CN115202259A - CPG control system of quadruped robot and parameter setting method thereof - Google Patents
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Abstract
The invention relates to a CPG control system of a quadruped robot and a parameter setting method thereof, the system comprises four oscillator units for correspondingly controlling hip joints of the quadruped robot, the oscillator units are connected to form a one-way annular network structure, the connection mode is time-lag coupling, the oscillator units realize multiple stable phase differences based on a spontaneous symmetry breaking mechanism under the action of time lag, and the parameter setting of the CPG control system is carried out through nonlinear dynamics analysis, so that multiple gait modes of the quadruped robot and the switching thereof are realized, wherein the multiple gait modes comprise quadruped jumping, lateral sequence walking, biped jumping, diagonal sequence walking, pacing and diagonal jogging. Compared with the prior art, the system of the invention has simple structure and is easy to implement in engineering; the parameter setting method is reliable, and the change of the gait mode can be realized by switching a single time lag parameter between rhythm areas; in a given rhythm area, the gait mode can not change along with the change of parameters, and the robustness is effectively ensured.
Description
Technical Field
The invention relates to the technical field of bionic robots, in particular to a CPG control system of a four-legged robot and a parameter setting method thereof.
Background
The research of bionic control has great significance for the development of robotics, and in recent years, the bionic control simulating a biological Central Pattern Generator (CPG) has become one of the research hotspots in the field of bionic control. The CPG can spontaneously generate stable rhythmic motion under the condition of lacking high-level control signals and external feedback, the motion has the advantages of easy adjustment by high-level commands, strong coupling, strong adaptability, simple structure and the like, and the workload of a control system can be reduced and the working time can be saved.
With the development of the quadruped robot and the rise of artificial intelligence in recent years, the robot has autonomy and intelligence become important components of the research of the quadruped robot, the quadruped robot gradually has the capabilities of sensing environment, autonomous planning and environment interaction, and researchers also pay more attention to improving the autonomy adaptability and functionality of the robot. At present, most quadruped robots can realize various movement gaits through a control algorithm and can complete simple tasks, in the field of gait control of the quadruped robots, a CPG (compact programmable gate) is one of the simplest control methods, and a proper rhythm controller is constructed to allocate one controller to each leg of the quadruped robot so that the quadruped robot can move according to a certain time sequence, but the method can realize the gait movement of the quadruped robot, but has the following main defects: (1) The proposed CPG structure unit is required to be a two-dimensional or more than two-dimensional oscillator model, and the network structure mostly adopts the full connection of four oscillator units, so that the dimension of the whole CPG system is high, and the computational complexity is improved; (2) A general and unified dynamics analysis method for parameter setting is not provided, only a group or a plurality of groups of fixed parameter values can be provided based on a specific motion mode of the robot by adopting a trial and error method or an optimization calculation method, the actual engineering realization is more complex, and the adjustability of the system and the robustness of the control system cannot be ensured.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a CPG control system of a quadruped robot and a parameter setting method thereof, which can realize a control system with a simple structure and improve the control performance of a gait mode and the robustness of the control system.
The purpose of the invention can be realized by the following technical scheme: the CPG control system of the quadruped robot comprises four oscillator units used for correspondingly controlling hip joints of the quadruped robot, the four oscillator units are connected to form a one-way annular network structure, the connection mode among the oscillator units is time-lag coupling, the oscillator units realize various stable phase differences based on a spontaneous symmetry breaking mechanism under the action of time lag, and through nonlinear dynamics analysis, parameter setting of the CPG control system is carried out, so that various gait modes of the quadruped robot and switching of the quadruped robot are realized, and the various gait modes comprise four-foot jumping (Pronk), side-sequence walking (L-S walk), two-foot jumping (Bound), diagonal walking (D-S walk), pacing (Pace) and diagonal running (Trot).
Further, the unidirectional ring network structure is specifically a single ring network to realize four gait modes, which are divided into three cases:
a. four-foot jumping, lateral walking, diagonal walking and two-foot jumping;
b. four-footed jumping, lateral sequence walking, diagonal sequence walking and pacing;
c. four-footed jumping, lateral sequence walking, diagonal sequence walking, and diagonal sprinting.
Further, the unidirectional ring network structure is specifically a superposition of three single ring networks, so as to realize six gait modes.
Furthermore, the oscillator units are connected by adopting a nonlinear time-lag coupling function or a linear time-lag coupling function.
Further, the oscillator unit employs a vibrator model having a periodic rhythm signal.
Further, the oscillator unit employs a node model having no periodic rhythm signal.
Further, the models and the coupling functions thereof adopted by the four oscillator units are the same, so that the CPG control system has symmetry.
Further, the nonlinear dynamics analysis is specifically Hopf bifurcation analysis, and based on the Hopf bifurcation theory, the CPG control system can generate stable switching of periodic rhythms under the action of time lag.
Further, the parameter region corresponding to the periodic rhythm can generate a stable phase difference based on a symmetrical break-up mechanism, namely the parameter region of the gait mode.
A CPG control system parameter setting method of a quadruped robot comprises the following steps:
s1, performing linearization processing near a balance point on a time-lag coupled nonlinear system to obtain a corresponding linear system and a corresponding characteristic equation;
s2, assuming that the characteristic equation has a pair of pure virtual roots with zero real parts, bringing the assumed pure virtual roots into the characteristic equation, separating the real parts and the imaginary parts to obtain a real part equation and an imaginary part equation, and obtaining an algebraic equation corresponding to the periodic rhythm according to a trigonometric function relationship;
s3, calculating an algebraic equation to obtain a corresponding frequency value, and performing back substitution on a real part equation and an imaginary part equation to calculate a critical time lag value;
s4, verifying a parameter plane determined by critical time lag, arbitrarily taking a value in a region, verifying that the region is a rhythm mode or a rest state mode by a numerical method, wherein the rhythm mode region and the rest state mode region alternately appear, and the corresponding rhythm mode region is sequentially distributed with four-foot jump (Pronk), side-sequence walk (L-S walk), two-foot jump (Bound) and diagonal walk (D-S walk) modes;
by adjusting the network topology, the parameter areas of the double-foot hopping (Bound) can further realize pacing (Pace) and diagonal sprint (Trot) modes.
Compared with the prior art, the invention has the following advantages:
1. the invention aims at the phase relation in the gait mode of the quadruped robot, realizes various stable phase differences based on a spontaneous symmetry breaking mechanism, provides a CPG quadruped robot gait control system with unidirectional annular time-lag coupling, comprises four oscillator units, adopts a unidirectional annular network topology structure among the units, has a simple network structure, can use only one node model expressed by a variable for each oscillator, is easy to implement in engineering, and determines parameter areas under different dynamic modes through nonlinear dynamics analysis, thereby realizing various gait modes and switching of the quadruped robot.
2. Aiming at the CPG gait control system provided by the invention, the invention also provides a general and unified kinetic analysis method for parameter setting, the parameter setting method is simple and easy to implement, the nonlinear kinetic analysis of the control system can provide a parameter area corresponding to an asynchronous state mode, the control of the gait mode is simple, a single time lag parameter is switched among rhythm areas to realize the change of the gait mode, only one gait mode exists in one parameter area, and the gait mode can not change along with the change of the parameter in the given rhythm area, so that the control system has good robustness.
Drawings
FIG. 1a is a schematic diagram of a first unidirectional ring network structure of the CPG of the quadruped robot of the present invention;
FIG. 1b is a schematic diagram of a second unidirectional ring network structure of the CPG of the quadruped robot of the present invention;
FIG. 1c is a schematic diagram of a third unidirectional ring network structure of the CPG of the quadruped robot of the present invention;
FIG. 1d is a schematic diagram of the superposed structure of three unidirectional ring networks of the CPG of the quadruped robot of the present invention;
FIG. 2 is a diagram illustrating parameter regions corresponding to an asynchronous mode in an embodiment;
FIG. 3 is a schematic diagram of CPG control signal output in the quadruped robot quadruped jumping (Pronk) gait mode in the embodiment;
FIG. 4 is a schematic diagram of CPG control signal output in the lateral walking (L-S walk) gait mode of the quadruped robot in one embodiment;
FIG. 5 is a schematic diagram of CPG control signal output in a biped robot biped jumping (Bound) gait mode in the embodiment;
FIG. 6 is a schematic diagram of CPG control signal output of the quadruped robot in the diagonal walking (D-S walk) gait mode in the embodiment;
FIG. 7 is a schematic diagram of CPG control signal output in pacing (Pace) gait mode of a four-foot robot in an embodiment;
fig. 8 is a schematic diagram of CPG control signal output in the diagonal Trot (Trot) gait mode of the quadruped robot in the embodiment.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
Examples
As shown in fig. 1a to 1D, a CPG control system of a quadruped robot comprises four oscillator units (as shown in osc.1, osc.2, osc.3, and osc.4 in the figure), the four oscillator units are connected to form a unidirectional ring network topology in a time-lag coupling manner, and the unidirectional ring network structure can be a single ring network (as shown in fig. 1a to 1 c), in which case, one of four gait modes, namely, two-foot jump (Bound), pace (Pace) and diagonal little run (Trot), and four-foot jump (Pronk), side walk (L-S walk), and diagonal walk (D-S walk) can be implemented;
or the superposition of three single ring networks (as shown in fig. 1D), namely all six gait modes of the four-footed robot, namely four-footed jump (Pronk), lateral-sequence walking (L-S walk), two-footed jump (Bound), diagonal-sequence walking (D-S walk), pacing (Pace) and diagonal sprinting (Trot), can be realized.
In practical applications, the four oscillator units for controlling the quadruped hip joint may be oscillator models with periodic rhythm signals or node models without periodic rhythm signals. In addition, the connection mode adopted between the oscillator units can be a linear function or a nonlinear function, but signals of the oscillator units need to be delayed time-lag coupling when interacting, and the time lag is a control parameter used for controlling the gait mode. In the embodiment, the same oscillator unit model and coupling function are selected, and the constructed CPG gait control system has symmetry under the one-way ring-shaped structure network topology structure.
After the CPG control system is constructed, parameter areas with periodic rhythms of output signals of all oscillator units are determined through nonlinear dynamics analysis so as to realize parameter setting of the CPG network system, and multiple gait modes and switching of the four-legged robot can be realized by using changes of time-lag parameters among the parameter areas.
In this embodiment, the parameter setting is specifically determined by bifurcation analysis of nonlinear dynamics, based on the Hopf bifurcation theory, the CPG control system can generate stable switching of periodic rhythm under the action of time lag, and the parameter region corresponding to the periodic rhythm is the parameter region of the gait pattern.
The specific steps of parameter setting are as follows: firstly, carrying out linearization processing near a balance point on a time-lag coupled nonlinear system to obtain a corresponding linear system and provide a corresponding characteristic equation;
to find the parametric conditions that can produce periodic rhythms, assume that the eigenequation has a pair of pure imaginary roots with zero real parts; the assumed pure virtual root is brought into a characteristic equation, a real part and an imaginary part are separated to obtain a real part equation and an imaginary part equation, and an algebraic equation corresponding to the periodic rhythm is obtained according to the trigonometric function relationship;
calculating an algebraic equation to obtain a corresponding frequency value, and back-substituting the frequency value into a real part equation and an imaginary part equation to calculate a critical time lag value;
inspecting a parameter plane determined by critical time lag, arbitrarily selecting a value in an area, and verifying that the area is a rhythm mode or a resting mode by a numerical method; the rhythm mode region and the resting state mode region alternately appear, and the corresponding rhythm mode region is distributed with four-foot jump (Pronk), lateral sequence walking (L-S walk), two-foot jump (Bound) and diagonal sequence walking (D-S walk) modes in sequence; by adjusting the network topology, the parameter areas of two-foot hopping (Bound) can realize pacing (Pace) and diagonal sprinting (Trot).
In this embodiment, a VDP oscillator expressed by a single variable is used, a simple linear time-lag coupling is used as a coupling function, and a unidirectional torus network topology structure in the sequence of 1 → 2 → 4 → 3 → 1 is selected in the network topology structure, as shown in a Type I structure in fig. 1a, the following four-footed robot CPG control system is constructed:
wherein the parameter alpha>0 and beta>0 for adjusting the frequency and amplitude, ε, of the periodic rhythm signal>0 is the nonlinear damping coefficient in VDP system for regulating the shape of periodic rhythm, tau>0 is the coupling time lag between VDP oscillators, k is the coupling weight, x i Is the output signal of the ith VDP oscillator,
corresponding velocity and acceleration signals, respectively.
Replacing x with a variable i ＝u i ,
An equivalent system model is obtained as follows:
aiming at the time-lag coupling CPG control system, a parameter area of periodic rhythm can be obtained by utilizing a Hopf bifurcation theory and a numerical method of time-lag dynamics, and the process is a general and uniform dynamics analysis method for system parameter setting. Specifically, the method comprises the following steps:
linearizing the nonlinear system near the equilibrium point to obtain a characteristic equation of the linear system, which is as follows:
g 1 (λ,τ)＝β+(k-εα)λ+λ 2 -kλe -λτ ＝0
g 2 (λ,τ)＝β+(k-εα)λ+λ 2 +kλe -λτ ＝0
g 3 (λ,τ)＝β+(k-εα)λ+λ 2 -ikλe -λτ ＝0
g 4 (λ,τ)＝β+(k-εα)λ+λ 2 +ikλe -λτ ＝0
under the action of time lag tau >0, a CPG system can generate a stable periodic rhythm signal, based on a Hopf bifurcation theory, lambda = i omega, and a real part and an imaginary part are separated to obtain:
at this time, the frequency of the periodic rhythm signal should satisfy the following algebraic equation:
ω 4 +(ε 2 α 2 -2β-2kεα)ω 2 +β 2 ＝0
and calculating to obtain an accurate solution of the frequency, namely:
at this time, omega ± The condition >0 must be satisfied so that the time lag threshold for periodic rhythms is calculated as follows:
according to the feature vector corresponding to the feature root, the feature root has the following feature vectors:
wherein, the vector eta + ＝(1,iω + ) Corresponding to the time lag threshold
Vector eta - ＝(1,iω - ) Correspond to
j =0,1, \8230n, that is, the periodic rhythm caused by time lag satisfies the phase difference, so that the phase relation of the gait patterns is formed, and various gait patterns are formed in different areas.
In order to prove that the parameter region set by the method can meet the gait mode of the quadruped robot, the parameter region of the periodic rhythm is given in the (tau, k) plane based on the analysis theory method, wherein the parameter region is fixed by the system parameters of alpha =1, beta =1 and epsilon =0.03, as shown in fig. 2.
In fig. 2, AD denotes the amplitude death region of the system, when each oscillator of the CPG system does not generate a periodic rhythm signal. The system can generate periodic rhythm mode outside the AD area, particularly, the Pronk area can generate periodic rhythm with completely synchronous four oscillators according to the characteristic vector corresponding to the characteristic root, namely, the four-foot jumping (Pronk) gait mode of the four-foot robot, and the output signal is shown in figure 3.
When the periodic rhythm passes through the AD zone, a delayed synchronization with a phase lag of 1/4 period is generated, corresponding to the lateral sequence walking (L-S walk) gait pattern of the quadruped robot, as shown in FIG. 4.
The periodic rhythm corresponding to the Bound region has a phase lag synchronization with a phase difference of 1/2 period, so that by changing the coupling connection direction between the units, a double-foot-jump (Bound) gait mode (as shown in fig. 5), a Pace (Pace) gait mode (as shown in fig. 7), and a diagonal little-race (Trot) gait mode (as shown in fig. 8) can be sequentially realized, and the corresponding network structures are Type I (corresponding to fig. 1 a), type II (corresponding to fig. 1 b), and Type III (corresponding to fig. 1 c), respectively. Therefore, in order to realize the above six gaits, a superposition of three unidirectional ring network structures of Type I, type II and Type III, i.e. the hybrid network structure in fig. 1d, may be adopted.
The periodic rhythm oscillations corresponding to the D-S walk area have phase difference of 1/4 period and phase lead synchronization, and at the moment, the corresponding gait mode of the quadruped robot is a diagonal walking (D-S walk) gait mode, as shown in FIG. 6.
In conclusion, the control system of the CPG quadruped robot provided by the technical scheme has a simple structure, each oscillator unit can be expressed by only one variable, and the engineering is easy to implement; the technical scheme utilizes the CPG system dynamics analysis to carry out parameter setting, compared with the traditional trial and error method, the parameter setting method is simple, and the parameter area under the asynchronous mode can be given out through the nonlinear dynamics analysis of the control system; the gait mode is simple to regulate and control, and the change of the gait mode can be realized by switching a single time lag parameter between rhythm areas; within a given rhythm area, the gait mode can not change along with the change of parameters, and the constructed control system has good robustness.
Claims (10)
1. A CPG control system of a quadruped robot is characterized by comprising four oscillator units for correspondingly controlling hip joints of the quadruped robot, the four oscillator units are connected to form a one-way annular network structure, the oscillator units are connected in a time-lag coupling mode, the oscillator units realize various stable phase differences based on a spontaneous symmetry breaking mechanism under the action of time lag, and parameter setting of the CPG control system is carried out through nonlinear dynamics analysis, so that various gait modes and switching of the quadruped robot are realized, and the various gait modes comprise quadruped jumping, lateral sequence walking, biped jumping, diagonal sequence walking, pacing and diagonal running.
2. The CPG control system of a quadruped robot as claimed in claim 1, wherein the unidirectional ring network structure is embodied as a single ring network to realize four gait patterns, which are divided into three cases:
a. four-foot jumping, lateral walking, diagonal walking and two-foot jumping;
b. four-footed jumping, lateral sequence walking, diagonal sequence walking and pacing;
c. four-footed jumping, lateral sequence walking, diagonal sequence walking, and diagonal sprinting.
3. The CPG control system of a quadruped robot as claimed in claim 2, wherein the unidirectional looped network structure is a superposition of three single looped networks to realize six gait patterns in all.
4. The CPG control system of a quadruped robot as claimed in claim 1, wherein the oscillator units are connected by a nonlinear time-lag coupling function or a linear time-lag coupling function.
5. A CPG control system of a quadruped robot as claimed in claim 1, characterized in that the oscillator unit employs a vibrator model with a periodic rhythm signal.
6. The CPG control system of a quadruped robot as claimed in claim 1, wherein the oscillator unit employs a nodal model with no periodic rhythm signal.
7. The CPG control system of a quadruped robot as claimed in claim 1, wherein the models and the coupling functions of the four oscillator units are the same, so that the CPG control system has symmetry.
8. The CPG control system of the quadruped robot as claimed in claim 1, wherein the nonlinear dynamics analysis is Hopf bifurcation analysis, and based on Hopf bifurcation theory, the CPG control system can generate stable switching of periodic rhythm under the action of time lag.
9. The CPG control system of a quadruped robot as claimed in claim 8, wherein the parameter region corresponding to the periodic rhythm generates a plurality of stable phase differences based on a mechanism of spontaneous symmetry loss, i.e. the parameter region of gait pattern.
10. A CPG control system parameter setting method of a quadruped robot is characterized by comprising the following steps:
s1, performing linearization processing near a balance point on a time-lag coupled nonlinear system to obtain a corresponding linear system and a corresponding characteristic equation;
s2, assuming that the characteristic equation has a pair of pure virtual roots with zero real parts, bringing the assumed pure virtual roots into the characteristic equation, separating the real parts and the imaginary parts to obtain a real part equation and an imaginary part equation, and obtaining an algebraic equation corresponding to the periodic rhythm according to a trigonometric function relationship;
s3, calculating an algebraic equation to obtain a corresponding frequency value, substituting the frequency value into a real part equation and an imaginary part equation, and calculating a critical time lag value;
s4, verifying a parameter plane determined by the critical time lag, arbitrarily selecting a value in the region, verifying that the region is a rhythm mode or a rest state mode by a numerical method, wherein the rhythm mode region and the rest state mode region alternately appear, and the corresponding rhythm mode region is sequentially distributed with four-foot jumping, lateral sequence walking, double-foot jumping and diagonal sequence walking modes;
by adjusting the network topology, the parameter areas of bipedal hopping can further enable pacing and diagonal sprint patterns.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116880293A (en) * | 2023-07-20 | 2023-10-13 | 济南大学 | Four-foot robot control method and control terminal based on explicit model predictive control |
| CN116880293B (en) * | 2023-07-20 | 2023-12-26 | 济南大学 | Four-foot robot control method and control terminal based on explicit model predictive control |
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