CN103750927B - Artificial leg knee joint adaptive iterative learning control method - Google Patents

Abstract

The invention discloses a kind of human body lower limbs movement of knee joints of artificial limbs control method, the adaptive iterative learning control method particularly during two rigid body two degrees of freedom artificial leg level walkings.First the present invention analyzes human body normal gait feature and artificial leg control overflow; Then by Newton-Euler algorithm, dynamic analysis is carried out to it, set up two rigid body two degrees of freedom artificial leg motor system models; Finally by adaptive iterative learning control algorithm application in this motor system model, its control algolithm flow process comprises: problem description, convergence, ask for boundedness, ask for incremental, ask for incremental.Adopt the present invention stably can reduce the tracking error of motion of knee joint within a certain period of time, reach good tracking effect.

Description

Artificial leg knee joint adaptive iterative learning control method

Technical field

The present invention relates to a kind of human body lower limbs artificial limb motion control method, particularly the method for adaptive iterative learning control during two rigid body two degrees of freedom artificial leg level walkings.

Background technology

The biomechanical system of human skeleton muscle system composition has extremely strong adaptive ability to walking.The main function components of artificial leg is knee joint and foot, especially important with artificial limb knee-joint.Good artificial limb knee-joint can ensure that patient is in the stability of support phase (from heel strike to toes liftoff period) and the motility of shaking peroid (from contacting to earth period to heel toeoff), naturally walking is completed, and make patient have good gait, be also whole artificial limb performance and the determiner in life-span simultaneously.

But, in the control of artificial thigh, theoretical research concentrates on the intelligent control methods such as general fuzzy control, common BP ANN Control, rule-based Multimode Control substantially, more complicated intelligent control method, as the also substantially non-practical application of the intelligence multiple control such as Neural Network Adaptive Control, Fuzzy Expert Control technology.Kalanovic etc. have studied the Neural Network Supervised Control that the BP network controller based on FEL (feedback-errorlearning) is combined with PD controller.This FEL control method owing to have employed BP nerve network controller, the poor real of its practical application.

Adaptive iterative learning control integrates the advantage of Self Adaptive Control and iterative learning control, and based on PD feedback control gain Automatic adjusument, iterative learning controller Correction and Control moment, this algorithm has asymptotic convergence performance fast.The present invention adopts the method to control artificial leg for this reason.

Summary of the invention

The present invention adopts adaptive iterative learning control method, reaches more satisfactory control overflow, stably can reduce tracking error within a certain period of time, reaches good tracking performance.

Object of the present invention can be achieved through the following technical solutions:

The present invention includes following steps:

Step 1. sets human normal gait feature and artificial leg control overflow.

Step 2. sets up artificial leg control imitation research kinetic model.

The adaptive iterative learning control of step 3. artificial leg motion of knee joint.

Wherein in step 1, the normal gait feature of human body can be divided into two stages, namely supports phase and shaking peroid, and concrete end is as follows:

Supporting latter stage, maximum vertical load produces, and knee joint bending starts soon later, for lower limb are prepared recovery phase, so knee joint bending resistance now should be minimum.When starting recovery phase, knee joint has bent 30 °, and maximum knee flexion angles is 55 ° ~ 65 °.Knee joint artificial limb with minimum bending resistance setting in motion, thus should adapt to the gait speed of certain limit automatically.

Artificial leg is expected to reach following control overflow: in support phase, has enough weight support stability and automatic safe reaction; There is the ability of automatic bending locking when tripping; Can to whole gait cycle, seat, to stand and the walking mode such as downstairs/descending controls; There is the ability of response leg speed transient change; The individual cultivation requirement of different wearer can be adapted to, realize the Self Adaptive Control without the need to training; There is the ability absorbing ground shock in heel contact position.

Wherein in step 2, artificial leg control imitation studies the foundation of kinetic model, based on two rigid body two degrees of freedom artificial leg motor systems, obtains the kinematic parameter of each rigid body, carries out dynamic analysis by Newton-Euler algorithm to it.First obtain the position coordinates of each rigid body barycenter, then its differentiate is obtained to the rate equation of each barycenter, introduce the broadest scope coordinate variable of respective link, ask for the outside force square that joint applies.

Wherein carry out adaptive iterative learning control to artificial leg motion of knee joint in step 3, make its movement locus level off to proper motion track, algorithm flow is through as follows:

(1) problem describes;

(2) convergence;

(3) W is asked for _ithe boundedness of (t);

(4) W is asked for ₀the incremental of (t);

(5) W is asked for _ithe incremental of (t);

Compared with prior art, the present invention has the following advantages:

1. establish fairly perfect artificial leg kinetic model, for the control method of artificial limb provides reference model.

2. this control method stably can reduce tracking error within a certain period of time, reaches good tracking performance.

Accompanying drawing explanation

Fig. 1 bis-rigid body two degrees of freedom artificial leg motor system model;

Figure 26 iteration trace location error;

Fig. 3 the 6th iteration follows the trail of rear velocity error;

The convergence process of position Error Absolute Value in Figure 46 iterative process;

The convergence process of Figure 56 iterative process medium velocity Error Absolute Value;

Fig. 1 shows two rigid body two degrees of freedom artificial leg motor systems, for the control algolithm of artificial leg provides reference model.

When Fig. 2 shows 6 iterative learnings, situation is followed the tracks of in knee joint position, has error between expected value and iterative value, and to increase error more and more less along with iterations.

Fig. 3 has fabulous Velocity Pursuit effect after showing the 6th iteration.

Fig. 4 shows position tracking error tracing process in 6 iterative process, and Fig. 5 shows 6 iterative process medium velocity tracking error tracing processs, and both tracking errors all reduce gradually with iterations.

Detailed description of the invention:

That expresses for making the object, technical solutions and advantages of the present invention clearly understands, is further described in detail the present invention below in conjunction with drawings and the specific embodiments again.

Main thought of the present invention considers that human body artificial limb system has the complication system such as model nonlinear and parameter uncertainty factor, design adaptive iterative learning control device collects it and controls research, uses the stability and the convergence that prove tracking error based on Lyapunov function.With set up artificial leg experimental prototype kinetic model for object, the controller of design is emulated.

Step 1: the normal gait feature of human body can be divided into two stages, namely supports phase and shaking peroid, and concrete end is as follows:

Supporting latter stage, maximum vertical load produces, and knee joint bending starts soon later, for lower limb are prepared recovery phase, so knee joint bending resistance now should be minimum.When starting recovery phase, knee joint has bent 30 °, and maximum knee flexion angles is 55 ° ~ 65 °.Knee joint artificial limb with minimum bending resistance setting in motion, thus should adapt to the gait speed of certain limit automatically.

Artificial leg is expected to reach following control overflow: in support phase, has enough weight support stability and automatic safe reaction; There is the ability of automatic bending locking when tripping; Can to whole gait cycle, seat, to stand and the walking mode such as downstairs/descending controls; There is the ability of response leg speed transient change; The individual cultivation requirement of different wearer can be adapted to, realize the Self Adaptive Control without the need to training; There is the ability absorbing ground shock in heel contact position.

Step 2: be the effect of the above-mentioned control program of simulation study, need the mathematical model setting up control object.Inverse dynamics can be summed up as traditionally: known trajectory plans speed and the acceleration of motion path and each point provided, and solves driving element and must be supplied to the generalized driving forces of initiatively closing (or displacement) in time and changing.In order to realize kneed Trajectory Tracking Control, only directly carry out Converse solved to kinetics equation according to the kinematics parameters of thigh, to obtain hip joint, kneed moment.But, in fact the joint moment parameter calculated accordingly cannot be used for the control needs of artificial thigh, because the joint moment (particularly knee joint torque) affecting thigh gait is normally controlled indirectly by non-thread damping, and the output of control microprocessor directly cannot carry out moment tracking according to the result of calculation of this mathematical model.Therefore, this patent, based on two rigid body two degrees of freedom artificial leg motor systems (see Fig. 1), carries out dynamic analysis, in Fig. 1 by Newton-Euler algorithm to it: l ₁and l ₂represent the length of human body lower limbs thigh and shank respectively; d ₁and d ₂represent the position of lower limb respective link barycenter; θ ₁and θ ₂for representing the broadest scope coordinate variable of respective link, meet right-hand rule; M ₁and M ₂represent the outside force square that joint applies; m ₁, m ₂with expression connecting rod quality, X _irepresent position coordinates (i=1,2).Its formula is as follows:

$\begin{array}{c}{M}_1=(m_1{d}_1^2+m_2{d}_2^2+m_2{l}_1^2+2m_2{l}_1{d}_2{\cos \mathrm{\θ}}_2){\stackrel{..}{\mathrm{\θ}}}_1+(m_2{d}_2^2+m_2{l}_1{d}_2{\cos \mathrm{\θ}}_2){\stackrel{..}{\mathrm{\θ}}}_2+\\ (-2m_2{l}_1{d}_2{\sin \mathrm{\θ}}_2){\stackrel{.}{\mathrm{\θ}}}_1{\stackrel{.}{\mathrm{\θ}}}_2+(-m_2{l}_1{d}_2{\sin \mathrm{\θ}}_2){{\stackrel{.}{\mathrm{\θ}}}_2}^2+(m_1{d}_1+m_2{d}_1)g*{\sin \mathrm{\θ}}_1+m_2{p}_{2}g\sin ({\mathrm{\θ}}_1+{\mathrm{\θ}}_2)\\ M_2=(m_2{d}_2^2+m_2{l}_1{d}_2{\cos \mathrm{\θ}}_2){\stackrel{..}{\mathrm{\θ}}}_1+m_2{d}_2^2{\stackrel{..}{\mathrm{\θ}}}_2+(-m_2{l}_1{\sin \mathrm{\θ}}_2+m_2{l}_1{d}_2{\sin \mathrm{\θ}}_2){\stackrel{.}{\mathrm{\θ}}}_1{\stackrel{.}{\mathrm{\θ}}}_2+\left(m_2{l}_1{d}_2{\sin \mathrm{\θ}}_2\right){{\stackrel{.}{\mathrm{\θ}}}_1}^2\\ +m_2{p}_{2}g\sin ({\mathrm{\θ}}_1+{\mathrm{\θ}}_2)\end{array}---\left(1\right)$

Get hip joint P ₀place is zero, sets up forward kinematics equation, obtains X ₁, X ₂coordinate is:

$\left\{\begin{array}{c}{X}_{p1}=X_{p0}+d_1{\sin \mathrm{\θ}}_1\\ Y_{p1}=Y_{p0}-d_1\cos {\mathrm{\θ}}_1\end{array}\right.---\left(2\right)$

$\left\{\begin{array}{c}{X}_{p2}=X_{p0}+l_1\sin {\mathrm{\θ}}_1+d_2{\sin \mathrm{\θ}}_2\\ Y_{p2}=Y_{p0}-l_1\cos {\mathrm{\θ}}_1-d_2{\cos \mathrm{\θ}}_2\end{array}\right.---\left(3\right)$

Differentiate is carried out to position equation, the rate equation of each barycenter that just can obtain leading leg, represents as follows:

$V_{p1}=\left(\begin{array}{c}\stackrel{.}{X_{p1}}\\ \stackrel{.}{Y_{p1}}\end{array}\right)=\left(\begin{array}{c}{d}_1\cos {\mathrm{\θ}}_1\\ d_1{\sin \mathrm{\θ}}_1\end{array}\right)\stackrel{.}{{\mathrm{\θ}}_1}---\left(4\right)$

$V_{p2}=\begin{array}{}\end{array}\left(\begin{array}{c}\stackrel{.}{X_{p2}}\\ \stackrel{.}{Y_{p2}}\end{array}\right)=\left(\begin{array}{c}{l}_1{\cos \mathrm{\θ}}_1\\ l_1{\sin \mathrm{\θ}}_1\end{array}\right){\stackrel{.}{\mathrm{\θ}}}_1+\left(\begin{array}{c}{d}_2{\cos \mathrm{\θ}}_2\\ d_2{\sin \mathrm{\θ}}_2\end{array}\right){\stackrel{.}{\mathrm{\θ}}}_2---\left(5\right)$

Step 3: the adaptive iterative learning control of artificial leg motion of knee joint.Its control algolithm is as follows:

(1) problem describes

Consider the uncertainty existed in reality, friction, inner knee joint damping, and the impact of external disturbance, the artificial leg device kinetics equation described in formula (1) can be written as:

$M\left(q_i\left(t\right)\right)\stackrel{..}{q_i}\left(t\right)+C(q_i\left(t\right),\stackrel{.}{q_i\left(t\right)})\stackrel{.}{q_i\left(t\right)}+G\left(q_i\left(t\right)\right)={\mathrm{\τ}}_i\left(t\right)-d_i\left(t\right)---\left(6\right)$

In formula (6): q _i(t)=θ _i(t), i=1,2 ..., t ∈ [0, T] is time variable, i ∈ Z ₊for iterations, q _i(t) ∈ R ⁿ, represent the joint angles of i-th iteration, angular velocity, angular acceleration amount.M (q _i) ∈ R ^n*nfor the inertial matrix of robot, represent centrifugal force and coriolis force, G (q _i) ∈ R ⁿfor gravity item, τ _i∈ R ⁿfor the turning moment on the i of joint, d _k∈ R ⁿfor knee joint damping and external disturbance.

(2) convergence

Assuming that kneed position and angular velocity obtain by feedback, then controlling of task designs a control rate τ exactly _it () makes q _it () is at [0, T] and arbitrarily i ∈ Z arbitrarily ₊all bounded, and as i → ∞ q _it () at any time t ∈ [0, T] all converges on the desired trajectory q in corresponding moment _d(t), wherein q _dt () is attainable joint reference locus angle.For reaching this control object, provide following basic assumption:

(A ₁) for and q _i(t), d _i(t) bounded;

(A ₂) right initial condition meets: $q_d\left(t\right)-q_i\left(t\right)=\stackrel{.}{q_d}\left(t\right)-\stackrel{.}{q_i}\left(t\right)=0;$

And meet following four characteristics:

(B ₁) M (q _i) ∈ R ^n*nfor bounded positive definite symmetric matrices;

(B ₂) for symmetrical matrix, $X^T(\stackrel{.}{M\left(q_i\right)}-2C(q_i,\stackrel{.}{q_i}))X=0,\∀X\∈R^n;$

(B ₃) $G\left(q_i\right)+2C(q_i,\stackrel{.}{q_i})\stackrel{.}{q_d}\left(t\right)=\mathrm{\ψ}(q_i,\stackrel{.}{q_i}){\mathrm{\ξ}}^T\left(t\right),\mathrm{\ψ}(q_i,\stackrel{.}{q_i})\∈R^{n\×m-1}$ For known matrix, ξ ^t(t) ∈ R ^m-1for unknown vector;

(B ₄) $\left|\right|C(q_i,\stackrel{.}{q_i})\left|\right|\&le;k_c\left|\right|\stackrel{.}{q_i}\left|\right|,\left|\right|G\left(q_i\right)\left|\right|<k_g,\&ForAll;t\&Element;[0,T],$ K _cand k _gfor arithmetic number.

Definition joint position tracking error and velocity error are respectively: the basis of the PD feedback control of classics overcome the unknown parameter of lower limb prosthetic systems by iteration item and disturb the uncertainty brought, and providing convergence:

Adopt control rate such as formula (7), (8):

In formula (7): and matrix K _p, K _d, Γ is symmetric positive definite matrix, then e _i(t), bounded, and $\underset{i\&RightArrow;\&infin;}{\lim }{e}_i\left(t\right)=\underset{i\&RightArrow;\&infin;}{\lim }\stackrel{.}{e_i}\left(t\right)=0,\&ForAll;t\&Element;[0,T].$

During i-th iteration, structure Lyapunov function:

$W_i(\stackrel{.}{e_i}\left(t\right),e_i\left(t\right),{\widetilde{\mathrm{\&theta;}}}_i\left(t\right))=V_i(\stackrel{.}{e}\left(t\right),e_i\left(t\right))+\frac{1}{2}{\&Integral;}_0^t{\tilde{q}}_i\left(t\right){\mathrm{\&Gamma;}}^{-1}{\widetilde{\mathrm{\&theta;}}}_i\left(t\right)\mathrm{d\&tau;}---\left(9\right)$

$V_i(\stackrel{.}{e_i}\left(t\right),e_i\left(t\right))=\frac{1}{2}\stackrel{.}{e_i^T}\left(t\right)M\left(q_i\right)\stackrel{.}{e_i}\left(t\right)+\frac{1}{2}{e}_i{\left(t\right)}^T{K}_p{e}_i\left(t\right)---\left(10\right)$

Due to namely then

${\widetilde{\mathrm{\&theta;}}}_i{\left(t\right)}^T{\mathrm{\&Gamma;}}^{-1}{\widetilde{\mathrm{\&theta;}}}_i\left(t\right)-\widetilde{{\mathrm{\&theta;}}_{i-1}}{\left(t\right)}^T{\mathrm{\&Gamma;}}^{-1}\widetilde{{\mathrm{\&theta;}}_{i-1}}\left(t\right)=-2{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_i{\left(t\right)}^T{\mathrm{\&Gamma;}}^{-1}{\widetilde{\mathrm{\&theta;}}}_i\left(t\right)-{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_i{\left(t\right)}^T{\mathrm{\&Gamma;}}^{-1}{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_i\left(t\right)---\left(11\right)$

(3) W is asked for _ithe boundedness of (t)

Consider the uncertainty existed in reality, friction, inner knee joint damping, and the impact of external disturbance, the artificial leg device kinetics equation described in formula (1) can be written as:

${\mathrm{\&Delta;W}}_i=W_i-W_{i-1}=V_i-V_{i-1}-1/2{\&Integral;}_0^t({\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_i{\left(t\right)}^T{\mathrm{\&Gamma;}}^{-1}{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_i\left(t\right)-{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_{i-1}{\left(t\right)}^T{\mathrm{\&Gamma;}}^{-1}{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_{i-1}\left(t\right))\mathrm{d\&tau;}---\left(12\right)$

By formula (6) and feature B ₂, B ₃:

$\left\{\begin{array}{c}{\stackrel{.}{e}}_i^{T}M{\stackrel{..}{e}}_i={\stackrel{.}{e}}_i^{T}M({\stackrel{..}{q}}_d-{\stackrel{..}{q}}_i)={\stackrel{.}{e}}_i^{T}M{\stackrel{..}{q}}_d-{\stackrel{.}{e}}_i^T(-C{\stackrel{.}{q}}_i-G+{\mathrm{\&tau;}}_i+d_i)\\ 1/2{\stackrel{.}{e}}_i^T\stackrel{.}{M}{\stackrel{.}{e}}_i={\stackrel{.}{e}}_i^{T}C{\stackrel{.}{e}}_i={\stackrel{.}{e}}_i^{T}C({\stackrel{.}{q}}_d-{\stackrel{.}{q}}_i)={\stackrel{.}{e}}_i^{T}C{\stackrel{.}{q}}_d-{\stackrel{.}{e}}_i^{T}C{\stackrel{.}{q}}_i\end{array}\right.---\left(13\right)$

Obtained by known

Then

Obtained by formula (8): ${{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_i}^T\left(t\right)={\left(\mathrm{\&Gamma;}{\mathrm{\&phi;}}^T{\stackrel{.}{e}}_i\right)}^T={\stackrel{.}{e}}_i^T\mathrm{\&phi;\&Gamma;},$ Have ${{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_i}^T{\mathrm{\&Gamma;}}^{-1}{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_i={\stackrel{.}{e}}_i^T\mathrm{\&phi;\&Gamma;}{\mathrm{\&Gamma;}}^{-1}\mathrm{\&Gamma;}{\mathrm{\&phi;}}^T{\stackrel{.}{e}}_i;$ ${{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_i}^T{\mathrm{\&Gamma;}}^{-1}{\widetilde{\mathrm{\&theta;}}}_i=2{\stackrel{.}{e}}_i^T{\mathrm{\&phi;\&Gamma;\&Gamma;}}^{-1}\mathrm{\&Gamma;}{\widetilde{\mathrm{\&phi;}}}_i=2{\stackrel{.}{e}}_i^T\mathrm{\&phi;}{\widetilde{\mathrm{\&phi;}}}_i---\left(16\right)$

By hypothesis A ₂obtain formula (16) is substituted into (12), has

$\begin{array}{c}{\mathrm{\&Delta;W}}_i=-V_{i-1}+V_i-1/2{\&Integral;}_0^t({{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_i}^T{\mathrm{\&Gamma;}}^{-1}{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_i+2{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_i^T{\mathrm{\&Gamma;}}^{-1}{\widetilde{\mathrm{\&theta;}}}_i)\mathrm{d\&sigma;}\&le;-V_{i-1}+\\ {\&Integral;}_0^t{\stackrel{.}{e}}_i^T(\mathrm{\&phi;}{\widetilde{\mathrm{\&theta;}}}_i-K_D{\stackrel{.}{e}}_i)\mathrm{d\&tau;}-1/2{\&Integral;}_0^t({\stackrel{.}{e}}_i^T\mathrm{\&phi;\&Gamma;}{\mathrm{\&phi;}}^T{\stackrel{.}{e}}_i+2{\stackrel{.}{e}}_i^T\mathrm{\&phi;}{\widetilde{\mathrm{\&theta;}}}_i)\mathrm{d\&tau;}\&le;-V_{i-1}\\ -1/2{\&Integral;}_0^t\left({\stackrel{.}{e}}_i^T(\mathrm{\&phi;\&Gamma;}{\mathrm{\&phi;}}^T+{2K}_D){\stackrel{.}{e}}_i\right)\mathrm{d\&tau;}\&le;0\end{array}---\left(17\right)$

Because V _i-1, Γ, K _dbe positive definite matrix, Δ W _i≤ 0, therefore W _ifor non-increasing sequence, then

Draw the following conclusions: if W ₀bounded, then W _ialso must bounded.

(4) W is asked for ₀the incremental of (t)

Obtained by formula (9) and formula (15):

Because k > 0, can draw:

In formula (19), ${\mathrm{\&beta;}}_1={\mathrm{\&lambda;}}_{\min }\left(K_D\right),{\mathrm{\&beta;}}_2=1/2{\mathrm{\&lambda;}}_{\min }\left({\mathrm{\&Gamma;}}^{-1}\right)-K{\mathrm{\&lambda;}}_{\max }^2\left({\mathrm{\&Gamma;}}^{-1}\right),K\&le;\frac{{\mathrm{\&lambda;}}_{\min }\left({\mathrm{\&Gamma;}}^{-1}\right)}{2{\mathrm{\&lambda;}}_{\max }^2\left({\mathrm{\&Gamma;}}^{-1}\right)},$ Therefore have:

${\stackrel{.}{W}}_0\left(t\right)\&le;\frac{1}{4K}{\left|\right|\mathrm{\&theta;}\left|\right|}^2,\&ForAll;t\&Element;[0,T]---\left(20\right)$

Because θ (t) is bounded continuously, release W ₀t () be continuous bounded also.

(5) W is asked for _ithe incremental of (t)

W _it () can be expressed as $W_i\left(t\right)=W_0+\underset{j=1}{\overset{i}{\mathrm{\&Sigma;}}}{\mathrm{\&Delta;W}}_j.$ Then can be obtained by formula (12):

$W_i\&le;W_0-\underset{j=1}{\overset{i}{\mathrm{\&Sigma;}}}{V}_{j-1}\&le;W_0-1/2\underset{j=1}{\overset{i}{\mathrm{\&Sigma;}}}{e}_{j-1}^T{K}_P{e}_{j-1}-1/2\underset{J=1}{\overset{I}{\mathrm{\&Sigma;}}}{{\stackrel{.}{e}}^T}_{j=1}{K}_P{\stackrel{.}{e}}_{j-1}---\left(21\right)$

So $(\underset{j=1}{\overset{i}{\mathrm{\&Sigma;}}}{e}_{j-1}^T{K}_P{e}_{j-1}-\underset{J=1}{\overset{I}{\mathrm{\&Sigma;}}}{{\stackrel{.}{e}}^T}_{j=1}{K}_P{\stackrel{.}{e}}_{j-1})\&le;2(W_0-W_i)\&le;{2W}_0,$ I.e. W _i(t) bounded.Can reach a conclusion: $\underset{i\&RightArrow;t}{\lim }{e}_i\left(t\right)=\underset{i\&RightArrow;t}{\lim }{\stackrel{.}{e}}_i\left(t\right)=0,\&ForAll;t\&Element;[0,T],$ Then W _ithe continuous bounded of (t).

This control method is applied to the model set up in step 2 controls, obtain knee joint position when Fig. 2 shows 6 iterative learnings after operation and follow the tracks of situation, between expected value and iterative value, have error, and to increase error more and more less along with iterations.Fig. 3 has fabulous Velocity Pursuit effect after showing the 6th iteration.Fig. 4 shows position tracking error tracing process in 6 iterative process, and Fig. 5 shows 6 iterative process medium velocity tracking error tracing processs, and both tracking errors all reduce gradually with iterations.

Claims (1)

1. the kneed adaptive iterative learning control method of artificial leg, is characterized in that the concrete steps of the method are:

Step 1. sets human normal gait feature and artificial leg control overflow, specifically:

The normal gait feature of described human body can be divided into two stages, namely supports phase and shaking peroid, is supporting latter stage, maximum vertical load produces, and knee joint bending starts soon afterwards, for lower limb are prepared recovery phase, so knee joint bending resistance now should be minimum; When starting recovery phase, knee joint has bent 30 °, and maximum knee flexion angles is 55 ° ~ 65 °; Knee joint artificial limb with minimum bending resistance setting in motion, thus should adapt to the gait speed of certain limit automatically;

Described artificial leg control overflow: there is enough weight support stability and automatic safe reaction in the support phase; There is the ability of automatic bending locking when tripping; Can to whole gait cycle, seat, to stand and downstairs/descending controls; There is the ability of response leg speed transient change; The individual cultivation requirement of different wearer can be adapted to, realize the Self Adaptive Control without the need to training; There is the ability absorbing ground shock in heel contact position;

Step 2. sets up artificial leg control imitation research kinetic model, specifically:

Based on two rigid body two degrees of freedom artificial leg motor systems, carry out dynamic analysis by Newton-Euler algorithm to it, expression formula is as follows:

$\begin{array}{c}{M}_1=\left(m_1{d}_1^2+m_2{d}_2^2+m_2{l}_1^2+2m_2{l}_1{d}_2{\mathrm{cos\&theta;}}_2\right){\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_1+\left(m_2{d}_2^2+m_2{l}_1{d}_2{\mathrm{cos\&theta;}}_2\right){\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_2+\\ \left(-2m_2{l}_1{d}_2{\mathrm{sin\&theta;}}_2\right){\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_1{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_2+\left(-m_2{l}_1{d}_2{\mathrm{sin\&theta;}}_2\right){{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_2}^2+\left(m_1{d}_1+m_2{d}_1\right)g*{\mathrm{sin\&theta;}}_1+m_2{p}_{2}g\sin \left({\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2\right)\\ M_2=\left(m_d{d}_2^2+m_2{l}_1{d}_2{\mathrm{cos\&theta;}}_2\right){\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_1+m_2{d}_2^2{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_2+\left(-m_2{l}_1{\mathrm{sin\&theta;}}_2+m_2{l}_1{d}_2{\mathrm{sin\&theta;}}_2\right){\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_1{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_2+\left(m_2{l}_1{d}_2{\mathrm{sin\&theta;}}_2\right){{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_1}^2\\ {\mathrm{+m}}_2{p}_{2}g\sin \left({\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2\right)\end{array}---\left(1\right)$

Wherein l ₁and l ₂represent the length of human body lower limbs thigh and shank respectively; d ₁and d ₂represent the position of lower limb respective link barycenter; θ ₁and θ ₂represent the broadest scope coordinate variable of respective link, meet right-hand rule; M ₁and M ₂represent the outside force square that joint applies; m ₁and m ₂represent connecting rod quality, X _irepresent position coordinates; I=1,2;

Get hip joint P ₀place is zero, sets up forward kinematics equation, obtains X ₁, X ₂coordinate is:

$\{\begin{array}{c}{X}_{p1}=X_{p0}+d_1{\mathrm{sin\&theta;}}_1\\ Y_{p1}=X_{p0}-d_1{\mathrm{cos\&theta;}}_1\end{array}---\left(2\right)$

$\left\{\begin{array}{c}{X}_{p2}=X_{p0}+l_1{\mathrm{sin\&theta;}}_1+d_2{\mathrm{sin\&theta;}}_2\\ Y_{p2}=Y_{p0}-l_1{\mathrm{cos\&theta;}}_1-d_2{\mathrm{cos\&theta;}}_2\end{array}\right.---\left(3\right)$

Differentiate is carried out to position equation, the rate equation of each barycenter that just can obtain leading leg, as follows

Represent: $V_{p1}=\left(\begin{array}{c}\stackrel{\&CenterDot;}{X_{p1}}\\ \stackrel{\&CenterDot;}{Y_{p1}}\end{array}\right)=\left(\begin{array}{c}{d}_{1}cos{\mathrm{\&theta;}}_1\\ d_1{\mathrm{sin\&theta;}}_1\end{array}\right)\stackrel{\&CenterDot;}{{\mathrm{\&theta;}}_1}---\left(4\right)$

$V_{p2}=\left(\begin{array}{c}\stackrel{\&CenterDot;}{X_{p2}}\\ \stackrel{\&CenterDot;}{Y_{p2}}\end{array}\right)=\left(\begin{array}{c}{l}_{1}cos{\mathrm{\&theta;}}_1\\ l_1{\mathrm{sin\&theta;}}_1\end{array}\right){\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_1+\left(\begin{array}{c}{d}_{2}cos{\mathrm{\&theta;}}_2\\ d_2{\mathrm{sin\&theta;}}_2\end{array}\right)\stackrel{\&CenterDot;}{{\mathrm{\&theta;}}_2}---\left(5\right)$

The adaptive iterative learning control of step 3. artificial leg motion of knee joint, specifically:

(1) problem describes

Consider the uncertainty existed in reality, friction, inner knee joint damping, and the impact of external disturbance, the artificial leg device kinetics equation described in formula (1) can be written as:

Q _i(t) ∈ R ⁿ, represent the joint angles of i-th iteration, angular velocity, angular acceleration amount; M (q _i) ∈ R ^n*nfor the inertial matrix of robot, represent centrifugal force and coriolis force, G (q _i) ∈ R ⁿfor gravity item, τ _i∈ R ⁿfor the turning moment on the i of joint, d _k∈ R ⁿfor knee joint damping and external disturbance;

(2) convergence

Assuming that kneed position and angular velocity obtain by feedback, then controlling of task designs a control rate τ exactly _it () makes q _it () is at [0, T] and arbitrarily i ∈ Z arbitrarily ₊all bounded, and as i → ∞ q _it () at any time t ∈ [0, T] all converges on the desired trajectory q in corresponding moment _d(t), wherein q _dt () is attainable joint reference locus angle; For reaching this control object, provide following basic assumption:

(A ₁) for and q _i(t), d _i(t) bounded;

(A ₂) right initial condition meets: $q_d\left(t\right)-q_i\left(t\right)={\stackrel{\&CenterDot;}{q}}_d\left(t\right)-{\stackrel{\&CenterDot;}{q}}_i\left(t\right)=0;$

And meet following four characteristics:

(B ₁) M (q _i) ∈ R ^n*nfor bounded positive definite symmetric matrices;

(B ₂) for symmetrical matrix, $X^T(\stackrel{\&CenterDot;}{M\left(q_i\right)}-2C(q_i,\stackrel{\&CenterDot;}{q_i}\left)\right)X=0,\&ForAll;X\&Element;R^n;$

(B ₃) $G\left(q_i\right)+2C(q_i,\stackrel{\&CenterDot;}{q_i})\stackrel{\&CenterDot;}{q_d}\left(t\right)=\mathrm{\&psi;}(q_i,\stackrel{\&CenterDot;}{q_i}){\mathrm{\&xi;}}^T\left(t\right),\mathrm{\&psi;}(q_i,\stackrel{\&CenterDot;}{q_i})\&Element;R^{n\&times;m-1}$ For known matrix,

ξ ^t(t) ∈ R ^m-1for unknown vector;

(B ₄) $\left|\right|C(q_i,\stackrel{\&CenterDot;}{q_i})\left|\right|\&le;k_c\left|\right|\stackrel{\&CenterDot;}{q_i}\left|\right|,\left|\right|G\left(q_i\right)\left|\right|<k_g,\&ForAll;t\&Element;\&lsqb;0,T\&rsqb;,$ K _cand k _gfor arithmetic number;

Definition joint position tracking error and velocity error are respectively:

$e\left(t\right)=q_d\left(t\right)-q_i\left(t\right),\stackrel{\&CenterDot;}{e}\left(t\right)=\stackrel{\&CenterDot;}{q_d}\left(t\right)-\stackrel{\&CenterDot;}{q_i}\left(t\right);$

The basis of the PD feedback control of classics overcome the unknown parameter of lower limb prosthetic systems by iteration item and disturb the uncertainty brought, and providing convergence:

Adopt control rate such as formula (7), (8):

In formula (7): and matrix K _p, K _d, Γ is symmetric positive definite matrix, then e _i(t), bounded, and

$\underset{i\&RightArrow;\mathrm{\&infin;}}{\lim }{e}_i\left(t\right)=\underset{i\&RightArrow;\mathrm{\&infin;}}{\lim }\stackrel{\&CenterDot;}{e_i}\left(t\right)=0,\&ForAll;t\&Element;\&lsqb;0,T\&rsqb;;$

Prove: during i-th iteration, structure Lyapunov function:

$W_i\left({\stackrel{\&CenterDot;}{e}}_i\right(t),e_i(t),{\widetilde{\mathrm{\&theta;}}}_i(t\left)\right)=V_i\left(\stackrel{\&CenterDot;}{e}\right(t),e_i(t\left)\right)+\frac{1}{2}{\&Integral;}_0^t{\tilde{q}}_i\left(t\right){\mathrm{\&Gamma;}}^{-1}{\widetilde{\mathrm{\&theta;}}}_i\left(t\right)d\mathrm{\&tau;}---\left(9\right)$

Wherein ${\widetilde{\mathrm{\&theta;}}}_i\left(t\right)={\mathrm{\&theta;}}_i\left(t\right)-{\widehat{\mathrm{\&theta;}}}_i\left(t\right),$ θ _i(t)＝[ξ ^T(t)β]， $\widehat{\mathrm{\&theta;}}\left(t\right)={\left[\begin{array}{cc}{\widehat{\mathrm{\&xi;}}}_i^T\left(t\right)& {\widehat{\mathrm{\&beta;}}}_i\left(t\right)\end{array}\right]}^T$ For the estimated value of θ (t); $\left|\right|M\left(q_i\right){\stackrel{\&CenterDot;\&CenterDot;}{q}}_d-d_i\left|\right|\&le;\mathrm{\&beta;};$ Get

$V_i\left({\stackrel{\&CenterDot;}{e}}_i\right(t),e_i\left(t\right))=\frac{1}{2}\stackrel{\&CenterDot;}{e_i^T}\left(t\right)M\left(q_i\right){\stackrel{\&CenterDot;}{e}}_i\left(t\right)+\frac{1}{2}{e}_i{\left(t\right)}^T{K}_p{e}_i\left(t\right)---\left(10\right)$

Due to namely then

$\widetilde{{\mathrm{\&theta;}}_i}{\left(t\right)}^T{\mathrm{\&Gamma;}}^{-1}\widetilde{{\mathrm{\&theta;}}_i}\left(t\right)-\widetilde{{\mathrm{\&theta;}}_{i-1}}{\left(t\right)}^T{\mathrm{\&Gamma;}}^{-1}\widetilde{{\mathrm{\&theta;}}_{i-1}}\left(t\right)=-2\stackrel{-}{{\mathrm{\&theta;}}_i}{\left(t\right)}^T{\mathrm{\&Gamma;}}^{-1}\widetilde{{\mathrm{\&theta;}}_i}\left(t\right)-\stackrel{-}{{\mathrm{\&theta;}}_i}{\left(t\right)}^T{\mathrm{\&Gamma;}}^{-1}\stackrel{-}{{\mathrm{\&theta;}}_i}\left(t\right)---\left(11\right)$

(3) W is asked for _ithe boundedness of (t)

Consider the uncertainty existed in reality, friction, inner knee joint damping, and the impact of external disturbance, the artificial leg device kinetics equation described in formula (1) can be written as:

${\mathrm{\&Delta;W}}_i=W_i-W_{i-1}=V_i-V_{i-1}-1/2{\&Integral;}_0^t\left(\stackrel{-}{{\mathrm{\&theta;}}_i}{\left(t\right)}^T{\mathrm{\&Gamma;}}^{-1}\stackrel{-}{{\mathrm{\&theta;}}_i}\left(t\right)-{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_{i-1}{\left(t\right)}^T{\mathrm{\&Gamma;}}^{-1}{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_{i-1}\left(t\right)\right)d\mathrm{\&tau;}---\left(12\right)$

By formula (6) and feature B ₂, B ₃:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{e}}_i^{T}M{\stackrel{\&CenterDot;\&CenterDot;}{e}}_i={\stackrel{\&CenterDot;}{e}}_i^{T}M\left({\stackrel{\&CenterDot;\&CenterDot;}{q}}_d-{\stackrel{\&CenterDot;\&CenterDot;}{q}}_i\right)={\stackrel{\&CenterDot;}{e}}_i^{T}M{\stackrel{\&CenterDot;\&CenterDot;}{q}}_d-{\stackrel{\&CenterDot;}{e}}_i^T\left(-C{\stackrel{\&CenterDot;}{q}}_i-G+{\mathrm{\&tau;}}_i+d_i\right)\\ 1/2{\stackrel{\&CenterDot;}{e}}_i^T\stackrel{\&CenterDot;}{M}{\stackrel{\&CenterDot;}{e}}_i={\stackrel{\&CenterDot;}{e}}_i^{T}C{\stackrel{\&CenterDot;}{e}}_i={\stackrel{\&CenterDot;}{e}}_i^{T}C\left({\stackrel{\&CenterDot;}{q}}_d-{\stackrel{\&CenterDot;}{q}}_i\right)={\stackrel{\&CenterDot;}{e}}_i^{T}C{\stackrel{\&CenterDot;}{q}}_d-{\stackrel{\&CenterDot;}{e}}_i^{T}C{\stackrel{\&CenterDot;}{q}}_i\end{array}\right.---\left(13\right)$

Obtained by known

Then

Obtained by formula (8): ${\stackrel{-}{{\mathrm{\&theta;}}_i}}^T\left(t\right)={\left({\mathrm{\&Gamma;\&phi;}}^T{\stackrel{\&CenterDot;}{e}}_i\right)}^T={{\stackrel{\&CenterDot;}{e}}_i}^T\mathrm{\&phi;}\mathrm{\&Gamma;},$ Have ${\stackrel{-}{{\mathrm{\&theta;}}_i}}^T{\mathrm{\&Gamma;}}^{-1}\stackrel{-}{{\mathrm{\&theta;}}_i}={{\stackrel{\&CenterDot;}{e}}_i}^T{\mathrm{\&phi;\&Gamma;\&Gamma;}}^{-1}{\mathrm{\&Gamma;\&phi;}}^T{\stackrel{\&CenterDot;}{e}}_i;$

${\stackrel{-}{{\mathrm{\&theta;}}_i}}^T{\mathrm{\&Gamma;}}^{-1}\widetilde{{\mathrm{\&theta;}}_i}=2{{\stackrel{\&CenterDot;}{e}}_i}^T{\mathrm{\&phi;\&Gamma;\&Gamma;}}^{-1}\mathrm{\&Gamma;}\widetilde{{\mathrm{\&phi;}}_i}=2{{\stackrel{\&CenterDot;}{e}}_i}^T\mathrm{\&phi;}\widetilde{{\mathrm{\&phi;}}_i}---\left(16\right)$

Because V _i-1, Γ, K _dbe positive definite matrix, Δ W _i≤ 0, therefore W _ifor non-increasing sequence, then draw the following conclusions: if W ₀bounded, then W _ialso must bounded;

(4) W is asked for ₀the incremental of (t)

Obtained by formula (9) and formula (15):

Because k > 0, can draw:

In formula (19), ${\mathrm{\&beta;}}_1={\mathrm{\&lambda;}}_{min}\left(K_D\right),{\mathrm{\&beta;}}_2=1/2{\mathrm{\&lambda;}}_{min}\left({\mathrm{\&Gamma;}}^{-1}\right)-{\mathrm{K\&lambda;}}_{max}^2\left({\mathrm{\&Gamma;}}^{-1}\right),K\&le;\frac{{\mathrm{\&lambda;}}_{min}\left({\mathrm{\&Gamma;}}^{-1}\right)}{2{\mathrm{\&lambda;}}_{max}^2\left({\mathrm{\&Gamma;}}^{-1}\right)},$ Therefore have:

${\stackrel{\&CenterDot;}{W}}_0\left(t\right)\&le;\frac{1}{4K}\left|\right|\mathrm{\&theta;}|{|}^2,\&ForAll;t\&Element;\&lsqb;0,T\&rsqb;---\left(20\right)$

Because θ (t) is bounded continuously, release W ₀t () be continuous bounded also;

(5) W is asked for _ithe incremental of (t)

W _it () can be expressed as then can be obtained by formula (12):

$W_i\&le;W_0-\underset{j=1}{\overset{i}{\mathrm{\&Sigma;}}}{V}_{j-1}\&le;W_0-1/2\underset{j=1}{\overset{i}{\mathrm{\&Sigma;}}}{e}_{j-1}^T{K}_P{e}_{j-1}-1/2\underset{J=1}{\overset{I}{\mathrm{\&Sigma;}}}{\stackrel{\&CenterDot;}{e}}_{j=1}^T{K}_P{\stackrel{\&CenterDot;}{e}}_{j-1}---\left(21\right)$

So $(\underset{j=1}{\overset{i}{\mathrm{\&Sigma;}}}{e}_{j-1}^T{K}_P{e}_{j-1}-\underset{J=1}{\overset{I}{\&Sigma;}}{\stackrel{\&CenterDot;}{e}}_{j=1}^T{K}_P{\stackrel{\&CenterDot;}{e}}_{j-1})\&le;2(W_0-W_i)\&le;2W_0,$ I.e. W _i(t) bounded; Can reach a conclusion: $\underset{i\&RightArrow;t}{\lim }{e}_i\left(t\right)=\underset{i\&RightArrow;t}{\lim }{\stackrel{\&CenterDot;}{e}}_i\left(t\right)=0,\&ForAll;t\&Element;\&lsqb;0,T\&rsqb;,$ Then W _ithe continuous bounded of (t);

This step method is applied in step 2 set up model on control.