CN106426176A - Method for analyzing dynamic load capacity work space of six-degree of freedom space manipulator - Google Patents

Abstract

The embodiment of the invention provides a method for analyzing a dynamic load capacity work space of a six-degree of freedom space manipulator. The method is used for realizing the analysis and evaluation for the dynamic load capacity of the work space of the six-degree of freedom space manipulator. The method comprises the following steps of: solving the work space of the six-degree of freedom space manipulator on the basis of Monte Carlo method; constructing a configuration set and a terminal velocity vector set of each point in the work space; compounding the configuration set with the terminal velocity vector set; and considering the maximum peak torque of the joint and solving the dynamic load capacity of each point, thereby acquiring the dynamic load capacity work space of the six-degree of freedom space manipulator. According to the technical scheme provided by the embodiment of the invention, the analysis and evaluation for the dynamic load capacity of the work space of the six-degree of freedom space manipulator can be realized.

Description

A kind of Six-freedom-degree space mechanical arm dynamic load capacity operation spacial analytical method

【Technical field】

The present invention relates to a kind of Six-freedom-degree space mechanical arm dynamic load capacity operation spacial analytical method, for realizing The dynamic load capability analysis of Six-freedom-degree space mechanical arm work space and assessment.

【Background technology】

With the continuous development of various countries' aerospace industry, space manipulator in-orbit load operation task such as space station build with And the carrying of large-scale load etc. is increasing, mechanical arm undertakes relatively large load and to be smoothed out spatial operation fast to space tasks Speed accurately completes also to play vital effect.Therefore, carry out the correlational study of space manipulator load operation, the mankind are visited Rope space has very big theory value and realistic meaning.

The method that the Workspace Analysis of mechanical arm are commonly used is Monte Carlo method, and it passes through the multigroup joint angle of random generation, Obtain the range coverage of mechanical arm tail end.But for bringing onto load space manipulator, the work space of mechanical arm is to a great extent On be limited to its end and take the impact to its joint moment of load-carrying quality and inertia, once joint moment exceeds mechanical arm institute Can bear to greatest extent it is possible to damage mechanical arm joint, now not only cannot complete task, also can cause bigger Loss.Therefore, the load capacity in analysis mechanical arm motor process, completes the dynamic load capability evaluation of its work space, that is, Solve dynamic load capacity operation space, load operation task is completed for space manipulator there is highly important reality meaning Justice.

【Content of the invention】

In view of this, embodiments provide a kind of Six-freedom-degree space mechanical arm dynamic load capacity operation space Analysis method, required dynamic load capacity operation space can be that the follow-up load operation of Six-freedom-degree space mechanical arm provides and protects Barrier.

In the solution procedure in above-mentioned Six-freedom-degree space mechanical arm dynamic load capacity operation space, the method used is at least Including：

According to Monte Carlo method, calculate the work space of Six-freedom-degree space mechanical arm.Set up six based on D-H parametric method certainly By degree space manipulator kinematics model, application homogeneous transform matrix derivation robot arm end effector is with respect to tool coordinates system Pose, according to the mapping relations in joint of mechanical arm space to work space, Six-freedom-degree space is solved using Monte Carlo method The work space of mechanical arm.

According to Mechanical transmission test location class against solution method, solve every bit in Six-freedom-degree space mechanical arm work space The be possible to configuration at place.Object pose with the every bit in work space as mechanical arm, using analytic method or analytic method knot Close Newton-Raphson approach, calculate the inverse solution of its location class respectively；Every bit in work space for the Six-freedom-degree space mechanical arm is How can correspond to and to obtain 8 groups of joint configuration, these configurations can form mechanical arm configuration collection corresponding at this point.

According to the feature of the trapezoidal planning of end of arm speed, take trapezoidal planning medium velocity maximum, acceleration maximum Speed and accekeration are as the tip speed of mechanical arm, acceleration magnitude.In spherical coordinate system, to the transmitting of space all directions Ray, the direction of every ray is considered as the velocity of mechanical arm tail end, obtains end of arm speed vector set with this.

According to the configuration collection at mechanical arm certain point in its work space and speed collection, with joint peak-peak moment it is Constraints, calculates the set of mechanical arm dynamic load ability at this point, takes minima therein as mechanical arm at this point Safety actuality load capacity value.Mechanical arm dynamic load energy is formed according to the Safety actuality load capacity value that every bit is tried to achieve Power work space.

In above-mentioned solution procedure, the process calculating Six-freedom-degree space mechanical arm work space includes：

The first step, sets up Six-freedom-degree space Mechanical transmission test model based on D-H parametric method, and certainly being built based on Cai is method Set up the link rod coordinate system ∑ being fixed on each connecting rod_i, 4 D-H parameters of each connecting rod are determined according to the definition of D-H parameter： Joint angle θ_i, biasing d_i, the long a of bar_iWith torsional angle α_i, and then obtain the D-H parameter list of mechanical arm；

Second step, based on the D-H parameter list of mechanical arm, according to coordinate system ∑_i-1To ∑_iTransformation matrix General Expression Formula：

Can in the hope of each connecting rod between transformation matrixAnd then can be obtained by forward kinematics equation Expression formula to end pose

3rd step, according to the mapping relations in joint of mechanical arm space to work space, solves six certainly using Monte Carlo method By the work space of degree space manipulator, comprise the following steps that：

(i) according to Mechanical transmission test normal solution, obtain robot arm end effector with respect to base coordinate system position to Amount [p_xp_yp_z]^TWith attitude vectors [α β γ]^T；

(ii) in each joint variable span [θ_imin,θ_imax] in, produced between N number of 0 to 1 using rand (j) function Random value is as arbitrary width variable (j=1,2 ..., N), i.e. (θ_imax-θ_imin) rand (j), thus obtain joint of mechanical arm becoming The pseudorandom values of amount：θ_i=θ_imin+(θ_imax-θ_imin) rand (j), wherein θ_iminFor joint variable lower limit, θ_imaxFor joint variable The upper limit；

(iii) pseudorandom values of the N number of joint variable tried to achieve in step (ii) are substituted into forward kinematics solution equation, and obtain Mechanical arm tail end point is with respect to the position of tool coordinates system and attitude vectors.Number of vectors is more, more can reflect the reality of mechanical arm Border work space.By gained mechanical arm tail end point position vector value proportionally, it is shown in computer graphical with described point mode and sets In standby, just obtain the work space point cloud chart of mechanical arm, namely the work space of mechanical arm.

In above-mentioned solution procedure, calculate the process bag of the configuration collection of every bit in Six-freedom-degree space mechanical arm work space Include：

The first step, using any point in institute's evaluation work space as the object pose [p of mechanical arm_xp_yp_zα β γ ]^T；

Second step, judges to be parallel to each other or meet at the pass of any with the presence or absence of three joints axes in sixdegree-of-freedom simulation Nodule structure；If existing, based on forward kinematics equation12 analytic equations can be obtained, it is parsed Solve and can get most 8 groups of joint angles, this several groups of joint angle combinations be may make up the configuration collection Q corresponding to this point；If no Exist, then need to be solved with reference to Newton-Raphson approach with analytic method, step is as follows：

I () assumes a certain improvement mechanical arm being biased to zero, constructing with spherical joint with biasing joint, and using solution Analysis method solves 8 groups of solutions；

(ii) set up the expression formula of site error Δ P (θ)

Wherein, subscript r represents actual machine arm parameter, and subscript m represents improvement mechanical arm parameter.

(iii) solved according to Newton-Raphson approach, that is, as k=1, made P_m=P_r；As k=k+1, make P_m= P_r-ΔP(θ_m), wherein θ_mFor improving the joint angle sequence that mechanical arm is tried to achieve by analytic method.Judge：If | | P_m(k)-P_m(k+1)| | >=ε, then return Analytic Method part, continue to solve joint angle θ_m；Otherwise, export θ_r=θ_m, complete asking of actual joint angle Solution.Solving result is multigroup solution, and the disaggregation being constituted is this configuration collection Q corresponding to point.

In above-mentioned solution procedure, the process calculating Six-freedom-degree space end of arm speed vector set includes：

The first step, has the characteristics that trapezoidal planning according to end of arm speed, that is, its velocity variations rule is：First to add Speed a increases to speed v, then keeps the uniform motion of certain time length, be finally reduced to speed with acceleration a is zero again, can Know：In the whole change procedure of its speed, acceleration and velocity amplitude are the point of maximum, as the end point of accelerator and The starting point of moderating process, at this point, acceleration is a, and speed is v.Due to the acceleration at certain point in work space cannot be known And velocity magnitude, therefore select the speed at this point and accekeration is operated the meter of the dynamic load capacity of all point in space Calculate.

Second step, because velocity attitude (acceleration is general with speed in the same direction) also affects the calculating of load capacity, in order to the greatest extent Amount covers all possible velocity attitude, is spaced θ traversal direction angle α and β at an angle, penetrates to space all directions Line, the direction of every ray is considered as the velocity of mechanical arm tail end, obtains end of arm speed set of vectors with this

In above-mentioned solution procedure, the process calculating Six-freedom-degree space mechanical arm dynamic load capacity operation space includes：

The first step, the configuration collection Q of certain point and velocity collection in work spaceIn respectively take out an element, two-by-two It is combined into the currently possible kinestate collection of mechanical armThis kinestate Collection contains mechanical arm and is moving to the state all that may be present at this point；

Second step, carries out Dynamic Modeling using Newton-Euler method to Six-freedom-degree space mechanical arm, in institute's established model Last root connecting rod end introduce varying duty, for any one kinestateIn conjunction with joint peak-peak power Square constraints, calculates its dynamic load ability.By calculating the dynamic load ability of all kinestates at this point, can get Dynamic load competence set M at this point, takes out the minimum M in quality set M_minSafety actuality as this point loads energy Power, step is as follows：

I () carries out Dynamic Modeling using Newton-Euler method to Six-freedom-degree space mechanical arm, each portion of system of deriving The stressing conditions dividing.

Recursion obtains the position of each connecting rod of space manipulator, attitude is：

Angular velocity, speed recurrence relation are：

Angular acceleration, acceleration recurrence relation are：

To bar k, act on the inertia force on its barycenter and moment of inertia is respectively F_k,N_k, according to Newton-Euller method, from The end of mechanical arm carries out recursion to pedestal, can obtain：

Suffered by each rod member, external force and moment are：

Each joint moment is

τ_k=n_k ^{T I}z_k(9)

Wherein, each parameter declaration and implication are as shown in table 1.

The explanation of table 1 kinetic parameter and implication

(ii) set up Manipulator Dynamic under loading condition, due to during mechanical arm load operation end load with Connecting rod keeps geo-stationary, therefore load and tail end connecting rod can be considered as one.Load and end effector can be considered as quality Concentrate on the particle of last root connecting rod end, under tail end connecting rod coordinate system, have

m_{n_new}=m_n+m_f(10)

I_{n_new}=I_n+I_f(11)

Wherein, m_fRepresent load quality, m_{n_new}Represent and introduce mechanical arm tail end connecting rod gross mass after end load, I_fRepresent It is supported on the inertia matrix of tail end connecting rod coordinate system, I_{n_new}Represent that after introducing end load, total rotation of mechanical arm tail end connecting rod is used to Amount, tail end connecting rod midpoint is passed through in its rotating shaft；P_{cn_new}Represent end load and tail end connecting rod assembly center-of-mass coordinate.

(iii) for any one kinestateIt is continuously increased the quality of its end load at certain intervals, meter Calculate the joint moment in each joint, make joint moment exceed its joint peak torque until end mass is increased to certain When to greatest extent, previous load quality is the dynamic load ability of mechanical arm under this kinestate.In other words, joint is maximum Peak torque is the constraints of space manipulator dynamic load ability, and dynamic load ability solution procedure can use following belt restraining Optimization problem description：

Wherein, i represents joint label,WithRepresent joint of mechanical arm speed and joint velocity respectively,WithRespectively Represent end of arm speed and acceleration,Represent the peak-peak moment in i-th joint.

By calculating the dynamic load ability of all kinestates at this point, the dynamic load capability set at this point can be obtained Close M, take out minima m in quality set M_minSafety actuality load capacity as this point.

3rd step, using said method calculate in work space Safety actuality load capacity a little, you can obtain The dynamic load capacity operation space M of Six-freedom-degree space mechanical arm_c.

The technical scheme of the embodiment of the present invention has the advantages that：

It is proposed that the dynamic load capacity operation of Six-freedom-degree space mechanical arm is empty in the technical scheme of the embodiment of the present invention Between concept, for representing the dynamic load energy of any point in mechanical arm work space in the case of given speed planning mode Power, and successfully complete the calculating in Six-freedom-degree space mechanical arm dynamic load capacity operation space.

【Brief description】

In order to be illustrated more clearly that the technical scheme of the embodiment of the present invention, below will be attached to use required in embodiment Figure be briefly described it should be apparent that, drawings in the following description are only some embodiments of the present invention, for this area For those of ordinary skill, without having to pay creative labor, can also be other attached according to the acquisition of these accompanying drawings Figure.

Fig. 1 is the Six-freedom-degree space mechanical arm dynamic load capacity operation spatial analysis that embodiment of the present invention is provided The schematic flow sheet of method；

Fig. 2 is the kinematics model figure of object of study in the embodiment of the present invention；

Fig. 3 is embodiment of the present invention medium velocity vector set figure；

Fig. 4 is the kinetic model figure of object of study in the embodiment of the present invention；

Fig. 5 is the dynamic load capacity operation space diagram of mechanical arm in the embodiment of the present invention.

【Specific embodiment】

1st, set up Six-freedom-degree space Mechanical transmission test model as shown in figure 1, its D-H parameter declaration is as shown in table 2.

Table 2 mechanical arm DH parameter

Using Monte Carlo method, arranging each joint angle slewing area is [- 180,180], and arranging random number of times is 5000 times, Generate its work space, as shown in Figure 3.

2nd, each point in work space is carried out with the inverse solution of location class, obtains Six-freedom-degree space mechanical arm configuration collection Q.To work As a example point [3.6, -4,2,90, -30, -90] in space (unit be m and °), corresponding configuration collection can be solved as shown in table 3.

Table 3 sixdegree-of-freedom simulation configuration collection

3rd, the maximum v of access speed and acceleration_max=0.1m/s, a_max=0.02m/s², in the range of [0,360] with 10 ° of traversal direction angle α and β in interval, obtain the sets of speeds of this pointAs shown in Figure 4.

4th, according to the configuration collection Q at every bit in this mechanical arm work space and speed collectionIn conjunction with joint peak-peak The moment upper limit, calculates the set of mechanical arm dynamic load ability at this point, and selects the minima of wherein dynamic load ability m_min.In work in combination space somewhat corresponding Safety actuality load capacity value, obtain the dynamic load ability of this mechanical arm Work space is as shown in Figure 5., from deep to shallow, its load capacity corresponding is ascending, permissible from figure in figure load capacity gray scale Find out, mechanical arm is in the majority in the boundary load capacity dark color close to its work space, illustrate in these position dynamic load energy Power is relatively low.In work space center, light color is in the majority, illustrates that it is higher in center dynamic load ability.

The foregoing is only presently preferred embodiments of the present invention, not in order to limit the present invention, all essences in the present invention Within god and principle, any modification, equivalent substitution and improvement done etc., should be included within the scope of protection of the invention.

The content not being described in detail in description of the invention belongs to the known technology of those skilled in the art.

Claims (4)

1. a kind of Six-freedom-degree space mechanical arm dynamic load capacity operation spacial analytical method：

According to Mechanical transmission test location class against solution method, solve at every bit in Six-freedom-degree space mechanical arm work space Be possible to configuration.Object pose with the every bit in work space as mechanical arm, combines cattle using analytic method or analytic method - the inferior method of pressgang, calculate the inverse solution of its location class respectively；Every bit in work space for the Six-freedom-degree space mechanical arm at most may be used Correspondence obtains 8 groups of joint configuration, and these configurations can form mechanical arm configuration collection corresponding at this point.

According to the feature of the trapezoidal planning of end of arm speed, take maximal rate in trapezoidal velocity planning and acceleration as end End motion state.In spherical coordinate system, to space all directions divergent-ray, the direction of every ray is considered as mechanical arm tail end Velocity, obtains end of arm speed vector set with this.

According to the configuration collection at mechanical arm certain point in its work space and speed collection, with joint peak-peak moment for constraint Condition, calculates the set of mechanical arm dynamic load ability at this point, takes minima therein peace as mechanical arm at this point Full dynamic load ability value.Mechanical arm dynamic load ability work is formed according to the Safety actuality load capacity value that every bit is tried to achieve Make space.

2. method according to claim 1 is it is characterised in that each in described Six-freedom-degree space mechanical arm work space The calculating of the configuration collection of point at least includes：

The first step, using any point in institute's evaluation work space as the object pose of mechanical arm

Second step, judges to be parallel to each other or meet at the pass nodule of any with the presence or absence of three joints axes in sixdegree-of-freedom simulation Structure；If existing, based on forward kinematics equation12 analytic equations can be obtained, Analytical Solution is carried out to it Can get most 8 groups of joint angles, this several groups of joint angle combinations be may make up the configuration collection Q corresponding to this point；If not existing, Then need to be solved with reference to Newton-Raphson approach with analytic method, step is as follows：

I () assumes a certain improvement mechanical arm being biased to zero, constructing with spherical joint with biasing joint, and utilize analytic method Solve 8 groups of solutions；

(ii) set up the expression formula of site error Δ P (θ)

$\mathrm{\Δ}P\left(\mathrm{\θ}\right)=P_r-P_m=\left[\begin{array}{c}{P}_{rx}\left(\mathrm{\θ}\right)-P_{mx}\left(\mathrm{\θ}\right)\\ P_{ry}\left(\mathrm{\θ}\right)-P_{my}\left(\mathrm{\θ}\right)\\ P_{rz}\left(\mathrm{\θ}\right)-P_{mz}\left(\mathrm{\θ}\right)\end{array}\right]$

Wherein, subscript r represents actual machine arm parameter, and subscript m represents improvement mechanical arm parameter.

(iii) solved according to Newton-Raphson approach, that is, as k=1, made P_m=P_r；As k=k+1, make P_m=P_r-ΔP (θ_m), wherein θ_mFor improving the joint angle sequence that mechanical arm is tried to achieve by analytic method.Judge：If | | P_m(k)-P_m(k+1) | | >=ε, Then return Analytic Method part, continue to solve joint angle θ_m；Otherwise, export θ_r=θ_m, complete the solution of actual joint angle.Ask Solution result is multigroup solution, and the disaggregation being constituted is this configuration collection Q corresponding to point.

3. method according to claim 1 is it is characterised in that described Six-freedom-degree space end of arm speed vector set Calculating at least include：

The first step, has the characteristics that trapezoidal planning according to end of arm speed, that is, its velocity variations rule is：First with acceleration A increases to speed v, then keeps the uniform motion of certain time length, last again with acceleration a be reduced to speed be zero it is known that：? In the whole change procedure of its speed, acceleration and velocity amplitude are the end point that maximum point is accelerator and moderating process Starting point, at this point acceleration be a, speed be v.It is big due to acceleration at certain point in work space and speed cannot be known Little, therefore select the speed at this point and accekeration is operated the calculating of the dynamic load capacity of all point in space.

Second step, because velocity attitude (acceleration is general with speed in the same direction) also affects the calculating of load capacity, in order to cover as far as possible Cover all possible velocity attitude, be spaced θ traversal direction angle α and β at an angle, to space all directions divergent-ray, The direction of every ray is considered as the velocity of mechanical arm tail end, obtains end of arm speed set of vectors with this

4. method according to claim 1 is it is characterised in that described Six-freedom-degree space mechanical arm dynamic load ability work The calculating making space at least includes：

The first step, the configuration collection Q of certain point and velocity collection in work spaceIn respectively take out an element, combination of two Become the currently possible kinestate collection of mechanical armThis kinestate Ji Bao Contained manipulator motion at this point when all states that may be present；

Second step, carries out Dynamic Modeling using Newton-Euler method to Six-freedom-degree space mechanical arm, in institute's established model A connecting rod end introduces varying duty, for any one kinestate afterwardsInterval is continuously increased at a certain angle The quality of its end load, calculates the joint moment in each joint, until end mass is increased to certain make joint moment Exceed its joint peak torque to greatest extent when, previous load quality is the dynamic load of mechanical arm under this kinestate Ability.In other words, peak-peak moment in joint is the constraints of space manipulator dynamic load ability, and dynamic load can be made every effort to Solution preocess can be described with the optimization problem of following belt restraining：

$\begin{array}{cc}\max & m_f\\ s.t.& g{(m_f,\stackrel{\·}{q}(\stackrel{\·}{X}),\stackrel{\·\·}{q}(\stackrel{\·}{X},\stackrel{\·\·}{X}\left)\right)}_i\≤{\mathrm{\τ}}_{\max }^i\end{array}$

Wherein, i represents joint label, m_fRepresent mechanical arm tail end load quality,WithRespectively represent joint of mechanical arm speed and Joint velocity,WithRepresent end of arm speed and acceleration respectively,Represent the peak-peak power in i-th joint Square.

By calculating the dynamic load ability of all kinestates at this point, the dynamic load competence set M at this point can be obtained, Take minima m in quality set M_minSafety actuality load capacity as this point.

3rd step, using said method calculate in work space Safety actuality load capacity a little, you can obtain six from Dynamic load capacity operation space M by degree space manipulator_c.