CN114102584A - Small-sized high-mobility rescue robot walking and operation stability control method - Google Patents

Small-sized high-mobility rescue robot walking and operation stability control method Download PDF

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CN114102584A
CN114102584A CN202111355916.5A CN202111355916A CN114102584A CN 114102584 A CN114102584 A CN 114102584A CN 202111355916 A CN202111355916 A CN 202111355916A CN 114102584 A CN114102584 A CN 114102584A
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stability
path
rescue robot
mobility
small
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秦绪坤
陈彤
张新
李兰芸
杨玲
宋黎
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Xinxing Jihua Group Co ltd
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Xinxing Jihua Group Co ltd
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/161—Hardware, e.g. neural networks, fuzzy logic, interfaces, processor
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1661—Programme controls characterised by programming, planning systems for manipulators characterised by task planning, object-oriented languages
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning

Abstract

The invention discloses a method for controlling walking and operation stability of a small high-mobility rescue robot, which comprises the following steps: obtaining a path stability index of the small-sized high-mobility rescue robot based on the pose estimator; the stress of the small-sized high-mobility rescue robot is obtained; obtaining a force angle stability margin index of the small-sized high-mobility rescue robot based on the path stability index and the stress index; establishing a stability cost function of the path based on a path stability index and a force angle stability margin index of the small-sized high-mobility rescue robot, so as to obtain the total time of path execution; or a path planning hypergraph model is established, and a required starting point and a required end point are selected from the path planning hypergraph model, so that a stable optimal path and a suboptimal path are obtained, and the small-sized high-mobility rescue robot selects the optimal path or the suboptimal path as required. Corresponding control device, electronic equipment and computer readable storage medium are also disclosed, which improve the stability control precision and effect.

Description

Small-sized high-mobility rescue robot walking and operation stability control method
Technical Field
The invention belongs to the technical field of intelligent rescue robot control, and particularly relates to a walking and operation stability control method for a small-sized high-mobility rescue robot.
Background
From the engineering perspective, the high-mobility rescue robot needs to simulate the inherent dynamic behaviors of human beings, such as walking and learning functions, in the rescue process, and due to the fact that the high-mobility rescue robot faces a complex disaster rescue environment, the stability of the high-mobility rescue robot in the walking and operation processes is higher than that of other types of robots.
The intelligent control adopts various intelligent technologies to achieve the aim of controlling a complex system, and the generation and development of the intelligent control reflect the development trend of modern automatic control and scientific technology. At present, there are four basic methods for controlling the walking and operation stability of the robot, and there is a trend of merging each other, including:
(1) robot variable structure control: the system is completely and ideally robust, and although containing uncertainty, the system has invariance to the external environment in the sliding mode, and is therefore suitable for control of the robot. The variable structure control does not need an accurate system model, and only needs to acquire the error range or the variation range of parameters in the model. Insensitive to bounded disturbances and parameter variations, thereby eliminating effects due to the effects of coriolis forces and viscous friction forces. The control algorithm is simple and easy to realize on line, but the buffeting phenomenon hinders the practical application of the buffeting algorithm on the rescue robot, and the weakening buffeting improvement algorithm effect of the dynamic adjustment sliding mode parameters and the on-line estimation sliding mode parameters which are proposed at present is not good.
(2) Fuzzy control of the robot: the control of a system by a robot simulator comprises fuzzification, fuzzy decision and precise calculation, wherein a fuzzy system is an estimator independent of a model, mainly depends on a fuzzy rule and a membership function of a fuzzy variable, does not need to know the mathematical dependency between input and output, and is an effective method for solving the control of an uncertain system.
(3) Robot hierarchical control: intelligent functions such as planning, decision and learning and the like outside the traditional control function are realized, the upper layer is used for simulating the behavior function of a person, the system is mainly based on knowledge, and the realized coordination of planning decision, learning, data access and tasks mainly processes the knowledge; the lower layer is used for executing specific control tasks of the robot.
(4) Neural network control of the robot: the identification and control of the complex nonlinear system can fully approximate any complex nonlinear system, learn and adapt to the dynamic characteristics of the uncertain system, and have strong robustness and fault tolerance. However, disaster prevention rescue environments are variable, so in the robot neural network dynamics control method, for multi-degree-of-freedom robot control, many input parameters, long learning time, low real-time performance and unfriendly calculation torque control and decomposition motion acceleration control cannot be applied to high-mobility rescue robots.
Disclosure of Invention
The invention aims to provide a method and a device for controlling walking and operation stability of a small-sized high-mobility rescue robot.
The invention provides a method for stably controlling walking and operation of a small-sized high-mobility rescue robot, which comprises the following steps:
step 1, obtaining a path stability index of the small-sized high-mobility rescue robot based on a pose estimator;
step 2, obtaining the stress of the small-sized high-mobility rescue robot;
step 3, obtaining a force angle stability margin index of the small-sized high-mobility rescue robot based on the path stability index and the stress index;
and 4, establishing a stability cost function of the path based on the path stability index of the small-sized high-mobility rescue robot and the force angle stability margin index, and implementing kinematic path constraint under the uneven terrain on the stability cost function so as to obtain the total execution time of the path.
Preferably, the step 4 may further include: and establishing a path planning hypergraph model based on the path stability index of the small-sized high-mobility rescue robot and the force angle stability margin index, and selecting a required starting point and a required end point in the path planning hypergraph model so as to obtain an optimal path and a suboptimal path based on stability, wherein the optimal path or the suboptimal path is selected by the small-sized high-mobility rescue robot according to requirements.
Preferably, the method further comprises a step 5 of adopting a stable compensation strategy aiming at the mechanical arm of the small-sized high-mobility rescue robot based on the stable influence of the mechanical arm motion of the small-sized high-mobility rescue robot on the crawler-type mobile chassis.
Preferably, the step 1 comprises:
step 11, defining a path, describing the path by using n position and posture sequences and n-1 time sequences, and expressing the position and posture of a path point as si＝[xi,yi,θi]TWherein x isi,yiThe position of the path point in the plane, θiThe sequence of the poses of the path is as follows:
Ps＝{si}i＝1,2...,n (1)；
the time series of paths represents the time interval between two adjacent poses as:
Ts＝{Δti}i＝1,2...,n-1 (2)；
to sum up, the path can be defined as: q: (P)s,Ts) (3)；
Step 12, designing a pose estimator, comprising:
acquiring a stability topographic map, and acquiring a digital elevation map of the post-disaster environment by using a laser radar, a CCD and the like:
H＝fdem(x,y) (4)
wherein f isdemThe method is characterized in that the method is a digital elevation model, H is the terrain height, x is the true east coordinate, and y is the true north coordinate; the supporting polygon of the rescue robot is a rectangle with the length of L and the width of H, and the width of a single crawler belt is d; the projection of the center coordinate of the rescue robot on the plane is (x)c,yc0), the course angle of the rescue robot is theta; and defining an included angle with the positive north direction, defining (-180,180), firstly rotating the rescue robot with a course angle of 0 at the origin of coordinates, then translating to obtain a supporting polygon projection at any position, wherein the supporting polygon coordinates at the origin are respectively Pbase1(-H/2, L/2, 0) Pbase2(H/2, L/2, 0) Pbase3(H/2, -L/2, 0) Pbase4(-H/2, -L/2, 0), and obtaining:
Figure BDA0003357614070000041
the coordinates after rotation are:
Pbase'＝Rot(θ)Pbase (6)；
the translation matrix is:
Figure BDA0003357614070000042
the projected coordinates of the support polygon at the specified position can thus be obtained: p ═ Rot (θ) Pbase+T (8)；
The approximate height between the rescue robot and the ground supporting point can be obtained according to the digital elevation model:
Pz＝fDEM(P) (9)；
by utilizing the approximate height of the supporting points, the pitch angle and the roll angle of the rescue robot can be estimated as follows:
α＝arctan((z1-z4+z2-z3)/(2L))
β＝arctan((z2-z1+z3-z4)/(2H)) (10)
using a pose estimator, from the pose s of the pathi＝[xi,yi,θi]TAnd a digital elevation model fdemObtaining the complete pose of the rescue robot:
Figure BDA0003357614070000051
step 13, calculating a path stability index, including:
the roll angle and the pitch angle of the rescue robot obtained based on the pose estimator are respectively alpha and beta; the vector of the gravity of the rescue robot under the gravity coordinate system is Gg＝[0 0 -mg]TAnd m is the total mass, the gravity vector under the body coordinate system is as follows:
fgrav＝Ry,βRx,αGg (12)；
wherein the content of the first and second substances,
Figure BDA0003357614070000052
adjacent pose is Si,Si+1The time interval between adjacent poses is DeltatiObtaining an approximate speed:
Figure BDA0003357614070000053
similarly, the approximate acceleration can be obtained from the adjacent velocities:
Figure BDA0003357614070000054
wherein, atran,arotaThe acceleration is translational acceleration and rotational acceleration; from an acceleration aiAnd the mass and the rotational inertia of the rescue robot, and the obtained inertia force and the inertia moment are as follows:
finertial＝m·atran
Figure BDA0003357614070000055
wherein, Jx,Jy,JzThe moment of inertia is the moment of inertia of the rescue robot under a coordinate system;
obtaining a load force by a force sensor mounted on the robot;
the stability of the rescue robot is obtained through each force (moment).
Preferably, the step 3 comprises:
step 31, defining a force angle stability margin:
βi＝diθi|fr|,i＝1,2 (16)
in this definition, the stability margin is the product of force, distance, angle; angle thetaiReflecting the height of the centroid, the higher the centroid is, thetaiThe smaller, the poorer the stability; distance diReflecting the effect of the moment of the effective resultant force on the stability when diThe system reaches the critical state of tipping when approaching 0; force frReflecting the sensitivity of the system when frWhen the voltage is very small, instability can be caused once external force interference exists; when beta isiWhen the value is 0, the system is in a critical stable state;
step 32, calculating the force angle stability margin
The contact projection of the crawler type rescue robot and the ground is a rectangle, and the vertex of the rectangle is defined as a contact point
Figure BDA0003357614070000061
The sides of the rectangle are defined as tilting edges, and the tilting edges are as follows:
ei＝Pi+1-Pi i＝1,2,3
e4＝P1-P4 (17)；
defining the gravity center position of the crawler-type rescue robot as Pc and the normal line from the gravity center to the tilting shaft as the tilting normal line, obtaining the tilting normal line liComprises the following steps:
Figure BDA0003357614070000062
the rescue robot is influenced by gravity, supporting force, load force and moment in the motion process, and according to the Alembert principle, the kinetic equation of the rescue robot is obtained through analysis and is as follows:
∑finertial＝∑(fgrav+fmanip+fsupport+fdist)
∑ninertial＝∑(ngrav+nmanip+nsupport+ndist) (19)
wherein f isinertial,ninertialIs an inertial force, an inertial moment, fgrav,ngravMoment, f, generated for the gravity and gravity of the robotmanip,nmanipFor load forces and load moments, fsupport,nsupportReaction forces and moments generated for the ground, fdist,ndistDisturbance forces and disturbance moments acting on the robot;
assuming that the resultant of all forces, except the ground acting force, applied to the robot is the position of the center of mass of the robot, where the resultant force acts on the robot, and the force is a main factor causing the robot to tip over, the resultant force is:
fr＝∑(fgrav+fmanip+fdist-finertial)
＝-∑fsupport (20)：
similarly, the resultant external moment is:
nr＝∑(ngrav+nmanip+ndist-ninertial)
＝-∑nsupport (21)；
when the robot rotates around a fixed tilting edge, the combined external force and the combined external moment of the tilting edge are as follows:
Figure BDA0003357614070000071
Figure BDA0003357614070000072
in power angle stability margin, use and close the contained angle judgement stability of external force vector and the normal that tumbles, convert the effect of moment to the turn-ups that tumbles into the equivalent couple, the equivalent couple that acts on the barycenter is:
Figure BDA0003357614070000073
wherein
Figure BDA0003357614070000074
The total resultant force vector along the fixed roll axis can thus be found to be:
Figure BDA0003357614070000075
definition of
Figure BDA0003357614070000076
The angle between the resultant force vector and the roll normal can be found to be:
Figure BDA0003357614070000077
wherein-pi is less than or equal to phii≤π，σiThe value of (a) is determined by the following formula:
Figure BDA0003357614070000078
wherein i is 1,2,3, 4; finally, the force angle stability margin of the rescue robot can be calculated as follows:
γ＝min(φi)||fr|| (27)。
preferably, the step 4 of establishing a stability cost function of the path based on the path stability index and the force angle stability margin index of the small-sized high-mobility rescue robot includes:
defining the stability of the robot in a horizontal state, in a state of not being subjected to other external forces except gravity, and in a state of zero speed and angular speed as a zero-interference stability margin phi of the rescue robot0Then, the variation of the stability margin caused by the environment is:
ΔΦ＝Φ0-γ (28)；
where γ is the stability margin of the current robot, thus giving the stability cost function of the whole path:
Figure BDA0003357614070000081
wherein, Δ Φi＝Φ0-γi。
The step 4 of constraining the kinematic path under the non-flat terrain comprises:
Figure BDA0003357614070000082
fvel＝∑eΓ(v)
facc＝∑eΓ(a) (30)；
the step 4 of obtaining the total time of the path execution comprises:
the execution time of the path is adopted to measure the execution efficiency of the path, and the delta t of the time sequence is usediAnd accumulating to obtain the total time of path execution:
Figure BDA0003357614070000083
preferably, the building of a path planning hypergraph model based on the path stability index of the small-sized high-mobility rescue robot and the force angle stability margin index selects a required starting point and a required end point in the path planning hypergraph model so as to obtain an optimal path and a suboptimal path based on stability, the small-sized high-mobility rescue robot selects the optimal path or the suboptimal path as required and adopts a path planning algorithm based on graph optimization, and a tracked robot uneven terrain path planning problem based on rollover stability can be converted into an optimization problem, which includes:
setting an optimization variable: path Q ═ Ps,Ts) Including a sequence of poses si＝[xi,yi,θi]TAnd time series Δ tiThe optimization target is better stability, the time cost is low, the speed and the acceleration are met, and the mathematical expression is as follows:
Figure BDA0003357614070000091
Figure BDA0003357614070000092
wherein eta iskIs a weight, fk() Evaluating functions for different constraints;
the stability-based path planning problem is converted into a hypergraph problem that can be solved by G2O. And selecting a required starting point and a required end point in the digital elevation model to obtain an optimal path and a suboptimal path based on stability, wherein an operator of the rescue robot selects the required path according to the actual condition.
Preferably, the step 5 comprises: and solving motion parameters of the mechanical arm by utilizing positive kinematics of the mechanical arm according to the known base force and moment required to be compensated, wherein the motion parameters comprise joint displacement, speed and acceleration. The overall stability is compensated by the aid of the redundant degree of freedom of the rescue robot through the compensation controller, and when the rescue robot is low in stability, the stability of the rescue robot is compensated by controlling the posture of the mechanical arm; or when one mechanical arm of the rescue robot works, the influence of the operation arm on the overall stability is compensated by controlling the motion of the other mechanical arm.
In a second aspect of the present invention, there is provided a small-sized high mobility rescue robot walking and work stabilization control device, including:
the path stability index calculation module is used for obtaining a path stability index of the small-sized high-mobility rescue robot based on the pose estimator;
one or more force sensors for obtaining the stress of the small-sized high-mobility rescue robot;
the force angle stability margin index calculation module is used for obtaining a force angle stability margin index of the small-sized high-mobility rescue robot based on the path stability index and the stress index;
the optimal path planning module is used for establishing a stability cost function of a path based on a path stability index and the force angle stability margin index of the small-sized high-mobility rescue robot and implementing kinematic path constraint under uneven terrain on the stability cost function so as to obtain the total execution time of the path;
and the stability compensation module is used for adopting a stability compensation strategy aiming at the mechanical arm of the small-sized high-mobility rescue robot based on the stability influence of the mechanical arm motion of the small-sized high-mobility rescue robot on the crawler-type mobile chassis.
A third aspect of the invention provides an electronic device comprising a processor and a memory, the memory storing a plurality of instructions, the processor being configured to read the instructions and to perform the method according to the first aspect.
A fourth aspect of the invention provides a computer readable storage medium storing a plurality of instructions readable by a processor and performing the method of the first aspect.
The invention provides a method and a device for stably controlling walking and operation of a small-sized high-mobility rescue robot and electronic equipment, and has the following beneficial effects:
a basic stability path plan is obtained through pose estimation and stability calculation based on the force angle stability margin, as an optimization mode, path planning can be carried out based on a graph optimization method, a further walking and operation stability control effect is obtained by using a dynamic stability compensation strategy, and the method is very suitable for stability control of walking and operation of a small-sized high-mobility rescue robot.
Drawings
Fig. 1 is a flow chart of a method for controlling walking and operation stability of a small-sized high-mobility rescue robot provided by the invention.
Fig. 2 is a schematic diagram of a two-dimensional simplified model of the force angle stability margin provided by the present invention.
Fig. 3 is a schematic diagram of a path planning hypergraph model provided by the present invention.
Fig. 4 is a schematic diagram of a stability path planning result provided by the present invention.
Fig. 5 is a schematic flow chart of the stability compensation algorithm provided by the present invention.
Fig. 6 is a schematic structural diagram of an embodiment of an electronic device provided in the present invention.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
Example one
As shown in fig. 1, a method for controlling walking and operation stability of a small-sized high-mobility rescue robot comprises the following steps:
s1, obtaining a path stability index of the small-sized high-mobility rescue robot based on the pose estimator;
s2, obtaining the stress of the small-sized high-mobility rescue robot;
s3, obtaining a force angle stability margin index of the small-sized high-mobility rescue robot based on the path stability index and the stress index;
s4, establishing a stability cost function of the path based on the path stability index and the force angle stability margin index of the small-sized high-mobility rescue robot, and implementing kinematic path constraint under uneven terrain on the stability cost function so as to obtain the total execution time of the path.
As a preferred embodiment, the S4 may further be: and establishing a path planning hypergraph model based on the path stability index of the small-sized high-mobility rescue robot and the force angle stability margin index, and selecting a required starting point and a required end point in the path planning hypergraph model so as to obtain an optimal path and a suboptimal path based on stability, wherein the optimal path or the suboptimal path is selected by the small-sized high-mobility rescue robot according to requirements.
As a preferred embodiment, the method further comprises step S5, and a stability compensation strategy for the mechanical arm of the small-sized high-mobility rescue robot is adopted based on the stability influence of the mechanical arm motion of the small-sized high-mobility rescue robot on the crawler-type mobile chassis.
As a preferred embodiment, the S1 includes:
(1) definition of paths
To facilitate the calculation of stability and path planning, the path is described using n sequences of positions and n-1 time sequences. Pose of a path point is represented as si＝[xi,yi,θi]TWherein x isi,yiThe position of the path point in the plane, θiIs the heading angle of the waypoint. Thus, the sequence of poses of the path is:
Ps＝{si}i＝1,2...,n (1)
the time series of paths represents the time interval between two adjacent poses:
Ts＝{Δti}i＝1,2...,n-1 (2)
to sum up, the path can be defined as:
Q:＝(Ps,Ts) (3)
(2) pose estimator design
Definition of path stability: when a specific robot passes through a designated path, the average value of the stability of the robot in the process is used as the stability of the path. Therefore, the stability of the path is not only related to the terrain, but also to the rescue robot stability model.
In order to obtain a stable topographic map, a digital elevation map of the post-disaster environment is obtained by utilizing a laser radar, a CCD and the like:
H＝fdem(x,y) (4)
wherein f isdemThe digital elevation model is represented by H, the terrain height, x, and y, respectively.
The supporting polygon of the rescue robot is a rectangle with the length of L and the width of H, and the width of a single crawler belt is d. The projection of the center coordinate of the rescue robot on the plane is (x)c,yc0), the heading angle of the rescue robot is theta (included angle with the north direction, the east direction is positive, and defines (-180, 180)). In order to obtain the approximate contact point coordinates of the rescue robot and the digital elevation map, the rescue robot with the course angle of 0 at the origin of the coordinates is firstly rotated and then translated to obtain the support polygon projection at any position.
The support polygon coordinates at the origin are respectively: pbase1(-H/2, L/2, 0) Pbase2(H/2, L/2, 0) Pbase3(H/2, -L/2, 0) Pbase4(-H/2, -L/2, 0), to obtain
Figure BDA0003357614070000131
The coordinates after rotation are:
Pbase'＝Rot(θ)Pbase (6)
the translation matrix is:
Figure BDA0003357614070000132
the projected coordinates of the support polygon at the specified position can thus be obtained:
P＝Rot(θ)Pbase+T (8)
the approximate height between the rescue robot and the ground supporting point can be obtained according to the digital elevation model:
Pz＝fDEM(P) (9)
by using the approximate height of the supporting points, the pitch angle and the roll angle of the rescue robot can be estimated to be respectively
α＝arctan((z1-z4+z2-z3)/(2L))
β＝arctan((z2-z1+z3-z4)/(2H)) (10)
Using a pose estimator, from the pose s of the pathi＝[xi,yi,θi]TAnd a digital elevation model fdemThe complete pose of the rescue robot can be obtained:
Figure BDA0003357614070000133
(3) path stability indicator calculation
Gravity is the most important factor for ensuring the roll stability of the robot. In FASM, for a specific robot, the pose of the robot affects the stability by affecting the direction of gravity. In order to realize calculation of the FASM, a gravity vector in a robot coordinate system needs to be obtained. And the roll angle and the pitch angle of the rescue robot are respectively alpha and beta by using the pose estimator in the previous section. The vector of the gravity of the rescue robot under the gravity coordinate system is Gg＝[0 0 -mg]TAnd m is the total mass, the gravity vector under the body coordinate system is as follows:
fgrav＝Ry,βRx,αGg (12)
wherein the content of the first and second substances,
Figure BDA0003357614070000141
the inertia force (moment) is an important factor affecting the roll stability of the robot. In most cases, the inertial forces (moments) impair the roll stability of the robot. According to the definition of the track of the tracked robot in the previous section, the adjacent poses are Si,Si+1The time interval between adjacent poses is DeltatiThe approximate speed can be obtained:
Figure BDA0003357614070000142
similarly, the approximate acceleration can be obtained from the adjacent velocities:
Figure BDA0003357614070000143
wherein, atran,arotaThe acceleration is translational acceleration and rotational acceleration. From an acceleration aiAnd the mass and the rotational inertia of the rescue robot, the obtained inertia force and the inertia moment are as follows:
finertial＝m·atran
Figure BDA0003357614070000144
wherein, Jx,Jy,JzThe moment of inertia is under the coordinate system of the rescue robot.
In addition to gravity and inertial forces, the stability of a tracked robot is also affected by load forces. Can be obtained by a force sensor mounted on the robot. The stability of the rescue robot is obtained through each force (moment).
As a preferred embodiment, the S3 includes:
and calculating the stress of the rescue robot by using a force angle stability margin defining and calculating method according to the path definition and the pose estimator, and finally obtaining the force angle stability margin of the rescue robot. Wherein:
(1) definition of force Angle stability margin
The definition of the power angle stability margin is given by the case of a two-dimensional plane. As shown in FIG. 2, the contact of the vehicle tire with the ground is simplified to point contact, and the position vector of the two contact points is p1，p2. The position vector of the center of mass of the vehicle is pc. There are two possible tipping modes in this case, namely tipping around p1 and tipping around p 2. Center of mass to p1，p2Are respectively | l1|，|l2L. Force frIn addition to ground reaction forcesThe resultant force of forces (including gravity, load force, inertia force, coriolis force) is called the effective resultant force. The ground reaction force is not considered because it does not contribute to the rollover. Theta1，θ2Is a1，l2And frThe included angle of (A); d1，d2Is p1，p2Vector end to effective resultant force frDistance of line of action.
The force angle stability margin is:
βi＝diθi|fr|,i＝1,2 (16)
in this definition, the stability margin is the product of force, distance, and angle. Angle thetaiReflecting the height of the centroid, the higher the centroid is, thetaiThe smaller, the poorer the stability; distance diReflecting the effect of the moment of the effective resultant force on the stability when diThe system reaches the critical state of tipping when approaching 0; force frReflecting the sensitivity of the system when frWhen the temperature is very low, instability can be caused once external force interference exists. When beta isiAt 0, the system is in a critical steady state.
(2) Force angle stability margin calculation method
The contact projection of the crawler type rescue robot and the ground is a rectangle, and in order to facilitate stability analysis, the vertex of the rectangle is defined as a contact point
Figure BDA0003357614070000151
The sides of the rectangle are defined as tilting edges, and the tilting edges are as follows:
ei＝Pi+1-Pi i＝1,2,3
e4＝P1-P4 (17)
defining the gravity center position of the crawler-type rescue robot as Pc and the normal line from the gravity center to the tilting shaft as the tilting normal line, obtaining the tilting normal line liComprises the following steps:
Figure BDA0003357614070000152
the rescue robot is influenced by gravity, supporting force, load force, moment and the like in the motion process, and according to the Alembert principle, the kinetic equation of the rescue robot is obtained through analysis and is as follows:
∑finertial＝∑(fgrav+fmanip+fsupport+fdist)
∑ninertial＝∑(ngrav+nmanip+nsupport+ndist) (19)
wherein f isininertial，ninertialIs an inertial force, an inertial moment, fgrav，ngravMoment, f, generated for the gravity and gravity of the robotmanip，nmanipFor load forces and load moments, fsupport，nsupportReaction forces and moments generated for the ground, fdist，ndistDisturbing forces and disturbing moments acting on the robot. The combination of all forces, except the ground acting force, applied to the robot is assumed to be the position of the mass center of the robot acted by the resultant external force, and the force is the main factor causing the robot to tip over. The resultant external force is:
fr＝∑(fgrav+fmanip+fdist-finertial)
＝-∑fsupport (20)
similarly, the resultant external moment is:
nr＝∑(ngrav+nmanip+ndist-ninertial)
＝--∑nsupport (21)
when the robot rotates around a fixed tilting edge, the external force and external moment of the tilting edge are as follows:
Figure BDA0003357614070000161
Figure BDA0003357614070000162
in the force angle stability margin, the stability is judged by using the included angle between the total external force vector and the tilting normal, so that the action of the moment on the tilting edge needs to be converted into an equivalent couple. The equivalent couple acting on the centroid is:
Figure BDA0003357614070000163
wherein
Figure BDA0003357614070000164
The total resultant force vector along the fixed roll axis can thus be found to be:
Figure BDA0003357614070000171
definition of
Figure BDA0003357614070000172
The angle between the resultant force vector and the roll normal can be found to be:
Figure BDA0003357614070000173
wherein-pi is less than or equal to phii≤π，σiThe value of (a) is determined by the following formula:
Figure BDA0003357614070000174
wherein i is 1,2,3, 4. Finally, the force angle stability margin of the rescue robot can be calculated as follows:
γ＝min(φi)||fr|| (27)。
preferably, in the step 4, a stability cost function of the path is established based on the path stability index of the small-sized high-mobility rescue robot and the force angle stability margin index, and the kinematics path constraint under the uneven terrain is implemented on the stability cost function, so as to obtain the total execution time of the path.
Wherein:
(1) the stability cost function of the path established based on the path stability index and the force angle stability margin index of the small-sized high-mobility rescue robot comprises the following steps:
in order to implement stable path planning, a stability cost function of a path needs to be defined. When the crawler-type rescue robot passes through uneven terrain, the speed is low, and the terrain is a main factor influencing the stability. Defining the stability of the robot in a horizontal state, in a state of not being subjected to other external forces except gravity, and in a state of zero speed and angular speed as a zero-interference stability margin phi of the rescue robot0Then, the variation of the stability margin caused by the environment is:
ΔΦ＝Φ0-γ (28)
wherein gamma is the stability margin of the current robot. Thus, the stability cost function for the entire path is given:
Figure BDA0003357614070000181
wherein, Δ Φi＝Φ0-γi。
(2) The kinematic path constraints under non-flat terrain comprise:
in the process that the rescue robot passes through a complex terrain, in order to ensure safety, incomplete constraints such as maximum speed and maximum acceleration need to be set, and the following kinematic constraints are given:
Figure BDA0003357614070000182
fvel＝∑eΓ(v)
facc＝∑e1(a) (30)
(3) the obtaining of the total time of execution of the path comprises:
to make the shoeThe belt type rescue robot reaches the destination as soon as possible, and the execution time of the path is used for measuring the execution efficiency of the path. Will be a time series of Δ tiAnd accumulating to obtain the total time of path execution:
Figure BDA0003357614070000183
as a preferred embodiment, a path planning hypergraph model is established based on the path stability index of the small-sized high-mobility rescue robot and the force angle stability margin index, a required starting point and a required end point are selected in the path planning hypergraph model, so that a stable optimal path and a stable suboptimal path are obtained, the small-sized high-mobility rescue robot selects the optimal path or the optimal path as required and adopts a path planning algorithm based on graph optimization, and a track type robot uneven terrain path planning problem based on rollover stability can be converted into an optimization problem. The method comprises the following steps:
wherein the optimization variables are: path Q: is ═ Ps，Ts) Including a sequence of poses si＝[xi，yi，θi]TAnd time series Δ ti. The optimization target is as follows: the method has good stability and low time cost, and meets the requirements of speed and acceleration. The mathematical expression is as follows:
Figure BDA0003357614070000191
Figure BDA0003357614070000192
wherein eta iskIs a weight, fk() The functions are evaluated for different constraints.
In graph theory, HyperGraph (HyperGraph) is a generalized graph featuring a hyper-edge that can connect multiple points. The path planning transformation problem of the present invention can be converted into a hypergraph as shown in fig. 3. Wherein, the top of the hypergraphWith points as pose sequences siAnd time series Δ tiThe cost function in the upper section constitutes the edge of the hypergraph.
G2O is a generic graph optimization framework that can be used to solve the above-mentioned nonlinear optimization problem, and is in the standard form:
Figure BDA0003357614070000193
Figure BDA0003357614070000194
where F (x) is an objective function, x represents the optimization solution variable, and z ij represents the observations of the link variables x i and xj. The degree to which the variables x i and xj satisfy the equation is evaluated using the error vector e (), with Ω i j being the information matrix. Converting the optimization formula of the path planning into a standard form of G2O, wherein x corresponds to the path point Q, ekCorrespond to
Figure BDA0003357614070000195
ΩijCorresponds to ηk。
Through the above process, the stability-based path planning problem is converted into a hypergraph problem that can be solved through G2O. By selecting the desired start and end points in the digital elevation model, the optimal path and the suboptimal path based on stability as shown in FIG. 4 can be obtained. The operator of the rescue robot can select the required path according to the actual situation.
Through analyzing the mechanism of influence of the motion of the mechanical arm on the stability of the crawler-type mobile chassis, a stability compensation strategy of the mechanical arm is provided. When the rescue robot is low in stability, the stability of the robot is compensated by controlling the posture of the mechanical arm. Or when one mechanical arm of the rescue robot works, the influence of the operation arm on the overall stability is compensated by controlling the motion of the other mechanical arm.
The key point of the compensation is to realize the decoupling of the mechanical arm action and the robot stability and the coupling effect of the two mechanical arms. In the stability compensation strategy, the operation of the rescue robot is divided into two working conditions, namely a working condition 1: one mechanical arm works, and the other mechanical arm does not work; working condition 2: the rescue robot only moves, and the two mechanical arms do not work. And for the working condition which is not in the stability compensation strategy, only overturning early warning is carried out, and the stability compensation of the double mechanical arms is not carried out. The implementation of the stability compensation is shown in fig. 5.
Condition 1 is analyzed here. In the rescue robot operation process, the control of the operation mechanical arm is realized through a teleoperation system, and the load of the mechanical arm can be measured through a six-dimensional force sensor of the end effector. Here the base force and moment of the work robot needs to be calculated:
Figure BDA0003357614070000201
wherein, FbaseIs the base force vector, MbaseFor moment received by the base, FsensorFor the force vector measured by the end effector force sensor, H is the coupling factor. Since the angles of the joints of the robot are known, the coupling factor H can be found by kinematics and mathematics of the robot arm. The influence of the operation arm on the overall stability of the rescue robot can be calculated through the stability criterion.
In order to compensate for stability of the operation arm, the amount of compensation of stability by the operation of the compensation arm should be equal to or greater than the influence of the operation arm. And simplifying the compensation arm by adopting a system centroid equivalent mechanical arm model. And solving the motion parameters (joint displacement, speed and acceleration) of the mechanical arm by utilizing the positive kinematics of the mechanical arm according to the known base force and moment required to be compensated. By the aid of the compensation controller, the overall stability is compensated by means of the redundant degree of freedom of the rescue robot.
In the second embodiment, the first embodiment of the method,
a walking and operation stability control device of a small-sized high-mobility rescue robot comprises:
the path stability index calculation module is used for obtaining a path stability index of the small-sized high-mobility rescue robot based on the pose estimator;
one or more force sensors for obtaining the stress of the small-sized high-mobility rescue robot;
the force angle stability margin index calculation module is used for obtaining a force angle stability margin index of the small-sized high-mobility rescue robot based on the path stability index and the stress index;
the optimal path planning module is used for establishing a stability cost function of a path based on a path stability index and the force angle stability margin index of the small-sized high-mobility rescue robot and implementing kinematic path constraint under uneven terrain on the stability cost function so as to obtain the total execution time of the path;
and the stability compensation module is used for adopting a stability compensation strategy aiming at the mechanical arm of the small-sized high-mobility rescue robot based on the stability influence of the mechanical arm motion of the small-sized high-mobility rescue robot on the crawler-type mobile chassis.
The device can implement the optimization method provided in the first embodiment, and the specific implementation method can be referred to the description in the first embodiment, which is not described herein again.
The invention also provides a memory storing a plurality of instructions for implementing the method according to the first embodiment.
As shown in fig. 6, the present invention further provides an electronic device, which includes a processor 301 and a memory 302 connected to the processor 301, where the memory 302 stores a plurality of instructions, and the instructions can be loaded and executed by the processor, so that the processor can execute the method according to the first embodiment.
The basic stability path planning is obtained through pose estimation and stability calculation based on the force angle stability margin, as an optimization mode, path planning can be carried out based on a graph optimization method, a further walking and operation stability control effect is obtained by using a dynamic stability compensation strategy, and the method is very suitable for stability control of walking and operation of a small-sized high-mobility rescue robot.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all such alterations and modifications as fall within the scope of the invention. It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (10)

1. A walking and operation stability control method for a small-sized high-mobility rescue robot is characterized by comprising the following steps:
step 1, obtaining a path stability index of the small-sized high-mobility rescue robot based on a pose estimator;
step 2, obtaining the stress of the small-sized high-mobility rescue robot;
step 3, obtaining a force angle stability margin index of the small-sized high-mobility rescue robot based on the path stability index and the stress index;
step 4, establishing a stability cost function of the path based on the path stability index of the small-sized high-mobility rescue robot and the force angle stability margin index, and implementing kinematic path constraint under the uneven terrain on the stability cost function so as to obtain the total execution time of the path; or a path planning hypergraph model is established based on the path stability index of the small-sized high-mobility rescue robot and the force angle stability margin index, a required starting point and a required terminal point are selected from the path planning hypergraph model, so that a stable optimal path and a suboptimal path are obtained, and the small-sized high-mobility rescue robot selects the optimal path or the suboptimal path as required.
2. The walking and operation stability control method for the small-sized high-mobility rescue robot is characterized by further comprising a step 5 of adopting a stability type compensation strategy aiming at a mechanical arm of the small-sized high-mobility rescue robot based on the stability type influence of the mechanical arm motion of the small-sized high-mobility rescue robot on a crawler-type moving chassis.
3. The walking and operation stability control method for the small-sized high-mobility rescue robot as claimed in claim 1, wherein the step 1 comprises:
step 11, defining a path, describing the path by using n position and posture sequences and n-1 time sequences, and expressing the position and posture of a path point as si＝[xi，yi，θi]TWherein x isi，yiThe position of the path point in the plane, θiThe sequence of the poses of the path is as follows:
Ps＝{si}i＝1，2...，n (1)；
the time series of paths represents the time interval between two adjacent poses as:
Ts＝{Δti}i＝1，2...，n-1 (2)；
to sum up, the path can be defined as: q: (P)s，Ts) (3)；
Step 12, designing a pose estimator, comprising:
acquiring a stability topographic map, and acquiring a digital elevation map of the post-disaster environment by using a laser radar, a CCD and the like:
H＝fdem(x，y) (4)
wherein f isdemThe method is characterized in that the method is a digital elevation model, H is the terrain height, x is the true east coordinate, and y is the true north coordinate; the supporting polygon of the rescue robot is a rectangle with the length of L and the width of H, and the width of a single crawler belt is d; the projection of the center coordinate of the rescue robot on the plane is (x)c，yc0), the course angle of the rescue robot is theta; defining an included angle with the true north direction, defining (-180,180) when the east direction is positive, firstly rotating the rescue robot with the course angle of 0 at the origin of coordinates, then translating to obtain the projection of a support polygon at any position, and supporting at the originThe polygon coordinates are: pbase1(-H/2, L/2, 0) Pbase2(H/2, L/2, 0) Pbase3(H/2, -L/2, 0) Pbase4(-H/2, -L/2, 0) to give:
Figure FDA0003357614060000021
the coordinates after rotation are:
Pbase'＝Rot(θ)Pbase (6)；
the translation matrix is:
Figure FDA0003357614060000022
the projected coordinates of the support polygon at the specified position can thus be obtained: p ═ Rot (θ) Pbase+T (8)；
The approximate height between the rescue robot and the ground supporting point can be obtained according to the digital elevation model:
Pz＝fDEM(P) (9)；
by utilizing the approximate height of the supporting points, the pitch angle and the roll angle of the rescue robot can be estimated as follows:
α＝arctan((z1-z4+z2-z3)/(2L))
β＝arctan((z2-z1+z3-z4)/(2H)) (10)
using a pose estimator, from the pose s of the pathi＝[xi，yi，θi]TAnd a digital elevation model fdemObtaining the complete pose of the rescue robot:
Figure FDA0003357614060000031
step 13, calculating a path stability index, including:
the roll angle and the pitch angle of the rescue robot obtained based on the pose estimator are respectively alpha and beta; the gravity of the rescue robot is under a gravity coordinate systemVector of (a) is Gg＝[0 0 -mg]TAnd m is the total mass, the gravity vector under the body coordinate system is as follows:
fgrav＝Ry，βRx，αGg (12)；
wherein the content of the first and second substances,
Figure FDA0003357614060000032
adjacent pose is Si，Si+1The time interval between adjacent poses is DeltatiObtaining an approximate speed:
Figure FDA0003357614060000033
similarly, the approximate acceleration can be obtained from the adjacent velocities:
Figure FDA0003357614060000034
wherein, atran，arotaThe acceleration is translational acceleration and rotational acceleration; from an acceleration aiAnd the mass and the rotational inertia of the rescue robot, and the obtained inertia force and the inertia moment are as follows:
finertial＝m·atran
Figure FDA0003357614060000041
wherein, Jx，Jy，JzThe moment of inertia is the moment of inertia of the rescue robot under a coordinate system;
obtaining a load force by a force sensor mounted on the robot;
the stability of the rescue robot is obtained through various forces or moments.
4. The walking and work stability control method of the small-sized high-mobility rescue robot as claimed in claim 1, wherein the step 3 comprises:
step 31, defining a force angle stability margin:
βi＝diθi|fr|，i＝1，2 (16)
in this definition, the stability margin is the product of force, distance, angle; angle thetaiReflecting the height of the centroid, the higher the centroid is, thetaiThe smaller, the poorer the stability; distance diReflecting the effect of the moment of the effective resultant force on the stability when diThe system reaches the critical state of tipping when approaching 0; force frReflecting the sensitivity of the system when frWhen the voltage is very small, instability can be caused once external force interference exists; when beta isiWhen the value is 0, the system is in a critical stable state;
step 32, calculating the force angle stability margin
The contact projection of the crawler type rescue robot and the ground is a rectangle, and the vertex of the rectangle is defined as a contact point
Figure FDA0003357614060000042
The sides of the rectangle are defined as tilting edges, and the tilting edges are as follows:
ei＝Pi+1-Pi i＝1，2，3
e4＝P1-P4 (17)；
defining the gravity center position of the crawler-type rescue robot as Pc and the normal line from the gravity center to the tilting shaft as the tilting normal line, obtaining the tilting normal line liComprises the following steps:
Figure FDA0003357614060000043
the rescue robot is influenced by gravity, supporting force, load force and moment in the motion process, and according to the Alembert principle, the kinetic equation of the rescue robot is obtained through analysis and is as follows:
∑finertial＝∑(fgrav+fmanip+fsupport+fdist)
∑ninertial＝∑(ngrav+nmanip+nsupport+ndist) (19)
wherein f isininertial，ninertialIs an inertial force, an inertial moment, fgrav，ngavMoment, f, generated for the gravity and gravity of the robotmanip，nmanipFor load forces and load moments, fsupport，nsupportReaction forces and moments generated for the ground, fdist，ndistDisturbance forces and disturbance moments acting on the robot;
assuming that the resultant of all forces, except the ground acting force, applied to the robot is the position of the center of mass of the robot, where the resultant force acts on the robot, and the force is a main factor causing the robot to tip over, the resultant force is:
fr＝∑(fgrav+fmanip+fdist-finertial)
＝-∑fsupport (20)：
similarly, the resultant external moment is:
nr＝∑(ngrav+nmanip+ndist-ninertial)
＝-∑nsupport (21)；
when the robot rotates around a fixed tilting edge, the combined external force and the combined external moment of the tilting edge are as follows:
Figure FDA0003357614060000051
Figure FDA0003357614060000052
in power angle stability margin, use and close the contained angle judgement stability of external force vector and the normal that tumbles, convert the effect of moment to the turn-ups that tumbles into the equivalent couple, the equivalent couple that acts on the barycenter is:
Figure FDA0003357614060000053
wherein
Figure FDA0003357614060000054
The total resultant force vector along the fixed roll axis can thus be found to be:
Figure FDA0003357614060000055
definition of
Figure FDA0003357614060000061
The angle between the resultant force vector and the roll normal can be found to be:
Figure FDA0003357614060000062
wherein-pi is less than or equal to phii≤π，σiThe value of (a) is determined by the following formula:
Figure FDA0003357614060000063
wherein i is 1,2,3, 4; finally, the force angle stability margin of the rescue robot can be calculated as follows:
γ＝min(φi)||fr|| (27)。
5. the method for controlling walking and work stability of a small-sized high-mobility rescue robot according to claim 1, wherein the step 4 of establishing a stability cost function of a path based on a path stability index and the force angle stability margin index of the small-sized high-mobility rescue robot comprises:
defining the stability of the robot in a horizontal state, in a state of not being subjected to other external forces except gravity, and in a state of zero speed and angular speed as a zero-interference stability margin phi of the rescue robot0Then, the variation of the stability margin caused by the environment is:
ΔΦ＝Φ0-γ (28)；
where γ is the stability margin of the current robot, thus giving the stability cost function of the whole path:
Figure FDA0003357614060000064
wherein, Δ Φi＝Φ0-γi；
The step 4 of constraining the kinematic path under the non-flat terrain comprises:
Figure FDA0003357614060000065
fvel＝∑eΓ(v)
facc＝∑e1(a) (30)；
the step 4 of obtaining the total time of the path execution comprises:
the execution time of the path is adopted to measure the execution efficiency of the path, and the delta t of the time sequence is usediAnd accumulating to obtain the total time of path execution:
Figure FDA0003357614060000071
6. the method for controlling walking and operation stability of the small-sized high-mobility rescue robot according to claim 1, wherein a path planning hypergraph model is established based on the path stability index and the force angle stability margin index of the small-sized high-mobility rescue robot, a required starting point and a required end point are selected from the path planning hypergraph model, so as to obtain an optimal path and a suboptimal path based on stability, the small-sized high-mobility rescue robot selects the optimal path or the suboptimal path as required as a path planning algorithm based on graph optimization, and a tracked robot uneven terrain path planning problem based on rollover stability can be converted into an optimization problem, and the method comprises the following steps:
setting an optimization variable: path Q ═ Ps，Ts) Including a sequence of poses si＝[xi，yi，θi]TAnd time series Δ tiThe optimization target is better stability, the time cost is low, the speed and the acceleration are met, and the mathematical expression is as follows:
Figure FDA0003357614060000072
Figure FDA0003357614060000073
wherein eta iskIs a weight, fk() Evaluating functions for different constraints;
the stability-based path planning problem is converted into a hypergraph problem which can be solved through G2O, a required starting point and a required end point are selected from the digital elevation model, an optimal path and a suboptimal path based on stability are obtained, and an operator of the rescue robot selects the required path according to actual conditions.
7. The walking and work stability control method of the small-sized high-mobility rescue robot as claimed in claim 2, wherein the step 5 comprises: solving motion parameters of the mechanical arm by utilizing positive kinematics of the mechanical arm according to the known base force and moment required to be compensated, wherein the motion parameters comprise joint displacement, speed and acceleration; the overall stability is compensated by the aid of the redundant degree of freedom of the rescue robot through the compensation controller, and when the rescue robot is low in stability, the stability of the rescue robot is compensated by controlling the posture of the mechanical arm; or when one mechanical arm of the rescue robot works, the influence of the operation arm on the overall stability is compensated by controlling the motion of the other mechanical arm.
8. A control device for implementing the walking and work stability control method of the small-sized high-mobility rescue robot according to any one of claims 1 to 7, characterized by comprising:
the path stability index calculation module is used for obtaining a path stability index of the small-sized high-mobility rescue robot based on the pose estimator;
one or more force sensors for obtaining the stress of the small-sized high-mobility rescue robot;
the force angle stability margin index calculation module is used for obtaining a force angle stability margin index of the small-sized high-mobility rescue robot based on the path stability index and the stress index;
the optimal path planning module is used for establishing a stability cost function of a path based on a path stability index and the force angle stability margin index of the small-sized high-mobility rescue robot and implementing kinematic path constraint under uneven terrain on the stability cost function so as to obtain the total execution time of the path;
and the stability compensation module is used for adopting a stability compensation strategy aiming at the mechanical arm of the small-sized high-mobility rescue robot based on the stability influence of the mechanical arm motion of the small-sized high-mobility rescue robot on the crawler-type mobile chassis.
9. An electronic device comprising a processor and a memory, the memory storing a plurality of instructions, the processor configured to read the instructions and perform the method of any of claims 1-7.
10. A computer-readable storage medium storing a plurality of instructions readable by a processor and performing the method of any one of claims 1 to 7.
CN202111355916.5A 2021-11-16 2021-11-16 Small-sized high-mobility rescue robot walking and operation stability control method Pending CN114102584A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115635485A (en) * 2022-11-09 2023-01-24 苏州智康机器人有限公司 Real-time human-computer interaction force control method of mobile rehabilitation robot
CN117067223A (en) * 2023-10-16 2023-11-17 哈尔滨理工大学 Six-foot robot free gait planning method based on motion stability estimation

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115635485A (en) * 2022-11-09 2023-01-24 苏州智康机器人有限公司 Real-time human-computer interaction force control method of mobile rehabilitation robot
CN115635485B (en) * 2022-11-09 2024-03-15 嘉兴智康机器人有限公司 Real-time human-computer interaction force control method of mobile rehabilitation robot
CN117067223A (en) * 2023-10-16 2023-11-17 哈尔滨理工大学 Six-foot robot free gait planning method based on motion stability estimation
CN117067223B (en) * 2023-10-16 2024-01-05 哈尔滨理工大学 Six-foot robot free gait planning method based on motion stability estimation

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