CN105988366A - Space robot minimal base disturbance trajectory planning method - Google Patents

Abstract

The invention relates to a space robot minimal base disturbance trajectory planning method, and particularly relates to a space robot minimal base disturbance trajectory planning method based on an improved chaotic particle swarm algorithm, which belongs to the technical field of aerospace. The method comprises steps: (1) a kinematics equation for the six-degree-of-freedom space robot is built; (2) a 7-order sine polynomial function is used for parameterizing joints; (3) an equation for a fitness function is built, and constraint conditions comprise position disturbance and attitude disturbance of the base, and joint velocity and angular velocity constraints; (3) in order not to fall into local optimum and quickly find the optimal solution, the chaotic particle swarm algorithm is improved; and (4) the improved chaotic particle swarm algorithm is used for solving unknown parameters, and the space robot optimal trajectory is obtained in a condition of minimal base position and attitude disturbance. The method of the invention mainly solves the problem of trajectory planning for the six-degree-of-freedom free-floating space robot, the improved chaotic particle swarm algorithm is used for finding the optimal motion trajectory for the space robot in the condition of minimal base position and attitude disturbance, and effects are good.

Description

A kind of robot for space minimum pedestal disturbance method for planning track

Technical field

The present invention relates to a kind of based on the robot for space minimum basis improving Chaos particle swarm optimization algorithm Seat disturbance method for planning track, belongs to calculating field of aerospace technology.

Background technology

Robot for space plays an irreplaceable role in On-orbit servicing, freely Space Robot System under floating state is unstable, when robot for space is held in space During row task, its athletic meeting produces disturbance, meanwhile, base position to position and the attitude of pedestal Change with attitude can produce again certain impact to the motion of robot for space, it is possible to causes appointing The failure of business, and then bring immeasurable loss.Position and attitude in order to maintain pedestal are protected Hold constant, reduce influencing each other between them, then need the movement locus to robot for space Plan so that it is in motor process, the disturbance to pedestal minimizes.

Problem for robot for space minimum pedestal disturbance trajectory planning always is research Focus and difficult point.1991, Dubowsky and Torres proposed a kind of enhanced disturbance map Technical method, the method can optimize the movement locus of robot for space and then reduce pedestal Disturbance, but only two-freedom space manipulator is proved, it is impossible to it is widely used in many Degree of freedom space manipulator；Calendar year 2001, Yoshida etc. proposes a kind of zero counteractive thought, Under the undisturbed constraint of pedestal attitude, space manipulator rail is carried out based on broad sense Jacobian matrix Mark is planned, but is not suitable for redundant space mechanical arm；2006, Panfeng Huang etc. carried Go out a kind of minimum pedestal disturbance path planning based on genetic algorithm, but the realization of genetic algorithm More complicated and convergence time is longer；2011, Wang Ming et al. proposed based on chaotic particle The trajectory planning of the pedestal disturbance torque minimum of group's algorithm, but do not consider the pose disturbance of pedestal Minimum；2014, the big grade of Xia Hong proposed pedestal attitude disturbance based on Chaos particle swarm optimization algorithm Minimum trajectory planning, but do not consider that the position disturbance of pedestal is minimum.

Up to the present, when robot for space trajectory planning and do not take into account robot for space Base position and attitude should be all that disturbance is minimum.

Summary of the invention

In order to overcome above-mentioned deficiency, it is an object of the invention to propose one based on improving chaos The robot for space minimum pedestal disturbance method for planning track of particle cluster algorithm, the method is by changing Enter Chaos particle swarm optimization algorithm and solve unknown parameter in the case of pedestal pose disturbance minimum, and then Obtain the optimal motion track of robot for space.

To achieve these goals, the technical solution adopted in the present invention is: a kind of space machine People's minimum pedestal disturbance method for planning track, it comprises the steps:

(1) broad sense Jacobian matrix is utilized to set up the kinesiology side of 6DOF robot for space Journey, is modeled robot for space in conjunction with D-H parametric method；

(2) geometric parameter of definition space robot, comprising: include the quantity in joint, The quality of the length of connecting rod, connecting rod and pedestal and the moment in joint between joint；

(3) utilize 7 rank sine polynomial functions that the joint of robot for space is carried out parametrization；

(4) with base position, the required precision of attitude, joint angle speed limits and angle is accelerated That spends is limited to constraints, sets up robot for space base position and the pass of attitude disturbance minimum Joint trajectory planning objective optimization model；

(5) use the Chaos particle swarm optimization algorithm improved to solve, export optimal value, and then obtain Robot for space optimal trajectory under pedestal pose disturbance minimum.

In described step (4), the object function in described objective optimization model is:

$F\left(\mathrm{\α}\right)=\frac{{\left|\right|{\mathrm{\δp}}_b\left|\right|}_2}{{\mathrm{\ω}}_p}+\frac{\left|\right|{\mathrm{\δq}}_b\left|\right|}{{\mathrm{\ω}}_q}+\frac{F_{\stackrel{\·}{\mathrm{\θ}}}}{{\mathrm{\ω}}_{\stackrel{\·}{\mathrm{\θ}}}}+\frac{F_{\stackrel{\·\·}{\mathrm{\θ}}}}{{\mathrm{\ω}}_{\stackrel{\·\·}{\mathrm{\θ}}}}$

Wherein, definitionδp_bFor the difference of base ends position Yu initial position, δq_bFor the difference of base ends attitude Yu initial attitude, ω_pFor the weight coefficient of site error, ω_q For the weight coefficient of attitude error,For the weight coefficient of joint angle constraint of velocity,For closing The weight coefficient of joint angular acceleration constraint,WithIt is respectively defined as following formula:

$F_{\stackrel{\·}{\mathrm{\θ}}}=\underset{1\≤i\≤6}{\max }\left(J_{{\stackrel{\·}{\mathrm{\θ}}}_i}\right),J_{{\stackrel{\·}{\mathrm{\θ}}}_i}=\left\{\begin{array}{c}\begin{array}{cc}0& {\stackrel{\·}{\mathrm{\θ}}}_{i\_\max }\≤{\stackrel{\·}{\mathrm{\θ}}}_{i\_\mathrm{lim\; it}}\end{array}\\ ({\stackrel{\·}{\mathrm{\θ}}}_{i\_\max }-{\stackrel{\·}{\mathrm{\θ}}}_{i\_\mathrm{lim\; it}})/{\stackrel{\·}{\mathrm{\θ}}}_{i\_\mathrm{lim\; it}}\end{array}\right.$

$F_{\stackrel{\·\·}{\mathrm{\θ}}}=\underset{1\≤i\≤6}{\max }\left(J_{{\stackrel{\·\·}{\mathrm{\θ}}}_i}\right),J_{{\stackrel{\·\·}{\mathrm{\θ}}}_i}=\left\{\begin{array}{c}\begin{array}{cc}0& {\stackrel{\·\·}{\mathrm{\θ}}}_{i\_\max }\≤{\stackrel{\·\·}{\mathrm{\θ}}}_{i\_\mathrm{lim\; it}}\end{array}\\ ({\stackrel{\·\·}{\mathrm{\θ}}}_{i\_\max }-{\stackrel{\·\·}{\mathrm{\θ}}}_{i\_\mathrm{lim\; it}})/{\stackrel{\·\·}{\mathrm{\θ}}}_{i\_\mathrm{lim\; it}}\end{array}\right.$

Wherein,It is the speed maximum in i-th joint,It it is the acceleration in i-th joint Maximum

In described step (5), the Chaos particle swarm optimization algorithm of improvement, its use nonlinear dynamically Inertia weight, i.e. inertia weight change automatically along with the target function value of particle；Add gold The thought of the ration of division, i.e. retaining fitness function value in colony is the particle of 38.2%；Select Sinusoidal function replaces Logistic function as chaos sequence generator.Algorithm concrete The process of realization is: (1) arranges the parameter of each particle；(2) each grain in random initializtion population The position of son and speed；(3) target function value of each particle is evaluated, by each particle current Position and target function value are stored in the pbest of each particle, by all of object function Value has most the position of individuality and its value to be stored in gbest；(4) speed of more new particle and position Put；(5) target function value of each particle is calculated, 38.2% that in reservation population, performance is best Particle；(6) the optimal particle preserved in population is carried out chaos Local Search, and more new particle Pbest and the gbest of population；(7) if meeting the stop condition (maximum usually preset Iterations or operational precision), stopping search, exporting optimal value, if be unsatisfactory for, then Transfer (8) to；(8) dynamic area contraction is carried out；(9) randomly generate in colony in the region shunk The particle of remaining 61.8%, goes to step (3).

The formula of described Nonlinear Dynamic inertia weight is as follows:

$\mathrm{\&omega;}=\left\{\begin{array}{cc}{\mathrm{\&omega;}}_{\max }-i\frac{{\mathrm{\&omega;}}_{\max }-{\mathrm{\&omega;}}_{\min }}{\max \_\mathrm{gen}}& f<f_{\mathrm{avg}}/2\\ {\mathrm{\&omega;}}_{\min }+\frac{(f-f_{\min })({\mathrm{\&omega;}}_{\max }-{\mathrm{\&omega;}}_{\min })}{f_{\mathrm{avg}}/2-f_{\min }}& f_{\mathrm{avg}}/2\&le;f\&le;f_{\mathrm{avg}}\\ {\mathrm{\&omega;}}_{\max }& f\&GreaterEqual;f_{\mathrm{avg}}/2\end{array}\right.$

Wherein, ω_minFor the minima of ω, ω_maxFor the maximum of ω, f is current particle Fitness function value, f_minFor the minimum fitness function value of all particles, f_avgIt is all The average fitness functional value of particle, i is current iterations, and max_gen is maximum changing Generation number.

The present invention compared with prior art has the advantages that the improvement that the present invention proposes mixes Ignorant particle cluster algorithm is used in the path planning of 6DOF free-floating space robot, examines Consider and arrived base position, the restriction of attitude disturbance minimum, joint angle speed, angular acceleration restriction Four constraintss of scope, have practicality；The Chaos particle swarm optimization algorithm utilizing improvement can be fast Speed effectively finds optimal solution, improves solving precision；The improvement chaotic particle that the present invention proposes Group's algorithm also can promote the path planning for 7 degree of freedom space manipulators.

Accompanying drawing explanation

Below by way of drawings and the specific embodiments, the present invention is described in detail.

Fig. 1 flow chart of the present invention；

Fig. 2 improves Chaos particle swarm optimization algorithm flow chart；

Fig. 3 base position change curve；

Fig. 4 pedestal attitudes vibration curve chart；

Fig. 5 joint change curve；

Fig. 6 joint angle speed change curves figure；

Fig. 7 joint angle acceleration change curve chart.

Detailed description of the invention

The invention will be further described below in conjunction with the accompanying drawings, as shown in Figure 1.

The present invention comprises the steps:

(1) broad sense Jacobian matrix is utilized to set up the kinesiology side of 6DOF robot for space Journey, is modeled robot for space in conjunction with D-H parametric method, defines the several of robot for space What parameter；

(2) utilize 7 rank sine polynomial functions that robot for space joint is carried out parametrization；

(3) setting up fitness function equation according to constraints, constraints includes pedestal position Put, the required precision of attitude, to joint angle speed and the restriction of angular acceleration；

(4) Chaos particle swarm optimization algorithm is improved；

(5) utilize the Chaos particle swarm optimization algorithm improved to solve unknown parameter, and then obtain space machine Device people optimal trajectory under pedestal pose disturbance minimum.

Embodiment 1

Embodiments of the invention are implemented under premised on technical solution of the present invention, give Go out detailed embodiment and concrete operating process, but protection scope of the present invention has been not limited to Following embodiment.

Being embodied as step is:

Step 1: for freely the most floating 6DOF robot for space, due to not by external force, Then system keeps the conservation of momentum, and kinematical equation is represented by:

$\left[\begin{array}{c}{v}_e\\ {\mathrm{\&omega;}}_e\end{array}\right]=J_b\left[\begin{array}{c}{v}_0\\ {\mathrm{\&omega;}}_0\end{array}\right]+J_r\stackrel{\&CenterDot;}{\mathrm{\&theta;}}$

Wherein: v_e∈R³, the linear velocity of end effector；ω_e∈R³, the angle speed of end effector Degree；v₀∈R³, the linear velocity of pedestal；ω₀∈R³, the angular velocity of pedestal；θ∈R⁶, machine The joint angle matrix of 6 joint angle compositions of device people.J_b∈R^6×6, the Jacobian matrix of pedestal； J_r∈R^6×6, the Jacobian matrix of robot.

Step 2: use 7 rank polynomial functions that joint angle is carried out parametrization in the present invention, As described by following formula:

θ_i(t)=Δ_i1sin(α_i7t⁷+α_i6t⁶+α_i5t⁵+α_i4t⁴

+α_i3t³+α_i2t²+α_i1t+α_i0)+Δ_i2

Wherein, i=1 ..., 7, α_i0～α_i7For multinomial coefficient

${\mathrm{\&Delta;}}_{i1}=\frac{{\mathrm{\&theta;}}_{i\max }-{\mathrm{\&theta;}}_{i\min }}{2},{\mathrm{\&Delta;}}_{i2}=\frac{{\mathrm{\&theta;}}_{i\max }+{\mathrm{\&theta;}}_{i\min }}{2},$

θ_{i_max}For the maximum of i-th joint angle, θ_{i_min}Minima for i-th joint angle.

In motor process, the joint angle speed of robot for space and angular acceleration are all limited System, and the smooth trajectory of robot for space to be ensured.Then the constraint to joint angle is as follows:

θ_i(t₀)=θ_i0,θ_i(t_f)=θ_if

${\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_i\left(t_0\right)={\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_i\left(t_f\right)=0,{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_i\left(t_0\right)={\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_i\left(t_f\right)=0$

θ_{i_min}≤θ_i(t)≤θ_{i_max}

Wherein, i=1 ..., 6, θ_i0For initial joint angle, θ_ifFor expectation joint angle.

It addition, the constraint of joint angle speed and angular acceleration is as follows:

$\left|{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_i\left(t\right)\right|\&le;{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_{i\_\mathrm{lim\; it}},\left|{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_i\left(t\right)\right|\&le;{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_{i\_\mathrm{lim\; it}}$

Wherein,For the limits value of joint angle speed,Restriction for joint angle acceleration Value.

Joint angle speed, as described by following formula:

$\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_i\left(t\right)={\mathrm{\&Delta;}}_{i1}\cos ({\mathrm{\&alpha;}}_{i7}{t}^7+{\mathrm{\&alpha;}}_{i6}{t}^6+{\mathrm{\&alpha;}}_{i5}{t}^5+{\mathrm{\&alpha;}}_{i4}{t}^4+\\ {\mathrm{\&alpha;}}_{i3}{t}^3+{\mathrm{\&alpha;}}_{i2}{t}^2+{\mathrm{\&alpha;}}_{i1}t+{\mathrm{\&alpha;}}_{i0})({7\mathrm{\&alpha;}}_{i7}{t}^6+{6\mathrm{\&alpha;}}_{i6}{t}^5+\\ {5\mathrm{\&alpha;}}_{i5}{t}^4+{4\mathrm{\&alpha;}}_{i4}{t}^3+{3\mathrm{\&alpha;}}_{i3}{t}^2+{2\mathrm{\&alpha;}}_{i2}t+{\mathrm{\&alpha;}}_{i1})\end{array}$

Joint angle acceleration, as described by following formula:

$\begin{array}{c}{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_i\left(t\right)=-{\mathrm{\&Delta;}}_{i1}\sin ({\mathrm{\&alpha;}}_{i7}{t}^7+{\mathrm{\&alpha;}}_{i6}{t}^6+{\mathrm{\&alpha;}}_{i5}{t}^5+{\mathrm{\&alpha;}}_{i4}{t}^4+\\ {\mathrm{\&alpha;}}_{i3}{t}^3+{\mathrm{\&alpha;}}_{i2}{t}^2+{\mathrm{\&alpha;}}_{i1}t+{\mathrm{\&alpha;}}_{i0})({7\mathrm{\&alpha;}}_{i7}{t}^6+{6\mathrm{\&alpha;}}_{i6}{t}^5+\\ {5\mathrm{\&alpha;}}_{i5}{t}^4+{4\mathrm{\&alpha;}}_{i4}{t}^3+{3\mathrm{\&alpha;}}_{i3}{t}^2+{2\mathrm{\&alpha;}}_{i2}+t+{\mathrm{\&alpha;}}_{i1})+\\ {\mathrm{\&Delta;}}_{i1}\cos ({\mathrm{\&alpha;}}_{i7}{t}^7+{\mathrm{\&alpha;}}_{i6}{t}^6+{\mathrm{\&alpha;}}_{i5}{t}^5+{\mathrm{\&alpha;}}_{i4}{t}^4+\\ {\mathrm{\&alpha;}}_{i3}{t}^3+{\mathrm{\&alpha;}}_{i2}{t}^2+{\mathrm{\&alpha;}}_{i1}t+{\mathrm{\&alpha;}}_{i0})({42\mathrm{\&alpha;}}_{i7}{t}^5+\\ {30\mathrm{\&alpha;}}_{i6}{t}^4+{20\mathrm{\&alpha;}}_{i5}{t}^3+{12\mathrm{\&alpha;}}_{i4}{t}^2+{6\mathrm{\&alpha;}}_{i3}t+{2\mathrm{\&alpha;}}_{i2})\end{array}$

Comprehensive above equation can obtain:

${\mathrm{\&alpha;}}_{i0}=\arcsin \left(\frac{{\mathrm{\&theta;}}_{i0}-{\mathrm{\&Delta;}}_{i2}}{{\mathrm{\&Delta;}}_{i1}}\right)$

α_i1=0, α_i2=0

${\mathrm{\&alpha;}}_{i3}=10\left(\begin{array}{c}\arcsin \frac{{\mathrm{\&theta;}}_{\mathrm{if}}-{\mathrm{\&Delta;}}_{i2}}{{\mathrm{\&Delta;}}_{i1}}-\\ \arcsin \frac{{\mathrm{\&theta;}}_{i0}-{\mathrm{\&Delta;}}_{i2}}{{\mathrm{\&Delta;}}_{i1}}\end{array}\right)-({3\mathrm{\&alpha;}}_{i7}{t}^7-{\mathrm{\&alpha;}}_{i6}{t}^6)/t^3$

${\mathrm{\&alpha;}}_{i4}=-15\left(\begin{array}{c}\arcsin \frac{{\mathrm{\&theta;}}_{\mathrm{if}}-{\mathrm{\&Delta;}}_{i2}}{{\mathrm{\&Delta;}}_{i1}}-\\ \arcsin \frac{{\mathrm{\&theta;}}_{i0}-{\mathrm{\&Delta;}}_{i2}}{{\mathrm{\&Delta;}}_{i1}}\end{array}\right)+({8\mathrm{\&alpha;}}_{i7}{t}^7+{3\mathrm{\&alpha;}}_{i6}{t}^6)/t^4$

${\mathrm{\&alpha;}}_{i5}=6\left(\begin{array}{c}\arcsin \frac{{\mathrm{\&theta;}}_{\mathrm{if}}-{\mathrm{\&Delta;}}_{i2}}{{\mathrm{\&Delta;}}_{i1}}-\\ \arcsin \frac{{\mathrm{\&theta;}}_{i0}-{\mathrm{\&Delta;}}_{i2}}{{\mathrm{\&Delta;}}_{i1}}\end{array}\right)-({6\mathrm{\&alpha;}}_{i7}{t}^7-{3\mathrm{\&alpha;}}_{i6}{t}^6)/t^5$

Being derived from above, the variable in joint angle, angular velocity and angular acceleration function is only α_i6And α_i7Not can determine that, be designated as following formula:

α=(α₁₆,α₁₇,…,α_i6,α_i7)

After it determines, then the joint of 6DOF robot for space is carried out trajectory planning.

Step 3: the present invention is the pass minimum based on robot for space base position and attitude disturbance Joint trajectory planning, then object function is defined as formula:

$F\left(\mathrm{\&alpha;}\right)=\frac{{\left|\right|{\mathrm{\&delta;p}}_b\left|\right|}_2}{{\mathrm{\&omega;}}_p}+\frac{\left|\right|{\mathrm{\&delta;q}}_b\left|\right|}{{\mathrm{\&omega;}}_q}+\frac{F_{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}}{{\mathrm{\&omega;}}_{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}}+\frac{F_{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}}{{\mathrm{\&omega;}}_{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}}$

Wherein,δp_bFor the difference of base ends position Yu initial position, δq_bFor the difference of base ends attitude Yu initial attitude, ω_pFor the weight coefficient of site error, ω_qFor the weight coefficient of attitude error,For the weight coefficient of joint angle constraint of velocity, The weight coefficient retrained for joint angle acceleration,WithThe formula not being defined as:

$F_{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}=\underset{1\&le;i\&le;6}{\max }\left(J_{{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_i}\right),J_{{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_i}=\left\{\begin{array}{cc}0& {\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_{i\_\max }\&le;{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_{i\_\mathrm{lim\; it}}\\ ({\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_{i\_\max }-{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_{i\_\mathrm{lim\; it}})/{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_{i\_\mathrm{lim\; it}}& \mathrm{else}\end{array}\right.$

$F_{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}=\underset{1\&le;i\&le;6}{\max }\left(J_{{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_i}\right),J_{{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_i}=\left\{\begin{array}{cc}0& {\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_{i\_\max }\&le;{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_{i\_\mathrm{lim\; it}}\\ ({\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_{i\_\max }-{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_{i\_\mathrm{lim\; it}})/{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_{i\_\mathrm{lim\; it}}& \mathrm{else}\end{array}\right.$

Wherein,It is the speed maximum in i-th joint,It it is i-th joint Acceleration maximum.

Step 4: the present invention proposes a kind of improvement Chaos particle swarm optimization algorithm, i.e. uses non-linear Dynamic inertia weight, i.e. inertia weight changes automatically along with the target function value of particle；Add Enter the thought of golden section proportion, i.e. retain in colony the grain of fitness function value is best 38.2% Son；Selection Sinusoidal function replacement Logistic function is as chaos sequence generator, whole Algorithm is as shown in flow chart 2.

Inertia weight determines the size that particle is affected by itself present speed, and suitable inertia is weighed The selection of weight can allow particle have exploring ability and the development ability of equilibrium.The present invention uses and changes The adaptive weighting method entered, the formula of Nonlinear Dynamic inertia weight is as follows:

$\mathrm{\&omega;}=\left\{\begin{array}{cc}{\mathrm{\&omega;}}_{\max }-i\frac{{\mathrm{\&omega;}}_{\max }-{\mathrm{\&omega;}}_{\min }}{\max \_\mathrm{gen}}& f<f_{\mathrm{avg}}/2\\ {\mathrm{\&omega;}}_{\min }+\frac{(f-f_{\min })({\mathrm{\&omega;}}_{\max }-{\mathrm{\&omega;}}_{\min })}{f_{\mathrm{avg}}/2-f_{\min }}& f_{\mathrm{avg}}/2\&le;f\&le;f_{\mathrm{avg}}\\ {\mathrm{\&omega;}}_{\max }& f\&GreaterEqual;f_{\mathrm{avg}}/2\end{array}\right.$

Wherein, ω_minFor the minima of ω, ω_maxFor the maximum of ω, f is current particle Fitness function value, f_minFor the minimum fitness function value of all particles, f_avgIt is all The average fitness functional value of particle, i is current iterations, and max_gen is maximum changing Generation number.

Different chaos sequence generators can be used in Chaos particle swarm optimization algorithm, 2013, Different chaotic maps functions is utilized standard to survey in article by AmirHosseinGandomi etc. Trial function is tested, and shows sinusoidal function and singer in most of optimization problems Function effect becomes apparent from, so have employed sinusoidal function in the present invention, it simplifies public affairs Formula is as follows:

x_k+1=sin (π x_k)

Chaos particle swarm optimization algorithm is chaos optimization and particle group optimizing combination between the two, and Chaos local search algorithm is related in algorithmic procedure.At the Chaos-Particle Swarm Optimization that the present invention improves In algorithmic procedure, the particle cluster algorithm first with adaptive weighting carries out global search, non-thread The formula of property dynamic inertia weight is as shown in equation；Complete to introduce afterwards golden section in search The thought of example, retains the outstanding particle of 38.2% in particle colony；Then sinusoidal letter is used Number is as the generator of chaos sequence, and the particle to 38.2% carries out chaos Local Search；Finally, In order to keep the multiformity of particle, in dynamic shrinkage region, randomly generate remaining 61.8% Particle.Dynamic shrinkage region formula is as follows:

x_min,j=max{x_min,j,x_g,j-r*(x_max,j-x_min,j), 0 ＜ r ＜ 1

x_max,j=min{x_min,j,x_g,j+r*(x_max,j-x_min,j), 0 ＜ r ＜ 1

Wherein, x_g,jRepresent the jth dimension variate-value of current optimal value.

Step 5: utilize the improvement Chaos particle swarm optimization algorithm that the present invention proposes for robot for space Minimum pedestal disturbance carries out trajectory planning, establishes one by freely floating pedestal and 6DOF The kinematics model of robot for space composition system, utilizes Matlab2013b platform to being proposed Method emulate and verify, it is assumed that trajectory planning time t=10s, the matter of robot for space Flow characteristic parameter is as shown in table 1, and D-H parameter is as shown in table 2.

Table 1 robot for space mass property parameter list

Wherein, l is the length of connecting rod, and m is the quality of pedestal and connecting rod, and I is the inertia of mechanical arm.

Table 2 robot for space D-H parameter list

Wherein, θ_iFor joint angle, α_i-1For the connecting rod corner of mechanical arm, a_i-1For joint shaft i-1 and pass The length of common vertical line, d between nodal axisn i_iFor connecting rod offset distance.

The initial joint angle of robot for space is θ_i0=[0 °, 0 °, 0 °, 0 °, 0 °, 0 °], it is desirable to Joint angle is θ_if=[12 °, 31 ° ,-17 ° ,-50 °, 26 ° ,-83 °].Joint angle in the range of:

-160°≤θ₁≤+160°,-160°≤θ₂≤+160°

-160°≤θ₃≤+160°,-179°≤θ₄≤+70°

-179°≤θ₅≤+70°,-160°≤θ₆≤+160°

Joint angle speed in the range of:

Joint angle acceleration in the range of:

The coefficient of definition fitness function is respectively as follows: ω_p=2 10^-3,ω_q=sin (π/360),

Optimized algorithm parameter is arranged:

N=30, c₁=c₂=2, ω_max=0.9, ω_min=0.2, x_max=0.1,

x_min=-0.1, M=100, MaxC=0.1, D=12

Wherein, N is number of particles, c₁、c₂For Studying factors, x_maxIt it is the maximum of independent variable region of search Value, x_minBeing the minima of independent variable region of search, M is maximum iteration time, and Maxc is chaos The maximum step number of search, D is the number of independent variable.

The Chaos particle swarm optimization algorithm that improves using the present invention carries out the optimum ginseng of trajectory planning Several and target function value after rounding up is:

$\left\{\begin{array}{c}\mathrm{\&alpha;}=\left[\begin{array}{c}-\mathrm{0.2422,0.0086},-\mathrm{0.1115,0.1953}\\ -0.2527,-0.2295,-0.0466,-0.0227\\ -0.0130,-\mathrm{0.0816,0.1270,0.0089}\end{array}\right]*{10}^{-5}\\ f\left(\mathrm{\&alpha;}\right)=14.3820\end{array}\right.$

In t, the position coordinates of pedestal is [-0.0015 ,-0.3177 ,-3.0883], and error is [-0.0015,0.0156 ,-0.0050], the attitude coordinate of pedestal be [0.0169 ,-0.0100,0.0497, 0.9986], error is [0.0169 ,-0.0100,0.0497 ,-0.0014].

The present invention is only by just planning the joint angle of 6DOF free-floating space robot Planned its movement locus, and take into account the minimum restriction of base position, attitude disturbance, Joint angle speed, angular acceleration limit four constraintss of scope, have practicality；Utilization changes The Chaos particle swarm optimization algorithm entered can find optimal solution fast and effectively, improves solving precision； The improvement Chaos particle swarm optimization algorithm that the present invention proposes also can be promoted for 7 degree of freedom space machines The path planning of people.

The above, the only present invention preferably detailed description of the invention, but the protection model of the present invention Enclosing and be not limited thereto, any those familiar with the art is in the skill of present disclosure In the range of art, according to technical scheme and inventive concept equivalent in addition thereof or change Become, all should contain within the scope of the present invention.

Claims (3)

1. a robot for space minimum pedestal disturbance method for planning track, it is characterised in that: it comprises the steps:

(1) utilize broad sense Jacobian matrix to set up the kinematical equation of 6DOF robot for space, in conjunction with D-H parametric method, robot for space is modeled；

(2) geometric parameter of definition space robot, comprising: include the quality of the length of connecting rod, connecting rod and pedestal between the quantity in joint, joint and the moment in joint；

(3) utilize 7 rank sine polynomial functions that the joint of robot for space is carried out parametrization；

(4) with base position, the required precision of attitude, the restriction of joint angle speed is limited to constraints with angular acceleration, sets up robot for space base position and the joint trajectory planning objective optimization model of attitude disturbance minimum；

(5) use the Chaos particle swarm optimization algorithm improved to solve, export optimal value, and then obtain robot for space optimal trajectory under pedestal pose disturbance minimum.

Robot for space minimum pedestal disturbance method for planning track the most according to claim 1, it is characterised in that: in described step (4), the object function in described objective optimization model is:

Wherein, definitionδp_bFor the difference of base ends position Yu initial position, δ q_bFor the difference of base ends attitude Yu initial attitude, ω_pFor the weight coefficient of site error, ω_qFor the weight coefficient of attitude error,For the weight coefficient of joint angle constraint of velocity,The weight coefficient retrained for joint angle acceleration,WithIt is respectively defined as following formula:

Wherein,It is the speed maximum in i-th joint,It it is the acceleration maximum in i-th joint.

Robot for space minimum pedestal disturbance method for planning track the most according to claim 1, it is characterized in that: it is characterized in that: in described step (5), the Chaos particle swarm optimization algorithm improved, it uses nonlinear dynamic inertia weight, i.e. inertia weight automatically to change along with the target function value of particle；Adding the thought of golden section proportion, i.e. retaining fitness function value in colony is the particle of 38.2%；Sinusoidal function is selected to replace Logistic function as chaos sequence generator.