CN113050645A - Spring-loaded inverted pendulum model of biped robot and gait planning method - Google Patents

Spring-loaded inverted pendulum model of biped robot and gait planning method Download PDF

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CN113050645A
CN113050645A CN202110301977.7A CN202110301977A CN113050645A CN 113050645 A CN113050645 A CN 113050645A CN 202110301977 A CN202110301977 A CN 202110301977A CN 113050645 A CN113050645 A CN 113050645A
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leg
foot
biped robot
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CN113050645B (en
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高亮
谢思诚
钟浩然
卢盛雨
胡成颢
董昊臻
李新宇
李培根
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Huazhong University of Science and Technology
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    • G—PHYSICS
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    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
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    • 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
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
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Abstract

The invention belongs to the technical field related to gait planning of a biped robot, and discloses a spring-loaded inverted pendulum model of the biped robot and a gait planning method, wherein the model comprises two legs and a mass center, and one ends of the two legs are connected to the mass center; the rigidity of the legs can be adjusted in a self-adaptive manner according to the step length of the biped robot; the model further comprises an ankle joint and a foot, and the other ends of the two legs are connected to the foot through the ankle joint respectively. The improved spring load inverted pendulum model containing the foot with the limited size has the foot with the limited size and the actively controlled ankle joint, can effectively improve the control performance and the motion performance of the robot, and can be applied to various double-foot or humanoid robots containing the active ankle joint and the foot; the model has the characteristic of adjustable leg rigidity, can realize flexible foot falling and reduce the impact of the foot and the ground, and can improve the step length range of the biped robot by combining a gait planning method of a self-adaptive leg stretching strategy.

Description

Spring-loaded inverted pendulum model of biped robot and gait planning method
Technical Field
The invention belongs to the technical field related to biped robot gait planning, and particularly relates to a spring-loaded inverted pendulum model of a biped robot and a gait planning method.
Background
The simplified model of the biped robot is an approximate dynamic model for abstracting the main characteristics of the robot. Because the biped robot has the characteristics of multiple joints, nonlinearity, strong coupling and variable structure, the control key points can be grasped by using the simplified model to control the robot, the motion planning is convenient, the control difficulty is effectively reduced, and the biped robot is widely applied to the aspects of biped robot gait planning and the like at present.
The Spring-Loaded Inverted Pendulum model (SLIP) is a simplified model of a biped robot with wide application, and consists of a mass center converging the whole body mass of the biped robot to one point and two legs which are free of mass, telescopic and have certain rigidity. The spring-loaded inverted pendulum model naturally has flexibility of legs, can absorb impact of foot bottom collision, simultaneously presents characteristics of ground reaction force, mass center track and the like similar to those of human beings in the walking process, and therefore can be used for predicting and generating running and walking gaits of the biped robot.
However, the traditional spring-loaded inverted pendulum model is an under-actuated model, and because the model does not have ankle joints and feet, and the spring stiffness of the two legs is fixed, the motion process is determined only by the physical parameters and initial state of the model, the motion capability and control performance of the biped robot are limited, and the biped robot is difficult to adapt to more complex external environments. The ankle joint and the foot play important roles of supporting, propelling, balancing and the like in the process of standing and walking of the human body, and are key components of a double-foot upright walking mode system. In addition, the rigidity of the legs of the human body can be adjusted within a certain range when the human body is in an asynchronous running environment, so that high robustness to a complex environment is shown. The conventional spring-loaded inverted pendulum model does not have the above characteristics and thus has limited its application in bipedal robots.
Disclosure of Invention
In view of the above drawbacks or needs for improvement of the prior art, the present invention provides a spring-loaded inverted pendulum model of a biped robot and a gait planning method, which realize the improvement of the model by exchanging point-like feet of a conventional spring-loaded inverted pendulum model into an ankle joint having one degree of freedom and a foot having no mass and limited size; meanwhile, a gait planning method based on a self-adaptive leg stretching strategy is provided, the centroid track in the motion process is obtained by combining optimization algorithm optimization, and walking control of the biped robot under the condition of accurate step length is realized.
To achieve the above objects, according to one aspect of the present invention, there is provided a spring-loaded inverted pendulum model of a biped robot, the model including two legs and a centroid, one end of each of the two legs being connected to the centroid; the rigidity of the legs can be adjusted in a self-adaptive manner according to the step length of the biped robot;
the model further comprises an ankle joint and a foot, and the other ends of the two legs are connected to the foot through the ankle joint respectively.
Further, the ankle joint is a one-degree-of-freedom ankle joint; the foot is a zero mass, limited size foot.
Furthermore, two legs are respectively called a supporting leg and a swinging leg, and i e is used as [ A, B ]]Is shown byiDenotes the leg length, kiRepresenting the equivalent stiffness of the leg, the contact angle theta representing the angle between the swing leg and the ground when the swing leg lands on the ground, xTDIndicating the position of the landing point; the dynamic formula of the centroid is:
Figure BDA0002986674940000021
where m is the mass of the centroid, pc＝[xc,zc]TIs the position of the center of mass, g is the acceleration of gravity, l0Is the original length of the leg, | | li| | is the actual length of the leg,
Figure BDA0002986674940000022
is a unit vector in the leg direction, τiIs the moment acting on the ankle joint.
According to another aspect of the present invention, there is provided a gait planning method of a biped robot, the gait planning method comprising the steps of:
(1) dividing the walking cycle of the biped robot based on the spring-loaded inverted pendulum model of the biped robot as described above;
(2) judging the gait cycle of the biped robot, and controlling the biped robot by adopting a self-adaptive leg stretching strategy according to the judgment result; the self-adaptive leg stretching strategy comprises moment control of ankle joints and adjustment of leg rigidity;
(3) the gait planning problem of the biped robot is converted into an optimization problem, optimization is carried out through an optimization algorithm to obtain control parameters, and the gait track of the biped robot is further obtained through solving of a differential equation.
Further, the step (1) includes a step of dividing one walking cycle of the biped robot into a monopod supporting period 1, a biped supporting period and a monopod supporting period 2 by using a finite state machine according to the model.
Further, if the biped robot is in the single-foot support period 1, a single-foot support control mode is adopted, wherein the single-foot support control mode comprises an early single-foot support control mode and an early swing control mode; wherein, the early stage single-foot supporting control mode adopts the following formula to control:
Figure BDA0002986674940000031
Figure BDA0002986674940000033
wherein the content of the first and second substances,m is the mass of the centroid; g is the acceleration of gravity; two legs adopt i epsilon [ A, B ∈]Carrying out representation; moment tau acting on ankle joint of leg AAsAdopting PD control; kp1And Kd1Control parameter for leg A, /)dThe shortest leg length that the A leg can reach at the stage is obtained, and the A leg can be adaptively adjusted according to the step length;
Figure BDA0002986674940000034
is the rate of change of leg length; l0Is the leg length; k is a radical ofAIs the stiffness of the A leg; iA| | is the actual length of the a leg;
Figure BDA0002986674940000035
is a unit vector in the direction of the a leg; p is a radical ofc＝[xc,zc]TIs the centroid position.
The early swing control mode uses a 5 th order bezier curve to generate a foot trajectory, which is controlled using the following formula:
Figure BDA0002986674940000032
wherein t is a normalized time coefficient; pi＝[xpi,zpi]Is a control point in the forward plane; b (t) ═ xBi,zBi]Is a point on the foot trajectory; n is the order of the bezier curve.
Further, if the biped robot is in the biped support mode, the biped support control mode is adopted, the biped support control mode comprises a first stage and a second stage, the first stage is that the gravity center gradually shifts to the leg B after the leg B falls to the ground;
the first stage is after the B leg falls to the ground and satisfies kB(l0-||lB| |) < 0.3mg, at which time the A leg still plays a major supporting role, controlled by the following formula:
Figure BDA0002986674940000041
the second stage is that the gravity center gradually shifts to the B leg and satisfies kB(l0-||lB| | is not less than 0.3mg, and the following formula is adopted for control:
Figure BDA0002986674940000042
Figure BDA0002986674940000047
in the formula, moment tau acting on ankle joint of B legBdUsing PD control, Kp3And Kd3For the purpose of its control parameters, the control parameters,
Figure BDA0002986674940000048
is the rate of change of leg length; two legs adopt i epsilon [ A, B ∈]Carrying out representation; m is the mass of the centroid; g is the acceleration of gravity; k is a radical ofAIs the stiffness of the A leg; iA| | is the actual length of the a leg;
Figure BDA0002986674940000043
is a unit vector in the direction of the a leg; k is a radical ofBIs the stiffness of the B leg; iB| | is the actual length of the B leg;
Figure BDA0002986674940000044
is a unit vector in the direction of the B leg; p is a radical ofc＝[xc,zc]TIs the centroid position; g is the acceleration of gravity; l0Is the leg length.
Further, if the biped robot is in the single-foot support period 2 mode, a late single-foot support control mode and a late swing control mode are adopted, wherein the late single-foot support control mode is controlled by adopting the following formula:
Figure BDA0002986674940000045
τBs＝Kp2(l0-||lB||)+Kd2lB
wherein the moment tau acting on the ankle joint of the leg BBsUsing PD control, Kp2And Kd2Control parameters for it;
Figure BDA0002986674940000049
is the rate of change of leg length; m is the mass of the centroid; g is the acceleration of gravity; k is a radical ofBIs the stiffness of the B leg; iB| | is the actual length of the B leg;
Figure BDA0002986674940000046
is a unit vector in the direction of the B leg; l0Is the leg length; p is a radical ofc＝[xc,zc]TIs the centroid position.
The late swing control mode adopts a 5-order Bezier curve to generate a foot track, and specifically adopts the following formula to control:
Figure BDA0002986674940000051
where t is a normalized time coefficient, Pi＝[xpi,zpi]Is a control point in the forward plane, b (t) ═ xBi,zBi]Is a point on the foot trajectory; n is the order of the bezier curve.
Further, step (3) comprises the following substeps:
3.1, determining an initial state and a terminal state of a gait cycle and an expression of parameters to be solved in a gait planning problem;
3.2 carrying out constraint analysis on the biped robot, wherein the constraint of the biped robot comprises foot overturning constraint and kinematic constraint;
3.3 based on the constraint conditions of the biped robot, optimizing the gait track by an optimization algorithm.
Further, the foot rollover constraint is:
-lf1≤xP≤lf2
the kinematic constraints are:
||li||≤l0
Figure BDA0002986674940000052
wherein the content of the first and second substances,
Figure BDA0002986674940000053
is the velocity of the centroid in the x direction; x is the number ofPThe position of the FRI in the x-axis direction of the foot end; lf1、lf2Is the geometric parameter of the foot; z is a radical ofcIs the height of the centroid in the z-axis direction.
The optimization problem is represented as:
Figure BDA0002986674940000054
the fitness function of the optimization problem is expressed as:
Figure BDA0002986674940000055
wherein f is ═ f1 f2 f3 f4 f5]Representing a weight factor; x is the number ofn、
Figure BDA0002986674940000061
znAnd
Figure BDA0002986674940000062
respectively representing the position and the speed of the mass center in the directions of the x axis and the z axis when the mass center is in the single-foot neutral state at the end of the nth step;
Figure BDA0002986674940000063
and
Figure BDA0002986674940000064
is the ideal shortest of the A leg in the n +1 stepLeg length and actual shortest leg length; ms isnRepresenting the state of the model in the neutral position of the single foot in the nth step, including the position and the speed of the centroid in the directions of the x axis and the z axis, and the shortest leg length which can be reached by the A leg in the n steps; ms is0Representing the state of the initial single-leg neutral position of the model; u. ofn+1Represents a set of control parameters including touchdown angle, biped stiffness, PD controller parameters for each stage, and the ideal shortest leg length for step a, step n + 1.
Generally, compared with the prior art, the spring-loaded inverted pendulum model and the gait planning method of the biped robot provided by the invention have the following beneficial effects:
1. the improved spring load inverted pendulum model with the limited-size foot has the limited-size foot and the actively controlled ankle joint, can effectively improve the control performance and the motion performance of the robot, and can be applied to various biped robots or humanoid robots with active ankle joints and feet.
2. The spring inverted pendulum model with the limited foot size has the characteristic of adjustable leg rigidity, can achieve flexible foot falling and reduce impact on the foot and the step planning method of the self-adaptive leg stretching strategy is combined, the step range of the biped robot can be increased, accurate foot falling control is achieved, and the robustness of the biped robot motion and the adaptability to the environment are effectively enhanced.
3. The invention can realize the accurate step length control of the biped robot, and then can realize the walking control of the robot on a discrete road surface.
4. The gait planning method is simple, easy to implement and high in applicability.
Drawings
FIG. 1 is a schematic diagram of a spring-loaded inverted pendulum model of a biped robot provided by the present invention;
fig. 2 (a) and (b) are schematic diagrams for comparing a spring-loaded inverted pendulum model of a conventional biped robot with a spring-loaded inverted pendulum model of the biped robot in fig. 1, respectively;
FIG. 3 shows the gait cycle division of the invention in (a), (b), (c) and (d);
FIG. 4 is a schematic diagram of the distribution of FRI points in a foot according to the present invention;
FIG. 5 is a schematic step range diagram for two models;
FIG. 6 is a centroid and foot trajectory of the VSLIP-FF model at maximum stride length;
FIG. 7 (a) and (b) are graphs of VSLIP-FF model ankle joint stress and moment in maximum step size.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Referring to fig. 1 and 2, the spring-loaded inverted pendulum model of the biped robot provided by the invention comprises two legs with adjustable rigidity, a center of mass, ankle joints and feet, wherein one end of each leg is connected to the center of mass, and the other end of each leg is connected to the feet through the ankle joints. Wherein the ankle joint is a one-degree-of-freedom ankle joint; the foot is a zero mass, limited size foot.
During the movement, the supporting legs and the swinging legs of the model are formed by i e to [ A, B ∈ [ ]]Is shown byiDenotes the leg length, kiRepresenting the equivalent stiffness of the leg, the contact angle theta representing the angle between the swing leg and the ground when the swing leg lands on the ground, xTDIndicating the position of the landing point; the dynamic formula of the centroid is:
Figure BDA0002986674940000071
wherein m is the mass of the centroid; p is a radical ofc＝[xc,zc]TIs the centroid position; g is the acceleration of gravity; l0Is the leg length; iiIs the actual length of the leg；
Figure BDA0002986674940000072
Is a unit vector in the leg direction; tau isiIs the moment acting on the ankle joint.
The invention also provides a gait planning method of the biped robot, which comprises the following steps:
the first step is to provide the spring-loaded inverted pendulum model of the biped robot, and to divide one walking cycle of the biped robot by using a finite state machine according to the model.
Specifically, one gait cycle is divided into a monopod support period 1(SS1), a bipedal support period (DS), and a monopod support period 2(SS2) using a finite state machine according to the spring-loaded inverted pendulum model, as shown in fig. 3.
The gait cycle starts from a single-foot neutral state (MS), specifically:
Figure BDA0002986674940000081
in the formula, zc0Is the initial height of the centroid;
Figure BDA0002986674940000082
is the velocity in the z-axis direction; x is the number ofTDiIs the position of the model support leg in the x-axis direction in step i. At this point, one-foot support period 1 is entered, leg a is in the early one-foot support control mode, and leg B is in the early swing control mode.
When model leg B Touches Down (TD), specifically:
Figure BDA0002986674940000083
at this time, the two-leg support period is entered, and both the leg a and the leg B are switched to the two-foot support control mode.
When the model leg a lifts off the ground (LO), specifically:
Figure BDA0002986674940000084
at this time, the single-leg support period 2 is entered, leg a is switched to the late swing control mode, and leg B is switched to the late single-foot support mode. When the model reaches the single-foot neutral state (MS) again, the single-leg support phase 2 is finished, and a complete gait cycle is completed.
Step two, judging the gait cycle of the biped robot, and controlling the biped robot according to the judgment result and the self-adaptive leg stretching strategy; wherein the adaptive leg stretching strategy comprises moment control of ankle joints and adjustment of leg stiffness.
Specifically, the strategy comprises moment control of ankle joints and adjustment of leg rigidity to realize adaptive leg stretching, and further complete control of the whole gait cycle. In monopod support period 1(SS1), the moment acting on the ankle of the A leg provides vertical support to the support leg (leg A), causing the leg to contract to an adaptive length. In the bipedal support period (DS), when the model center of gravity is transferred to the B leg, the moment acting on the ankle of the B leg stretches the A leg to the original leg length. In one-leg support period 2(SS2), leg B becomes the new support leg, with its ankle moment driving the center of mass back to the original height. In the whole gait process, the leg rigidity is self-adaptively adjusted according to the step length.
If the biped robot is in the single-foot support period 1, adopting a single-foot support control mode, wherein the single-foot support control mode comprises an early single-foot support control mode and an early swing control mode; wherein, the early stage single-foot supporting control mode adopts the following formula to control:
Figure BDA0002986674940000091
τAs＝-(Kp1(||lA||-ld)-Kd1lA)
wherein the moment tau acting on the ankle joint of the leg AAsUsing PD control, Kp1And Kd1For its control parameters. ldIs reached at this stage by the A legThe shortest leg length and can be adaptively adjusted according to the step length.
Figure BDA0002986674940000092
Is the rate of change of leg length; k is a radical ofAIs the stiffness of the A leg; iA| | is the actual length of the a leg;
Figure BDA0002986674940000093
is a unit vector in the a-leg direction.
The early swing control mode uses a 5 th order bezier curve to generate a foot trajectory, which is controlled using the following formula:
Figure BDA0002986674940000094
wherein t is a normalized time coefficient; pi＝[xpi,zpi]Is a control point in the forward plane; b (t) ═ xBi,zBi]Is a point on the foot trajectory; n is the order of the bezier curve. In order to avoid impact with the ground, the position, the speed and the acceleration of the initial moment and the terminal moment of the foot track are restrained, and the method specifically comprises the following steps:
TABLE 1 early swing control mode constraint parameters
Figure BDA0002986674940000095
Wherein
Figure BDA0002986674940000096
The velocity of the swing leg in the one-foot neutral state is the same as the initial velocity of the center of mass.
And if the biped robot is in the biped support mode, adopting the biped support control mode, wherein the biped support control mode comprises a first stage and a second stage, and after the B leg falls to the ground, the gravity center is gradually shifted to the B leg in the second stage.
The first stage is after the B leg falls to the ground and satisfies kB(l0-||lB| |) < 0.3mg, at which time the A leg still plays a major supporting role, controlled by the following formula:
Figure BDA0002986674940000101
the second stage is that the gravity center gradually shifts to the B leg and satisfies kB(l0-||lB| | is not less than 0.3mg, and the following formula is adopted for control:
Figure BDA0002986674940000102
Figure BDA0002986674940000109
in the formula, moment tau acting on ankle joint of B legBdAdopting PD control; kp3And Kd3Control parameters for it;
Figure BDA0002986674940000103
is the rate of change of leg length; k is a radical ofAIs the stiffness of the A leg; iA| | is the actual length of the a leg;
Figure BDA0002986674940000104
is a unit vector in the direction of the a leg; k is a radical ofBIs the stiffness of the B leg; iB| | is the actual length of the B leg;
Figure BDA0002986674940000105
is a unit vector in the direction of the B leg.
If the biped robot is in the single-foot support period 2 mode, a late single-foot support control mode and a late swing control mode are adopted, wherein the late single-foot support control mode is controlled by adopting the following formula:
Figure BDA0002986674940000106
Figure BDA0002986674940000107
wherein the moment tau acting on the ankle joint of the leg BBsUsing PD control, Kp2And Kd2For its control parameters.
Figure BDA00029866749400001010
Is the rate of change of leg length; k is a radical ofBIs the stiffness of the B leg; iB| | is the actual length of the B leg;
Figure BDA0002986674940000108
is a unit vector in the direction of the B leg.
The late swing control mode adopts a 5-order Bezier curve to generate a foot track, and specifically adopts the following formula to control:
Figure BDA0002986674940000111
wherein t is a normalized time coefficient; pi＝[xpi,zpi]Is a control point in the forward plane; b (t) ═ xBi,zBi]Is a point on the foot trajectory; n is the order of the bezier curve. In order to avoid impact with the ground, the position, the speed and the acceleration of the initial moment and the terminal moment of the foot track are restrained, and the method specifically comprises the following steps:
TABLE 2 late swing control mode constraint parameters
Figure BDA0002986674940000112
Wherein the content of the first and second substances,
Figure BDA0002986674940000113
the velocity of the swing leg in the one-foot neutral state is the same as the initial velocity of the center of mass.
And step three, converting the gait planning problem of the biped robot into an optimization problem, optimizing through an optimization algorithm to obtain control parameters, and further solving through a differential equation solving method to obtain the gait track of the biped robot.
Specifically, step three includes the following substeps:
3.1 determining the initial state and the terminal state of the gait cycle and the expression of the parameters to be solved in the gait planning problem.
The initial state and the terminal state of the gait cycle and the expressions of the parameters to be solved in the gait planning problem are respectively as follows:
msn+1＝H(msn,un+1)
Figure BDA0002986674940000114
Figure BDA0002986674940000115
Figure BDA0002986674940000116
in the formula, H represents a regression map of a one-foot neutral state; ms isnRepresenting the state of the model in the neutral position of the single foot in the nth step, including the position and the speed of the centroid in the directions of the x axis and the z axis, and the shortest leg length which can be reached by the A leg in the n steps; ms is0Representing the state of the initial single-leg neutral position of the model; u. ofn+1Represents a set of control parameters including touchdown angle, biped stiffness, PD controller parameters for each stage, and the ideal shortest leg length for step a, step n + 1.
And 3.2, carrying out constraint analysis on the biped robot, wherein the constraints of the biped robot comprise foot overturning constraints and kinematic constraints.
Referring to fig. 4, a Foot-turning Indicator (FRI) is adopted for Foot turning constraint, when the FRI point is located within the Foot supporting range, the force and moment applied to the ankle joint can be balanced with the ground reaction force, the Foot cannot be turned, and the model keeps balance; when the FRI point is located outside the foot supporting range, the foot end generates a net moment, the foot turns over and the model is unbalanced, and the position of the FRI point can be expressed as:
xP＝-(Fixhf+τi)/Fiz
Fi＝ki(l0-||li||)
in the formula, xPThe position of the FRI point in the x-axis direction of the foot end (the ankle joint is taken as the origin of coordinates); fiThe force applied to the ankle joints of each leg; fixAnd FizIs the component force in the directions of the x axis and the z axis; lf1、lf2And hfIs the geometric parameter of the foot. The foot rollover constraint is:
-lf1≤xP≤lf2。
the kinematic constraint is added for avoiding the failure condition of gait planning, and specifically comprises the following steps:
||li||≤l0
Figure BDA0002986674940000121
wherein the content of the first and second substances,
Figure BDA0002986674940000122
is the velocity of the centroid in the x direction; z is a radical ofcIs the height of the centroid in the z-axis direction.
3.3 based on the constraint conditions of the biped robot, optimizing the gait track by an optimization algorithm.
Specifically, the trajectory generation method may be a longge-kutta method or an euler method, and the optimization algorithm may be a genetic algorithm or a differential evolution algorithm.
Optimizing the gait trajectory through an optimization algorithm, wherein the gait planning problem can be transformed into an optimization problem of the trajectory, which can be expressed as:
Figure BDA0002986674940000131
the fitness function of the optimization problem may be expressed as:
Figure BDA0002986674940000132
wherein f is ═ f1 f2 f3 f4 f5]Representing a weight factor; x is the number ofn、
Figure BDA0002986674940000133
znAnd
Figure BDA0002986674940000134
respectively representing the position and the speed of the mass center in the directions of the x axis and the z axis when the mass center is in the single-foot neutral state at the end of the nth step;
Figure BDA0002986674940000135
and
Figure BDA0002986674940000136
the ideal shortest leg length and the actual shortest leg length of the A leg in the step (n + 1); u. ofn+1Represents a set of control parameters including touchdown angle, biped stiffness, PD controller parameters for each stage, and the ideal shortest leg length for step a, step n + 1.
The invention is described in further detail below with reference to a specific embodiment.
By using the model and the gait planning method of the invention, the mass of the gait planning model is 115kg, the original length of the leg is 1m, and the geometric parameter l of the foot is measuredf1Is 0.25m, lf2Is 0.05m, hfThe gait planning is carried out on the biped robot with the speed of 0.1m, the initial speed of 1m/s in the x-axis direction, the initial speed of 0m/s in the z-axis direction and the height of the center of mass of the biped robot in the single-foot neutral state of 0.97m so as to obtain continuous periodic gait.
Fig. 5 shows the gait planning step range under the same condition for two models, wherein the improved spring-loaded inverted pendulum model with the foot of limited size adopts a gait planning method based on an adaptive leg stretching strategy, and the traditional spring-loaded inverted pendulum model adopts the same gait planning method except for the ankle joint. It can be seen that the actual shortest leg length of the leg of the model A is in a descending trend along with the increase of the step length; in contrast, the improved spring-loaded inverted pendulum model with limited foot size has a step size range that is increased by 19.35%, demonstrating the effectiveness and advancement of the model and method of the present invention.
Fig. 6 is a centroid trace and a foot trace of a modified spring-loaded inverted pendulum model with a finite-sized foot at a maximum step size of 0.97m, and fig. 7 is a force and moment curve to which an ankle joint is subjected.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (10)

1. The utility model provides a spring load inverted pendulum model of biped robot which characterized in that:
the model comprises two legs and a mass center, and one ends of the two legs are connected to the mass center; the rigidity of the legs can be adjusted in a self-adaptive manner according to the step length of the biped robot;
the model further comprises an ankle joint and a foot, and the other ends of the two legs are connected to the foot through the ankle joint respectively.
2. The spring-loaded inverted pendulum model of a biped robot according to claim 1, characterized in that: the ankle joint is a degree-of-freedom ankle joint; the foot is a zero mass, limited size foot.
3. The spring-loaded inverted pendulum model of a biped robot according to claim 1, characterized in that: two legs are respectively called supporting leg and swinging leg, and i is an e [ A, B ]]Is shown byiDenotes the leg length, kiRepresenting the equivalent stiffness of the leg, the contact angle theta representing the angle between the swing leg and the ground when the swing leg lands on the ground, xTDIndicating the position of the landing point; the dynamic formula of the centroid is:
Figure FDA0002986674930000011
wherein m is the mass of the centroid; p is a radical ofc＝[xc,zc]TIs the position of the center of mass, g is the acceleration of gravity, l0Is the original length of the leg, | | li| | is the actual length of the leg,
Figure FDA0002986674930000012
is a unit vector in the leg direction, τiIs the moment acting on the ankle joint.
4. A gait planning method of a biped robot is characterized by comprising the following steps:
(1) dividing a walking cycle of the biped robot based on the spring-loaded inverted pendulum model of the biped robot according to any one of claims 1 to 3;
(2) judging the gait cycle of the biped robot, and controlling the biped robot by adopting a self-adaptive leg stretching strategy according to the judgment result; the self-adaptive leg stretching strategy comprises moment control of ankle joints and adjustment of leg rigidity;
(3) the gait planning problem of the biped robot is converted into an optimization problem, optimization is carried out through an optimization algorithm to obtain control parameters, and the gait track of the biped robot is further obtained through solving of a differential equation.
5. The gait planning method of a biped robot according to claim 4, characterized in that: the step (1) also comprises a step of dividing a walking cycle of the biped robot into a single-foot supporting period 1, a double-foot supporting period and a single-foot supporting period 2 by using a finite state machine according to the model.
6. The gait planning method of a biped robot according to claim 5, characterized in that: if the biped robot is in the single-foot support period 1, adopting a single-foot support control mode, wherein the single-foot support control mode comprises an early single-foot support control mode and an early swing control mode; wherein, the early stage single-foot supporting control mode adopts the following formula to control:
Figure FDA0002986674930000021
Figure FDA0002986674930000022
wherein m is the mass of the centroid; g is the acceleration of gravity; two legs adopt i epsilon [ A, B ∈]Carrying out representation; moment tau acting on ankle joint of leg AAsAdopting PD control; kp1And Kd1Control parameter for leg A, /)dThe shortest leg length that the A leg can reach at the stage is obtained, and the A leg can be adaptively adjusted according to the step length;
Figure FDA0002986674930000023
is the rate of change of leg length; l0Is the leg length; k is a radical ofAIs the stiffness of the A leg; iA| | is the actual length of the a leg;
Figure FDA0002986674930000024
is a unit vector in the direction of the a leg; p is a radical ofc＝[xc,zc]TIs the centroid position;
the early swing control mode uses a 5 th order bezier curve to generate a foot trajectory, which is controlled using the following formula:
Figure FDA0002986674930000025
wherein t is a normalized time coefficient; pi＝[xpi,zpi]Is a control point in the forward plane; b (t) ═ xBi,zBi]Is a point on the foot trajectory; n is the order of the bezier curve.
7. The gait planning method of a biped robot according to claim 5, characterized in that: if the biped robot is in the biped support mode, adopting the biped support control mode, wherein the biped support control mode comprises a first stage and a second stage, and the first stage is that the gravity center gradually shifts to the leg B after the leg B falls to the ground;
the first stage is after the B leg falls to the ground and satisfies kB(l0-||lB| |) < 0.3mg, at which time the A leg still plays a major supporting role, controlled by the following formula:
Figure FDA0002986674930000031
the second stage is that the gravity center gradually shifts to the B leg and satisfies kB(l0-||lB| | is not less than 0.3mg, and the following formula is adopted for control:
Figure FDA0002986674930000032
Figure FDA0002986674930000033
wherein the moment tau acting on the ankle joint of the leg BBdUsing PD control, Kp3And Kd3For the purpose of its control parameters, the control parameters,
Figure FDA0002986674930000034
is the rate of change of leg length; two legs adopt i epsilon [ A, B ∈]Carrying out representation; m is the mass of the centroid; g is the acceleration of gravity; k is a radical ofAIs the stiffness of the A leg; iA| | is the actual length of the a leg;
Figure FDA0002986674930000035
is a unit vector in the direction of the a leg; k is a radical ofBIs the stiffness of the B leg; iB| | is the actual length of the B leg;
Figure FDA0002986674930000036
is a unit vector in the direction of the B leg; p is a radical ofc＝[xc,zc]TIs the centroid position; g is the acceleration of gravity; l0Is the leg length.
8. The gait planning method of a biped robot according to claim 5, characterized in that: if the biped robot is in the single-foot support period 2 mode, a late single-foot support control mode and a late swing control mode are adopted, wherein the late single-foot support control mode is controlled by adopting the following formula:
Figure FDA0002986674930000037
Figure FDA0002986674930000038
wherein the moment tau acting on the ankle joint of the leg BBsUsing PD control, Kp2And Kd2For the purpose of its control parameters, the control parameters,
Figure FDA0002986674930000039
is the rate of change of leg length; m is the mass of the centroid; g is the acceleration of gravity; k is a radical ofBIs the stiffness of the B leg; iB| | is the actual length of the B leg;
Figure FDA00029866749300000310
is a unit vector in the direction of the B leg; l0Is the leg partOriginal length; p is a radical ofc＝[xc,zc]TIs the centroid position;
the late swing control mode adopts a 5-order Bezier curve to generate a foot track, and specifically adopts the following formula to control:
Figure FDA0002986674930000041
where t is a normalized time coefficient, Pi＝[xpi,zpi]Is a control point in the forward plane, b (t) ═ xBi,zBi]Is a point on the foot trajectory; n is the order of the bezier curve.
9. A gait planning method of a biped robot according to any one of claims 4 to 8, characterized in that: the step (3) comprises the following substeps:
3.1, determining an initial state and a terminal state of a gait cycle and an expression of parameters to be solved in a gait planning problem;
3.2 carrying out constraint analysis on the biped robot, wherein the constraint of the biped robot comprises foot overturning constraint and kinematic constraint;
3.3 based on the constraint conditions of the biped robot, optimizing the gait track by an optimization algorithm.
10. The gait planning method of a biped robot according to claim 9, characterized in that: the foot rollover constraint is:
-lf1≤xP≤lf2
the kinematic constraints are:
||li||≤l0
Figure FDA0002986674930000042
wherein the content of the first and second substances,
Figure FDA0002986674930000043
is the velocity of the centroid in the x direction; x is the number ofPThe position of the FRI point in the x-axis direction of the foot end; lf1、lf2Is the geometric parameter of the foot; l0Is the original length of the leg; z is a radical ofcIs the height of the centroid in the z-axis direction;
the optimization problem is represented as:
Figure FDA0002986674930000044
the fitness function of the optimization problem is expressed as:
Figure FDA0002986674930000045
wherein f is ═ f1 f2 f3 f4 f5]Representing a weight factor; x is the number ofn、
Figure FDA0002986674930000051
znAnd
Figure FDA0002986674930000052
respectively representing the position and the speed of the mass center in the directions of the x axis and the z axis when the mass center is in the single-foot neutral state at the end of the nth step;
Figure FDA0002986674930000053
and
Figure FDA0002986674930000054
the ideal shortest leg length and the actual shortest leg length of the A leg in the step (n + 1); ms isnRepresenting the state of the model in the neutral position of the single foot in the nth step, including the position and the speed of the centroid in the directions of the x axis and the z axis, and the shortest leg length which can be reached by the A leg in the n steps; ms is0Representing the state of the initial single-leg neutral position of the model; u. ofn+1Represents a set of control parameters including a touchdown angle,The rigidity of the two legs, the PD controller parameters of each stage and the ideal shortest leg length of the A leg of the (n + 1) th step.
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