CN112015088A - Fault-tolerant motion planning method for joint locking fault six-legged robot - Google Patents

Fault-tolerant motion planning method for joint locking fault six-legged robot Download PDF

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CN112015088A
CN112015088A CN202010945877.3A CN202010945877A CN112015088A CN 112015088 A CN112015088 A CN 112015088A CN 202010945877 A CN202010945877 A CN 202010945877A CN 112015088 A CN112015088 A CN 112015088A
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leg
joint
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尤波
刘大权
李佳钰
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Harbin University of Science and Technology
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Abstract

The invention relates to a fault-tolerant motion planning method for a joint locking fault hexapod robot. At present, foot robots have better terrain adaptability, however, when the robot is working remotely, the malfunction of the actuator is a serious problem. A fault-tolerant motion planning method for a joint locking fault six-legged robot comprises the following steps: the robot comprises a six-legged robot body, the six-legged robot body is composed of a body (1) and six legs (2), the body is of a regular hexagon structure, the six legs comprise a first leg (2-1), a second leg (2-2), a third leg (2-3), a fourth leg (2-4), a fifth leg (2-5) and a sixth leg (2-6), the following joints (3) are rotary joints, the body and a base joint are connected, the hip joints (4) are first-level pitching joints, the base joint and a thigh are connected, and the knee joints (5) are second-level pitching joints and are connected with the thigh and the shank. The invention relates to a fault-tolerant motion planning method of a hexapod robot applied to joint locking faults.

Description

Fault-tolerant motion planning method for joint locking fault six-legged robot
The technical field is as follows:
the invention relates to a fault-tolerant motion planning method for a joint locking fault hexapod robot.
Background art:
the foot robot has better terrain adaptability. They may be dispatched to perform tasks that are not human-safe. However, when the robot is working remotely, the malfunction of the actuator is a serious problem. The failure may be caused by a variety of reasons, such as communication failure, motor overload protection braking, and mechanical damage. Whereas hexapod robots can find many fault tolerant gaits, such as tripodal and quadruped gaits. Hexapod robots with problematic legs can still perform omnidirectional walking, turning, following a lead gait, and the like. The fault tolerant gait of a hexapod robot is far from being discovered. Periodic crab walking and optimized two-phase intermittent gait are provided. There is a degree of similarity between them: once the leg is diseased, the entire leg and body are considered stationary. In the support phase, the failing leg does not actively swing, and only participates in the body support work. In the transfer phase, once lifted away, the faulty leg will perform a passive movement with the displacement of the robot body, i.e. the position relative to the robot body will not change. According to this method, if two actuators fail on different legs, both legs will be fixed to the body. This would make walking very difficult. Another common point of existing fault-tolerant gaits is that the body direction is undefined. In general, the direction of the body is usually parallel to the ground or defined by other criteria. This reduces 3 planning degrees of freedom. The motion of the hexapod robot has strong coupling, and the robot can be disturbed by the fault of any joint, thereby causing serious consequences.
The invention content is as follows:
the invention aims to provide a hexapod robot fault-tolerant motion planning method for joint locking faults.
The above purpose is realized by the following technical scheme:
a fault-tolerant motion planning method for a joint locking fault six-legged robot comprises the following steps: six sufficient robot bodies, six sufficient robot bodies constitute by organism and six legs, wherein the organism adopt regular hexagon structure, six legs include a leg, No. two legs, No. three legs, No. four legs, No. five legs and No. six legs, just six legs evenly distributed in the organism outside, the structure homogeneous phase of every leg is the same, all has three degree of freedom, wherein is rotary joint with the joint, connects organism and base joint, the hip joint is one-level every single move jointThe base joint is connected with the thigh, the knee joint is a two-stage pitching joint and is connected with the thigh and the shank, the angles of rotation of the heel joint, the hip joint and the knee joint are respectively alpha, beta and gamma, and the length of the base joint is L1Thigh length L2The length of the shank is L3。
The joint locking fault six-legged robot fault-tolerant motion planning method is characterized in that a world coordinate system and a robot coordinate system are respectively
Figure BDA0002675305980000021
And
Figure BDA0002675305980000022
no. one leg, No. two legs, No. three legs, No. four legs, No. five legs and No. six legs are related to a coordinate system of the body
Figure BDA0002675305980000023
The first leg, the fourth leg, the third leg and the sixth leg are symmetrical relative to a machine body coordinate system
Figure BDA0002675305980000024
When the joint rotation angle is zero, the second leg and the fifth leg are collinear with the axis, and in an initial state, a world coordinate system
Figure BDA0002675305980000025
Coordinate system with machine body
Figure BDA0002675305980000026
And (4) overlapping.
The fault-tolerant motion planning method of the joint locking fault six-legged robot defines sigma G-XgYgZgIs a world coordinate system, sigma O-XoYoZoIs a coordinate system of the machine body, sigma B-XbYbZbFor the coordinate system of the heel joint, sigma H-XhYhZhIs a hip joint coordinate system, sigma K-XkYkZkIs a knee joint coordinate system, sigma F-XfYfZfIs a foot end coordinate system, and in an initial state,the world coordinate system is superposed with the body coordinate system;
Figure BDA0002675305980000027
the jacobian matrix for a single leg of a hexapod robot is:
Figure BDA0002675305980000028
the fault-tolerant motion planning method for the hexapod robot comprises the following steps:
quintic bezier curve expression is written:
f＝c0(1-t)5+5c1(1-t)4t+10c2(1-t)3t2+10c3(1-t)2t3+5c4(1-t)t4+c5t5 (3)
Figure BDA0002675305980000031
Figure BDA0002675305980000032
Figure BDA0002675305980000033
is sigma G-XgYgZgJacobian matrix in a coordinate system, JiIs sigma O-XoYoZoJacobian matrix in a coordinate system, RBA rotation matrix of the robot body relative to a world coordinate system;
Figure BDA0002675305980000034
BPi＝[BPix BPiy BPiz]Tthe coordinates of the foot end of the ith leg in a coordinate system of the machine body are obtained;
Figure BDA0002675305980000035
Figure BDA0002675305980000036
is the velocity of the foot end in the world coordinate system,
Figure BDA0002675305980000037
is the speed in the broad sense of the word,
Figure BDA0002675305980000038
is LiA Jacobian matrix with a foot end in a world coordinate system;
Figure BDA0002675305980000039
Figure BDA00026753059800000310
Figure BDA00026753059800000311
wherein,GPiis the coordinate of the foot end under the ground coordinate system,
Figure BDA00026753059800000312
is the coordinate of the foot end under the body coordinate system, XBRepresenting the position of the origin of the body coordinate system in the ground coordinate system, RBA rotation matrix representing a robot body coordinate system to a ground coordinate system;
Figure BDA00026753059800000313
Figure BDA00026753059800000314
ensuring that the mass center of the machine body is positioned in the supporting polygon is an important condition for ensuring the motion stability of the robot, so that the displacement of the machine body COM on the X, Y axis is more important than other degrees of freedom in static gait;
Figure BDA0002675305980000041
in the formula:
Figure BDA0002675305980000042
suppose a faulty leg LiIf the j (j ═ 1, 2, and 3) th joint has a locking failure, the angular velocity of the joint is known to be 0, and the following formula can be obtained:
Figure BDA0002675305980000043
Figure BDA0002675305980000044
and
Figure BDA0002675305980000045
each represents JTAnd JRJ-th line of (1), VB＝[vx vy vz]T,ωB＝[ωx ωy ωz]T
When the hexapod robot is in the walking phase, vxvyvzMore important for the stability of the body, and thus as a known quantity, ωx、ωy、ωzCan be used as an unknown quantity;
Figure BDA0002675305980000046
it can be seen that if θ is made to be [ roll pitch yaw ]]TIn order to optimally solve the redundancy equation, a projection matrix corresponding to the jacobian matrix is first constructed as follows:
Figure BDA0002675305980000047
obtaining a minimum value of the joint variable value theta of g (theta) on the premise of satisfying the formula that f (theta) is equal to x*The following requirements need to be satisfied;
Figure BDA0002675305980000048
in the formula [ theta ]*Indicates the joint configuration at which g (θ) reaches the optimum value. It is worth noting that the jacobian matrix
Figure BDA0002675305980000049
The rank is m, the rank of phi (theta) is n-m, GiCombining the constraints of these optimal values with f (θ) x to obtain the equation that θ needs to satisfy:
Figure BDA00026753059800000410
simultaneous differentiation of both sides yields the relationship between joint velocity and tip velocity as follows:
Figure BDA0002675305980000051
Figure BDA0002675305980000052
Figure BDA0002675305980000053
although in fault tolerant gait by adjusting ω is requiredx、ωy、ωzTo ensure the accuracy of the COM trajectory and the foot end trajectory of the machine body, we still want the deviation between the adjusted attitude angle and the planned attitude angle to be as small as possible, so the optimization objective function can be set as follows:
g(θ)＝(roll-rolld)2+(pitch-pitchd)2+(yaw-yawd)2 (22)
in the above formula, roll, pitch, and yaw are adjustment values of the fault-tolerant body attitude angle, respectively. And is a rolld、pitchd、yawdAttitude angle expectation in normal gait. After the optimization objective function is determined, the optimized ω can be obtained according to the formulax、ωy、ωz。
Has the advantages that:
1. the fault-tolerant gait planning method is suitable for fault-tolerant gait planning of joint locking faults. Establishing a redundancy equation at a locked joint through a floating body kinematics model of the hexapod robot; and (4) utilizing the augmented Jacobian matrix to complete the solution of a redundancy equation containing an optimization function, thereby realizing fault-tolerant gait planning. The feasibility and the effectiveness of the method are verified through simulation analysis and prototype tests. The results show that compared with the existing method, the fault-tolerant gait planning method can effectively improve the efficiency of fault-tolerant gait.
2. According to the method, a redundancy equation is established at a locked joint through the floating body kinematics, and then the redundancy equation solution containing an optimization function is completed by utilizing an augmented Jacobian matrix. And the feasibility and the effectiveness of the method are verified through simulation analysis and prototype test. Compared with the prior planning method, the method provided by the invention has the following innovation points:
(1) the fault-tolerant gait planning problem under the joint locking fault is converted into the solution of a redundancy equation by adopting the floating body kinematics.
(2) The redundancy equation converted by the fault-tolerant gait is combined with the optimization function to form an extended Jacobian matrix, and the extended Jacobian matrix is used for solving the fault-tolerant gait, so that the movement efficiency of the fault-tolerant gait of the robot is effectively improved. In this context, sudden changes in acceleration during robot centromere motion are the main cause of body wobble in fault-tolerant gait. In subsequent research, the influence of a foot end track and a robot centroid motion track on fault-tolerant gait stability is researched from an acceleration level so as to further improve the stability of the algorithm.
Description of the drawings:
FIG. 1 is a schematic diagram of the overall configuration of the hexapod robot.
Fig. 2 is a schematic view of the single leg configuration of fig. 1.
In the figure: 1. the novel leg-strengthening and leg-strengthening chair comprises a body, 2, six legs, 2-1, first leg, 2-2, second leg, 2-3, third leg, 2-4, fourth leg, 2-5, fifth leg, 2-6, sixth leg, 3 heel joint, 4 hip joint and 5 knee joint.
The specific implementation mode is as follows:
example 1:
a fault-tolerant motion planning method for a joint locking fault six-legged robot comprises the following steps: the six-legged robot comprises a six-legged robot body, wherein the six-legged robot body is composed of a body 1 and six legs 2, the body is of a regular hexagon structure, the six legs comprise a first leg 2-1, a second leg 2-2, a third leg 2-3, a fourth leg 2-4, a fifth leg 2-5 and a sixth leg 2-6, the six legs are uniformly distributed on the outer side of the body, the structure of each leg is the same and has three degrees of freedom, a heel joint 3 is a rotary joint, the body is connected with a base joint, a hip joint 4 is a first-level pitching joint, the base joint is connected with a thigh, a knee joint 5 is a second-level pitching joint and is connected with the thigh and the calf, the heel joint, the hip joint and the knee joint are respectively alpha, beta and gamma, and the base joint is L in length1Thigh length L2The length of the shank is L3。
Example 2:
according to the method for planning the fault-tolerant motion of the hexapod robot with the joint locking fault in the embodiment 1, the world coordinate system and the body coordinate system are respectively
Figure BDA0002675305980000061
And
Figure BDA0002675305980000062
no. one leg, No. two legs, No. three legs, No. four legs, No. five legs and No. six legs are related to a coordinate system of the body
Figure BDA0002675305980000063
The first leg, the fourth leg, the third leg and the sixth leg are symmetrical relative to a machine body coordinate system
Figure BDA0002675305980000064
When the joint rotation angle is zero, the second leg and the fifth leg are collinear with the axis, and in an initial state, a world coordinate system
Figure BDA0002675305980000065
Coordinate system with machine body
Figure BDA0002675305980000066
And (4) overlapping.
Example 3:
the method for fault-tolerant motion planning of a hexapod robot with joint locking failure as described in embodiment 1 or 2, defined as world coordinate system, Σ O-XoYoZoIs a coordinate system of the machine body, sigma B-XbYbZbFor the coordinate system of the heel joint, sigma H-XhYhZhIs a hip joint coordinate system, sigma K-XkYkZkIs a knee joint coordinate system, sigma F-XfYfZfThe system is a foot end coordinate system, and in an initial state, a world coordinate system is superposed with a body coordinate system;
Figure BDA0002675305980000071
the jacobian matrix for a single leg of a hexapod robot is:
Figure BDA0002675305980000072
example 4:
a method for fault-tolerant motion planning for a hexapod robot with joint locking failure as described in any one of embodiments 1-3, the method comprising the steps of:
quintic bezier curve expression is written:
f＝c0(1-t)5+5c1(1-t)4t+10c2(1-t)3t2+10c3(1-t)2t3+5c4(1-t)t4+c5t5 (25)
Figure BDA0002675305980000073
Figure BDA0002675305980000074
Figure BDA0002675305980000075
is sigma G-XgYgZgJacobian matrix in a coordinate system, JiIs sigma O-XoYoZoJacobian matrix in a coordinate system, RBA rotation matrix of the robot body relative to a world coordinate system;
Figure BDA0002675305980000081
BPi＝[BPix BPiy BPiz]Tthe coordinates of the foot end of the ith leg in a coordinate system of the machine body are obtained;
Figure BDA0002675305980000082
Figure BDA0002675305980000083
is the velocity of the foot end in the world coordinate system,
Figure BDA0002675305980000084
is the speed in the broad sense of the word,
Figure BDA0002675305980000085
is LiA Jacobian matrix with a foot end in a world coordinate system;
Figure BDA0002675305980000086
Figure BDA0002675305980000087
Figure BDA0002675305980000088
wherein,GPiis the coordinate of the foot end under the ground coordinate system,
Figure BDA0002675305980000089
is the coordinate of the foot end under the body coordinate system, XBRepresenting the position of the origin of the body coordinate system in the ground coordinate system, RBA rotation matrix representing a robot body coordinate system to a ground coordinate system;
Figure BDA00026753059800000810
Figure BDA00026753059800000811
ensuring that the mass center of the machine body is positioned in the supporting polygon is an important condition for ensuring the motion stability of the robot, so that the displacement of the machine body COM on the X, Y axis is more important than other degrees of freedom in static gait;
Figure BDA00026753059800000812
in the formula:
Figure BDA00026753059800000813
suppose a faulty leg LiIf the j (j ═ 1, 2, and 3) th joint has a locking failure, the angular velocity of the joint is known to be 0, and the following formula can be obtained:
Figure BDA00026753059800000814
Figure BDA00026753059800000815
and
Figure BDA00026753059800000816
each represents JTAnd JRJ-th line of (1), VB＝[vx vy vz]T,ωB＝[ωx ωy ωz]T
When the hexapod robot is in the walking phase, vx vy vzMore important for the stability of the body, and thus as a known quantity, ωx、ωy、ωzCan be used as an unknown quantity;
Figure BDA00026753059800000817
it can be seen that if θ is made to be [ roll pitch yaw ]]TIn order to optimally solve the redundancy equation, a projection matrix corresponding to the jacobian matrix is first constructed as follows:
Figure BDA0002675305980000091
obtaining a minimum value of the joint variable value theta of g (theta) on the premise of satisfying the formula that f (theta) is equal to x*The following requirements need to be satisfied;
Figure BDA0002675305980000092
in the formula [ theta ]*Indicates the joint configuration at which g (θ) reaches the optimum value. It is worth noting that the jacobian matrix
Figure BDA0002675305980000093
The rank is m, the rank of phi (theta) is n-m, GiCombining the constraints of these optimal values with f (θ) x to obtain the equation that θ needs to satisfy:
Figure BDA0002675305980000094
simultaneous differentiation of both sides yields the relationship between joint velocity and tip velocity as follows:
Figure BDA0002675305980000095
Figure BDA0002675305980000096
Figure BDA0002675305980000097
although in fault tolerant gait by adjusting ω is requiredx、ωy、ωzTo ensure the accuracy of the COM track and the foot end track of the machine body, but we still want the adjusted attitude angle and the planned attitude angleThe deviation between them is as small as possible, so the optimization objective function can be set as:
g(θ)＝(roll-rolld)2+(pitch-pitchd)2+(yaw-yawd)2 (44)
in the above formula, roll, pitch, and yaw are adjustment values of the fault-tolerant body attitude angle, respectively. And is a rolld、pitchd、yawdAttitude angle expectation in normal gait. After the optimization objective function is determined, the optimized ω can be obtained according to the formulax、ωy、ωz。

Claims (4)

1. A fault-tolerant motion planning method for a joint locking fault six-legged robot comprises the following steps: six sufficient robot bodies, characterized by: the six-legged robot body comprises a body and six legs, wherein the body adopts a regular hexagon structure, the six legs comprise a first leg, a second leg, a third leg, a fourth leg, a fifth leg and a sixth leg, the six legs are uniformly distributed on the outer side of the body, the structure of each leg is identical and has three degrees of freedom, the following joints are rotary joints and are connected with the body and the base joint, the hip joints are first-level pitching joints and are connected with the base joint and the thigh, the knee joints are second-level pitching joints and are connected with the thigh and the calf, the following joints, the hip joints and the knee joints have corners of alpha, beta and gamma respectively, and the length of the base joint is L1Thigh length L2The length of the shank is L3。
2. The joint locking failure hexapod robot fault-tolerant motion planning method of claim 1, wherein: the world coordinate system and the body coordinate system are respectively
Figure FDA0002675305970000011
And
Figure FDA0002675305970000012
no. one leg, No. two legs, No. three legs, No. four legs, No. five legs and No. six legsLeg-to-body coordinate system
Figure FDA0002675305970000013
The first leg, the fourth leg, the third leg and the sixth leg are symmetrical relative to a machine body coordinate system
Figure FDA0002675305970000014
When the joint rotation angle is zero, the second leg and the fifth leg are collinear with the axis, and in an initial state, a world coordinate system
Figure FDA0002675305970000015
Coordinate system with machine body
Figure FDA0002675305970000016
And (4) overlapping.
3. The joint locking failure hexapod robot fault-tolerant motion planning method of claim 2, wherein: definition of ∑ G-XgYgZgIs a world coordinate system, sigma O-XoYoZoIs a coordinate system of the machine body, sigma B-XbYbZbFor the coordinate system of the heel joint, sigma H-XhYhZhIs a hip joint coordinate system, sigma K-XkYkZkIs a knee joint coordinate system, sigma F-XfYfZfThe system is a foot end coordinate system, and in an initial state, a world coordinate system is superposed with a body coordinate system;
Figure FDA0002675305970000017
the jacobian matrix for a single leg of a hexapod robot is:
Figure FDA0002675305970000018
4. a method for fault-tolerant motion planning of a joint locking fault hexapod robot according to any one of claims 1-3, characterized by: the method comprises the following steps:
quintic bezier curve expression is written:
f＝c0(1-t)5+5c1(1-t)4t+10c2(1-t)3t2+10c3(1-t)2t3+5c4(1-t)t4+c5t5 (3)
Figure FDA0002675305970000021
Figure FDA0002675305970000022
Figure FDA0002675305970000023
is sigma G-XgYgZgJacobian matrix in a coordinate system, JiIs sigma O-XoYoZoJacobian matrix in a coordinate system, RBA rotation matrix of the robot body relative to a world coordinate system;
Figure FDA0002675305970000024
BPi＝[BPix BPiy BPiz]Tthe coordinates of the foot end of the ith leg in a coordinate system of the machine body are obtained;
Figure FDA0002675305970000025
Figure FDA0002675305970000026
is the velocity of the foot end in the world coordinate system,
Figure FDA0002675305970000027
is the speed in the broad sense of the word,
Figure FDA0002675305970000028
is LiA Jacobian matrix with a foot end in a world coordinate system;
Figure FDA0002675305970000029
Figure FDA00026753059700000210
Figure FDA00026753059700000211
wherein,GPiis the coordinate of the foot end under the ground coordinate system,
Figure FDA00026753059700000212
is the coordinate of the foot end under the body coordinate system, XBRepresenting the position of the origin of the body coordinate system in the ground coordinate system, RBA rotation matrix representing a robot body coordinate system to a ground coordinate system;
Figure FDA00026753059700000213
Figure FDA00026753059700000214
ensuring that the mass center of the machine body is positioned in the supporting polygon is an important condition for ensuring the motion stability of the robot, so that the displacement of the machine body COM on the X, Y axis is more important than other degrees of freedom in static gait;
Figure FDA0002675305970000031
in the formula:
Figure FDA0002675305970000032
suppose a faulty leg LiIf the j (j ═ 1, 2, and 3) th joint has a locking failure, the angular velocity of the joint is known to be 0, and the following formula can be obtained:
Figure FDA0002675305970000033
Figure FDA0002675305970000034
and
Figure FDA0002675305970000035
each represents JTAnd JRJ-th line of (1), VB＝[vx vy vz]T,ωB＝[ωx ωy ωz]T
When the hexapod robot is in the walking phase, vx vy vzMore important for the stability of the body, and thus as a known quantity, ωx、ωy、ωzCan be used as an unknown quantity;
Figure FDA0002675305970000036
it can be seen that if θ is made to be [ roll pitch yaw ]]TTo cope with redundancyPerforming optimization solution on the redundancy equation, and firstly constructing a projection matrix corresponding to the Jacobian matrix as follows:
Figure FDA0002675305970000037
obtaining a minimum value of the joint variable value theta of g (theta) on the premise of satisfying the formula that f (theta) is equal to x*The following requirements need to be satisfied;
Figure FDA0002675305970000038
in the formula [ theta ]*The Jacobian matrix representing the configuration of the joint when g (theta) reaches an optimum value
Figure FDA0002675305970000039
The rank is m, the rank of phi (theta) is n-m, GiCombining the constraints of these optimal values with f (θ) x to obtain the equation that θ needs to satisfy:
Figure FDA00026753059700000310
simultaneous differentiation of both sides yields the relationship between joint velocity and tip velocity as follows:
Figure FDA0002675305970000041
Figure FDA0002675305970000042
Figure FDA0002675305970000043
although in fault tolerant gait by adjusting ω is requiredx、ωy、ωzSo as to ensure the accuracy of the COM track and the foot end track of the machine body, and the deviation between the adjusted attitude angle and the planning attitude angle is as small as possible, so that the optimization objective function can be set as the following formula:
g(θ)＝(roll-rolld)2+(pitch-pitchd)2+(yaw-yawd)2 (22)
in the above formula, roll, pitch and yaw are respectively the adjustment values of the fault-tolerant body attitude angle, and are rolld、pitchd、yawdAfter the attitude angle expected value in normal gait is determined and the optimization objective function is determined, the optimized omega is obtained according to the formulax、ωy、ωz。
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