CN111284584B - Single-foot support phase step planning method for biped robot - Google Patents

Single-foot support phase step planning method for biped robot Download PDF

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CN111284584B
CN111284584B CN202010086909.9A CN202010086909A CN111284584B CN 111284584 B CN111284584 B CN 111284584B CN 202010086909 A CN202010086909 A CN 202010086909A CN 111284584 B CN111284584 B CN 111284584B
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CN111284584A (en
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袁海辉
沈方岩
顾建军
朱世强
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Zhejiang Lab
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B62—LAND VEHICLES FOR TRAVELLING OTHERWISE THAN ON RAILS
    • B62D—MOTOR VEHICLES; TRAILERS
    • B62D57/00—Vehicles characterised by having other propulsion or other ground- engaging means than wheels or endless track, alone or in addition to wheels or endless track
    • B62D57/02—Vehicles characterised by having other propulsion or other ground- engaging means than wheels or endless track, alone or in addition to wheels or endless track with ground-engaging propulsion means, e.g. walking members
    • B62D57/032—Vehicles characterised by having other propulsion or other ground- engaging means than wheels or endless track, alone or in addition to wheels or endless track with ground-engaging propulsion means, e.g. walking members with alternately or sequentially lifted supporting base and legs; with alternately or sequentially lifted feet or skid

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Abstract

The invention discloses a single-foot support phase step planning method for a biped robot. The method estimates the landing time of the under-actuated free robot based on a simplified model, further considers possible landing time errors, enables the robot to move to a target pose in advance, and then keeps the pose to land; in addition, in order to avoid scraping between the swinging feet of the robot and the ground, the method decomposes the action process of the swinging legs of the single-foot support, including leg lifting action and leg swinging action. Based on the single-foot support phase step planning method provided by the invention, the robot can be effectively helped to reach the expected foot landing point on the single-foot support phase and can be prevented from being scraped with the ground, so that the walking movement and task operation of the biped robot can be realized.

Description

Single-foot support phase step planning method for biped robot
Technical Field
The invention belongs to the technical field of robots, and particularly relates to a single-foot support phase step planning method for a biped robot.
Background
In recent years, the development of biped robots has received unprecedented attention at home and abroad, and a series of biped robot development plans have been developed. At present, prototypes of biped robots have been designed in many countries, such as Atlas of boston power company, Cassie of Agility robotics company, ASIMO of japan honda company, HRP series of AIST, HUBO series of KAIST of korea, eucub of european open source robot, colleague series of beijing physicists university of china, WLR-II and GoRoBoT of harbin industries university, XT of china science and technology university, kukou of zhejiang university, and THU-Strider of qinghua university, etc. In general, although the biped robot technology has made a great breakthrough, there is still a certain gap between the overall performance and the human requirement.
Gait planning of the biped robot is the key content of technical research of the biped robot, and is related to walking energy efficiency, stability and humanoid effect of the robot. The gait of the biped robot mainly comprises a single-foot supporting phase and a biped supporting phase, wherein the walking time of the single-foot supporting phase generally accounts for more than 75% of the whole walking cycle, so that the quality of the single-foot supporting phase step-wise planning has a very important influence on the whole gait of the robot. In order to improve walking efficiency, the ankles of the supporting legs of the biped robot are always in a passive state in the whole single-foot supporting phase, the center of mass of the robot naturally moves forwards under the action of gravity, and in the process, the swinging feet of the robot rapidly move forwards to a target foot-falling point and are prevented from being scraped with the ground. However, due to the underactuation caused by the passive state of the ankle, it is difficult to control the robot to reach a given pose at a certain time to achieve a target landing point and avoid scraping with the ground. The document "assisted stable walking of a five-link interfaced 3-D bipolar robot" realizes the single-foot support phase step-wise planning of the under-actuated ankle biped robot by a nonlinear constraint optimization mode, but the method needs to consume larger calculated amount and is difficult to achieve the effect of real-time planning and control; the literature, "mechanical positioning steps for bipedal walking" first estimates the landing time based on a simplified model, and then plans out an expected landing point, however, the simplified model causes a certain error between the actual landing time of the robot and the estimated landing time.
Disclosure of Invention
The invention aims to provide a single-foot support phase dynamic planning method of a biped robot aiming at the defects of the prior art.
The purpose of the invention is realized by the following technical scheme: a single-foot support phase dynamic planning method of a biped robot is characterized by comprising the following steps:
(1) according to the initial state and the final state of the single-foot support phase of the robot, the landing time t of the robot on a forward plane is estimatedfronAnd the landing time t of the robot on the lateral planelatThen the landing time t of the robotland＝φ*min{tfron,tlatWhere φ ∈ (0, 1).
(2) Planning the track of each joint of the supporting leg of the single-foot supporting phase as follows: supporting ankle joint freedom q in the forward planeankle,rollSupporting the degree of freedom q of the ankle joint in the lateral planeankle,stEtc. are all in passive state; degree of freedom q of other joints of supporting legstThe motion trail of (1) is:
Figure BDA0002382384890000021
wherein q isst＝[qknee,st,qyaw,st,qroll,st,qpitch,st]T，qknee,stFor supporting the knee joint degree of freedom, qyaw,stFor rotational freedom of the hip joint of the supporting leg, qroll,stFor the swinging freedom of the hip joint of the supporting leg, qpitch,stThe pitch freedom degree of hip joints of the supporting legs; alpha is alphakIs qstB is a Bessel polynomial coefficient;
Figure BDA0002382384890000022
(3) planning the track of each joint of the swing leg of the single-foot support phase, comprising the following substeps:
(3.1) floor time t of robotlandDivided into leg-lifting action time lambda1tlandAnd leg swing action time lambda2tland，tland＝λ1tland+λ2tland。
(3.2) when lifting legs, swinging the hip joints of the legs to have the pitching degree of freedom qpitch,swDegree of freedom q of knee joint of swing legknee,swAnd the pitching degree of freedom q of the ankle joint of the swinging legankle,swThe action plan is as follows:
Figure BDA0002382384890000023
Figure BDA0002382384890000024
Figure BDA0002382384890000025
wherein the content of the first and second substances,
Figure BDA0002382384890000026
β1,k、β2,k、β3,kare each qpitch,sw、qknee,sw、qankle,swThe bessel polynomial coefficients of (a).
(3.3) degree of freedom q of joint of swing leg during leg swingswThe action plan is as follows:
Figure BDA0002382384890000027
wherein q issw＝[qankle,sw,qknee,sw,qyaw,sw,qroll,sw,qpitch,sw]T，qyaw,swFor rotational freedom of the hip joint of the swing leg, qroll,swThe degree of freedom of the swing of the hip joint of the swing leg;
Figure BDA0002382384890000031
ζkis qswThe bessel polynomial coefficients of (a).
(3.4) when t is more than or equal to tlandAnd when the robot is in use, each joint of the swing leg is locked, so that the robot can keep the target posture to land.
Further, the knee joint degree of freedom q of the supporting legknee,stRotational degree of freedom q of hip joint of supporting legyaw,stAnd the swinging freedom q of hip joint of supporting legroll,stPitching degree of freedom q of hip joint of supporting legpitch,stRotational degree of freedom q of hip joint of swing legyaw,swAnd the degree of freedom of swing q of the hip joint of the swing legroll,swPitching degree of freedom q of hip joint of swing legpitch,swDegree of freedom q of knee joint of swing legknee,swAnd the pitching degree of freedom q of the ankle joint of the swinging legankle,swAll of the end state angular velocities of (1) are 0.
Further, in the step (1), the landing time t of the robot in the forward planefronComprises the following steps:
Figure BDA0002382384890000032
wherein the content of the first and second substances,
Figure BDA0002382384890000033
g is the gravity acceleration, h is the height of the mass center;
Figure BDA0002382384890000034
ycom,1is the target end state position of the center of mass of the robot in the forward plane, ycom,0Is the initial position of the center of mass of the robot in the forward plane,
Figure BDA0002382384890000035
is the initial velocity of the robot centroid in the forward plane.
Further, in the step (1), the landing time t of the robot in the lateral planelatComprises the following steps:
Figure BDA0002382384890000036
wherein the content of the first and second substances,
Figure BDA0002382384890000037
xcom,1is the target end state position, x, of the robot centroid in the lateral planecom,0Is the initial position of the robot centroid in the lateral plane,
Figure BDA0002382384890000038
is the initial velocity of the robot's center of mass in the lateral plane.
Further, in the step (1.3), Φ is 0.85.
Further, in the step (3.1), λ1＝0.6，λ2＝0.4。
Further, the Bessel polynomial coefficient α in the step (2)kObtained by the following formula:
Figure BDA0002382384890000039
wherein q isst,0Is qstThe initial joint angle of (a) is,
Figure BDA0002382384890000041
is qstInitial joint angular velocity of qst,1Is qstThe angle of the joint in the final state of (1),
Figure BDA0002382384890000042
is qstThe final state of joint angular velocity.
Further, the Bessel polynomial coefficient β in the step (3.2)1,k、β2,k、β3,kObtained by the following formula:
Figure BDA0002382384890000043
wherein q ispitch,0And
Figure BDA0002382384890000044
is qpitch,swInitial angle and angular velocity of qpitch,1And
Figure BDA0002382384890000045
is qpitch,swAngle and angular velocity of end state qknee,0And
Figure BDA0002382384890000046
is qknee,swInitial angle and angular velocity of qknee,1And
Figure BDA0002382384890000047
is qknee,swAngle and angular velocity of end state qankle,0And
Figure BDA0002382384890000048
is qankle,swInitial angle and angular velocity of qankle,1And
Figure BDA0002382384890000049
is qankle,swAngle and angular velocity of end state。
Further, the Bessel polynomial coefficient ζ in the step (3.3)kObtained by the following formula:
Figure BDA00023823848900000410
wherein q issw,0And
Figure BDA00023823848900000411
is qswInitial angle and angular velocity of qsw,1And
Figure BDA00023823848900000412
is qswEnd state angle and angular velocity.
The invention has the beneficial effects that: the method estimates the landing time of the robot with the under-actuated degree of freedom based on a simplified model, further considers possible landing time errors, enables the robot to move to a target pose in advance, and then keeps the pose to land; in addition, in order to avoid scraping between the swinging feet of the robot and the ground, the invention decomposes the action process of swinging the legs of the monopod support phase, including leg lifting action and leg swinging action. Based on the single-foot support phase step planning method provided by the invention, the robot can be effectively helped to reach the expected foot landing point on the single-foot support phase and can be prevented from being scraped with the ground, so that the walking movement and task operation of the biped robot can be realized.
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FIG. 1 is a schematic diagram of a model of an 11 degree-of-freedom 3D biped robot;
fig. 2 shows the action process of the single-foot supporting phase swinging leg.
Detailed Description
The invention is further illustrated by the following figures and examples.
As shown in FIG. 1, this embodiment considers a biped robot with 11 degrees of freedom, qankle,rollTo support the degree of freedom of the ankle joint in the forward plane, qankle,stTo support the degree of freedom of the ankle joint in the lateral plane, qknee,stFor supporting the knee joint degree of freedom, qyaw,stFor rotational freedom of the hip joint of the supporting leg, qroll,stFor the swinging freedom of the hip joint of the supporting leg, qpitch,stFor the pitch freedom of the hip joint of the supporting leg, qyaw,swFor rotational freedom of the hip joint of the swing leg, qroll,swFor swinging freedom of the hip joint of the swinging leg, qpitch,swFor the degree of freedom of pitch of the hip joint of the swing leg, qknee,swFor swinging the knee joint, qankle,swFor swinging the ankle joint of the leg with a pitching degree of freedom, wherein qankle,rollIs an under-actuated degree of freedom without motor actuation, and the degree of freedom qankle,stIs in a passive state during walking.
The single-foot support phase step planning method provided by the invention estimates the landing time of the robot containing the under-actuated free space based on a simplified model, further considers possible landing time errors, enables the robot to move to a target pose in advance, then keeps the pose to land, and decomposes the action process of the swing leg of the single-foot support phase to avoid scraping the swing leg of the robot with the ground, wherein the action process comprises leg lifting action and leg swinging action; the method specifically comprises the following steps:
the method comprises the following steps: and setting the target end state of the single-foot supporting phase. The target end state of the single-foot supporting phase of the robot meets the expected foot drop point, and the degree of freedom q of the ankle joint is removedankle,roll、qankle,stBesides, the free angular velocity of the other driving joints is 0.
Step two: planning the landing time t of the robot based on the simplified modelland. Firstly, according to the target end state of the robot, the centroid position (x) of the robot at the moment is determinedcom,1,ycom,1) (ii) a Then, according to the centroid state of the final state and the initial state of the robot single-foot supporting phase
Figure BDA0002382384890000051
Linear inverted pendulum model pair based on simplificationLanding time t of robot on forward plane and lateral planefron、tlatAnd (4) estimating:
according to the linear inverted pendulum theory, the landing time t of the robot in a forward planefronCan be estimated as
Figure BDA0002382384890000052
Wherein
Figure BDA0002382384890000053
g is the gravity acceleration, h is the height of the mass center,
Figure BDA0002382384890000054
xcom,1is the final state coordinate, y, of the target of the robot centroid in the lateral planecom,1Is the target end state coordinate, y, of the center of mass of the robot in the forward planecom,0Is the initial position of the center of mass of the robot in the forward plane,
Figure BDA0002382384890000055
the corresponding initial speed.
According to the linear inverted pendulum theory, the landing time t of the robot in a lateral planelatCan be estimated as
Figure BDA0002382384890000061
Wherein
Figure BDA0002382384890000062
Wherein x iscom,0Is the initial position of the robot centroid in the lateral plane,
Figure BDA0002382384890000063
the corresponding initial speed.
Then, the estimated landing time t of the robotland,aTaking the smaller value of the estimated time, i.e. tland,a＝min{tfron,tlat}. Considering the errors caused by various factors in the estimation process, in order to ensure that the swing leg of the robot has enough time margin to complete the swing, the planned landing time tlandIs taken as
tland＝φtland,a
Where Φ ∈ (0,1), Φ may be 0.85.
Step three: planning the track of each joint of the supporting legs of the single-foot supporting phase. Ankle joint degree of freedom q of supporting legankle,roll、qankle,stIn a passive state, supporting the other joint degrees of freedom qstIs expressed in the form of a piecewise function as follows:
Figure BDA0002382384890000064
wherein q isst＝[qknee,st,qyaw,st,qroll,st,qpitch,st]T，
Figure BDA0002382384890000065
Vector alphak(k is 0,1,2,3) is qstThe Bessel polynomial coefficients of (1) can be calculated based on the initial state and the final state of the single-foot supporting phase:
Figure BDA0002382384890000066
wherein q isst,0Is qstThe initial joint angle of (a) is,
Figure BDA0002382384890000067
is qstInitial joint angular velocity of qst,1Is qstThe angle of the joint in the final state of (1),
Figure BDA0002382384890000068
is qstThe final state of joint angular velocity.
Step four: planning the track of each joint of the swing leg of the single-foot support phase.
Firstly, the motion process of the single-foot support-phase leg swinging is decomposed by imitating the motion characteristics of human bodies, and the motion process comprises a leg lifting motion and a leg swinging motion, as shown in fig. 2. When the leg-raising action is carried out, the thigh is raised, the shank is raised to prevent the swinging foot from scraping the ground, and when the leg-swinging action is carried out, the thigh is pressed down, and the knee joint is quickly opened to prepare for landing;
then, the time proportion of each decomposition action is divided by referring to the data of human, and the time proportion is the leg lifting action time lambda1tlandTime of leg swing operation λ2tlandSatisfy tland＝λ1tland+λ2tlandOptionally, λ is selected1＝0.6，λ2＝0.4；
And then, carrying out trajectory planning on the leg lifting action and the leg swinging action:
1) leg lifting action planning:
Figure BDA0002382384890000071
Figure BDA0002382384890000072
Figure BDA0002382384890000073
wherein q ispitch,swFor the degree of freedom of pitch of the hip joint of the swing leg, qknee,swFor swinging the knee joint, qankle,swIn order to swing the pitch freedom of the ankle joint of the leg,
Figure BDA0002382384890000074
scalar beta1,k、β2,k、β3,kK is 0,1,2,3, each qpitch,sw、qknee,sw、qankle,swThe Bessel polynomial coefficient can be based on a single-foot supporting phaseAnd given the end state of the leg-lifting action:
Figure BDA0002382384890000075
wherein q ispitch,0And
Figure BDA0002382384890000076
is qpitch,swInitial angle and angular velocity of qpitch,1And
Figure BDA0002382384890000077
is qpitch,swAngle and angular velocity of end state qknee,0And
Figure BDA0002382384890000078
is qknee,swInitial angle and angular velocity of qknee,1And
Figure BDA0002382384890000079
is qknee,swAngle and angular velocity of end state qankle,0And
Figure BDA00023823848900000710
is qankle,swInitial angle and angular velocity of qankle,1And
Figure BDA00023823848900000711
is qankle,swEnd state angle and angular velocity. The given leg lifting action end state meets the condition that the swing legs of the robot are positioned in front of the support legs, and the leg lifting height of the swing legs meets certain requirements so as to solve the scraping problem.
2) Planning leg swinging actions:
Figure BDA00023823848900000712
λ1tland≤t≤λ1tland+λ2tland
wherein the degree of freedom q of the swing leg jointsw＝[qankle,sw,qknee,sw,qyaw,sw,qroll,sw,qpitch,sw]T，qyaw,swFor rotational freedom of the hip joint of the swing leg, qroll,swIn order to swing the degree of freedom of the hip joint of the swing leg,
Figure BDA00023823848900000713
and vector ζk(k is 0,1,2,3) is qswThe Bessel polynomial coefficient can be calculated through the initial state of the leg swing action stage and the final state of the single-foot support phase:
Figure BDA0002382384890000081
wherein q issw,0And
Figure BDA0002382384890000082
is qswInitial angle and angular velocity of qsw,1And
Figure BDA0002382384890000083
is qswEnd state angle and angular velocity. The leg swing action plan mainly realizes the action of pressing down the thigh and quickly opening the knee joint.
Finally, when t is more than or equal to tlandAnd when the robot lands, all joints of the swing legs are locked, so that the robot keeps the target posture to land.
The above embodiments are only used for illustrating the design idea and features of the present invention, and the purpose of the present invention is to enable those skilled in the art to understand the content of the present invention and implement the present invention accordingly, and the protection scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes and modifications made in accordance with the principles and concepts disclosed herein are intended to be included within the scope of the present invention.

Claims (9)

1. A single-foot support phase dynamic planning method of a biped robot is characterized by comprising the following steps:
(1) according to the initial state and the final state of the single-foot support phase of the robot, the landing time t of the robot on a forward plane is estimatedfronAnd the landing time t of the robot on the lateral planelatThen the landing time t of the robotland＝φ*min{tfron,tlatφ ∈ (0, 1);
(2) planning the track of each joint of the supporting leg of the single-foot supporting phase as follows: supporting ankle joint freedom q in the forward planeankle,rollSupporting the degree of freedom q of the ankle joint in the lateral planeankle,stEtc. are all in passive state; degree of freedom q of other joints of supporting legstThe motion trail of (1) is:
Figure FDA0002756740090000011
wherein q isst＝[qknee,st,qyaw,st,qroll,st,qpitch,st]T，qknee,stFor supporting the knee joint degree of freedom, qyaw,stFor rotational freedom of the hip joint of the supporting leg, qroll,stFor the swinging freedom of the hip joint of the supporting leg, qpitch,stThe pitch freedom degree of hip joints of the supporting legs; alpha is alphakIs qstB is a Bessel polynomial coefficient;
Figure FDA0002756740090000012
(3) planning the track of each joint of the swing leg of the single-foot support phase, comprising the following substeps:
(3.1) floor time t of robotlandDivided into leg-lifting action time lambda1tlandAnd leg swing action time lambda2tland，tland＝λ1tland+λ2tland；
(3.2) when lifting legs, swinging the hip joints of the legs to have the pitching degree of freedom qpitch,swDegree of freedom q of knee joint of swing legknee,swAnd the pitching degree of freedom q of the ankle joint of the swinging legankle,swThe action plan is as follows:
Figure FDA0002756740090000013
Figure FDA0002756740090000014
Figure FDA0002756740090000015
wherein the content of the first and second substances,
Figure FDA0002756740090000016
β1,k、β2,k、β3,kare each qpitch,sw、qknee,sw、qankle,swB is a Bessel polynomial coefficient;
(3.3) degree of freedom q of joint of swing leg during leg swingswThe action plan is as follows:
Figure FDA0002756740090000021
wherein q issw＝[qankle,sw,qknee,sw,qyaw,sw,qroll,sw,qpitch,sw]T，qyaw,swFor rotational freedom of the hip joint of the swing leg, qroll,swThe degree of freedom of the swing of the hip joint of the swing leg;
Figure FDA0002756740090000022
ζkis qswB is a Bessel polynomial coefficient;
(3.4) when t is more than or equal to tlandAnd when the robot is in use, each joint of the swing leg is locked, so that the robot can keep the target posture to land.
2. Root of herbaceous plantThe biped robot single-foot support phase gait planning method according to claim 1, characterized in that the support leg knee joint degree of freedom qknee,stRotational degree of freedom q of hip joint of supporting legyaw,stAnd the swinging freedom q of hip joint of supporting legroll,stPitching degree of freedom q of hip joint of supporting legpitch,stRotational degree of freedom q of hip joint of swing legyaw,swAnd the degree of freedom of swing q of the hip joint of the swing legroll,swPitching degree of freedom q of hip joint of swing legpitch,swDegree of freedom q of knee joint of swing legknee,swAnd the pitching degree of freedom q of the ankle joint of the swinging legankle,swAll of the end state angular velocities of (1) are 0.
3. The biped robot single-foot support phase step planning method according to claim 1, wherein in the step (1), the landing time t of the robot in the forward plane isfronComprises the following steps:
Figure FDA0002756740090000023
wherein the content of the first and second substances,
Figure FDA0002756740090000024
g is the gravity acceleration, h is the height of the mass center;
Figure FDA0002756740090000025
ycom,1is the target end state position of the center of mass of the robot in the forward plane, ycom,0Is the initial position of the center of mass of the robot in the forward plane,
Figure FDA0002756740090000026
is the initial velocity of the robot centroid in the forward plane.
4. The biped robot single-foot support phase step planning method according to claim 1, wherein in the step (1), the robot is inTime to ground t in the lateral planelatComprises the following steps:
Figure FDA0002756740090000027
wherein the content of the first and second substances,
Figure FDA0002756740090000028
xcom,1is the target end state position, x, of the robot centroid in the lateral planecom,0Is the initial position of the robot centroid in the lateral plane,
Figure FDA0002756740090000029
is the initial velocity of the robot's center of mass in the lateral plane.
5. The biped robot one-foot support phase step planning method according to claim 1, wherein in step (1.3), Φ is 0.85.
6. The biped robot one-foot support phase step planning method according to claim 1, wherein in step (3.1), λ1＝0.6，λ2＝0.4。
7. The biped robot single-foot support phase step planning method according to claim 1, wherein the Bessel polynomial coefficient α in the step (2)kObtained by the following formula:
Figure FDA0002756740090000031
wherein q isst,0Is qstThe initial joint angle of (a) is,
Figure FDA0002756740090000032
is qstInitial joint angular velocity of qst,1Is qstThe angle of the joint in the final state of (1),
Figure FDA0002756740090000033
is qstThe final state of joint angular velocity.
8. The biped robot single-foot support phase step planning method according to claim 1, wherein the Bessel polynomial coefficient β in the step (3.2)1,k、β2,k、β3,kObtained by the following formula:
Figure FDA0002756740090000034
wherein q ispitch,0And
Figure FDA0002756740090000035
is qpitch,swInitial angle and angular velocity of qpitch,1And
Figure FDA0002756740090000036
is qpitch,swAngle and angular velocity of end state qknee,0And
Figure FDA0002756740090000037
is qknee,swInitial angle and angular velocity of qknee,1And
Figure FDA0002756740090000038
is qknee,swAngle and angular velocity of end state qankle,0And
Figure FDA0002756740090000039
is qankle,swInitial angle and angular velocity of qankle,1And
Figure FDA00027567400900000310
is qankle,swEnd state angle and angular velocity.
9. The biped robot single-foot support phase step planning method according to claim 1, wherein the Bessel polynomial coefficient ζ in step (3.3)kObtained by the following formula:
Figure FDA0002756740090000041
wherein q issw,0And
Figure FDA0002756740090000042
is qswInitial angle and angular velocity of qsw,1And
Figure FDA0002756740090000043
is qswEnd state angle and angular velocity.
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