CN113359729A - Electric drive foot type robot slippage inhibition method - Google Patents

Electric drive foot type robot slippage inhibition method Download PDF

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CN113359729A
CN113359729A CN202110646526.7A CN202110646526A CN113359729A CN 113359729 A CN113359729 A CN 113359729A CN 202110646526 A CN202110646526 A CN 202110646526A CN 113359729 A CN113359729 A CN 113359729A
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foot
force
normal
robot
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刘宇飞
高海波
丁亮
江磊
苏波
邢伯阳
王志瑞
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Intelligent Mobile Robot Zhongshan Research Institute
China North Vehicle Research Institute
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Intelligent Mobile Robot Zhongshan Research Institute
China North Vehicle Research Institute
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0223—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving speed control of the vehicle
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0276—Control of position or course in two dimensions specially adapted to land vehicles using signals provided by a source external to the vehicle

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Abstract

The invention relates to a method for inhibiting slippage of an electrically-driven foot type robot, and belongs to the technical field of motion control of foot type robots. Through research on a method for suppressing the slippage of the electrically-driven foot type robot, the electrically-driven foot type robot provided by the invention has a slippage suppression function in the traction direction and the lateral movement process, can realize the foot slippage suppression function through the detected foot slippage amount, and can improve the motion stability of the control of the foot type robot.

Description

Electric drive foot type robot slippage inhibition method
Technical Field
The invention belongs to the technical field of motion control of foot robots, and particularly relates to a method for inhibiting slippage of an electrically-driven foot robot.
Background
The electric drive foot type robot slippage inhibition method is an important key technology for the stable control of a foot type system, and plays an important role in converting external environment disturbance into specific slippage inhibition motion control. Aiming at ensuring the motion stability, flexibility, robustness and convenience in operation of the foot type platform, the electric drive foot type robot slippage inhibition method focuses on the walking function and stability control performance of the foot type system.
At present, foot robots in China start late, and the foot robots generally have the defects of low autonomous stability, poor terrain adaptability, low slip inhibition control level, strong dependence on working terrain environments and the like. Because the ground contact information of each leg of the legged robot is not completely the same, the motion deviation in different degrees can be caused in the traction direction and the tangential direction, so that the legs in the traction direction can not realize synchronous support, and the internal force between the support legs in the tangential direction is increased. The foot type robot increases the complexity of a control system due to various degrees of freedom, lacks the capability of inhibiting real-time foot ground slippage in the motion process, is mainly oriented to field rugged ground, mostly focuses on the realization of walking function and has little focus on the slippage inhibition problem of the foot type robot at present.
Disclosure of Invention
Technical problem to be solved
The technical problem to be solved by the invention is as follows: the problems that the robot generally has the defects of low autonomous stability, poor terrain adaptability, poor slip inhibition capability of a foot type robot and the like, the degree of freedom is large, the complexity of a control system is increased, and the real-time foot slip inhibition capability is lacked in the motion process are solved.
(II) technical scheme
In order to solve the technical problem, the invention provides a method for inhibiting slippage of an electrically-driven foot robot, which comprises the following steps:
step one, analyzing and resolving the coupling of the foot force of the foot type robot: coupling analysis is carried out on supporting foot forces of three-foot, four-foot and five-foot of the foot robot, normal foot force coupling characteristics based on topographic information are analyzed according to a foot-ground contact model and normal deviation of a single-foot distance contact surface, a three-dimensional moment balance equation borne by the centroid of the foot robot is established, under the condition that the supporting feet have the same control input, a normal force coupling expression of the foot robot with multiple supporting feet is obtained through calculation, and a supporting foot force coupling expression of the foot robot with multiple supporting feet is obtained;
step two, estimating a slope angle by using a plane fitting method according to the position of a foot end by using the foot force coupling expression of the foot type robot obtained by calculation in the step one, establishing a plane estimation equation and calculating to obtain the slope angle and a vertical distance parameter, adjusting the pitch angle and the roll angle of the robot body in real time according to the slope change of the ground and the limit position of a joint according to the estimation of the slope terrain to adapt to the terrain change, and calculating to obtain a mechanical transformation matrix for correcting the stress of the foot end, wherein the mechanical transformation matrix is as follows:
Figure BDA0003109973700000021
in the formula (I), the compound is shown in the specification,
Figure BDA0003109973700000022
is a rotation matrix between the slope ground and the horizontal ground; glegiA weight matrix for each leg;
Figure BDA0003109973700000023
estimating an angle for the slope;
step three, establishing normal and tangential stress balance equations of the foot robot by using the mechanical transformation matrix obtained by calculation in the step two, and establishing a roll torque balance equation suffered by the mass center of the robot based on the stress balance equations:
Figure BDA0003109973700000031
in the formula (I), the compound is shown in the specification,LFNzinormal supporting force for each foot；LFTyiIs the tangential force of each foot;LPxi,LPyi,LPzicoordinates of the advancing direction, the tangential direction and the normal direction of each foot;LPx,LPy,LPzis the advancing direction of the machine body; coordinates of the tangential direction and the normal direction;
according to the stress and moment balance equation, the foot force optimization problem is converted into a quadratic programming problem:
Figure BDA0003109973700000032
in the formula, F is an m-dimensional column vector and represents a normal force and a tangential force of a foot end; g is an n-order symmetric matrix; g is an m-dimensional column vector; a is an mxn matrix; bwIs an m-dimensional column vector;
and (3) solving by a Lagrange method, and converting an objective equation for solving the unknown foot force into a Lagrange function:
Figure BDA0003109973700000033
in the formula, ArA foot force corresponding matrix to be solved is obtained; frSolving the result of the foot force; grIs an n-order symmetric matrix; grIs an m-dimensional column vector; lambda is a characteristic solution vector;
finally, the optimal solution of unknown foot force is obtained as follows:
Fr *＝-grH+Tbw (5)
in the formula, grIs an m-dimensional column vector; bwIs an m-dimensional column vector; h is an m-dimensional row vector;
step four, an optimization target equation in a foot force inhibition state in a slippage state is provided by using the optimal solution of the foot force obtained by calculation in the step three;
the optimization target equation of the normal force and the tangential force of the foot end in the slip suppression state is as follows:
Figure BDA0003109973700000041
in the formula (I), the compound is shown in the specification,LFTxi,LFTyia forward traction force for each foot;LFNziis the normal force of each foot;
Figure BDA0003109973700000042
is the forward acceleration of the body;
Figure BDA0003109973700000043
is the tangential acceleration of the machine body; i isBIs the inertia tensor of the body;
Figure BDA0003109973700000044
is yaw acceleration of the machine body;LPxithe position of the foot end in the single leg traction direction;LPyithe position of the foot end in the tangential direction of the single leg is shown;BPxis the position of the center of mass in the traction direction of the machine body;BPyis the position of the mass center of the machine body in the tangential force direction;
constructing a function L by a multiplier methodμ(FNs,FTs) Establishing an augmented Lagrange equation of a constructor:
Figure BDA0003109973700000045
in the formula, FTsA forward traction force for each foot; fNsIs the normal force of each foot; Δ FTsIs the amount of change in the forward traction of each foot;
Figure BDA0003109973700000046
is a multiplier coefficient; mu.sNTsIs a friction cone characteristic value; fsIs a foot-end three-way force; gNs,GTsIs an n-order symmetric matrix; a. thesIs an m multiplied by n matrix; bsIs an m-dimensional column vector;
if the obtained optimal solution cannot meet the inequality constraint, establishing an objective function of the inequality constraint as follows:
Figure BDA0003109973700000047
in the formula (I); fNsIs the normal force of each foot; Δ FTsIs the amount of change in the forward traction of each foot; Δ MTsIs the normal force variation of each foot; mu.sgIs the foot ground friction cone coefficient;
according to an inequality constrained target function, establishing an augmented Lagrange equation under a non-equality constraint condition as follows:
Figure BDA0003109973700000051
in the formula, FTsA forward traction force for each foot; fNsIs the normal force of each foot; Δ FTsIs the amount of change in the forward traction of each foot; Δ MTsIs the normal force variation of each foot; giIs a characteristic variable; gNs,GTs,GMTsIs an n-order symmetric matrix; mu is the foot ground friction coefficient; lambda [ alpha ]siIs a multiplier coefficient;
and step five, realizing the solving process of the foot force optimization and slip suppression method by using the objective function and the augmented Lagrange equation obtained by calculation in the step four.
The invention also provides application of the method in the technical field of motion control of the foot type robot.
(III) advantageous effects
Through research on a method for suppressing the slippage of the electrically-driven foot type robot, the electrically-driven foot type robot provided by the invention has a slippage suppression function in the traction direction and the lateral movement process, can realize the foot slippage suppression function through the detected foot slippage amount, and can improve the motion stability of the control of the foot type robot.
Drawings
FIG. 1 is a schematic diagram of a slip suppression method for an electrically driven foot robot according to the present invention;
FIG. 2 is a schematic diagram of the three-legged support contact mechanics analysis of the legged robot of the present invention;
FIG. 3 is a schematic diagram of the four-foot support contact mechanics analysis of the legged robot of the present invention;
FIG. 4 is a schematic diagram of the mechanical foot conversion of a legged robot based on terrain estimation according to the present invention;
FIG. 5 is a flow chart of the optimal solution for foot force under slip suppression according to the present invention.
Detailed Description
In order to make the objects, contents, and advantages of the present invention clearer, the following detailed description of the embodiments of the present invention will be made in conjunction with the accompanying drawings and examples.
As shown in fig. 2 and fig. 3, the method for suppressing slippage of an electrically-driven foot robot provided by the invention is specifically completed according to the following steps:
step one, analyzing and resolving the coupling of the foot force of the foot type robot: coupling analysis is carried out on supporting foot forces of three-foot, four-foot and five-foot of the foot robot, normal foot force coupling characteristics based on topographic information are analyzed according to a foot-ground contact model and normal deviation of a single-foot distance contact surface, a three-dimensional moment balance equation borne by the centroid of the foot robot is established, under the condition that the supporting feet have the same control input, a normal force coupling expression of the foot robot with multiple supporting feet is obtained through calculation, and a supporting foot force coupling expression of the foot robot with multiple supporting feet is obtained;
and step two, estimating the slope angle by using the foot force coupling expression of the foot type robot obtained by calculation in the step one and adopting a plane fitting method according to the position of a foot end, establishing a plane estimation equation and calculating to obtain parameters such as the slope angle, the vertical distance and the like. According to the estimation of the slope terrain, the pitching and rolling angles of the robot body are adjusted in real time to adapt to the terrain change according to the slope change of the ground and the joint limit position, and a mechanical transformation matrix is obtained through calculation and used for correcting the stress of the foot end, and is as follows:
Figure BDA0003109973700000061
in the formula (I), the compound is shown in the specification,
Figure BDA0003109973700000062
is a rotation matrix between the slope ground and the horizontal ground; glegiA weight matrix for each leg;
Figure BDA0003109973700000063
an angle is estimated for the slope.
Step three, establishing normal and tangential stress balance equations of the foot robot by using the mechanical transformation matrix obtained by calculation in the step two, and establishing a roll torque balance equation suffered by the mass center of the robot based on the stress balance equations:
Figure BDA0003109973700000071
in the formula (I), the compound is shown in the specification,LFNzinormal support force for each foot;LFTyiis the tangential force of each foot;LPxi,LPyi,LPzicoordinates of the advancing direction, the tangential direction and the normal direction of each foot;LPx,LPy,LPzis the advancing direction of the machine body; tangential and normal direction coordinates.
According to the stress and moment balance equation, the foot force optimization problem is converted into a quadratic programming problem:
Figure BDA0003109973700000072
in the formula, F is an m-dimensional column vector and represents a normal force and a tangential force of a foot end; g is an n-order symmetric matrix; g is an m-dimensional column vector; a is an mxn matrix; bwIs an m-dimensional column vector.
And (3) solving by a Lagrange method, and converting an objective equation for solving the unknown foot force into a Lagrange function:
Figure BDA0003109973700000073
in the formula, ArA foot force corresponding matrix to be solved is obtained; frSolving the result of the foot force; grIs an n-order symmetric matrix; grIs an m-dimensional column vector; λ is the feature solution vector.
Finally, the optimal solution of unknown foot force is obtained as follows:
Fr *＝-grH+Tbw (5)
in the formula, grIs an m-dimensional column vector; bwIs an m-dimensional column vector; h is an m-dimensional row vector.
Step four, an optimization target equation in a foot force inhibition state in a slippage state is provided by using the optimal solution of the foot force obtained by calculation in the step three;
the optimization target equation of the normal force and the tangential force of the foot end in the slip suppression state is as follows:
Figure BDA0003109973700000081
in the formula (I), the compound is shown in the specification,LFTxi,LFTyia forward traction force for each foot;LFNziis the normal force of each foot;
Figure BDA0003109973700000082
is the forward acceleration of the body;
Figure BDA0003109973700000083
is the tangential acceleration of the machine body; i isBIs the inertia tensor of the body;
Figure BDA0003109973700000084
is yaw acceleration of the machine body;LPxithe position of the foot end in the single leg traction direction;LPyithe position of the foot end in the tangential direction of the single leg is shown;BPxis the position of the center of mass in the traction direction of the machine body;BPyis the body tangential force direction mass centerLocation.
Constructing a function L by a multiplier methodμ(FNs,FTs) Establishing an augmented Lagrange equation of a constructor:
Figure BDA0003109973700000085
in the formula, FTsA forward traction force for each foot; fNsIs the normal force of each foot; Δ FTsIs the amount of change in the forward traction of each foot;
Figure BDA0003109973700000086
is a multiplier coefficient; mu.sNTsIs a friction cone characteristic value; fsIs a foot-end three-way force; gNs,GTsIs an n-order symmetric matrix; a. thesIs an m multiplied by n matrix; bsIs an m-dimensional column vector.
If the obtained optimal solution cannot meet the inequality constraint, establishing an objective function of the inequality constraint as follows:
Figure BDA0003109973700000091
in the formula, FNsIs the normal force of each foot; Δ FTsIs the amount of change in the forward traction of each foot; Δ MTsIs the normal force variation of each foot; mu.sgIs the foot ground friction cone coefficient.
According to the inequality constrained target function of the step four, establishing an augmented Lagrange equation under the non-equality constraint condition as follows:
Figure BDA0003109973700000092
in the formula, FTsA forward traction force for each foot; fNsIs the normal force of each foot; Δ FTsIs the amount of change in the forward traction of each foot; Δ MTsIs the normal force variation of each foot; giIs a characteristic variable; gNs,GTs,GMTsIs an n-order symmetric matrix; mu is the foot ground friction coefficient; lambda [ alpha ]siAre multiplier coefficients.
In the first step, the three-foot support and foot force coupling analysis of the foot type robot is carried out, and the three-dimensional moment balance equation of the centroid of the foot type robot is established as follows:
Figure BDA0003109973700000093
wherein the three-dimensional force acting on the center of mass of the robot isBFx,BFy,BFzAnd a three-dimensional moment vector is defined asBMx,BMy,BMzThe three-dimensional foot force of each supporting leg is defined asLFTxi,LFTyi,LFNziThe distance between the center of mass of the robot and the ground is h,BPxis the position of the center of mass in the traction direction of the machine body;BPyis the position of the mass center of the machine body in the tangential force direction.
Under the condition of ensuring that the supporting feet have the same control input, calculating to obtain a normal force coupling expression of the foot type robot with an odd number of groups of the three supporting feet;
in the first step, by utilizing the established three-dimensional moment balance equation, the foot force coupling analysis of the four-foot support of the foot robot is carried out, the normal foot force coupling characteristic based on the terrain information is analyzed according to the foot-ground contact model and the normal deviation of the single-foot distance contact surface, and the organism balance equation when the four-foot support is established is as follows:
Figure BDA0003109973700000101
wherein the three-dimensional force acting on the center of mass of the robot isBFx,BFy,BFzAnd a three-dimensional moment vector is defined asBMx,BMy,BMz；kNThe normal contact force stiffness coefficient;
Figure BDA0003109973700000102
the position difference of the contact surfaces of the 1, 2, 4 and 5 feet in the normal direction of the ground is obtained;LPxithe position of the foot end in the traction direction;LPyiis the lateral direction position of the foot end;
Figure BDA0003109973700000103
the difference in the contact surface position of the foot in the normal direction of the ground.
Establishing a position deviation geometric condition of the foot end position to obtain a support foot force coupling expression of the four-foot supported foot type robot;
and in the second step, estimating the slope angle by using the coupling analysis result of the multi-foot support foot force of the foot type robot and adopting a plane fitting method according to the position of the foot end, establishing a plane estimation equation and calculating to obtain parameters such as the slope angle, the vertical distance and the like. According to the slope normal vector, the slope estimation angle
Figure BDA0003109973700000104
Comprises the following steps:
Figure BDA0003109973700000105
in the formula (I), the compound is shown in the specification,Sxi is a slope three-dimensional normal vector under the world coordinate system.
According to estimation of slope terrain, the pitching and rolling angles of the robot body are adjusted in real time to adapt to terrain change according to slope change of the ground and the joint limit position, and a mechanical transformation matrix is obtained through calculation and used for correcting foot end stress, as shown in a terrain estimation-based foot mechanical transformation schematic diagram of a foot type robot shown in fig. 4, the mechanical transformation matrix is as follows:
Figure BDA0003109973700000111
in the formula (I), the compound is shown in the specification,
Figure BDA0003109973700000112
is a rotation matrix between the slope ground and the horizontal ground; glegiA weight matrix for each leg;
Figure BDA0003109973700000113
an angle is estimated for the slope.
And in the third step, the calculated mechanics conversion matrix based on terrain estimation is utilized to carry out foot force optimization under steady-state walking, normal and tangential stress balance equations of the foot type robot are established, and a rolling moment balance equation borne by the center of mass of the robot is established based on the stress balance equation.
As shown in fig. 5, the solving process of the method for realizing the foot power optimization and the slip suppression by using the objective function and the augmented lagrangian equation obtained by the fourth step is divided into the following three steps:
step 1: judging the motion state of the foot type robot according to the slip state estimation;
step 2: judging whether the foot end slips by using the motion state of the foot type robot obtained in the step 1, establishing a foot force optimization objective function, establishing an organism balance equation, constructing a Lagrange objective function through the established objective function, and solving to finally obtain a foot force three-dimensional optimal solution;
and step 3: and (3) establishing a foot force inhibition optimization objective function in the slippage state by utilizing the motion state and foot ground force of the foot type robot obtained by calculation in the steps (1) and (2), constructing an augmented Lagrange objective function, solving an unconstrained problem, and finally obtaining a three-dimensional optimal solution of the foot force in the slippage state.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (9)

1. An electrically driven legged robot slip suppression method, comprising the steps of:
step one, analyzing and resolving the coupling of the foot force of the foot type robot: coupling analysis is carried out on supporting foot forces of three-foot, four-foot and five-foot of the foot robot, normal foot force coupling characteristics based on topographic information are analyzed according to a foot-ground contact model and normal deviation of a single-foot distance contact surface, a three-dimensional moment balance equation borne by the centroid of the foot robot is established, under the condition that the supporting feet have the same control input, a normal force coupling expression of the foot robot with multiple supporting feet is obtained through calculation, and a supporting foot force coupling expression of the foot robot with multiple supporting feet is obtained;
step two, estimating a slope angle by using a plane fitting method according to the position of a foot end by using the foot force coupling expression of the foot type robot obtained by calculation in the step one, establishing a plane estimation equation and calculating to obtain the slope angle and a vertical distance parameter, adjusting the pitch angle and the roll angle of the robot body in real time according to the slope change of the ground and the limit position of a joint according to the estimation of the slope terrain to adapt to the terrain change, and calculating to obtain a mechanical transformation matrix for correcting the stress of the foot end, wherein the mechanical transformation matrix is as follows:
Figure FDA0003109973690000011
in the formula (I), the compound is shown in the specification,
Figure FDA0003109973690000012
is a rotation matrix between the slope ground and the horizontal ground; glegiA weight matrix for each leg;
Figure FDA0003109973690000013
estimating an angle for the slope;
step three, establishing normal and tangential stress balance equations of the foot robot by using the mechanical transformation matrix obtained by calculation in the step two, and establishing a roll torque balance equation suffered by the mass center of the robot based on the stress balance equations:
Figure FDA0003109973690000021
in the formula (I), the compound is shown in the specification,LFNzinormal support force for each foot;LFTyiis the tangential force of each foot;LPxi,LPyi,LPzicoordinates of the advancing direction, the tangential direction and the normal direction of each foot;LPx,LPy,LPzis the advancing direction of the machine body; coordinates of the tangential direction and the normal direction;
according to the stress and moment balance equation, the foot force optimization problem is converted into a quadratic programming problem:
Figure FDA0003109973690000022
in the formula, F is an m-dimensional column vector and represents a normal force and a tangential force of a foot end; g is an n-order symmetric matrix; g is an m-dimensional column vector; a is an mxn matrix; bwIs an m-dimensional column vector;
and (3) solving by a Lagrange method, and converting an objective equation for solving the unknown foot force into a Lagrange function:
Figure FDA0003109973690000023
in the formula, ArA foot force corresponding matrix to be solved is obtained; frSolving the result of the foot force; grIs an n-order symmetric matrix; grIs an m-dimensional column vector; lambda is a characteristic solution vector;
finally, the optimal solution of unknown foot force is obtained as follows:
Fr *＝-grH+Tbw (5)
in the formula, grIs an m-dimensional column vector; bwIs an m-dimensional column vector; h is an m-dimensional row vector;
step four, an optimization target equation in a foot force inhibition state in a slippage state is provided by using the optimal solution of the foot force obtained by calculation in the step three;
the optimization target equation of the normal force and the tangential force of the foot end in the slip suppression state is as follows:
Figure FDA0003109973690000031
in the formula (I), the compound is shown in the specification,LFTxi,LFTyia forward traction force for each foot;LFNziis the normal force of each foot;
Figure FDA0003109973690000032
is the forward acceleration of the body;
Figure FDA0003109973690000033
is the tangential acceleration of the machine body; i isBIs the inertia tensor of the body;
Figure FDA0003109973690000034
is yaw acceleration of the machine body;LPxithe position of the foot end in the single leg traction direction;LPyithe position of the foot end in the tangential direction of the single leg is shown;BPxis the position of the center of mass in the traction direction of the machine body;BPyis the position of the mass center of the machine body in the tangential force direction;
constructing a function L by a multiplier methodμ(FNs,FTs) Establishing an augmented Lagrange equation of a constructor:
Figure FDA0003109973690000035
in the formula, FTsA forward traction force for each foot; fNsIs the normal force of each foot; Δ FTsIs the amount of change in the forward traction of each foot;
Figure FDA0003109973690000036
is a multiplier coefficient; mu.sNTsTo be rubbedA cone eigenvalue; fsIs a foot-end three-way force; gNs,GTsIs an n-order symmetric matrix; a. thesIs an m multiplied by n matrix; bsIs an m-dimensional column vector;
if the obtained optimal solution cannot meet the inequality constraint, establishing an objective function of the inequality constraint as follows:
Figure FDA0003109973690000037
in the formula (I); fNsIs the normal force of each foot; Δ FTsIs the amount of change in the forward traction of each foot; Δ MTsIs the normal force variation of each foot; mu.sgIs the foot ground friction cone coefficient;
according to an inequality constrained target function, establishing an augmented Lagrange equation under a non-equality constraint condition as follows:
Figure FDA0003109973690000041
in the formula, FTsA forward traction force for each foot; fNsIs the normal force of each foot; Δ FTsIs the amount of change in the forward traction of each foot; Δ MTsIs the normal force variation of each foot; giIs a characteristic variable; gNs,GTs,GMTsIs an n-order symmetric matrix; mu is the foot ground friction coefficient; lambda [ alpha ]siIs a multiplier coefficient;
and step five, realizing the solving process of the foot force optimization and slip suppression method by using the objective function and the augmented Lagrange equation obtained by calculation in the step four.
2. The method of claim 1, wherein in the first step, the three-leg support and leg force coupling analysis of the legged robot establishes a three-dimensional moment equilibrium equation of the centroid of the legged robot as follows:
Figure FDA0003109973690000042
wherein the three-dimensional force acting on the center of mass of the robot isBFx,BFy,BFzAnd a three-dimensional moment vector is defined asBMx,BMy,BMzThe three-dimensional foot force of each supporting leg is defined asLFTxi,LFTyi,LFNziThe distance between the center of mass of the robot and the ground is h,BPxis the position of the center of mass in the traction direction of the machine body;BPyis the position of the mass center of the machine body in the tangential force direction;
under the condition of ensuring that the supporting feet have the same control input, calculating to obtain a normal force coupling expression of the foot type robot with an odd number of groups of the three supporting feet.
3. The method according to claim 2, wherein in the first step, the three-dimensional moment balance equation is established, the foot force coupling analysis of the four-foot support of the legged robot is performed, the normal foot force coupling characteristic based on the terrain information is analyzed according to the foot-ground contact model and the normal deviation of the single-foot distance contact surface, and the body balance equation during the four-leg support is established as follows:
Figure FDA0003109973690000051
wherein the three-dimensional force acting on the center of mass of the robot isBFx,BFy,BFzAnd a three-dimensional moment vector is defined asBMx,BMy,BMz；kNThe normal contact force stiffness coefficient; deltaLP1 n,
Figure FDA0003109973690000052
The position difference of the contact surfaces of the 1, 2, 4 and 5 feet in the normal direction of the ground is obtained;LPxithe position of the foot end in the traction direction;LPyiis the lateral direction position of the foot end;
Figure FDA0003109973690000053
the position difference of the contact surface of the foot in the normal direction of the ground;
and establishing a position deviation geometric condition of the foot end position to obtain a support foot force coupling expression of the four-foot supported foot type robot.
4. The method according to claim 3, wherein in the first step, the established three-dimensional moment balance equation is used for analyzing the force coupling characteristics of the five-foot support of the legged robot, the normal force coupling characteristics of the five-foot support based on the terrain information are analyzed according to the established foot-ground contact model and the normal deviation of two non-coplanar foot distance contact surfaces, and the body balance equation during the establishment of the five-foot support is as follows:
Figure FDA0003109973690000061
wherein the three-dimensional force acting on the center of mass of the robot isBFx,BFy,BFzAnd a three-dimensional moment vector is defined asBMx,BMy,BMz；kNThe normal contact force stiffness coefficient; deltaLP1 n,
Figure FDA0003109973690000062
The position difference of the contact surfaces of the 1, 2, 3, 5 and 6 feet in the ground normal direction is shown;LPxithe position of the foot end in the traction direction;LPyiis the lateral direction position of the foot end;
Figure FDA0003109973690000063
the position difference of the contact surface of the foot in the normal direction of the ground;
and establishing a position deviation geometric condition of the foot end position to obtain a five-foot supported foot force coupling expression of the foot type robot support.
5. The method according to claim 4, wherein in the second step, the slope angle is estimated by using the coupling analysis result of the multi-foot support foot force of the legged robot and adopting a plane fitting method according to the position of the foot end, a plane estimation equation is established, and parameters such as the slope angle and the vertical distance are obtained through calculation. According to the slope normal vector, the slope estimation angle
Figure FDA0003109973690000064
Comprises the following steps:
Figure FDA0003109973690000065
in the formula (I), the compound is shown in the specification,Sxi is a slope three-dimensional normal vector under the world coordinate system.
6. The method of claim 5, wherein in step two,
according to estimation of slope terrain, the pitching and rolling angles of the robot body are adjusted in real time to adapt to terrain change according to slope change of the ground and the joint limit position, and a mechanical transformation matrix is obtained through calculation and used for correcting foot end stress, wherein the mechanical transformation matrix is as follows:
Figure FDA0003109973690000071
in the formula (I), the compound is shown in the specification,
Figure FDA0003109973690000072
is a rotation matrix between the slope ground and the horizontal ground; glegiA weight matrix for each leg;
Figure FDA0003109973690000073
an angle is estimated for the slope.
7. The method as claimed in claim 6, wherein in the third step, the calculated mechanical transformation matrix based on the terrain estimation is used for optimizing the foot force under steady walking, normal and tangential force balance equations of the foot type robot are established, and a roll moment balance equation suffered by the center of mass of the robot is established based on the force balance equations.
8. The method according to claim 7, wherein in the fifth step, the solving process of the foot force optimization and slip suppression method is divided into the following three steps:
step 1: judging the motion state of the foot type robot according to the slip state estimation;
step 2: judging whether the foot end slips or not by utilizing the motion state of the foot type robot obtained in the step 1, establishing a foot force optimization objective function, establishing an organism balance equation, constructing a Lagrange objective function through the established objective function, and solving to finally obtain a foot force three-dimensional optimal solution; (ii) a
And step 3: and (3) establishing a foot force inhibition optimization objective function in the slippage state by utilizing the motion state and foot ground force of the foot type robot obtained by calculation in the steps (1) and (2), constructing an augmented Lagrange objective function, solving an unconstrained problem, and finally obtaining a three-dimensional optimal solution of the foot force in the slippage state.
9. Use of the method according to any one of claims 1 to 8 in the field of legged robot motion control technology.
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