CN104290092A - Loop analysis method for kinematics of driving robot with N freedom degrees through 2N wires - Google Patents

Abstract

The invention discloses a loop analysis method for kinematics of driving a robot with N freedom degrees through 2N wires. According to the method, a loop matrix and a motor drive space equivalent-radius matrix can be used for fast describing the kinematics mapping relation between a wire transmission robot joint space and a motor drive space. The loop matrix and the equivalent-radius matrix can be directly listed by observing a planar transmission schematic diagram of the wire transmission robot; because first branches and second branches in loops correspond to forward rotation and reverse rotation of wheels making contact with the branches when the branches generate positive wire displacement, the element symbols in the corresponding loops are oppositely selected, the two matrixes can be written just by determining the element symbol of one branch in each loop, a kinematics mapping relation model can be built, the modeling and analysis process of the wire transmission robot kinematics is quickened and simplified, and a foundation is laid for the design of a wire transmission mechanism and kinematics analysis and control.

Description

The kinematic loop analysis method of a 2N bar silk driving N degree of freedom robot

Technical field

The present invention relates to a kind of kinematic loop analysis method of a 2N bar silk driving N degree of freedom robot, space equivalent redius matrix can be driven to describe a transmission machinery person joint space and motor fast with circuit matrix and motor and drive kinematics mapping relations between space.

Background technology

Silk drive technology is applicable to remote transmission and moves and power, be easy to change direction in transmission process, power source can being arranged on the fixed pedestal away from joint of robot place thus simplifying drive mechanism, the field such as industry, space flight that is widely used in is as hawser traction artificial satellite in the lifting of elevator, aviation etc.; In addition, the drive mechanism that silk transmission has is simple, compact, allows multiple degrees of freedom in little space to arrange; Insensitive for structure mismachining tolerance; Without return difference when tensioning; Available buffer damping, the feature such as make the motion of end-of-arm tooling more steady also can meet the requirement of medical environment, multiple silk drive mechanism by Successful utilization in the design such as medical robot and operating theater instruments.

In order to realize the effective control to silk transmission machinery people, need to set up rotor angular displacement and the mapping relations model between robot end position and attitude.Its kinematics analysis mainly comprises two steps: 1) derive the mapping relations model between joint space and cartesian space by vector method, D-H method and spinor method etc.; 2) according to silk transmission principle, introducing fundamental circuit equation, coaxial condition and drive line set up the mapping relations between silk displacement and joint angle displacement, and the mapping relations between silk displacement and rotor angular displacement form equation, thus obtain joint space and motor and drive mapping relations model between space.In second step, need to judge positive and negative according to the actuation types of silk, row write out fundamental circuit equation, three connecting rod angle displacement chain type rules are write out by coaxial condition row, a fundamental circuit is write for often taking turns row, the mapping relations converting and just can obtain between wire vent displacement and joint angle displacement of carrying out deriving in conjunction with fundamental circuit equation and coaxial condition according to drive line; Mapping relations between silk displacement and rotor angular displacement need to arrange to the electric-motor drive unit containing decelerator the mapping relations write between a displacement and rotor angular displacement respectively.Need to carry out a large amount of walking direction, the derivation of equation in model construction, formula replacement and equation build, its process comparatively very complicated and easily makeing mistakes.

Summary of the invention

The object of this invention is to provide a kind of kinematic loop analysis method of a 2N bar silk driving N degree of freedom robot, the method directly can be arranged by the layout of observing silk writes circuit matrix and motor driving space equivalent redius matrix, thus sets up the mapping relations model between joint angle displacement and rotor angular displacement fast.

In order to achieve the above object, scheme of the present invention is:

First define several concept: (1) branch road: be made up of a silk, one end and the connecting rod of silk are fixed, wheel on the other end and motor reducer output shaft fixes.(2) path: silk the route of process, be made up of branch road and the wheel that contacts with silk.(3) loop: the closed path be made up of two branch roads.

Therefore, every bar loop is made up of two branch roads, is expressed as B ₁and B ₂.The wheel that contacts on joint shaft with silk is concerned about and with silk two end in contact and the wheel of fixing silk, wheel contact with silk beyond joint shaft need not be considered, they only play the effect of support or change silk transmission direction, do not have an impact to analysis result at this.

For the ease of the kinematics analysis of silk transmission machinery people, parallel rotating is carried out in other joint of robot for space, to make it with joint one in same plane and joints axes is parallel each other, thus obtain clear and intuitive plane transmission principle figure, as joint 1-1 in Fig. 1,1-2 transforms schematic diagram, and connecting rod 1-3 is in order to ensure that two close the fixing centre-to-centre spacing of internode.

Positive direction specifies: because silk can only bear pulling force, can not bear pressure, and simultaneously motor is active cell, and therefore regulation points to the direction of electric-motor drive unit is silk positive displacement direction, namely in Fig. 2 mark 2-1, the direction of 2-2,2-3,2-4,2-5,2-6; Regulation is counterclockwise the positive direction of rotor angular displacement and joint angle displacement, namely in Fig. 2 mark 2-16,2-17,2-18 and 2-19, the direction of 2-20,2-21.

On the basis of silk transmission machinery people kinematics analysis, defined loop matrix is L _{2n × n}, be used for describing and add mapping relations between joint of robot angular displacement and rotor angular displacement after silk, wheel.If when silk does not have the wheel of layout on corresponding joint axle, the element of circuit matrix relevant position is taken as zero; If during the wheel of silk layout on corresponding joint axle, the element of circuit matrix relevant position is just being got or negative wheel radius, by silk pass by positive displacement time, drive the direction of rotation of corresponding joint axle contact wheel with it to determine.Get positive sign when direction of rotation is consistent with joint angle displacement positive direction, otherwise get negative sign, wherein circuit matrix L can be described as:

Wherein, L ₁, L ₂l _nfor 1 to loop, loop n, every primary Ioops comprises two branch road B ₁and B ₂; B in the corresponding corresponding circuit of odd-numbered line difference in matrix ₁branch road, B in the corresponding corresponding circuit of even number line ₂branch road; J ₁, J ₂j _nfor joint angle θ ₁to θ _ncorresponding joint shaft, r in matrix _i1j, i, j=1,2 ... n is the radius of branch road 1 in i-th loop contact wheel with it on a jth joint shaft, r _i2j, i, j=1,2 ... n is the wheel radius that the branch road 2 in the i-th loop contacts with it on a jth joint shaft, if branch road does not contact with the wheel on joint shaft, then corresponding entry is zero.When silk produces positive displacement, branch road 1 corresponding to each loop and branch road 2 control the rotating of contact wheel with it respectively, and therefore only need determine the symbol of a branch road element in each loop, another branch road in contrast, thus obtain circuit matrix fast, set up mapping relations model.

Definition R _m1for motor drives space equivalent redius matrix, be used for describing the mapping relations between silk displacement and rotor angular displacement, R _m1can be expressed as:

Row in matrix each branch road corresponding, arranges corresponding electric-motor drive unit M ₁, M ₂m _nthe element of corresponding position is radius that reducer output shaft the is taken turns speed reducing ratio divided by decelerator, if after decelerator transmission, the direction of rotation of reducer output shaft is consistent with the direction of rotation of motor, then when silk is passed by positive displacement, when the direction of rotation that reducer output shaft is taken turns is identical with the positive direction of motor angular displacement, the element of equivalent redius matrix corresponding position gets positive sign, otherwise gets negative sign.If after decelerator transmission, the direction of rotation of reducer output shaft and the direction of rotation of motor inconsistent, then the sign of equivalent redius matrix corresponding position element is chosen on the contrary.The rotating that reducer output shaft is taken turns drives branch road 1 and branch road 2 in the same circuit to produce positive silk displacement respectively, therefore the same circuit that branch road 1 and branch road 2 are formed can be seen as a line of matrix, choosing of the corresponding symbol of element is just the opposite, only need determine the symbol of element of odd-numbered line in matrix, can R be obtained _m=diag (D ₁d ₂d _id _n), wherein, $D_i={\left[\begin{array}{cc}\±\frac{r_{\mathrm{mi}}}{n_i}& \underset{+}{\‾}\frac{r_{\mathrm{mi}}}{n_i}\end{array}\right]}^T.$

According to above-mentioned analytical method, be easy to mapping relations model L θ=R between joint angle displacement and rotor angular displacement by observation _m1θ _mrow write out, and wherein θ is that joint angle motion vector is tieed up, θ in n × 1 _mfor rotor angle of electric machine motion vector is tieed up in n × 1, this row write method is referred to as " the kinematic loop analysis method of a 2N bar silk driving N degree of freedom robot ".

The present invention has following beneficial effect for the mapping relations model set up between the joint angle displacement of a transmission machinery people and rotor angular displacement: 1. loop analysis method of the present invention can by observation and the concept introducing loop, utilize the feature of two branch roads corresponding in each loop, quick writing circuit matrix and equivalent redius matrix, have the advantage of simple, intuitive, precise and high efficiency; 2. loop analysis method of the present invention decoupling zero causes between joint of robot due to silk transmission sports coupling, in conjunction with the angular displacement of open-loop chain joint of robot and the mapping relations between end effector of robot position and pose, achieve motor and drive space, kinematics complete between joint space and cartesian space mapping, simplify a kinematic modeling process of transmission machinery people, for the kinematics of silk transmission machinery people and dynamics Controlling are laid a good foundation.

Accompanying drawing explanation

Fig. 1 is the silk transmission principle schematic diagram that space of the present invention-plane transforms;

Fig. 2 is plane silk transmission principle schematic diagram of the present invention.

Detailed description of the invention

Below in conjunction with specific embodiment, loop analysis method of the present invention is described in detail.

To simplify the analysis, silk transmission machinery people follows following assumed condition: (1) all silks are in tensioning state all the time, and ignores the silk elongation because tensile force causes; Frictional force between silk and wheel is enough large, and making does not have Relative sliding to move between silk and wheel; Silk is lightweight, and the inertia of silk, bending and shearing effect are ignored.(2) mechanism follows general free degree equation, and mechanism is joint type, and removes silk and Lun Hou mechanism becomes an open-loop chain robot.Each is taken turns a revolute on its axis, and for obtaining centre-to-centre spacing constant between two-wheeled, often pair of being connected by silk wheel has a common supporter.

The direction that regulation points to electric-motor drive unit is the positive moving direction of silk, and namely electric-motor drive unit is pointed in the direction of branch road; Regulation is counterclockwise the positive direction of joint angle displacement and rotor angular displacement.

Drive 3 free degree silk transmission machinery artificially routine with 6 silks, draw the plane transmission principle figure of a transmission machinery people according to Fig. 1, write out circuit matrix by viewing plane transmission principle figure row: as shown in Figure 2, when the displacement that silk 2-1 passes by positive, drive radius is r ₁₀wheel 2-10 be rotated counterclockwise, wheel 2-10 direction of rotation is consistent with joint angle displacement positive direction, then the element of matrix corresponding position is designated as+r ₁₀, when the displacement that silk 2-2 passes by positive, drive radius is r ₁₀wheel 2-10 turn clockwise, wheel 2-10 direction of rotation is contrary with joint angle displacement positive direction, then the element of matrix corresponding position is designated as-r ₁₀, in like manner can be extrapolated to loop L ₂, L ₃.Branch road 1 when silk produces positive displacement corresponding to each loop and branch road 2 control the rotating of contact wheel with it respectively, and therefore only need determine the symbol of element of odd-numbered line in matrix, even number line in contrast, can obtain circuit matrix L fast, can be described as:

$L=\left[\begin{array}{ccc}+r_{10}& 0& 0\\ -r_{10}& 0& 0\\ -r_{11}& +r_{13}& 0\\ +r_{11}& -r_{13}& 0\\ -r_{12}& -r_{14}& -r_{15}\\ +r_{12}& +r_{14}& +r_{15}\end{array}\right]$

Motor drives space equivalent redius matrix R _m1in the corresponding each branch road of row, row each electric-motor drive unit corresponding, the element of corresponding position is radius that reducer output shaft the is taken turns speed reducing ratio divided by decelerator.As shown in Figure 2, suppose that the direction of rotation of reducer output shaft is consistent with the direction of rotation of motor after decelerator 2-22 transmission, when radius on reducer output shaft is r ₇wheel 2-7 when being rotated counterclockwise, band movable wire 2-1 passes by positive displacement, and the direction of rotation of wheel 2-7 is consistent with rotor angular displacement positive direction, then the element of equivalent redius matrix corresponding position is designated as when reducer output shaft being taken turns 7 and turning clockwise, drive 2-2 to pass by positive displacement, wheel 2-7 direction of rotation is contrary with rotor angular displacement positive direction, then the element of matrix corresponding position is designated as in like manner can be extrapolated to loop L ₂, L ₃the rotating that reducer output shaft is taken turns drives branch road 1 and branch road 2 in the same circuit to produce positive silk displacement respectively, therefore the same circuit that branch road 1 and branch road 2 are formed can be seen as a line of matrix, choosing of the corresponding symbol of element is just the opposite, equivalent redius matrix R _m1can be described as:

$R_{m1}=\left[\begin{array}{ccc}+\frac{r_7}{n_{22}}& 0& 0\\ -\frac{r_7}{n_{22}}& 0& 0\\ 0& -\frac{r_8}{n_{23}}& 0\\ 0& +\frac{r_8}{n_{23}}& 0\\ 0& 0& -\frac{r_9}{n_{24}}\\ 0& 0& +\frac{r_9}{n_{24}}\end{array}\right]$

According to above-mentioned analytical method, be easy to kinematics mapping relations model L θ=R between joint angle displacement and rotor angular displacement _m1θ _mrow write out.Therefore, the step utilizing loop analysis method to carry out kinematics analysis can be summarized as: (1) draws the plane transmission principle figure of a transmission machinery people; (2) specify that electric-motor drive unit is pointed in the positive displacement direction of silk, regulation is counterclockwise the positive direction of joint angle displacement and rotor angular displacement; (3) space equivalent redius matrix is driven by observing the layout of silk and the positive direction quick writing circuit matrix of regulation and motor; (4) the kinematics mapping relations model in joint space and motor driving space is write according to the equation row built.

Claims (3)

1. The kinematic loop analysis method of a 1.2N bar silk driving N degree of freedom robot, it is characterized in that: in the kinematics analysis of silk transmission machinery people, introducing circuit matrix L is described the mapping relations model between a displacement and joint angle displacement, if when silk does not have the wheel of layout on corresponding joint axle, the element of circuit matrix corresponding position is taken as zero; If during the wheel of silk layout on corresponding joint axle, the element of circuit matrix corresponding position is just being got or negative wheel radius, by silk pass by positive displacement time, the direction of rotation of corresponding joint axle contact wheel is with it driven to determine, when silk produces positive displacement, branch road 1 corresponding to each loop and branch road 2 control the rotating of contact wheel with it respectively, only need determine the symbol of element of a branch road in each loop, another branch road in contrast, therefore directly can be arranged by the plane transmission principle figure observing silk transmission machinery people and write back road matrix L.
2. 2. according to the kinematic loop analysis method of a 2N bar silk driving N degree of freedom robot according to claim 1, it is characterized in that: in the kinematics analysis of silk transmission machinery people, introduce motor and drive space equivalent redius matrix R _m1be described the mapping relations model between a displacement and rotor angular displacement, the corresponding each branch road of row in matrix, row each electric-motor drive unit corresponding, the element of corresponding position is radius that reducer output shaft the is taken turns speed reducing ratio divided by decelerator, the sign of element depends on after decelerator transmission, whether the direction of rotation of reducer output shaft is consistent with the direction of rotation of motor, and the direction of rotation of reducer output shaft being taken turns when the displacement that silk is passed by positive, the rotating that reducer output shaft is taken turns drives branch road 1 and branch road 2 in the same circuit to produce positive silk displacement respectively, the same circuit that branch road 1 and branch road 2 are formed can be seen as a line of matrix, choosing of the corresponding symbol of element is just the opposite, therefore directly can be arranged by the plane transmission principle figure observing silk transmission machinery people and write motor driving space equivalent redius matrix R _m1.
3. 3. according to the kinematic loop analysis method of a 2N bar silk driving N degree of freedom robot according to claim 1, it is characterized in that: according to being arranged the circuit matrix L and motor driving space equivalent redius matrix R that write out in claim 1 and claim 2 by observation _m1, directly can arrange and write out a transmission machinery person joint angular displacement and rotor angular displacement θ _mbetween kinematics mapping relations model be L θ=R _m1θ _m.