CN108873686B - A kind of control method for series elastic driver - Google Patents
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Abstract
The present invention provides a kind of control method for series elastic driver, and method includes: 100, obtains angle/position q, SEA spring stress value τ that load-side contacts ports, desired angle/position qd, desired joint stiffness Ks；101, angle/position q, the desired angle/position q of port are contacted according to load-sided, desired joint stiffness Ks, obtain the output valve ν of controller outer ring；102, according to τs, ν and selection controller inner ring parameter information, obtain the output valve w of controller inner ring；103, according to w, setting and τsAssociated numerical value obtains the control force τ of motor in SEAm.The above method makes the mechanical output mouth of SEA that the rigidity value of any desired can be presented, while can break through traditional SEA and can not surmount the limitation of actual physics rigidity, while can guarantee and contact stabilization with external environment.
Description
Technical Field
The invention relates to a control method for a series elastic driver.
Background
In addition to the advantages of safety, impact mitigation and energy storage in terms of mechanical structure, the SEA, as shown in fig. 1, has an important advantage in terms of control, that is, the stress value of the spring is converted into the position variation of the spring for processing, because the variation of the spring is proportional to the output force; the other advantage is that the damping and decoupling effect is achieved on the inertia of the motor, and the reflection mass of equipment such as an actuator is reduced. However, SEA is known to have problems of bandwidth limitation, rigidity limitation, stability limitation and the like in control.
Concept of port impedance: the port impedance is derived from the mechanical impedance and is used primarily to describe the interaction control. "interactive control" refers to regulating the dynamic behavior of the robot with the environment through an interactive port. An interactive port is a place where energy is exchanged with the environment, defined by a set of motion and force variables, P ═ Ftv, e.g. vector v of velocity (or angular velocity) moves in different degrees of freedom at the point of contact, FtIs the corresponding force (moment) vector, P is the power flow between the robot and the environment. Impedance is used to fully describe how a robotic arm interacts with various environments, and in principle, any behavior can be achieved if any impedance can be achieved.
Concept of stable contact with external environment: a system with passive port impedance can never output more energy than input at the interaction port at any time, and the contact is stable. I.e. when the environment is passive, the interaction process is stable if the contacted controlled object is also passive. Passivity is generally used to characterize whether the contact with the external environment is stable in the control system. Passive means stable in contact with the environment, and non-passive means unstable in contact with the environment. Passivity is generally judged by whether a phase angle diagram in a frequency response diagram of port impedance is +/-90 degrees, passive systems are in a range of +/-90 degrees, namely interactive stability is realized, and passive systems are in a range beyond the range, namely interactive instability is realized.
Impedance control mainly controls the feeling of contact, for example, the lower the impedance presented by a controlled object, the softer the feeling when touched by a human hand; the higher the impedance presented by the controlled object, the harder it will feel when touched by a human hand.
There are generally two methods to achieve variable impedance control, one is mechanical (variable stiffness drive) and the other is control. As shown in fig. 2, a Variable Stiffness Actuators (VSA) that varies the joint output motion by a motor to allow a motor to perform spring rate adjustment, as shown in fig. 2 (a); if the rigidity adjusting motor is removed, the rigidity adjustment can be realized by using a control algorithm, and the method is a virtual rigidity changing method. As shown in fig. 2 (b).
For the above-mentioned SEA control methods, there are various control methods provided in the prior art, such as three control methods as illustrated below:
(1) position control block diagram of motor as feedback (as shown in figure 3)
Let thetad0, namely:
the complex number in the alternative formula (2)Obtaining a frequency response Z (j omega), and calculating a desired stiffness value K according to a frequency characteristic curve shown in figure 4desiredAnd a final stiffness value KfinalSee formula (3).
The curve ① in fig. 4 represents the frequency response of the port impedance z(s), the curve ② represents the desired stiffness frequency response (frequency response shown for cross-port impedance), and the curve ③ represents the frequency response of the spring's inherent stiffness.
For the low frequency band omega → 0, the planned stiffness can be realized, and the stiffness value is K in the formula (3)desiredHowever, as can be derived, the stiffness value is always less than the inherent stiffness value K of the spring; for the high frequency band ω → ∞, it is known that the displayed interaction port impedance will approach the mechanical spring rate of SEA. Therefore, it can be seen that the port impedance presented by this control method is always limited by the inherent stiffness of the spring when interacting.
(2) Cascade PI control
The control method proposed below has a port impedance that may exceed the inherent stiffness of the spring, but affects the stability of the interaction, i.e., if the interaction is to be stable, the port impedance cannot exceed the inherent stiffness of the spring. The control block is shown in fig. 5.
The control law and the dynamic model are as the following formula (4), and P is a stiffness controller parameter:
the port impedance transfer function can be derived:
obtaining:
as shown in a port impedance frequency response curve shown in FIG. 6, it can be known through analysis that the port impedance of the control method exceeds the inherent stiffness value of the mechanical spring in a low frequency band, but the stability during interaction is affected, namely, a phase angle diagram exists more than-90 degrees, namely, an passivity condition is not met, and it can be known through proving that the port impedance cannot exceed the inherent stiffness of the spring if the interaction stability is ensured.
(3) Single loop feedback in the presence of resonance conditions
When cascade control is not employed, control thereof in the case of link-side position feedback is as shown in the block diagram of fig. 7: the control law and the dynamic model are as follows:
the port impedance transfer function can be derived:
as shown in the port impedance frequency response curve of fig. 8, the curve ① represents the port impedance frequency response of only the position loop, and the curve ② represents the actual stiffness frequency response curve of the spring, it can be clearly seen from fig. 8 that there is a resonance frequency point in the middle frequency band, the impedance of the high frequency band approaches the actual spring stiffness, and it can be known from the phase angle diagram that the method does not satisfy the passivity condition, and there is an unstable situation when interacting with the environment.
Each of the above methods has drawbacks, and for this reason, how to provide a mechanical output port of SEA that exhibits any desired stiffness value, and that can exceed the limit of actual physical stiffness, is a problem that needs to be solved currently.
Disclosure of Invention
To address the problems in the prior art, the present invention provides a control method for a series elastic driver.
In a first aspect, the present invention provides a control method for a series elastic driver, comprising:
100. obtaining the angle/position q of the load side contact port, the spring force value tau of the series elastic driver SEAsExpectation ofAngle/position q ofdDesired joint stiffness Ks；
101. According to the angle/position q of the load side contact port, the desired angle/position qdDesired joint stiffness KsAcquiring an output value v of the outer ring of the controller;
102. according to the spring stress value tausAcquiring an output value w of the inner ring of the controller according to the output value v and the selected parameter information of the inner ring of the controller;
103. according to the output value w of the inner ring of the controller, the set value and the spring stress value tausAssociated values to obtain the control force tau of the motor in the SEAm。
Specifically, the step 101 includes:
v＝(qd-q)×(KS+Kds)
wherein, KdIn order to be the differential coefficient,is represented by (q)d-q)×KdThe derivation operation of (1).
Specifically, the step 102 includes:
wherein,the parameter information of the inner ring of the controller,to representThe derivation operation of (1).
In particular, a set stress value tau associated with said springsThe associated numerical values are specifically: tau issAnd +/-C and C are preset values.
Specifically, q isdWhen equal to 0, the port impedance, i.e. the spring force value τsAnd load speedThe transfer function of the division:
order complex numberSubstituting the frequency response Z (j omega) into the formula (A3) to obtain the impedance frequency characteristic of the port; and the number of the first and second groups,
desired stiffness value KdesiredAnd a final stiffness value KfinalThe method specifically comprises the following steps:
where B is the loaded position and K is the spring rate of SEA.
In particular, said desired angle/position qdGiven or obtained by more than one torque loop/impedance loop/position loop nested through the controller outer loop.
The invention has the following beneficial effects:
the method of this embodiment, which is itself based on a motion control framework, allows the mechanical output port of the SEA to exhibit any desired stiffness value through a control algorithm, generating the desired interaction, which breaks the limitation that conventional SEA cannot exceed the actual physical stiffness. In practical application, the method not only keeps the basic performance of the SEA, but also has the design concept of the VSA, and other cascade control algorithms based on the method have excellent realization effects.
Drawings
FIG. 1 is a block diagram of a prior art SEA;
FIG. 2 is a schematic diagram of a prior art virtual variable stiffness controller model;
FIG. 3 is a block diagram of a position control method for coordinated feedback of a motor according to the prior art;
fig. 4 is a graph of the frequency characteristic shown in fig. 3;
FIG. 5 is a schematic diagram of another control method provided in the prior art;
FIG. 6 is a graph of the frequency response of FIG. 5 for unsatisfied passivity;
FIG. 7 is a schematic control block diagram of a control method provided in the prior art;
FIG. 8 is a schematic diagram of the frequency response of the port impedance of FIG. 7;
FIG. 9 is a schematic diagram of the corresponding positions of part of the system variables;
FIG. 10 is a block schematic diagram of a virtual variable stiffness controller of the present invention;
FIG. 11 is a schematic diagram of a VVSC controlled port impedance frequency response curve;
FIG. 12 is a graph illustrating stiffness versus impedance comparison in a cascade method of the present invention and prior art motor parity feedback;
FIG. 13 is a schematic illustration of the experimental platform with SEA flexible joint provided in this example;
fig. 14 is a schematic diagram of the experimental results of the experimental platform shown in fig. 13.
Detailed Description
For the purpose of better explaining the present invention and to facilitate understanding, the present invention will be described in detail by way of specific embodiments with reference to the accompanying drawings.
The virtual variable stiffness method provided by the embodiment of the application is based on a motion control frame, the mechanical output port of the SEA can present any expected stiffness value through a control algorithm, expected interaction is generated, and the limit that the traditional SEA cannot exceed actual physical stiffness is broken through. In practical application, the method not only keeps the basic performance of the SEA, but also has the design concept of the VSA, and the control algorithm is used as a basic control algorithm, and the series/parallel connection of other control algorithms has excellent realization effect.
The definition of the model and some variables is given below:
as shown in fig. 9, the system variables define: tau ismThe magnetic force applied to the motor rotor can also be called control force for controlling the motor; tau issThe force applied to the load is also known as contact force, spring force or external force; θ is the angle/position of the motor; q is the angle/position of the load, also called the spring output position, link side position; b is the motor mass; k is the spring rate;is the acceleration of the motor.
The system differential equation is written according to the model column shown in fig. 9:
in this embodiment, by connecting two controllers in series, the feedback information of the first controller (outer controller loop) is the angle/position q feedback of the load, and the feedback information of the second controller (inner controller loop) is the spring moment, as shown in fig. 10. In the embodiment, for convenience of analysis, factors such as friction and damping are ignored.
Specifically, the control method for the series elastic actuator in the present embodiment, i.e., the control method of the "virtual variable stiffness controller" can be described as:
101. the first controller (outer loop) expects an angle/position q through a given loaddSubtracted from the angle/position q on the load side to obtain a value α;
102. the value α is used as input to the first controller (outer loop), multiplied by Ks+Kds (where KsIs a proportionality coefficient, named joint stiffness desired to exhibit, KdIs a differential coefficient named joint damping expected to exhibit, s is an arithmetic signRepresents the pair u × KdSubsequent derivation operation) to obtain an output value v;
103. output value v and stress value tau of springsThe subtracted value is β multiplied by the parameter information of the second controller, and the output value w is obtained through the operation of the second controller;
104. the output value w needs to be added/subtracted by a value, which can be the spring stress value taus(in this example, the spring force value τ is usedsThis value may be greater or less than τ, depending on the method of uses) Finally, the control force tau of the motor is obtainedm。
The second controller can be selected from a variety of forms but must include a common factor kin(A simple proportional-derivative controller is chosen here
Desired position: it is desired that the control link is at that position, e.g. the position at the side of the desired link is 90 °I.e. without interference, the link-side position ends up at 90 °, this desired position being the horizontal position of the silver link in fig. 13, and q for fig. 10dA value of (d);
a load side position: that is, q value in fig. 10, spring output position/link-side position/load-side position; the outer ring of the controller: according to FIG. 10, at τmTwo frames in front, from taumThe most recent is the inner ring; the inner ring of the controller: one frame outside the inner ring is the outer ring.
KsTo the joint stiffness desired to exhibit, KdJoint damping is desired to exhibit. The controller of the inner loop can be selected in various forms but must have a high gain factor kin(A simple proportional-derivative controller is chosen hereThe controllers of this inner loop are not of a particular kind and may be combined as desired, but must be able to extract a common factor, kinThe number is usually at least 5 or more as long as it can be increased, and the larger the number, the better.
The specific calculation model is as follows (a 2):
qdwhen 0, the port impedance, i.e. the load force τ, is written according to the above formulasAnd load speedThe transfer function of the division:
order complex numberThe frequency response Z (j omega) is obtained by substituting the formula (A3), and the impedance frequency characteristic of the port can be obtained by analyzing the frequency response of the port impedance transfer function. The frequency characteristic curve is shown in FIG. 11, and the expected rigidity value K is calculateddesiredAnd a final stiffness value Kfinal，
FIG. 11 shows frequency response plots for FIG. 11(a) without exceeding the physical spring rate and FIG. 11(b) with the physical spring rate exceeded, respectively, and curve ① in FIG. 11 represents the port impedanceCurve ② represents the desired stiffness frequency response (frequency response for cross-port impedance display), curve ③ represents the frequency response for the physical spring rate, and curve ④ represents the final rate exhibited at high frequencies.
Viewing the asymptote of this fig. 11 allows a more intuitive understanding of SEA behavior. For the low frequency range ω → 0, the planned stiffness can be achieved, with a stiffness value of K in equation (a4)desiredThe value of the stiffness is independent of the value of the inherent stiffness K of the spring, as can be derived; for the high band ω → ∞, it can be seen that the displayed interaction port impedance will be close to K in equation (a4)finalStiffness, which is proportional to the value of the spring inherent stiffness K, is related to the motor mass and controller parameters, and it can be seen from the phase angle diagram that passivity is guaranteed regardless of whether the spring stiffness is exceeded or not. In summary, in the cascade control method, when interacting, the presented port impedance is not limited by the inherent stiffness of the spring, and the spring stiffness presented by the port is limited by the parameters of the controller.
In addition, it should be noted that the above formula (A3) is a formula for the case where damping or friction is ignored, and if damping or friction is increased, the formula A3 is changed appropriately.
As is apparent from comparison of fig. 12(a), the static stiffness exhibited by the control method of the present embodiment is not affected by the stiffness of the mechanical spring, and the static stiffness of the motor parity feedback cannot exceed the spring stiffness all the time; in fig. 12(b), it can be seen that the "virtual variable stiffness controller" can achieve the same port impedance characteristic as the coordinated feedback in the low frequency band, and gradually surpasses the characteristic of the mechanical spring with the increase of frequency, and exhibits a spring characteristic related to the controller parameter, while the motor coordinated feedback can only gradually approach the mechanical spring characteristic. The "virtual variable stiffness controller" also exhibits a spring characteristic at high frequencies, and therefore also has safety (touch or a spring feel at high frequencies).
Further, in the above method, it is possible to achieve different control effects by nesting again in the outer ring, for example, by nesting a moment ring (or a position ring/resistance ring, etc.) outside, i.e., force control, etc.
Additional details are provided below to provide a better understanding of the method of embodiments of the invention.
1) The controller of the inner loop can be selected in various forms but must have a high gain factor kin：
Explanation is made based on the above formula (a 3):
the formula (A3) is a development of the formula
When the formula is divided by kinWhen it is obtained
With kinIs increased, whereinAndthe two terms gradually approach to zero, and then the formula of the upper and lower terms is approximately removedThen obtain
In the formulaIs the removal of k from the inner ringinSo when the common factor k is removedinOther parameters of the inner ring can be not required.
2)KsTo the joint stiffness desired to exhibit, KdTo illustrate the joint damping that is expected to be exhibited:
in the control process adopting advanced algorithms of variable impedance control/interactive matching control/predictive control and the like, KsAnd KdThe specific value of the representative port impedance can be changed in real time according to the requirement in the control process, and is not a constant value.
To better understand the control method of the embodiment of the present invention, the following description is made with reference to the experimental apparatus shown in fig. 13.
In fig. 13, when the link is controlled to the horizontal 90 ° balance position, the desired stiffness value K of the controller is setsBy adding a weight to the end of the link, the positional change information on the link side is obtained, and a positional error map under different weight loads is obtained, and as shown in fig. 14(a), the positional difference Δ x and the weight G of the weight are converted into the stiffness values to be exhibitedFIG. 14(b) shows the desired stiffness value K by setting it when using this algorithm (the method of the present invention)sAnd (3) obtaining a corresponding stiffness graph of the exhibited stiffness value K of the system through experiments, and verifying the correctness of the algorithm from the graph (b) in FIG. 14.
The above embodiments may be referred to each other, and the present embodiment does not limit the embodiments.
Finally, it should be noted that: the above-mentioned embodiments are only used for illustrating the technical solution of the present invention, and not for limiting the same; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (2)
1. A control method for a series elastic actuator, comprising:
100. obtaining the angle/position q of the load side contact port, the spring force value tau of the series elastic driver SEAsDesired angle/position qdDesired joint stiffness Ks；
101. According to the angle/position q of the load side contact port, the desired angle/position qdDesired joint stiffness KsAcquiring an output value v of the outer ring of the controller;
102、according to the spring stress value tausAcquiring an output value w of the inner ring of the controller according to the output value v and the selected parameter information of the inner ring of the controller;
103. according to the output value w of the inner ring of the controller, the set value and the spring stress value tausAssociated values to obtain the control force tau of the motor in the SEAm；
Wherein the step 101 comprises:
v＝(qd-q)×(KS+Kds)；
wherein, KdIn order to be the differential coefficient,is represented by (q)d-q)×KdThe derivation operation of (1);
the step 102 comprises:
wherein,parameter information indicative of an inner loop of the controller,to representThe derivation operation of (1);
in addition, the set stress value tau to the springsThe associated numerical values are specifically: tau issC, C is a preset value;
qdwhen equal to 0, the port impedance, i.e. the spring force value τsAnd load speedThe transfer function of the division:
order complex numberSubstituting the frequency response Z (j omega) into the formula (A3) to obtain the impedance frequency characteristic of the port; and the number of the first and second groups,
desired stiffness value KdesiredAnd a final stiffness value KfinalThe method specifically comprises the following steps:
wherein B is the mass or moment of inertia of the motor, and K is the spring rate of SEA.
2. The method of claim 1,
the desired angle/position qdGiven or obtained by more than one torque loop/impedance loop/position loop nested through the controller outer loop.
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| CN109773792B (en) * | 2019-02-14 | 2021-07-06 | 中科新松有限公司 | Position control device and method for series elastic driver, storage medium and equipment |
| CN110262218A (en) * | 2019-05-20 | 2019-09-20 | 北京航空航天大学 | Control method, device, equipment and the storage medium of machine fish |
| CN112987812B (en) * | 2021-02-24 | 2021-12-10 | 深圳市优必选科技股份有限公司 | Torque control method and device, terminal equipment and storage medium |
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