment of the two-foot supporting period is KT, the starting moment of the single-leg supporting period is KT + Tss, the moment when the ankle joint reaches the highest position is KT + Tsh, the ending moment of the single-leg supporting period is KT + Tse, and the moment when the ankle joint returns to the two-leg supporting period again is KT + T.
Further, the first robot and the second robot keep communication through a wireless message channel; during transport, the center of gravity of the first and second robots is maintained within the support area with the feet level with the ground.
Further, first robot and second robot all adopt the NAO robot of the same model, and every leg of first robot and second robot all has six rotational degrees of freedom, wherein include: three degrees of freedom for the hip joint, one degree of freedom for the knee joint, and two degrees of freedom for the ankle joint.
The technical scheme adopted by the invention has the following beneficial effects:
the invention solves the problem of singularity existing when adjacent connecting rods are parallel by newly introducing a parameter, an orthogonal reference coordinate system is arranged at the joint of each connecting rod and comprises connecting rod parameters, joint variables, angles and other information, and joint positions and postures are deduced through a series of sequential transformation so as to show the transformation relation between the connecting rods. The invention utilizes cubic polynomial interpolation to respectively carry out gait planning of stair climbing on two robots, obtain the time-related tracks of hip joints and ankle joints, obtain the motion rules of all joints in the complete gait cycle, and realize that the two robots cooperatively carry a wood board to go upstairs. In the process, the overall gravity center track is changed by adjusting the angle of the knee joint, so that the stability of the two robots in the stair climbing process is kept.
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FIG. 1 is a flow chart of a coordinated control-based stair climbing gait planning method for a biped robot according to the invention;
FIG. 2 is a flow chart of parameter setting and gait control of the stair climbing gait planning method of the biped robot based on cooperative control according to the invention;
FIG. 3 is a model diagram of leg links of a first robot and a second robot of the stair climbing gait planning method of the biped robot based on cooperative control according to the present invention;
FIG. 4 is an inverse kinematics model diagram of a first robot and a second robot of the stair climbing gait planning method of the biped robot based on cooperative control according to the present invention;
FIG. 5 is a diagram of a motion trajectory model of a first robot and a second robot of the stair climbing gait planning method of the biped robot based on cooperative control according to the present invention;
fig. 6 is a simulation diagram of the transported object of the first robot and the second robot based on the coordinated control biped robot stair climbing gait planning method.
Detailed Description
The following are specific embodiments of the present invention and are further described with reference to the drawings, but the present invention is not limited to these embodiments.
This example
The embodiment provides a stair climbing gait planning method of a biped robot based on cooperative control, and as shown in fig. 1, the method comprises the following steps: s10: establishing a kinematic model of a first robot and a second robot for conveying objects according to a preset D-H parameter method; s20: planning a first preset gait track of the first robot through cubic polynomial interpolation, obtaining the angle of the knee joint of the first robot based on a preset algorithm, and controlling the first robot to finish a first preset gait motion; s30: after the first robot finishes the first preset gait motion, the gravity center of the first robot after finishing the first preset gait motion is reduced by adjusting the angle of the knee joint of the first robot; s40: planning a second preset gait track of the second robot according to the terminal speed of the movement of the conveyed object and the cubic polynomial interpolation value, and controlling the second robot to finish second preset gait motion; s50: after the second robot finishes the second preset gait motion, the first robot is enabled to restore the upright state by adjusting the angle of the knee joint of the first robot, and the first preset gait motion and the second preset gait motion are repeated to carry out the gait track of the next step.
Specifically, a preset D-H parameter method is used for constructing a forward and reverse kinematics model for carrying the wood plates by the first robot and the second robot. The D-H representation of the rigid rod depends on the following four parameters of the connecting rod: alpha is alphai-1Is along Xi-1Direction Zi-1And ZiThe included angle between them; . a isi-1Is along Xi-1Direction Zi-1And ZiThe distance between them; thetaiIs along ZiDirection Xi-1And XiThe included angle between them; diIs along ZiDirection Xi-1And XiThe distance between them; the specific parameters of the preset D-H parameter method are as follows:
TABLE 1
Wherein the kinematics model comprises a positive kinematics model and an inverse kinematics model.
Establishing a positive kinematic model for the leg of the first robot according to a preset D-H parameter method, establishing a world coordinate system sigma W at the central position of the right ankle joint of the right foot of the first robot, and obtaining a homogeneous transformation matrix T of the right leg movement of the first robot as follows:
the local coordinate system of the left ankle joint of the second robot is Σ α, and the homogeneous transformation coordinate with respect to the world coordinate system Σ W is:
specifically, by establishing the world coordinate system Σ W at the center of the right ankle joint of the first robot, the transformation matrix that can convert the position of any one point in the coordinate system Σ i to the coordinate system Σ i-1 is converted to be one that is only associated with the joint variable qiThe function concerned is:
wherein, c θiIs cos thetaiAbbreviation, s θiIs sin thetaiAbbreviation, c αi-1Is cos alphai-1Abbreviation, s.alpha.i-1Is sin alphai-1Abbreviations.
After the first robot finishes the gait of the first step, the instability of gravity center upward movement caused by the second robot going upstairs is reduced by adjusting the angle of the knee joint. The first robot keeps the wooden board parallel to the ground by lowering the center of gravity, so the coordinate position of the lowered knee joint in the z direction should satisfy:
0＜zknee(t)-zknee(t)′≤Sh
therefore, the stability in the cooperative movement process is improved, the position of the center of gravity is changed, and the quality of the template born by the second robot is reduced.
Referring to fig. 2, by setting parameters such as step length and landing point positions of the first robot and the second robot, the movement trajectories of the hip joint and the ankle joint are planned by 3-degree polynomial interpolation; the preset algorithm comprises the steps of calculating angles of other joints through an inverse kinematics model, judging the stability of the first robot and the second robot based on a ZMP formula, and if so, controlling each joint to finish stair climbing gaits; if not, the pose is corrected, the 3 rd-order polynomial interpolation is adopted to plan the motion tracks of the hip joint and the ankle joint, namely the first preset gait track of the first robot is planned through the third-order polynomial interpolation, then other joint angles are calculated continuously through the inverse kinematics model, and the stability of the first robot and the second robot is judged based on the ZMP formula.
Referring to fig. 3 and 4, an inverse kinematics model is established for the leg of the first robot according to a preset D-H parameter method, and inverse kinematics solution is performed on joint coordinates of the ankle joint and joint coordinates of the hip joint through a geometric method to obtain a hip joint position vector in an ankle joint coordinate system as follows:
wherein the joint coordinate of the ankle joint is (P)0，R0) The hip joint coordinates are (P)4，R4) The center of the ankle joint is the origin of a world coordinate system sigma W;
the distance between the ankle joint and the hip joint obtained by using the pythagorean theorem is as follows:
according to the cosine theorem: l is2＝Lknee 2+Lhip 2-2LkneeLhipcos(π-θ3)
Obtaining the angle theta of the knee joint3Comprises the following steps:
specifically, the included angle of the position vectors of the swing leg, the ankle joint and the hip joint is alpha, and in a right-angled triangle formed by connecting lines of the ankle joint, the hip joint and the knee joint, the included angle is as follows according to the cosine law:
in an ankle joint coordinate system, a pitch angle and a roll angle of the ankle joint can be obtained according to a position vector of the hip joint, wherein the pitch angle and the roll angle are respectively as follows:
θ1＝a tan2(Ly，Lz)
where sign (x) is a sign function that returns +1 when x is positive and returns-1 when x is negative.
For three angles of swing, rolling and pitching of the hip joint, the pose relationship among the connecting rods is as follows:
R1＝R4Rz(θ6)Rx(θ5)Ry(θ4)Ry(θ2+θ3)Rx(θ1)
variations on the above equation may result:
the left equation is expanded and the right value is calculated, i.e.:
comparing the elements of the left matrix, the expressions for the various angles of the hip joint can be obtained as follows:
θ6＝a tan2(-R12，R22)
θ5＝a tan2(R32，-R12sθ6+R22cθ6)
θ4＝a tan2(-R31，R33)
referring to fig. 5 and 6, the trajectory expression of the first robot hip joint is:
wherein, [ y ]hs，zhs]TAs the initial position of the hip joint of the first robot, [ v ]yhs，vzhs]TIs the initial velocity of the first robot hip joint, [ yhe，zhe]TFor the end position of the hip joint of the first robot, [ v ]yhe，vzhe]TThe gait cycle is T, the step length is Ls, the middle moment of the two-foot supporting period is KT, the starting moment of the single-leg supporting period is KT + Tss, the moment when the ankle joint reaches the highest position is KT + Tsh, the ending moment of the single-leg supporting period is KT + Tse, and the moment when the ankle joint returns to the two-leg supporting period again is KT + T.
Specifically, a cubic polynomial is used: z is a radical ofhip(t)＝a0+a1(t-kT)+a2(t-kT)2+a3(t-kT)3；
The parameters of the movement trajectory of the hip joint in the z-axis direction of the first robot are determined by initial and terminal constraints.
Wherein the trajectory in the y-axis direction is composed of two functions of a two-foot support period and a single-foot support period, and the parameters of a cubic polynomial thereof can be derived by the following constraints:
it is assumed that the initial acceleration and tip velocity are determined so that a hip trajectory can be generated that satisfies the physical constraints. A cubic polynomial is used for planning the track of the ankle joint in the single foot supporting period, and the constraint conditions which must be met are as follows:
wherein the content of the first and second substances,
when the second robot lands on the left swinging foot, the first robot returns to the standing state, the overall gravity center track is influenced, and the influence is accumulated with time to cause the instability of the robot cooperation control to increase. Therefore, after the second robot completes a gait cycle, the second robot stops moving for a period of time, which is beneficial to eliminating accumulated errors.
Suppose sum (x)G1，yG1，zG1) And (x)G2，yG2，zG2) Are the barycentric coordinates, M, of the first and second robots, respectively1And M2The masses of the two robots, respectively, and the mass of the object to be transported is M3The coordinate of the centroid is (x)G3，yG3，zG3). So that the barycentric coordinates of the whole can be calculated as
The formula for calculating each joint motion and ZMP of the robot according to the planning is as follows:
the first robot and the second robot keep communication through a wireless message channel; during transport, the center of gravity of the first and second robots is maintained within the support area with the feet level with the ground.
First robot and second robot all adopt the NAO robot of the same model, and every leg of first robot and second robot all has six rotational degrees of freedom, wherein includes: three degrees of freedom for the hip joint, one degree of freedom for the knee joint, and two degrees of freedom for the ankle joint.
Wherein, the three degrees of freedom of the hip joint include: pitch, roll, and yaw; one degree of freedom of the knee joint includes: pitching; the two degrees of freedom of the ankle joint include: pitch and roll.
The invention respectively plans the motion tracks of hip joints and ankle joints of two robots by cubic polynomial interpolation, changes the gravity center position by adjusting the angle of the knee joint to keep the stability in the walking process, and then obtains the motion angle corresponding to each joint by solving the inverse solution of a positive kinematics model to control the foot movement. ZMP is used as a judgment basis for dynamic walking stability, and the ZMP is ensured to be always positioned in a support polygon formed by the feet of the robot and the ground.
The NAO robot model is used in a V-REP environment and is subjected to joint simulation with MATLAB software. The method utilizes an inverse kinematics algorithm in MATLAB and controls the leg of the virtual robot to move to a specified position and posture in VREP through an Application Programming Interface (API) interface, thereby verifying the correctness simulation and experimental results of the inverse kinematics algorithm.
The invention utilizes cubic polynomial interpolation to respectively carry out gait planning of stair climbing on two robots, obtain the time-related tracks of hip joints and ankle joints, obtain the motion rules of all joints in the complete gait cycle, and realize that the two robots cooperatively carry a wood board to go upstairs. In the process, the overall gravity center track is changed by adjusting the angle of the knee joint, so that the stability of the two robots in the stair climbing process is kept.
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.
Claims (8)
1. A biped robot stair climbing gait planning method based on cooperative control is characterized by comprising the following steps:
s10: establishing a kinematic model of a first robot and a second robot for conveying objects according to a preset D-H parameter method;
s20: planning a first preset gait track of the first robot through cubic polynomial interpolation, obtaining the angle of the knee joint of the first robot based on a preset algorithm, and controlling the first robot to finish a first preset gait motion;
s30: after the first robot finishes the first preset gait motion, the gravity center of the first robot after finishing the first preset gait motion is reduced by adjusting the angle of the knee joint of the first robot;
s40: planning a second preset gait track of the second robot according to the terminal speed of the movement of the conveyed object and the cubic polynomial interpolation value, and controlling the second robot to finish second preset gait motion;
s50: after the second robot finishes the second preset gait motion, the first robot is enabled to restore the upright state by adjusting the angle of the knee joint of the first robot, and the first preset gait motion and the second preset gait motion are repeated to carry out the gait track of the next step.
2. The cooperative control based biped robotic stair climbing gait planning method of claim 1, wherein the kinematics model comprises a forward kinematics model and an inverse kinematics model.
3. The stair climbing gait planning method for the biped robot based on cooperative control as claimed in claim 2, characterized in that a positive kinematics model is established for the leg of the first robot according to a preset D-H parameter method, a world coordinate system sigma W is established at the center position of the right ankle joint of the first robot, and a homogeneous transformation matrix T of the right leg movement of the first robot is obtained as follows:
4. the cooperative control based biped robot stair climbing gait rule method according to claim 3, characterized in that the local coordinate system of the left ankle joint of the second robot is Σ α, and the homogeneous transformation coordinates with respect to the world coordinate system Σ W are:
5. the cooperative control-based stair climbing gait rule method for the biped robot as claimed in claim 2, wherein an inverse kinematics model is established for the leg of the first robot according to a preset D-H parameter method, inverse kinematics solution is performed on joint coordinates of the ankle joint and joint coordinates of the hip joint through a geometric method, and the hip joint position vector in the ankle joint coordinate system is obtained as follows:
wherein the joint coordinate of the ankle joint is (P)0，R0) The hip joint coordinates are (P)4，R4) The center of the ankle joint is the origin of a world coordinate system sigma W;
the distance between the ankle joint and the hip joint obtained by using the pythagorean theorem is as follows:
according to the cosine theorem:
L2＝Lknee 2+Lhip 2-2LkneeLhipcos(π-θ3)
obtaining the angle theta of the knee joint3Comprises the following steps:
6. the cooperative control-based stair climbing gait rule method of the biped robot according to claim 5, characterized in that the trajectory expression of the hip joint of the first robot is as follows:
wherein, [ y ]hs，zhs]TIs the initial position of the first robot hip joint,[vyhs，vzhs]Tis the initial velocity of the first robot hip joint, [ yhe，zhe]TFor the end position of the hip joint of the first robot, [ v ]yhe，vzhe]TThe gait cycle is T, the step length is Ls, the middle moment of the two-foot supporting period is KT, the starting moment of the single-leg supporting period is KT + Tss, the moment when the ankle joint reaches the highest position is KT + Tsh, the ending moment of the single-leg supporting period is KT + Tse, and the moment when the ankle joint returns to the two-leg supporting period again is KT + T.
7. The cooperative control based biped robot stair climbing gait rule method according to claim 1, characterized in that the first robot and the second robot are in communication through a wireless message channel; during transport, the center of gravity of the first and second robots is maintained within the support area with the feet level with the ground.
8. The cooperative control based biped robot stair climbing gait rule method according to claim 1, characterized in that the first robot and the second robot both use NAO robots of the same model, and each leg of the first robot and the second robot has six rotational degrees of freedom, which includes: three degrees of freedom for the hip joint, one degree of freedom for the knee joint, and two degrees of freedom for the ankle joint.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114442649A (en) * | 2021-12-22 | 2022-05-06 | 之江实验室 | Hybrid dynamics modeling and motion planning method for biped robot |
| CN114661057A (en) * | 2022-05-23 | 2022-06-24 | 武汉跨克信息技术有限公司 | Intelligent bionic biped inspection robot |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN114442649A (en) * | 2021-12-22 | 2022-05-06 | 之江实验室 | Hybrid dynamics modeling and motion planning method for biped robot |
| CN114442649B (en) * | 2021-12-22 | 2024-04-19 | 之江实验室 | Biped robot hybrid dynamics modeling and motion planning method |
| CN114661057A (en) * | 2022-05-23 | 2022-06-24 | 武汉跨克信息技术有限公司 | Intelligent bionic biped inspection robot |
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Application publication date: 20211217 |